Fourth Grade MATHEMATICSmyvolusiaschools.org/K12-Curriculum/Curriculum Maps and Guides/Ma… · Fourth Grade MATHEMATICS ... Topic 12: Comparing decimal ... multiplication of 2‐digit

Fourth Grade

MATHEMATICS Curriculum Map

2017 – 2018

Volusia County Schools

Mathematics Florida Standards

1 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department May 2017

2 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department May 2017

Elementary Instructional Math Block

Time Components Description

5-15 minutes

Number Talks

Short, daily fluency routine that engages students in meaningful conversations around purposefully crafted computation problems that are solved using number relationships and the structure of numbers. Students are asked to communicate their thinking when presenting and justifying solutions to problems they solve mentally while the teacher records their ideas with mathematical precision. These exchanges lead to the development of more accurate, efficient, and flexible strategies.

5 minutes

Opening: Hook/Coherence Connection

The teacher will engage students to create interest for the whole group lesson or review prerequisite standards to prepare students to make explicit connections that will allow students to apply and extend previous learning when interacting with the lesson’s grade-level content.

15 minutes

Whole Group: Mini Lesson/Guided Practice

Used prior to small group to introduce/practice new knowledge and skills or after small group to refine/practice strategies discovered by students.

The lesson focuses on the depth of grade-level cluster(s), grade-level content standard(s), or part(s) thereof, intentionally targeting the aspect(s) of rigor (conceptual understanding, procedural skill and fluency, application) called for by the standard(s) being addressed.

During this time, the teacher makes the mathematics of the lesson explicit using clear and correct explanations, representations, tasks, and/or examples. The teacher provides opportunities for all students to work with and practice grade-level problems and exercises, deliberately checking for understanding throughout the lesson and adapting the lesson according to student understanding. The teacher poses high-quality questions and problems that prompt students to share their developing thinking about the content of the lesson. Class created anchor charts are constructed by strategically adding key concepts throughout the topic’s lessons.

30-40 minutes

Small Collaborative Groups/ Independent Practice

The teacher encourages reasoning and problem solving by posing challenging problems that offer opportunities for student choice of appropriate tools and promote productive struggle. Students work in small, flexible collaborative groups to engage in mathematical tasks while the teacher circulates and asks questions to elicit thinking, providing support or extensions as needed. The teacher asks students to explain and justify work, connecting and developing students’ informal language to precise mathematical language appropriate to their grade, and provides feedback that helps students revise initial work. The teacher makes observations to select and sequence appropriate strategies for students to share during the class discussion.

5 minutes

Closure: Summarize

The teacher strengthens all students’ understanding of the content by strategically sharing a variety of students’ representations and solution methods. The teacher facilitates the summary of the mathematics with references to student work and by creating the conditions for student conversations where students are encouraged to talk about each other’s thinking in order to reinforce the purpose of the lesson.

Formative techniques occur throughout the framework to drive instruction, guide collaborative grouping, and evaluate which students will need intervention/enrichment.

Grade 4 Math Curriculum Map July 2017

3 Volusia County Schools Grade 4 Math Curriculum Map Mathematics Department July 2017

Year At A Glance

Unit 1: August 14 – October 25

Topic 1: Exploring multiples and factors Topic 2: Using multiplication and division strategies with larger numbers Topic 3: Decomposing and composing fractions for addition and subtraction Topic 4: Applying place value concepts in whole number addition and subtraction

Unit 2: October 26 – January 23

Topic 5: Understanding fraction equivalence and comparison Topic 6: Introducing measurement conversions Topic 7: Solving problems using multiplicative comparison Topic 8: Solving measurement problems using the four operations

Unit 3: January 24 – March 30

Topic 9: Solving addition and subtraction problems involving fractions and mixed numbers Topic 10: Angle measurement Topic 11: Multiplying fractions by whole numbers Topic 12: Comparing decimal fractions and understanding notation

Unit 4: April 2 – May 30

Topic 13: Recognizing and analyzing attributes of 2-dimensional shapes Topic 14: Problem solving with whole numbers Topic 15: Revisiting solving addition and subtraction problems involving fractions and mixed

number data present in line plots Topic 16: Revisiting using conversions to solve measurement problems


Unit 1 PACING: August 14 – October 25

Topic 1: Exploring multiples and factors Pacing: August 14 – 28

In this topic students develop understanding of multiples and factors, applying their understanding of multiplication from the previous year. This understanding lays a strong foundation for generalizing strategies learned in previous grades to develop, discuss, and use efficient, accurate, and generalizable computational strategies involving multi-digit numbers. These concepts and the terms “prime” and “composite” are new to Grade 4, so they are introduced early in the year to give students ample time to develop and apply this understanding.

Standards Academic Language

Investigate factors and multiples. a. Find all factor pairs for a whole number in the range 1–100. b. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. c. Determine whether a given whole number in the range 1–100 is prime or composite.

NOTE: This standard has been amended in Florida.

MAFS.4.OA.2.4

composite factor factor pairs multiple prime feature numeric pattern rule sequence term

Students will:

• determine factor pairs of whole numbers in the range 1-100.

• recognize that a whole number is a multiple of each of its factors.

• determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number.

• determine if a number in the range 1-100 is prime or composite.


Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

MAFS.4.OA.3.5

Students will:

• generate a number pattern that follows a given one- or two-step rule.

E.g., Rule: Multiply by 2 and then subtract 4. The first number in the pattern is 6. Show the next three numbers in the pattern. Answer: 8,12, 20

• identify features in a number pattern after following a given one- or two-step rule.

E.g.,

3. Construct viable arguments and critique the reasoning of others. 7. Look for and make use of structure.

MAFS.K12.MP.3.1 MAFS.K12.MP.7.1

Topic Comments:

While working on OA.2.4, students use manipulatives to determine whether a number is prime or composite. Although there are

shape patterns in arrays, the focus of this topic is number patterns. OA.3.5 is repeated in topic 13, where the focus will be on

identifying shape patterns.

The focus of this topic is not necessarily to become fluent in finding all factor pairs, but to use student’s understanding of the concept and language to discuss the structure of multiples and factors (MP.3, MP.7).


Topic 1 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

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Topic 1 One Number Indivisible

Teacher Guide p. 5

Reproducibles p. 3

Daily Math Journal pp. 2, 4, 7, 8, 10, 13, 14

Pick A Problem #12, 13, 14, 15, 16, 17, 18

How Did You Solve It? #11, 12, 13, 14

Factor Triangles

Find all the Factor Pairs Multiples of Six Factor Pairs Prime or Composite

www.cpalms.org Creating Factor Pair Trees

https://www.illustrativemathematics.org/content-standards Locker Game

www.IXL.com/signin/volusia D.4, D.3, A.10, A.11

https://learnzillion.com/ Unit 1: Exploring Multiples and Factors (lessons 1-7) http://achievethecore.org No aligned resources

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Topic 1 Key Codes

Teacher Guide p. 6

Reproducible p. 3


Pick A Problem #7, 8, 11, 19, 20


Multiply by Four Dot Patterns Baseball Cards

www.cpalms.org Chips Ahoy!

Rules, Number Patterns and Tables

https://www.illustrativemathematics.org/content-standards Double Plus One

Multiples of Nine

Multiples of 3,6, and 7

www.IXL.com/signin/volusia D.29, H.2, L.5, L.7

https://learnzillion.com/ Unit 1: Exploring Multiples and Factors (lessons 8-10) http://achievethecore.org No aligned resources

http://www.cpalms.org/Resource/mfas.aspx

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/OneNumberIndivisible.pdf?authToken=eyJ0eXAiOiJKV1QiLCJhbGciOiJSUzI1NiIsIng1dCI6Ik81YXN1TXdZWXdMUS1QVGRvS2lHcm1UdXJHVSJ9.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.CO3W5IVQG3Wj2e0d1gQBzdXA7ti8FHE3cv-SLpvTqjZmDJb-Hr8E11nTPhXCfNfz76aLGhfBfOUlqYEvYTYzYiqtUSNWuMABTBkngQ2lJW7aiJRKLKqOtw9jQEkIGvlMUULvnOpgYS2AVXcj6Wjnl31xKQz0eiRZZwBjX_8jbcJLs2yBwnI8ffHw3Vh2QUUhl6RHbsST52Begvbtm9wi_uRUUCK3SfN8ycScvAbABiwMjTiWqQitZdCtntS-oF_o7txb07WN4f5wy2aDVarlLSsLZAriBVY7WeHz5qfpb08XDUkN7w7cYtbbUk8NMiiZ34rwrighaqTd0JUBxDIcIw&client-request-id=1b2d4b00-c623-0000-bbaf-2d1b23c6d201

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/OneNumberIndivisible.pdf?authToken=eyJ0eXAiOiJKV1QiLCJhbGciOiJSUzI1NiIsIng1dCI6Ik81YXN1TXdZWXdMUS1QVGRvS2lHcm1UdXJHVSJ9.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.CO3W5IVQG3Wj2e0d1gQBzdXA7ti8FHE3cv-SLpvTqjZmDJb-Hr8E11nTPhXCfNfz76aLGhfBfOUlqYEvYTYzYiqtUSNWuMABTBkngQ2lJW7aiJRKLKqOtw9jQEkIGvlMUULvnOpgYS2AVXcj6Wjnl31xKQz0eiRZZwBjX_8jbcJLs2yBwnI8ffHw3Vh2QUUhl6RHbsST52Begvbtm9wi_uRUUCK3SfN8ycScvAbABiwMjTiWqQitZdCtntS-oF_o7txb07WN4f5wy2aDVarlLSsLZAriBVY7WeHz5qfpb08XDUkN7w7cYtbbUk8NMiiZ34rwrighaqTd0JUBxDIcIw&client-request-id=1b2d4b00-c623-0000-bbaf-2d1b23c6d201

https://intranet.volusia.k12.fl.us/departments/elementarymath/Lakeshore%204/Grade%204_Guide.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/Lakeshore%204/Grade%204_Reproducibles.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/Lakeshore%204/Grade%204_Daily%20Math%20Practice%20Journal.pdf

http://www.cpalms.org/Public/PreviewResourceAssessment/Preview/55151




http://www.cpalms.org/

https://www.illustrativemathematics.org/content-standards/4/OA/B/4/tasks/938

http://www.ixl.com/signin/volusia

https://learnzillion.com/resources/64472-1st-grade-math


https://learnzillion.com/resources/64178-exploring-multiples-and-factors


http://achievethecore.org/

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/KeyCodes.pdf








http://www.cpalms.org/Public/PreviewResourceUrl/Preview/24468

http://www.cpalms.org/Public/PreviewResourceLesson/Preview/43527



https://www.illustrativemathematics.org/content-standards/4/OA/C/5/tasks/1481

https://www.illustrativemathematics.org/content-standards/4/OA/C/tasks/1484








Topic 2: Using multiplication and division strategies with larger numbers Pacing: August 29 – September 25 In this topic students continue using computational and problem-solving strategies, with a focus on building conceptual understanding of multiplication of greater numbers and division with remainders. Area and perimeter of rectangles provide one context for developing such understanding.


Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

MAFS.4.OA.1.3

area model comparative relational

thinking distributive property dividend divisor factor formula mental computation reasonableness rectangular array remainder quotient unknown factor unknown quantity variable

Students will:

• solve multi-step word problems that involve multiplication and/or division using strategies for this grade level (e.g, rectangular arrays, area models, properties of operations, etc).

• represent a multi-step word problem using equations involving a variable represented by a letter for the unknown number.

• interpret remainders that result from multi-step word problems.

• assess the reasonableness of answers to multi-step word problems using estimation strategies and mental computation.

NOTE: The expectations for multi-step word problems in this topic include

multiplication of 2‐digit by 1‐digit or a multiple of 10 by a 1‐digit and division of

2‐digit by 1‐digit.

The context of a word problem must be considered when interpreting remainders. Here are some ways remainders can be addressed:

• remainder as a leftover

• discard remainder leaving only the whole number answer

• increase the whole number answer by one

*Students will write remainders as fractions in Grade 5


Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

MAFS.4.NBT.2.5

Students will:

• use manipulatives or drawings of rectangular arrays and/or array models to solve and explain multi-digit multiplication problems that extend to 4-digit by 1-digit or up to 2-digit by 2-digit.

E.g.,

Rectangular Array (Concrete) Rectangular Array (Representational) Area Model

• solve multi-digit multiplication problems that extend to 4-digit by 1-digit or up to 2-digit by 2-digit using strategies based on place value and the properties of operations, and record the calculation using equations. E.g.,

Distributive Property Partial Products

NOTE: Use of the standard algorithm for multiplication is a Grade 5 standard. Although these strategies are precursors to the standard algorithm, students should not be moved too quickly to the algorithm, as the standard algorithm is not the only end goal. Perhaps more importantly, students must become flexible in their use of place value and properties of operations when multiplying in Grade 4 in order to be successful later in Algebra when using the Distributive Property.


Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

MAFS.4.NBT.2.6

Students will:

• use manipulatives or drawings of rectangular arrays and/or array models to solve and explain division problems that involve the division of a multi-digit dividend (with up to four digits) by a one-digit divisor.

E.g.,

Rectangular Array (Concrete) Rectangular Array (Representational) Area Model

• solve division of a multi-digit dividend (with up to four digits) by a one-digit divisor using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division, and record the calculation using equations.

E.g.,

Distributive Property Partial Quotients Multiplying Up

NOTE: Use of the standard algorithm for division is a Grade 6 standard.

Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

MAFS.4.MD.1.3

Students will:

• apply the perimeter formula (P = 2l + 2w) in real world and mathematical situations.

• apply the area formula (A = l × w) in real world and mathematical situations.

• solve for missing dimensions of rectangles when provided with the perimeter and/or area.

• solve problems involving area of a composite figure composed of rectangles.

Note: Students need to be provided with the Grade 4 FSA Mathematics Reference Sheet in order to practice using the tool. Exponential notation for unit abbreviations (e.g., cm2 ) is not introduced until Grade 5.


Determine whether an equation is true or false by using comparative relational thinking. For example, without adding 60 and 24, determine whether the equation 60 + 24 = 57 + 27 is true or false. NOTE: This standard has been added in Florida.

MAFS.4.OA.1.a

Students will:

NOTE: Due to this standard’s emphasis on mental math, it will be introduced and then embedded through the use of Number Talks.

• determine if a given equation is true or false by comparing, composing, and/or decomposing the numbers without solving. E.g.,

NOTE: Whole number equations are limited to: addition and subtraction within 1,000, multiplication of 2‐digit by 1‐digit or a multiple of 10 by a 1‐digit, or division of 2‐digit by 1‐digit

Determine the unknown whole number in an equation relating four whole numbers using comparative relational thinking. For example, solve 76 + 9 = n + 5 for n by arguing that nine is four more than five, so the unknown number must be four greater than 76. NOTE: This standard has been added in Florida.

MAFS.4.OA.1.b

Students will: NOTE: Due to this standard’s emphasis on mental math, it will be introduced and then embedded through the use Number

Talks.

• compare the two sides of an equation to determine the unknown value without solving. E.g., 27 + n = 25 + 42 Student, “25 is 2 less than 27, so n must be 2 less than 42.” NOTE: Whole number equations are limited to: addition and subtraction within 1,000, multiplication of 2‐digit by 1‐digit or a

multiple of 10 by a 1‐digit, or division of 2‐digit by 1‐digit.


1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 8. Look for and express regularity in repeated reasoning.

MAFS.K12.MP.1.1 MAFS.K12.MP.2.1 MAFS.K12.MP.8.1

Topic Comments: OA.1.3 is the first time students are expected to interpret remainders based upon the context. All four operations will be addressed in topic 8, and the standard will be finalized in topic 14. MD.1.3 provides the context of area and perimeter of rectangles to use for problem solving. Students are first introduced to formulas in this topic and make sense of the formulas using their prior work with area and perimeter. Students make sense of multi-‐step problems (MP.1) and reason about how the formulas connect to the context (MP.2). The use of generalized strategies and formulas provides an opportunity to investigate and use regularity in repeated reasoning (MP.8).



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Topic 2 Picturing Clues Party Planning

Teacher Guide p. 4

Reproducibles p. 3


Pick A Problem #1, 2, 32


Estimating the Solution Juice Boxes

www.cpalms.org I love Leftovers!

Aaron and Anya's Quilt Challenge

https://www.illustrativemathematics.org/content-standards Carnival Tickets

www.IXL.com/signin/volusia D.27, E.7, E.11 *Practice after NBT.2.5, NBT.2.6 and MD.1.3 are taught.

https://learnzillion.com/ No aligned resources http://achievethecore.org No aligned resources

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.2.5

Topic 2 Multiplication Stretch

Teacher Guide: p. 10

Reproducibles: p. 3

Daily Math Journal pp. 17, 20, 27, 31, 33

Pick A Problem #30, 31, 37, 38, 39

How Did You Solve It? #27, 28, 29

Reading Challenge Partial Products Multiplying by Using an Array or Area Model The Produce Shop

www.cpalms.org 2-Digit Array Multiplication

Boxing Math

https://www.illustrativemathematics.org/content-standards No aligned resources

www.IXL.com/signin/volusia D.5, D.6, D.11, D.15, D.18, D.24

https://learnzillion.com/ Unit 2: Multiplication and division strategies with larger numbers (Lessons 1-5) http://achievethecore.org No aligned resources


https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/PicturingClues.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/PartyPlanning.pdf










https://www.illustrativemathematics.org/content-standards/4/OA/A/3/tasks/1289





https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/MultiplicationStretch.pdf
















https://learnzillion.com/resources/64180-using-multiplication-and-division-strategies-with-larger-numbers







4.N

BT

.2.6

Topic 2 Pack 10 Trading Center Candy Factory


Reproducibles: p. 3

Daily Math Journal pp. 18, 22, 23, 25, 26, 29, 32, 40

Pick A Problem #33, 34, 35, 36


Dividing Using an Area Model Book Drive Interpreting Division Dividing Using Place Value

www.cpalms.org Share and Share Alike

https://www.illustrativemathematics.org/content-standards Mental Division Strategy

www.IXL.com/signin/volusia E.4, E.5, E.8, E.14

https://learnzillion.com/ Unit 2: Multiplication and division strategies with larger numbers (Lessons 6-10) http://achievethecore.org How Many Teams?

4.M

D.1

.3

Topic 2 No aligned resources

Teacher Guide pp. 20-21

Reproducible pp. 3, 15

Daily Math Journal pp. 57, 58, 60, 64

Pick A Problem #74, 75, 76, 77, 78


Area Tiles

Party Math Geometry Problem Solving Kit Activity Cards 5-6

Using Area and Perimeter Fencing a Garden What is the Perimeter of the Lettuce Section? Applying Area and Perimeter

www.cpalms.org New Puppy Pen

https://www.illustrativemathematics.org/content-standards Karl’s Garden

www.IXL.com/signin/volusia BB.1 (uses a variety of shapes), BB.6, BB.9, BB.10, BB.11, BB.13



https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/Pack10TradingCenters.pdf


https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/CandyFactory.pdf












https://www.illustrativemathematics.org/content-standards/4/NBT/B/6/tasks/1774








http://achievethecore.org/page/1053/how-many-teams













https://www.illustrativemathematics.org/content-standards/4/MD/A/3/tasks/876











4.O

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.a


Teacher Guide p. 4

Problem Solving Strategy Puzzles

Are the Equations True? Determining if an Equation is True True and False Division Equations True and False Multiplication Equations

www.cpalms.org Is My Equation TRUE or FALSE?


www.IXL.com/signin/volusia No aligned resources


4.O

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.b

Topic 2 Zoo Books

Teacher Guide p. 4

Reproducibles p. 4


Comparative Relational Thinking in a Division Equation Comparative Relational Thinking in a Multiplication Equation Comparative Relational Thinking in a Subtraction Equation Comparative Relational Thinking in an Addition Equation

www.cpalms.org Can You Compare and Find the Missing Number in an Equation?





















https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%203/ZooBooks.pdf
























Topic 3: Decomposing and composing fractions for addition and subtraction Pacing: September 26 – October 6 In this topic students extend their prior knowledge of unit fractions with denominators of 2, 3, 4, 6, and 8 from Grade 3 to include denominators of 5, 10, 12, and 100. In Grade 4, they use their understanding of partitioning to find unit fractions to compose and decompose fractions in order to add fractions with like denominators. This is foundational for further work with fractions later in the year, such as comparing fractions and multiplying fractions by a whole number.


Understand a fraction 𝑎

𝑏 with a > 1 as a sum of fractions

1

𝑏.

a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction

model. Examples: 3

8=

1

8 +

1

8 +

1

8 ;

3

8 =

1

8 +

2

8 ; 2

1

8 = 1 + 1 +

1

8 ; 2

1

8 =

8

8 +

8

8 +

1

8 .

MAFS.4.NF.2.3

decompose denominator equation equivalent fraction numerator sum unit fraction whole

Students will:

• demonstrate with concrete and visual models (i.e., number lines, rectangles, squares, and circles) that adding fractions referring to the same sized whole is joining parts of the whole.

• demonstrate with concrete and visual models that subtracting fractions referring to the same sized whole is separating parts of the whole.

NOTE: Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

• decompose a fraction into a sum of fractions with the same denominator in more than one way using visual models.

• record the decomposition of a fraction by an equation and justify the decomposition.

E.g.,

7. Look for and make use of structure. MAFS.K12.MP.7.1

Topic Comments: 4.NF.2.3 will be revisited in topic 9 to address adding and subtracting mixed numbers.

Students use their previous experiences with composing and decomposing whole numbers to understand the structure of fraction composition (MP 7).




4.N

F.2

.3 (

a, b

)

Topic 3 Shady Fractions Cindy's Carpet Emporium


Reproducibles pp. 3, 7, 11, 12

Daily Math Journal pp. 34, 35, 48

Pick A Problem #46, 47, 48, 49, 50, 55

How Did You Solve It? #38, 39, 40, 41, 42, 43, 44, 45

Daily Dose of Fractions & Decimals #1-120

Giant Magnetic Fraction Circles and Bars

Decomposing Three-Fifths

www.cpalms.org Decomposing Fractions

Relay Races

https://www.illustrativemathematics.org/content-standards Making 22 seventeenths in different ways

Plastic Building Blocks

Cynthia’s Perfect Punch

Peaches

www.IXL.com/signin/volusia Q.4, Q.5, Q.6, Q.7, Q.8, Q. 13, Q.1, Q.2, Q.3

https://learnzillion.com/ Unit 3: Decomposing and composing fractions for addition and subtraction (lessons 1-9)

http://achievethecore.org No aligned resources


https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/ShadyFractions.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/CindysCarpetEmporium.pdf










https://www.illustrativemathematics.org/content-standards/4/NF/B/3/tasks/837








https://learnzillion.com/resources/64181-decomposing-and-composing-fractions-for-addition-and-subtraction





Topic 4: Applying place value concepts in whole number addition and subtraction Pacing: October 9 – 25 The focus of this topic is to provide students time to develop and practice efficient addition and subtraction of multi-digit whole numbers while developing place

value concepts.


Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

MAFS.4.NBT.1.1

base-ten numeral compose (a ten, hundred, thousand, etc.) decompose (a ten, hundred, thousand, etc.) digit expanded form greater than symbol (>) less than symbol (<) multi-digit number names place standard algorithm value

Students will:

• demonstrate with models that in a multi-digit whole number, a digit in one place represents ten times the value of the place to its right. E.g.,

• explain that a digit in one place is worth ten times the value of the place to its right. E.g., 10 × 540 = 5,400; the 5 in 5,400 represents 5 thousands which is 10 times as much as the 5 hundreds in 540. NOTE: While students may discover the pattern of adding a “0” at the end of a number, they need to be able to justify this pattern

in terms of place value. When you multiply a number by 10, the value becomes 10 times greater, so every digit shifts one place to the left, or in 10 x 4, ten groups of 4 ones is 40 ones, which is equivalent to 4 tens, or 40.


Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

MAFS.4.NBT.1.2

Students will:

• read and write multi-digit numbers through one million in base-ten numerals (standard form), number names (word form), and expanded form. NOTE: Expanded form of 285 can be 200 + 80 + 5. However, students should have opportunities to explore the idea that 285

could also be 28 tens plus 5 ones or 1 hundred, 18 tens and 5 ones (necessary for fluent regrouping using the standard algorithm).

• compare two multi-digit numbers to 1,000,000 using place value and record the comparison numerically using the following symbols: <, >, or =.

Use place value understanding to round multi-digit whole numbers to any place. MAFS.4.NBT.1.3

Students will:

• use place value understanding to round multi-digit whole numbers to any place between 1,000 and 1,000,000.

E.g.,

curved number line


Fluently add and subtract multi-digit whole numbers using the standard algorithm MAFS.4.NBT.2.4

Students will:

• apply an understanding of addition and subtraction, place value, and flexibility with multiple strategies to use the standard algorithms for addition and subtraction of whole numbers with solutions greater than 1,000 and within 1,000,000.

NOTE: Computational fluency is defined as accuracy, efficiency, and flexibility. Grade 4 is the first grade-level in which students are expected to be fluent with the standard algorithm to add and subtract. Fluency with the standard algorithm is an end of the year grade level expectation.

6. Attend to precision. 8. Look for and express regularity in repeated reasoning.


Topic Comments:

NBT.1.1 will be revisited in topic 6 connected to conversions within the metric system of measurement. NBT.1.3 will be revisited in topic 7 with multiplication and division as a context. NBT.2.4 will be revisited in topic 8 and finalized in topic 14 for fluency in addition and subtraction of multi‐digit whole numbers.

Students use the structure of the base‐ten system to generalize their strategies and to discuss reasonableness of their computations and work towards fluency (MP.6, MP.8).



4.N

BT

.1.1

Topic 4 Modeling A Million


Reproducibles pp. 3, 5

Daily Math Journal pp. 16, 22, 24, 26, 28, 30

Whole Number Place Value Magnets

How Did You Solve It? #19, 20

Base Ten Place Value Family Vacations Seven Hundred Seventy Seven Comparing Amounts of Baseball Cards

www.cpalms.org 10XBigger!

Terrific Tim’s Ten Tiny Toes

https://www.illustrativemathematics.org/content-standards Thousands and Millions of Fourth Graders

Threatened and Endangered

www.IXL.com/signin/volusia A.1, A.4, B.6, C.4

https://learnzillion.com/ Unit 4: Lesson 1- Understand place-value, the power of 10 http://achievethecore.org No aligned resources


https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/ModelingMillion.pdf














https://www.illustrativemathematics.org/content-standards/4/NBT/A/1/tasks/1808







https://learnzillion.com/lesson_plans/3436-1-understand-place-value-the-power-of-10-c

https://learnzillion.com/lesson_plans/3436-1-understand-place-value-the-power-of-10-c





4.N

BT

.1.2

Topic 4 Modeling A Million I'm The Greatest Place Value Patterns


Reproducibles p. 3

Daily Math Journal pp. 16, 18, 20, 21, 22, 24, 27, 28, 30, 32




Reading Greater Numbers Using Word and Expanded Form Writing Number Names to a Million Collections Numbers in Expanded Form

www.cpalms.org Help Me Build a Roller Coaster

https://www.illustrativemathematics.org/content-standards Ordering 4-digit numbers

www.IXL.com/signin/volusia A.2, A.3, A.5, A.6, A.7, A.8, A.15, K.1 *A.7 & A.8 go to hundred million *A.15 goes to billion

https://learnzillion.com/ Unit 4: Applying place value concepts in whole number addition and subtraction (Lessons 2-4 & 8,9)


4.N

BT

.1.3

Topic 4 Making The Rounds

Teacher Guide: pp. 8-9

Reproducibles: pp. 3




Rounding Numbers Rounding to the Thousands Place Rounding to Ten Thousands Place Rounding to the Hundreds Thousands Place

www.cpalms.org Round Me!

Adventure Falls Bus Purchase

https://www.illustrativemathematics Rounding on the number line

Rounding to the nearest 100 and 1000

Rounding to the nearest 1000

www.IXL.com/signin/volusia A.12, B.8, B.9, C.6, C.7

https://learnzillion.com/ Unit 4: Applying place value concepts in whole number addition and subtraction (Lessons 5-7)





https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/ImTheGreatest.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/ImTheGreatest.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/PlaceValuePatterns.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/PlaceValuePatterns.pdf




















https://learnzillion.com/resources/64182-applying-place-value-concepts-in-whole-number-addition-and-subtraction





https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/MakingTheRounds.pdf
































4.N

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.2.4

Topic 4 Palindromic Ponderings Subtraction Palindromes Two-Digit Turn Around

Teacher Guide: p. 9

Reproducibles: p. 3

Daily Math Journal pp. 17, 19, 21, 23, 25, 28, 31, 32 Pick A Problem #27, 28, 29 How Did You Solve It? #25, 26

Find the Error Fill in the Missing Number Addition Using the Standard Algorithm Subtracting Using the Standard Algorithm

www.cpalms.org Let’s Make a Movie


www.IXL.com/signin/volusia B.1, B.3, C.1, C.3


http://achievethecore.org Addition & Subtraction Mini Assessment


https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/PalindromicPonderings.pdf


https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/SubtractionPalindromes.pdf


https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/TwoDigitTurnAround.pdf





















http://achievethecore.org/page/2778/multi-digit-addition-and-subtraction-mini-assessment



Unit 2 PACING: October 26 – January 23

Topic 5: Understanding fraction equivalence and comparison Pacing: October 26 – November 13 In this topic students develop an understanding of fraction equivalence and various methods for comparing fractions. Students should understand that when comparing fractions, it is not always necessary to generate equivalent fractions. Other methods, such as comparing fractions to a benchmark, can be used to discuss relative sizes. The justification of comparing or generating equivalent fractions using visual models is an emphasis of this topic.


Explain why a fraction 𝑎

𝑏 is equivalent to a fraction

𝑛 ×𝑎

𝑛 ×𝑏 by using visual fraction models, with attention to how

the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

MAFS.4.NF.1.1

benchmark fraction common denominator common numerator denominator equivalent fractions fraction greater than 1 greater than symbol (>) less than symbol (<) numerator unit fraction whole

Students will:

• explain, using visual representation, how and why fractions can be equivalent even though the number and size of the parts are not the same.

• recognize and generate equivalent fractions by partitioning number lines, rectangles, squares, and circles using visual models. E.g.,

NOTE: Denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, 100.

• apply the identity property of multiplication (you can multiply any number by 1 and it keeps its identity; the number maintains the same value) to generate equivalent fractions numerically.

E.g.,

Start with 1

3. Multiply

1

3 by 1 in the form of a fraction as shown below.

1

3 ×

2

2 =

2

6

1

3 ×

4

4 =

4

12

Compare two fractions with different numerators and different denominators, e.g., by creating common

denominators or numerators, or by comparing to a benchmark fraction such as 1

2 . Recognize that comparisons

MAFS.4.NF.1.2


are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Students will:

• explain that fractions can only be compared when they refer to the same sized whole (e.g., 1

2 of a small pizza is not the same

size as 1

2 of a large pizza).

NOTE: Denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, 100.

• compare two fractions with different numerators and different denominators by:

o using benchmark fractions (e.g., 5

8 is close to

1

2 and

1

10 is close to 0, therefore

5

8 >

1

10.

o reasoning about their size or location on a number line. o multiplying by a fraction equivalent to 1 to create common numerators. o multiplying by a fraction equivalent to 1 to create common denominators.

• record the results of comparisons with the symbols <, > or =.

• justify the conclusions of comparisons.

NOTE: Fractions may be greater than 1 (e.g., 6

5).

Students need to be able to generate equivalent fractions, but will NOT use the language, “least common denominator”.

3. Construct viable arguments and critique the reasoning of others. 5. Use appropriate tools strategically.


Topic Comments:

Students justify their methods for generating equivalent fractions and comparing fractions by using their conceptual understanding and models (MP.3, MP.5).




4.N

F.1

.1

Topic 5 Fraction Fringe: On the Cutting Edge Same Name Frame Shady Fractions








Eating Cake Are the Fractions Equivalent Equivalence Using the Number Line Equivalent Fractions on a Number Line

www.cpalms.org Chocolate Fractions

https://www.illustrativemathematics.org/content-standards Explaining Fraction equivalence with pictures

Fractions and rectangles

www.IXL.com/signin/volusia P.5, P.6, P.7, P.8, P.9 *P.8 – goes to 1,000

https://learnzillion.com/ Unit 5: Understanding fraction equivalence and comparison (Lessons 7-10)


4.N

F.1

.2

Topic 5 Ordering Up Fractions Half Track Between Zero and One


Reproducibles pp. 3, 6, 8, 9, 10


Pick A Problem #44, 45,



Comparing Four-Fifths and Three-Fourths Compare Fractions Comparing Fractions Using Benchmark Fractions Corn Farms

www.cpalms.org Fractional Clothesline

https://www.illustrativemathematics.org/content-standards Doubling Numerators and denominators

Listing Fractions in increasing size

Using benchmarks to compare numbers

Comparing Fractions using benchmark game

www.IXL.com/signin/volusia P.14, P.15, P.16, P.17, P.21, R.16

https://learnzillion.com/ Unit 5: Understanding fraction equivalence and comparison (Lessons 1-6 & 11-15)

http://achievethecore.org Human-Sized Number Lines: Let’s Compare Fractions!

Fraction Concept Mini-Assessment


https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/FractionFringeOnCuttingEdge.pdf



https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/SameNameFrame.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/SameNameFrame.pdf














https://www.illustrativemathematics.org/content-standards/4/NF/A/1/tasks/743







https://learnzillion.com/resources/64183-understanding-fraction-equivalence-and-comparison




https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/OrderingUpFractions.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/OrderingUpFractions.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/HalfTrack.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/BetweenZeroAndOne.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/BetweenZeroAndOne.pdf



























http://achievethecore.org/page/2850/human-sized-number-lines-let-s-compare-fractions

http://achievethecore.org/page/2850/human-sized-number-lines-let-s-compare-fractions

http://achievethecore.org/page/1056/fraction-concepts-mini-assessment


Topic 6: Introducing measurement conversions Pacing: November 14 – December 1 In this topic students build a conceptual understanding of the relative sizes of units of measure within a single system of measurement. Measurement conversions are used to introduce multiplication as a comparison. The concepts in this topic are foundational for the concepts in topic 7 and topic 8.


Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

MAFS.4.OA.1.1

equation multiplicative

comparison conversions customary units digit metric units place

Students will:

• interpret a basic multiplication equation as a comparison (e.g., if a = n × b, then a is n times as much as b).

• represent verbal statements of multiplicative comparison as multiplication equations.

NOTE: Statements for comparative language: times as tall as, times as long as, times as heavy as, times as much as, etc. (rather than times taller, times longer, times heavier, etc.).

Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

MAFS.4.NBT.1.1

Students will:

• explain that a digit in one place is worth ten times the value of the place to its right by connecting to measurement conversions within the metric system. E.g.,

Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; L, mL; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …

MAFS.4.MD.1.1

Students will: NOTE: Students need to be provided with the Grade 4 FSA Mathematics Reference Sheet in order to practice using the tool.


• know relative size of measurement units within one system.

• convert larger units of measure into smaller equivalent units (required units are listed on Grade 4 FSA Mathematics Reference Sheet).

• complete a two-column table (function table) showing measurement equivalents and relate measurement conversions to multiplicative comparisons (e.g., 1 yard is 3 times as long as 1 foot).

E.g.,

2. Reason abstractly and quantitatively. 6. Attend to precision. 7. Look for and make use of structure.


Topic Comments: OA.1.1 is repeated in topic 11, in which the focus is on multiplication of fractions. NBT.1.1 was addressed in topic 4, in which the focus was on addition and subtraction. In this topic, metric measurement provides an opportunity to deepen the students’ understanding of place value in relation to multiples of 10. MD.1.1 introduces units of measure new to Grade 4. In this topic students look for patterns in different measurement systems (MP.2, MP.7) and discuss precisely how many times larger one unit is than another (MP.6)



4.O

A.1

.1

Topic 6 Estimating Everything

Teacher Guide p. 3

Reproducibles p. 3



Pet Snakes Kate and Her Doll Animal Photographs Writing an Equation to Match a Word Problem

www.cpalms.org Bar Model Math – Twice as Nice


www.IXL.com/signin/volusia D.1, D.2

https://learnzillion.com/ This concept is built into the conversion lessons. http://achievethecore.org No aligned resources


https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/EstimatingEverything.pdf


















4.N

BT

.1.1

Topic 6 Modeling A

Million



Daily Math Journal pp. 16, 22, 24, 26, 28, 30



Base Ten Place Value Family Vacations Seven Hundred Seventy Seven Comparing Amounts of Baseball Cards Repeated resources from Topic 4

www.cpalms.org Making your first Million

https://www.illustrativemathematics.org/content-standards Thousands and Millions

Threatened and Endangered

www.IXL.com/signin/volusia D.8, E.13

https://learnzillion.com/ Unit 6: Lesson 1- Conversions with metric units using a place value chart


4.M

D.1

.1

Topic 6

Measure for Measure

Reproducible p. 3




Conversions in the Metric System

Conversions in the Metric System Part Two

Conversions in the Customary System

Converting Units of Time

Relative Sizes of Measurement Units for Weight

Relative Sizes of Measurement Units for Length

www.cpalms.org Lets Think in Small Units

https://www.illustrativemathematics.org/content-standards Who is the tallest?

www.IXL.com/signin/volusia N.2, N.3, N.4, N.5, N.6, N.7, N.11, N.12, N.13, N.14, N.15, N.16, O.1

https://learnzillion.com/ Unit 6: Introducing measurement conversions (Lessons 2-10) http://achievethecore.org No aligned resources













http://www.cpalms.org/Public/PreviewResourceUrl/Preview/1870







https://learnzillion.com/lesson_plans/2572-1-conversions-with-metric-units-using-a-place-value-chart-c




https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/MeasureForMeasure.pdf






















https://learnzillion.com/resources/64184-introducing-measurement-conversions




Topic 7: Solving problems using multiplicative comparison Pacing: December 4 – 20 In this topic students are introduced to multiplicative compare problems, extending their conceptual work with multiplicative comparison from topic 6. For students to develop this concept, they must be provided rich problem situations that encourage them to make sense of the relationships among the quantities involved, model the situation, and check their solution using a different method. The Common Multiplication and Division Table (see page 68) is an important resource for understanding multiplicative comparison problems, which are new to Grade 4 students.


Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

MAFS.4.OA.1.2

additive comparison balanced equation comparative relational thinking intervals of time linear models multiplicative comparison place unknown number

Students will:

• distinguish multiplicative comparison (e.g., Tonya has 3 times as many cousins as Matthew) from additive comparison (e.g., Tonya has 3 more cousins than Matthew).

NOTE: In an additive comparison, the underlying question is what amount would be added to one quantity in order to result in the other. In a multiplicative comparison, the underlying question is what factor would multiply one quantity in order to result in the other.

• solve word problems involving multiplicative comparison (situations may include 2-digit by 1-digit expressions or a multiple of 10 by a 1-digit expression).

E.g., A red hat costs $18 and a blue hat costs $6. How many times as much as the blue hat does the red hat cost?

The red hat costs 3 times as much as the blue hat.

Use place value understanding to round multi-digit whole numbers to any place. MAFS.4.NBT.1.3

Students will:

• use place value understanding to round multi-digit whole numbers to any place between 1,000 and 1,000,000.

Use the four operations to solve word problems involving distances, intervals of time, and money, including problems involving simple fractions or decimals. Represent fractional quantities of distance and intervals of time using linear models. NOTE: This is an amended Florida Standard.

MAFS.4.MD.1.2

Students will:

• use multiplication and division to solve multiplicative comparison word problems involving distances (i.e., inch, feet, yard, mile; millimeter, centimeter, meter, kilometer), including problems that require expressing measurements given in a larger unit in terms of a smaller unit, involving whole numbers only.

• use multiplication and division to solve multiplicative comparison word problems involving intervals of time including whole numbers only and represent the intervals of time using linear models.

• use multiplication and division to solve multiplicative comparison word problems involving money including whole numbers only.



MAFS.4.OA.1.a

Students will: NOTE: Due to this standard’s emphasis on mental math, it will be embedded through the use of Number Talks.

• determine if a given equation is true or false by comparing, composing, and/or decomposing the numbers without solving.

NOTE: Equations in this topic may include: Multiplication of 2-digit by 1-digit or a multiple of 10 by 1-digit, division of 2-digit by 1-digit or a multiple of 10 by 1-digit.


MAFS.4.OA.1.b


• compare the two sides of an equation to determine the unknown value without solving. NOTE: Equations in this topic may include: Multiplication of 2-digit by 1-digit or a multiple of 10 by 1-digit, division of 2-digit by 1-digit or a multiple of 10 by 1-digit.

1. Make sense of problems and persevere in solving them. MAFS.K12.MP.1.1

Topic Comments: OA.1.2 is also addressed in topic 14 because of the time it takes to master the concepts and its importance to future mathematics. NBT.1.3 was addressed in topic 4 with a focus on addition and subtraction. In this topic, the focus is on multiplication and division. MD.1.2 is used as a context for multiplicative compare problems with whole numbers only. This standard is revisited in topic 8 to include the four operations, and addressed in topic 12 with decimal fractions. Students use charts and diagrams to explain their own methods as well make sense of approaches taken by others (MP.1).




4.O

A.1

.2

Topic 7 Zoo Books

Teacher Guide p. 3

Reproducibles p. 3


Pick A Problem #9, 10


Books and Yarn Throwing Footballs Making Necklaces Dogs as Pets

www.cpalms.org Travels and More

https://www.illustrativemathematics.org/content-standards Comparing Money Raised


https://learnzillion.com/ Unit 7: Solving problems using multiplicative comparisons (Lessons 1-3)

http://achievethecore.org Comparing Money Raised

4.N

BT

.1.3

Topic 7 Making The Rounds

Teacher Guide pp. 8-9 Reproducibles pp. 3




Rounding Numbers Rounding to the Thousands Place Rounding to Ten Thousands Place Rounding to the Hundreds Thousands Place Resources repeated from Topic 4

www.cpalms.org Round Me! [Also in Topic 4]

Adventure Falls Bus Purchase [Also in Topic 4]

https://www.illustrativemathematics.org/content-standards Rounding on the number line

Rounding to the nearest 100 and 1000

Rounding to the nearest 1000

www.IXL.com/signin/volusia D.12, D.13, D.14, F.3



















https://learnzillion.com/resources/64185-solving-problems-using-multiplicative-comparison




http://achievethecore.org/page/615/comparing-money-raised


































4.M

D.1

.2

Topic 7 Step By Step Mix-Ups and Mysteries

Reproducible p. 3


Pick A Problem #56, 57, 58, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72

How Did You Solve It? #59, 60, 61, 62, 63

Shopping List Kesha and Juan Remote Control Motorcycle Piano Lessons

www.cpalms.org Amazing Race – Elapsed Time

https://www.illustrativemathematics.org/content-standards Margie Buys Apples


https://learnzillion.com/ Unit 7: Lesson 10- Apply converting measurements in order to compare amounts


4.O

A.1

.a


Teacher Guide p. 4


Are the Equations True?

Determining if an Equation is True

True and False Division Equations

True and False Multiplication Equations

Resources repeated from Topic 2

www.cpalms.org Is My Equation TRUE or FALSE?




4.O

A.1

.b

Topic 7 Zoo Books

Teacher Guide p. 4

Reproducibles p. 4


Comparative Relational Thinking in a Division Equation

Comparative Relational Thinking in a Multiplication Equation

Comparative Relational Thinking in a Subtraction Equation

Comparative Relational Thinking in an Addition Equation


www.cpalms.org Can You Compare and Find the Missing Number In an Equation?





https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/StepByStep.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/MixUpsAndMysteries.pdf
















https://learnzillion.com/lesson_plans/3844-10-apply-converting-measurements-in-order-to-compare-amounts-a












































Topic 8: Solving measurement problems using the four operations Pacing: January 8 - 23 In this topic students combine competencies from different domains to solve measurement problems using the four operations. Measurement is included in this topic to provide a context for problem solving. All of the problem types in the Common Addition and Subtraction and Multiplication and Division Tables (see pg. 67 and 68) should be addressed in this topic.



MAFS.4.OA.1.3

comparative relational thinking estimation linear model intervals of time mental computation reasonableness remainder standard algorithm unknown quantity variable

Students will:

• solve multi-step word problems (i.e., up to 3 steps) that involve the four operations using strategies for this grade level (e.g, rectangular arrays, area models, properties of operations, etc).




NOTE: The expectations for multi-step word problems include addition and subtraction within 1,000, multiplication of 2‐digit by 1‐digit or a multiple of 10 by a 1‐digit, and division of 2‐digit by 1‐digit

Fluently add and subtract multi-digit whole numbers using the standard algorithm. MAFS.4.NBT.2.4

Students will:

• apply an understanding of addition and subtraction, place value, and flexibility with multiple strategies to use the standard algorithms for addition and subtraction.

NOTE: Addition expressions may contain up to three addends.


MAFS.4.MD.1.2

Students will:

• use the four operations to solve word problems involving distances (i.e., inch, feet, yard, mile; millimeter, centimeter, meter, kilometer), including problems that require expressing measurements given in a larger unit in terms of a smaller unit, involving whole numbers only.

• use the four operations to solve word problems involving intervals of time including whole numbers only and represent the intervals of time using linear models.

• use the four operations to solve word problems involving money including whole numbers only. NOTE: All of the problem types in the Common Addition and Subtraction and Multiplication and Division Tables (see pg. 67 and 68) should be addressed in this topic.



MAFS.4.OA.1.a


• determine if a given equation is true or false by comparing, composing, and/or decomposing the numbers without solving.


MAFS.4.OA.1.b


• compare the two sides of an equation to determine the unknown value without solving. NOTE: Equations may include:

o Addition and subtraction with 1,000. o Multiplication of 2-digit by 1-digit, or a multiple of 10 by 1-digit. o Division of 2-digit by 1-digit or a multiple of 10 by 1-digit.

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 6. Attend to precision.


Topic Comments: OA.1.3 and NBT.2.4 are repeated here to include all four operations and will be finalized in topic 14. Repeating these standards throughout the year provides students multiple opportunities to develop these skills—which are major areas of focus for this grade level. MD.1.2 is repeated from the previous topic, but in this topic the emphasis is on using the four operations and all problem types. This standard will be finalized in topic 12 to include decimal fractions. Students use various diagrams and precise language to solve measurement problems and explain their strategies (MP.1, MP.6). They make connections between abstract representations and the problem situations (MP.2).




4.O

A.1

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Topic 8 Picturing Clues Party Planning

Teacher Guide p. 4

Reproducibles p. 3




Picking Strawberries Estimating the Solution Juice Boxes Resources repeated from Topic 2

www.cpalms.org Express Yourself with Math Story Chains

Birthday Balloon Planner

Florida Tours Company


Karl’s Garden

www.IXL.com/signin/volusia D.13, D.14, E.11, E.15, F.3, F.6

https://learnzillion.com/ This concept is addressed through lessons aligned with MD.1.2. http://achievethecore.org Mini Assessment

4.N

BT

.2.4


Teacher Guide p. 9 Reproducibles p. 3 Daily Math Journal pp. 17, 19, 21, 23, 25, 28, 31, 32



Find the Error Fill in the Missing Number Addition Using the Standard Algorithm Subtraction Using the Standard Algorithm Resources repeated from Topic 4

www.cpalms.org Let’s Make a Movie [Also in Topic 4]


www.IXL.com/signin/volusia B.1, B.2, B.3, C.1, C.2, C.3 Resources repeated

https://learnzillion.com/ Unit 8: Lesson 8- Solving multi-step measurement word problems using the standard algorithm

http://achievethecore.org Fluency practice Addition & Subtraction Mini Assessment






















http://achievethecore.org/page/1031/multi-step-problems-using-the-four-operations-mini-assessment






















https://learnzillion.com/lesson_plans/2032-8-solving-multi-step-measurement-word-problems-using-the-standard-algorithm-fp




http://achievethecore.org/page/2948/fluency-resources-for-grade-level-routines






4.M

D.1

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Reproducible p. 3


Pick A Problem #56, 57, 58, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72


Shopping List

Kesha and Juan

Remote Control Motorcycle

Piano Lessons Resources repeated from Topic 7

www.cpalms.org Money Managers!

https://www.illustrativemathematics.org/content-standards Margie Buys Apples [Also in Topic 7]

www.IXL.com/signin/volusia O.5, O.7, O.8

https://learnzillion.com/ Unit 8: Lesson 7- Solving multi-step problems Unit 8: Lesson 10- Solving multi-step measurement problems http://achievethecore.org No aligned resources

4.O

A.1

.a


Teacher Guide p. 4


Are the Equations True?

Determining if an Equation is True

True and False Division Equations

True and False Multiplication Equations

Repeated resources from Topics 2 and 7

www.cpalms.org Is My Equation TRUE or FALSE? [Also in Topic 2, 7]




4.O

A.1

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Topic 8 Zoo Books

Teacher Guide p. 4

Reproducibles p. 4


Comparative Relational Thinking in a Division Equation

Comparative Relational Thinking in a Multiplication Equation

Comparative Relational Thinking in a Subtraction Equation

Comparative Relational Thinking in an Addition Equation

Repeated resources from Topics 2 and 7

www.cpalms.org Can You Compare and Find the Missing Number In an Equation? [Also in Topic 2, 7]


www.IXL.com/signin/volusia No aligned resources https://learnzillion.com/ No aligned resources http://achievethecore.org No aligned resources

















https://learnzillion.com/lesson_plans/2006-7-solving-multi-step-problems-c

https://learnzillion.com/lesson_plans/2006-7-solving-multi-step-problems-c

https://learnzillion.com/lesson_plans/4130-10-solving-multi-step-measurement-problems-a

https://learnzillion.com/lesson_plans/4130-10-solving-multi-step-measurement-problems-a









































Unit 3 PACING: January 24 – March 30

Topic 9: Solving addition and subtraction problems involving fractions and mixed numbers

Pacing: January 24 – February 5

In this topic students will use their understanding of adding and subtracting fractions and generating equivalent fractions to solve problems involving fractions and mixed numbers. Students rely on their previous work with whole numbers as fractions to compose and decompose whole numbers into fractional quantities. Data is used in this topic to support students’ understanding of fractional quantities both less than and greater than 1.




1

𝑏.

c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. d. Solve word problems involving the addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

MAFS.4.NF.2.3

data set decomposition denominator equation equivalent fraction fraction greater than 1 line plot mixed number numerator sum unit fraction whole

Students will:

• decompose a mixed number into a sum of fractions equal to 1 and a fraction less than 1 to find an equivalent fraction to replace the mixed number in an addition or subtraction situation. E.g.,

21

8+

3

8

17

8+

3

8 =

20

8

• find equivalent sums or differences by converting fractions greater than 1 to mixed numbers by decomposing the fraction into a sum of fractions equal to 1 and fractions less than 1. E.g.,

• add and subtract mixed numbers with like denominators using equivalent fractions, and/or by using properties of operations and the relationship between addition and subtraction.

E.g., 3 3

4. + 2

1

4


E.g., Students use their knowledge of decomposition (17

6 =

12

6 +

5

6) to calculate

17

6 –

5

6 =

12

6.

• solve word problems involving addition and subtraction of fractions and mixed numbers with like denominators using visual fraction models (i.e., circular models, rectangular models, and number line models) and/or equations.

E.g., Lindsey and Brooke need 3 3

8 feet of ribbon to design costumes for a performance. Lindsey has 1

1

8 and Brooke has 2

5

8 feet

of ribbon. If they combine what they have, will that be enough for the project? Explain why or why not.

Ribbon needed for the project 33

8 ft. =

8

8 ft. +

8

8 ft. +

8

8 ft.+

3

8ft.=

27

8ft.

Lindsey’s 9

8 ft. + Brooke’s

21

8 ft. =

30

8 ft.

30

8 ft. is greater than

27

8ft. So they have enough ribbon for the costumes.

NOTE: Denominators of given fractions are limited to: 2, 3, 4, 5, 6, 8, 10, 12, 100.


Make a line plot to display a data set of measurements in fractions of a unit (1

2,

1

4,

1

8). Solve problems involving

addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

MAFS.4.MD.2.4

Students will:

• create a line plot to display measurement data including fraction units of halves, quarters, and eighths.

E.g., Thomas’ father cuts a wooden rod into 8 smaller pieces. He records the measurements of each piece on a line plot.

• use the measurement data on a line plot to solve problems involving the addition and subtraction of fractions with like denominators.

E.g., A small group of students in Mr. Tordini’s class measure the antennae of different insects to the nearest eighth of an inch. They display the measurements on the line plot shown below. Answer the following questions based on the line plot.

o What is the difference between the longest and shortest antennae of all the insects that were measured?

(Answer:12

8−

1

8 =

11

8 inches)

o If the antennae with the longest length were laid end to end, what would their total length be?

(Answer: 12

8 +

12

8 =

24

8 inches)


2. Reason abstractly and quantitatively. 4. Model with mathematics.


Topic Comments: 4.MD.2.4 extends students’ work from Grade 3 with simple fractions on a line plot (3.MD.2.4) to include eighths and to now solve addition and subtraction problems using the data. Students reason about fractions by using abstract models to represent both the data and the fractional quantities (MP.2, MP.4).



4.N

F.2

.3 (

c, d

)

Topic 9 Shady Fractions Cindy's Carpet Emporium




Pick A Problem #46, 47, 48, 49, 50, 55




Anna Marie and the Pizza Fraction Word Problems Adding and Subtracting Mixed Numbers

www.cpalms.org Learning to Love Like Denominators

https://www.illustrativemathematics.org/content-standards Cynthia’s Perfect Punch

Peaches


Writing a Mixed Number as an Equivalent Fraction

www.IXL.com/signin/volusia P.4, P.23, Q.11, Q.12, Q.14

https://learnzillion.com/ Unit 3: Decomposing and composing fractions for addition and subtraction (lessons 10-12) Unit 9: Solving addition and subtraction word problems involving fractions and mixed numbers (Lessons 1-4 & 6-9)


4.M

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Topic 9 Hook, Line, & Sticker

Teacher Guide p. 21

Reproducible p. 3




Race Cars Part One Race Cars Part Two Science Experiment Part One Science Experiment Part Two

www.cpalms.org No aligned resources

https://www.illustrativemathematics.org/content-standards Button Diameters

www.IXL.com/signin/volusia J.6, J.7, J.8

https://learnzillion.com/ Unit 9: Lesson 5- Analyzing Line plots with fractions greater than 1. http://achievethecore.org No aligned resources






























https://learnzillion.com/resources/64187-solving-addition-and-subtraction-word-problems-involving-fractions-and-mixed-numbers





https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%203/HookLineSticker.pdf












https://www.illustrativemathematics.org/content-standards/4/MD/B/4/tasks/1039




https://learnzillion.com/lesson_plans/9633-5-analyzing-line-plots-with-fractions-greater-than-one-a




Topic 10: Angle measurement Pacing: February 6 – 21 This topic is an introduction to angles and angle measurement. Students start this topic drawing points, lines, segments, rays and angles since it is foundational to the other standards in this topic. Students use their understanding of equal partitioning and unit measurement to understand angle and turn measure.


Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.

a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the

circle. An angle that turns through 1

360 of a circle is called a “one-degree angle,” and can be used to

measure angles. b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

MAFS.4.MD.3.5

acute angle angle measure degree endpoint line line segment obtuse one-degree angle point protractor ray right rotation

Students will:

• recognize an angle as a geometric shape that is formed when two rays share a common endpoint.

• explain the relationship between a circle and the number of degrees in an angle (i.e., an angle is measured in reference to a circle—its center is the endpoint for each of the rays that make up the angle).

• explain an angle as a series of “one-degree turns” and the total number of “one-degree turns” is the measure of the angle in

degrees ().

E.g., A water sprinkler rotates one-degree at each interval. If the sprinkler rotates a total of 100 one-degree turns, what is the measure of the sprinkler’s rotation in degrees?

• explain that since it takes 360 “one-degree turns” to rotate through a circle, 1

360 of a circle is a “one-degree angle”.

E.g.,


Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. MAFS.4.MD.3.6

Students will:

• measure an angle to the nearest whole number degrees using a protractor. E.g.,

• use a protractor to sketch an angle given a specific measurement.

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

MAFS.4.G.1.1

Students will:

• draw points, lines, line segments, rays, right angles (exactly 90), acute angles (less than 90), obtuse angles (greater than 90

and less than 180). E.g.,

4. Model with mathematics. 5. Use appropriate tools strategically.


Topic Comments: In this topic, 4.G.1.1 focuses on drawing points, lines, line segments, rays, and different types of angles. The standard will be addressed in its entirety in topic 13. Students select and use a protractor to measure angles and represent the angles with drawings (MP.4, MP.5).




4.M

D.3

.5



Reproducible: p. 3

Daily Math Journal p. 60


Angles Measurement Center

Lawn Sprinkler Circle the Angles Determining an Angle's Measure This Angle

www.cpalms.org No aligned resources https://www.illustrativemathematics.org/content-standards No aligned resources

www.IXL.com/signin/volusia Z.2

https://learnzillion.com/ Unit 10: Angle measurement

(Lessons 4-7) http://achievethecore.org No aligned resources

4.M

D.3

.6

Topic 10 Protractor Ground School Flight Paths Mirrors That Multiply Hall of Mirrors


Reproducible: p. 3

Daily Math Journal pp. 59, 62



Protractors

Measuring Angles with a Protractor Drawing and Measuring Angles Town of Happyville Using a Protractor to Measure Angles

www.cpalms.org Runway Rotations

https://www.illustrativemathematics.org/content-standards Finding an Unknown Angle

Measuring Angles

www.IXL.com/signin/volusia Z.3

https://learnzillion.com/ Unit 10: Angle measurement (Lessons 8-9) http://achievethecore.org No aligned resources

4.G

.1.1

Topic 10 Hall of Mirrors Lines to Design


Reproducible: p. 3


Pick A Problem #86, 87, 88, 89, 90, 91, 92


2-D Geometric Shapes Tub

Geometry in the Real World Photo Magnets

Locating Points, Lines, and Rays All About Angles

www.cpalms.org Angle Your Way Around

https://www.illustrativemathematics.org/content-standards Addressed in Topic 13

www.IXL.com/signin/volusia W.4, Z.1

https://learnzillion.com/ Unit 10: Angle measurement (Lessons 1-3)















https://learnzillion.com/resources/64188-angle-measurement



https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/ProtractorGroundSchool.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/ProtractorGroundSchool.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/FlightPaths.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/MirrorsThatMultiply.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/MirrorsThatMultiply.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/HallOfMirrors.pdf

















https://www.illustrativemathematics.org/content-standards/4/MD/C/7/tasks/1168









https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/LinesToDesign.pdf














Topic 11: Multiplying fractions by whole numbers Pacing: February 22 – March 8 In this topic students apply their understanding of composing and decomposing fractions to develop a conceptual understanding of multiplication of a fraction by a whole number. Students also use and extend their previous understandings of operations with whole numbers and relate that understanding to fractions.


Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

MAFS.4.OA.1.1 decompose denominator equivalent fraction multiplicative comparison numerator times as many times as much unit fraction whole number

Students will:

• interpret an equation involving multiplying a fraction by a whole number as a verbal comparison (e.g., if 5

4 = 5 x

1

4, then

5

4 is 5 times

as much as 1

4).

• represent verbal statements of multiplicative comparison involving multiplying a fraction by a whole number as a multiplication

equation (e.g., Rob’s stick is 6 times as long as Todd’s. Todd’s stick is 1

5 yard long. A multiplication equation that represents the

situation is 6 x 1

5 =

6

5.)

NOTE: Multiplying by a fraction (i.e., 𝑎

𝑏 x n) is not an expectation of the Standards in Grade 4, so situations should be limited to

contexts where the multiplier is a whole number and the number being multiplied can realistically be represented by a fraction (such as measurement situations).

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

a. Understand a fraction 𝑎

𝑏 as a multiple of

1

𝑏. For example, use a visual fraction model to represent

5

4 as the product 5 x (

1

4), recording the conclusion by the equation

5

4 = 5 x (

1

4).

b. Understand a multiple of 𝑎

𝑏 as a multiple of

1

𝑏, and use this understanding to multiply a fraction by

a whole number. For example, use a visual fraction model to express 3 x (2

5) as 6 x (

1

5),

recognizing this product as 6

5. (In general, n x (

𝑎

𝑏) = (

𝑛 𝑥 𝑎)

𝑏).

c. Solve word problems involving multiplication of a fraction by a whole number, e.g. by using visual fraction models and equations to represent the problem. For example, if each person at a party will

eat 3

8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast

beef will be needed? Between what two whole numbers does your answer lie?

MAFS.4.NF.2.4

Students will:

• decompose a fraction into unit fractions (i.e., fractions with a numerator of one) and record the conclusion with a multiplication equation.

E.g.,

3 groups of 1

7 is

3

7, so 3 x

1

7 =

3

7


• Recognize that a fraction 𝑎

𝑏 is a multiple of

1

𝑏

• Recognize that a multiple of 𝑎

𝑏 is also a multiple of

1

𝑏 (e.g., 3 groups of

2

5 has the same value as 6 groups of

1

5) and use this

understanding to multiply a fraction by a whole number.

E.g.,

• solve word problems that involve multiplying a fraction by a whole number using visual models and equations.

E.g., If each person at a party eats 3

8 of a pound of roast beef, and there are 5 people at the party, how many pounds of roast beef

are needed?

NOTE: Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

1. Make sense of problems and persevere in solving them. 6. Attend to precision.


Topic Comments:

4.OA.1.1 is readdressed in this topic to include multiplication of fractions and apply the understanding of “times as much” (i.e. multiplication as comparison) to multiplying a fraction by a whole number.

4.NF.2.4 is limited to multiplying fractions by whole numbers (e.g., 3 x 2

5). Students do not multiply whole numbers by fractions (e.g.,

2

5 x 3) or

fractions by fractions until Grade 5.

Students use precise language to communicate their comprehension of the problem situations and defend their various solution methods (MP.1, MP.6)




4.O

A.1

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Topic 11 Estimating Everything

Teacher Guide: p. 3

Reproducibles: p. 3



Pet Snakes Kate and Her Doll Animal Photographs Writing an Equation to Match a Word Problem Resources repeated from Topic 6

www.cpalms.org Exploring Fraction Multiplication

https://www.illustrativemathematics.org/content-standards This concept is addressed through lessons aligned with NF.2.4.


https://learnzillion.com/ Unit 11: Multiplying fractions by whole numbers (Lessons 8-10). http://achievethecore.org No aligned resources

4.N

F.2

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Teacher Guide: pp. 17-18

Reproducibles: pp. 3, 6

Daily Math Journal: pp. 37, 38, 41, 44, 47, 49, 51, 53, 54


How Did You Solve It? #46, 47, 48, 49, 50, 51


Problem Solving Strategy Puzzles- Blue Set


Fractions and Multiples How Many One Fourths? How Much Sugar? Training For A Race

www.cpalms.org Multiply Fractions and Whole Numbers with Models

https://www.illustrativemathematics.org/content-standards Extending Multiplication from Whole Number to Fractions

Sugar in Six Cans of Soda

www.IXL.com/signin/volusia S.1, S.2, S.5, S.6, S.7, S.8, S.10, S.12, S.14, S.15

https://learnzillion.com/ Unit 11: Multiplying fractions by whole numbers (Lessons 1-7).




















https://learnzillion.com/resources/64189-multiplying-fractions-by-whole-numbers


























Topic 12: Comparing decimal fractions and understanding notation Pacing: March 19 – March 30 In this topic of study students use their previous work with fractions to represent special fractions in a new way. Students use their understanding of equivalent fractions to begin to use decimal notation—however, it is not the intent at this grade level to connect this notation to the base-ten system. The focus is on solving word problems involving simple fractions or decimals. Work with money can support this work with decimal fractions.


Express a fraction with denominator 10 as an equivalent fraction with denominator 100 and use this technique

to add two fractions with respective denominators 10 and 100. For example, express 3

10 as

30

100, and add

3

10 +

4

100 =

34

100.

MAFS.4.NF.3.5

decimal fractions decimal notation denominator equivalent fraction hundredths intervals of time numerator tenths digit equivalence place value

Students will:

• represent fractions with a denominator of 10 and fractions with a denominator of 100 using models (e.g., grids, base ten blocks, and number lines).

• express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100.

E.g.,

NOTE: While students may be able to easily see the pattern of adding a “0” at the end of a numerator when creating these equivalent fractions, they need to be able to justify why this works.

• add two fractions with denominators 10 and/or 100 by finding equivalent fractions with like denominators.


Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62

100; describe

length as 0.62 meters; locate 0.62 on a number line diagram. MAFS.4.NF.3.6

Students will:

• demonstrate place value of decimals through the hundredths using concrete materials (e.g., decimal grids, base ten blocks, number lines).

E.g.,

• translate a fraction with a denominator of 10 or 100 into its equivalent decimal form.

• translate a decimal to the tenths or hundredths place into its equivalent fraction form.

• represent a decimal value on a number line.

Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

MAFS.4.NF.3.7

Students will:

• explain that decimals can only be compared when they refer to the same sized wholes.

NOTE: Decimals may be greater than 1.

• compare decimals with and without models (such as decimal grids or base ten blocks) and record the comparison numerically using symbols: <, > or =.

• justify the comparison by reasoning about the size of the decimal.

E.g., To compare 1.32 and 1.6, students create a model to show that 1.32 < 1.6



MAFS.4.MD.1.2

Students will:

• use the four operations to solve word problems involving distances (i.e., inch, feet, yard, mile; millimeter, centimeter, meter, kilometer), including simple fractions or decimals.

• represent fractional quantities of distance using linear models.

E.g., Billy has been training for a half-marathon. Each day he runs on the treadmill 2 2

4 miles and runs on the outdoor track for 3

1

4

miles. In all, how many miles does Billy run each day?

• use the four operations to solve word problems involving intervals of time including simple fractions and represent these intervals of time using linear models.

E.g., Jim got to the fair at 5:45 P.M. He spent 1 hour playing games, 11

4 hours riding rides, and

1

4 hour eating dinner before

leaving. What time did Jim leave?

• use the four operations to solve word problems involving money including simple decimals.

E.g., Helen bought popcorn at the movies. She bought 2 large bags, and each one cost $1.30. How much change did she receive from $5?

NOTE: Decimal amounts should be limited to hundredths in multiples of 10 (e.g., $0.10, $0.20, $0.30, $ 0.40…) in order to relate to fractions. Computational fluency with fractions and decimals is not the goal for students at this grade level.

3. Construct viable arguments and critique the reasoning of others. 7. Look for and make use of structure.


Topic Comments:

4.MD.1.2 was addressed in topic 7. It is important to note that students are not expected to do computations with quantities in

decimal notation. Students can use visual fraction models to solve problems involving simple fractions or decimals.

Students compare decimals fractions and justify their comparisons using either a fraction model or their understanding of the notation (MP.3, MP.7).




4.N

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Topic 12 What's The Point



Daily Math Journal pp. 34, 38, 42, 45, 47, 48, 51, 52, 54


Daily Dose of Fractions & Decimals 121-150

Adding Five Tenths Hundredths and Tenths Seven Tenths Tenths and Hundredths

www.cpalms.org How many Tenths and Hundredths

https://www.illustrativemathematics.org/content-standards Adding Tenths and Hundredths

Fraction Equivalence

www.IXL.com/signin/volusia P.8, R.5, R.6

https://learnzillion.com/ Unit 12: Comparing decimal fractions and understanding notation (Lessons 5 & 6)


4.N

F.3

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Topic 12 What's The Point

Teacher Guide p. 19

Reproducible p. 3

Daily Math Journal pp. 46, 50, 52



Using Benchmark Fractions on a Number Line Using Benchmark Decimals on a Number Line Fractions to Decimals Decimals to Fractions

www.cpalms.org Fractions Undercover

https://www.illustrativemathematics.org/content-standards Dimes and Pennies

Expanded Fractions and Decimals

How Many Tenths and Hundredths

www.IXL.com/signin/volusia T.1, T.2, T.4, T.6, T.7, T.8, T.9, T.10, T.11 *T.10 goes to thousandths

https://learnzillion.com/ Unit 12: Comparing decimal fractions and understanding notation (Lessons 1-3)



https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/WhatsThePoint.pdf









http://www.cpalms.org/Public/PreviewResourceUpload/Preview/43259

http://www.cpalms.org/Public/PreviewResourceUpload/Preview/43259

https://www.illustrativemathematics.org/content-standards/4/NF/C/5/tasks/153






https://learnzillion.com/resources/64190-comparing-decimal-fractions-and-understanding-notation




https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/WhatsThePoint.pdf





























4.N

F.3

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Topic 12 Dueling Decimals Show Me The Money




How Did You Solve It? #56


Decimal Place Value Magnets

Decimal Grids

Compare Decimals Comparing Four Tenths Using Models to Compare Decimals Comparing Decimals in Context

www.cpalms.org Using Models to Compare Decimals

https://www.illustrativemathematics.org/content-standards Using Place Value

www.IXL.com/signin/volusia T.5, T.14, T.15, T.16, T.17

https://learnzillion.com/ Unit 12: Comparing decimal fractions and understanding notation (Lessons 7-10)


4.M

D.1

.2


Reproducible p. 3


Pick A Problem #56, 57, 58, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72


Shopping List Kesha and Juan Remote Control Motorcycle Piano Lessons Resources repeated from Topics 7 and 8

www.cpalms.org Amazing Race – Elapsed Time [Also in Topic 7]

Money Managers! [Also in Topic 8]

https://www.illustrativemathematics.org/content-standards Margie Buys Apples [Also in Topic 7, 8]

www.IXL.com/signin/volusia M.4, M.6, M.7, O.5, O.6, O.7, Q.11, S.6, S.12, S.15



https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/DuelingDecimals.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/ShowMeTheMoney.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/ShowMeTheMoney.pdf









































Unit 4 PACING: April 2 – May 30

Topic 13: Recognizing and analyzing attributes of 2-dimensional shapes Pacing: April 2 - 17 In this topic students develop their spatial reasoning skills by using a wide variety of attributes to talk about 2-‐dimensional shapes. Students analyze geometric figures based on angle measurement, parallel and perpendicular lines, and symmetry.


Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

MAFS.4.OA.3.5 attributes acute angle additive angle angle measure category classify decompose degree endpoint feature generate line line segment line symmetrical line symmetry nonoverlapping numeric pattern obtuse angle parallel lines perpendicular lines point protractor ray right angle right triangle rule sequence shape pattern term variable

Students will:

• generate a number or shape pattern that follows a given one- or two-step rule.

• identify features in number or shape patterns after following a given one- or two-step rule.

E.g, The pattern repeats every five steps and goes in this order, circle, hexagon, right triangle, square, square. Can you draw the next four shapes in the pattern?

Can you tell what the 51st shape in the pattern will be without drawing all of the shapes? How did you determine what the 51st shape would be?

“The pattern is circle, hexagon, right triangle, square, square, and the pattern repeats every five numbers. I looked at 50 and knew the 50th shape would be a square, so the 51st shape will begin the pattern again and it is a circle.”

Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

MAFS.4.MD.3.7

Students will:

• recognize angle measure as additive, explaining that the angle measurement of a larger angle is the sum of the angle measures of its decomposed parts.

• solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.

E.g.,


Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

MAFS.4.G.1.1

Students will:

• draw points, lines, line segments, rays, right angles (exactly 90), acute angles (less than 90), obtuse angles (greater than 90

and less than 180), and perpendicular and parallel lines. E.g.,

• identify the two-dimensional attributes shown above in two-dimensional shapes. E.g., List the two-dimensional attributes within this trapezoid:

NOTE: Students can and should make geometric distinctions about angles without measuring or mentioning degrees. Angles

should be classified in comparison to right angles, such as greater than (obtuse) or less than (acute) a right angle.


Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

MAFS.4.G.1.2

Students will:

• classify two-dimensional shapes into the following categories: those with parallel lines, those with perpendicular lines, those with both parallel and perpendicular lines, those with no parallel or perpendicular lines.

• classify two-dimensional shapes into categories based on the presence or absence of acute, obtuse, or right angles.

• recognize that right triangles form a category of triangles and identify triangles that fit in this category. E.g., Do you agree with the label on each of the ovals in the Venn diagram? Why or why not? Explain why some shapes fall in the overlapping sections of the ovals.

Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

MAFS.4.G.1.3

Students will:

• explain line symmetry and identify figures that have line symmetry (e.g., fold a figure or draw a line so it has two parts that match exactly).

• draw lines of symmetry in both regular and non-regular polygons. E.g.,

NOTE: This standard only includes line symmetry, NOT rotational symmetry.


3. Construct viable arguments and critique the reasoning of others. 5. Use appropriate tools strategically. 7. Look for and make use of structure.


Topic Comments:

In this topic, 4.OA.3.5 includes repeated and growing shape patterns. 4.G.1.1 was first addressed in topic 10, and is addressed in its entirety in this topic to include perpendicular and parallel lines. The concepts in this topic lend themselves to using technology applications (MP.5). Students understand that geometric figures can be classified by analyzing various properties (MP.7) and justify their conclusions by using viable arguments (MP.3).



OA

.3.5

Topic 13 Key Codes

Teacher Guide p. 6

Reproducible p. 3


Pick A Problem #7, 8, 11, 19, 20


Multiply by Four Dot Patterns Baseball Cards Resources repeated from Topic 1

www.cpalms.org Pattern Fun

https://www.illustrativemathematics.org/content-standards Double Plus One [Also in Topic 1]

Multiples of Nine [Also in Topic 1]

Multiples of 3,6, and 7 [Also in Topic 1]

www.IXL.com/signin/volusia L.1, L.2, L.4

https://learnzillion.com/ Unit 13: Lesson 9- Understand patterns that follow a rule Unit 13: Lesson 10- Explore patterns that follow rules http://achievethecore.org No aligned resources


https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/KeyCodes.pdf










https://www.illustrativemathematics.org/content-standards/4/OA/C/5/tasks/1481

https://www.illustrativemathematics.org/content-standards/4/OA/C/tasks/1484




https://learnzillion.com/lesson_plans/4210-9-understand-patterns-that-follow-a-rule-c

https://learnzillion.com/lesson_plans/4210-9-understand-patterns-that-follow-a-rule-c

https://learnzillion.com/lesson_plans/2168-10-explore-patterns-that-follow-rules-a

https://learnzillion.com/lesson_plans/2168-10-explore-patterns-that-follow-rules-a





4.M

D.3

.7



Reproducible p. 3





Protractors

Turns on a Skateboard

Using Known Angles Understanding Angles What is the Measure of the Angle?

www.cpalms.org Adding up the Angles

Edible Angles: Decomposing Angles into Parts of a Whole

What’s My Degree? Coming Full Circle

https://www.illustrativemathematics Finding an Unknown Angle

Measuring Angles

www.IXL.com/signin/volusia Z.3 Repeated resource

https://learnzillion.com/ Unit 13: Recognizing and analyzing attributes of 2-dimensional shapes (Lessons 4-6)


4.G

.1.1

Topic 13 Hall of Mirrors Lines to Design


Reproducible p. 3


Pick A Problem #86, 87, 88, 89, 90, 91, 92


2-D Geometric Shapes Tub

Geometry in the Real World Photo Magnets

Locating Points, Lines, and Rays All About Angles Lines, Rays, and Line Segments Parallel and Perpendicular Sides Some resources repeated from Topic 10

www.cpalms.org Geometric Math Makers

Points, Lines, and Angles, Oh My!

Geometry at the County Fair

Geometry, USA

Parallel and Perpendicular Lines

https://www.illustrativemathematics.org/content-standards The Geometry of Letters

What’s the Point?

www.IXL.com/signin/volusia W.5

https://learnzillion.com/ Unit 13: Recognizing and analyzing attributes of 2-dimensional shapes (Lessons 1-2)
























https://learnzillion.com/resources/64192-recognizing-and-analyzing-attributes-of-2-dimensional-shapes


























https://www.illustrativemathematics.org/content-standards/4/G/A/1/tasks/1263













4.G

.1.2

Topic 13 Classifying Quadrilaterals

Teacher Guide p. 24 Reproducible pp. 3, 16 Daily Math Journal pp. 66, 68, 69, 70, 71 Pick A Problem #93, 94, 95, 96, 98 How Did You Solve It? #80, 81, 82, 83, 84, 85 Protractors

Grouping Triangles Sketching Quadrilaterals Sketching Triangles

www.cpalms.org A Closer Look at Quadrilaterals: The Parallelogram Connection

Polygon Express

https://www.illustrativemathematics Are These Rights?

Defining Attributes of Rectangles and Parallelograms

What is a Trapezoid (Part 1)

What Shape and I?

www.IXL.com/signin/volusia X.3, X.4, X.5

https://learnzillion.com/ Unit 13: Lesson 3- Use perpendicular and parallel lines to describe 2D figures http://achievethecore.org No aligned resources

4.G

.1.3

Topic 13 Line Symmetry, Naturally

Teacher Guide p. 24 Reproducible p. 3 Pick A Problem #97, 99, 100 Daily Math Journal pp. 66, 67, 68, 70 How Did You Solve It? #86, 87, 88, 89, 90

Squares and Lines of Symmetry Using Line of Symmetry Line Symmetry Identifying and Explaining Symmetry

www.cpalms.org ABC Symmetry

Symmetrical Solutions

The Secret Agent Symmetry Man!

https://www.illustrativemathematics.org/content-standards Finding Lines of Symmetry

Lines of Symmetry for Circles

Lines of Symmetry for Quadrilaterals

Lines of Symmetry for Triangles

www.IXL.com/signin/volusia Y.1, Y.2, Y.3

https://learnzillion.com/ Unit 13: Lesson 8- Create lines of symmetry



https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%205/ClassifyingQuadrilat.pdf

https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%205/ClassifyingQuadrilat.pdf






















https://learnzillion.com/lesson_plans/2162-3-use-perpendicular-and-parallel-lines-to-describe-2d-figures-a




https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/LineSymmetryNaturally.pdf



























https://learnzillion.com/lesson_plans/2166-8-create-lines-of-symmetry-fp

https://learnzillion.com/lesson_plans/2166-8-create-lines-of-symmetry-fp



Topic 14: Problem solving with whole numbers Pacing: April 18 - May 11 This is a culminating topic in which students focus on problem solving in order to demonstrate fluency with the standard algorithms in addition and subtraction. They demonstrate computational fluency with all problem types. All standards in this topic have been addressed in prior topics. These concepts require greater emphasis due to the depth of the ideas, the time they take to master, and/or their importance to future mathematics.


Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

MAFS.4.OA.1.2

area model multiplicative

comparison properties of operations rectangular array standard algorithm

Students will:

• distinguish multiplicative comparison (e.g., Tonya has 3 times as many cousins as Matthew) from additive comparison (e.g., Tonya has 3 more cousins than Matthew).

• solve word problems involving multiplicative comparison (situations may include 2-digit by 1-digit expressions or a multiple of 10 by a 1-digit expression).


MAFS.4.OA.1.3

Students will:

• solve multi-step word problems (i.e., up to 3 steps) that involve the four operations using strategies for this grade level (e.g, rectangular arrays, area models, properties of operations, etc).




NOTE: The expectations for multi-step word problems include addition and subtraction within 1,000, multiplication of 2‐digit by 1‐digit or a multiple of 10 by a 1‐digit, and division of 2‐digit by 1‐digit.

Fluently add and subtract multi-digit whole numbers using the standard algorithm. MAFS.4.NBT.2.4

Students will:

• fluently add and subtract multi-digit whole numbers using the standard algorithm.

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

MAFS.4.NBT.2.5

Students will:

• solve multi-digit multiplication problems that extend to 4-digit by 1-digit or up to 2-digit by 2-digit using strategies based on place value and the properties of operations, and explain the calculation by using equations, rectangular arrays, and/or area models.

NOTE: Use of the standard algorithm for multiplication is a Grade 5 standard. Although these strategies are precursors to the standard algorithm, students should not be moved too quickly to the algorithm, as the standard algorithm is not the only end goal. Perhaps more importantly, students must become flexible in their use of place value and properties of operations when multiplying in Grade 4 in order to be successful later in Algebra when using the Distributive Property.


Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

MAFS.4.NBT.2.6

Students will:

• solve division of a multi-digit number (with up to four digits) by a one-digit number using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division, and explain the calculation using equations, rectangular arrays, and/or area models.

NOTE: Use of the standard algorithm for division is a Grade 6 standard.

2. Reason abstractly and quantitatively. 8. Look for and express regularity in repeated reasoning.


Topic Comments:

In demonstrating fluency, students explain and flexibly use properties of operations and place value to solve problems, looking for shortcuts and applying generalized strategies (MP.2, MP.8).



4.O

A.1

.2

Topic 14 Zoo Books

Teacher Guide p. 3

Reproducibles p. 3


Pick A Problem #9, 10


Books and Yarn Throwing Footballs Making Necklaces Dogs as Pets Resources repeated from Topic 7

www.cpalms.org Cruising for a Great Value

https://www.illustrativemathematics.org/content-standards Comparing Money Raised [Also in Topic 7]


























4.O

A.1

.3

Topic 14 Picturing Clues Party Planning Hall Of Mirrors

Teacher Guide p. 4

Reproducibles p. 3




Estimating the Solution Juice Boxes Resources repeated from Topics 2 and 8

www.cpalms.org Edible Angles


Karl’s Garden [Also in Topic 8]

www.IXL.com/signin/volusia D.27, F.6, E.7, D.13, D.14, E.11, E.15, F.3, F.6 Repeated resources

https://learnzillion.com/ No aligned resources

http://achievethecore.org How Many Teams?

4.N

BT

.2.4


Teacher Guide p. 9 Reproducibles p. 3 Daily Math Journal pp. 17, 19, 21, 23, 25, 28, 31, 32



Find the Error Fill in the Missing Number Addition Using the Standard Algorithm Subtracting Using the Standard Algorithm Resources repeated from Topics 4 and 8

www.cpalms.org Let’s Make a Movie [Also in topics 2,4]


www.IXL.com/signin/volusia B.1, B.2, B.3, C.1, C.2, C.3 Repeated resources


http://achievethecore.org Fluency practice Addition & Subtraction Mini Assessment












































http://achievethecore.org/page/2948/fluency-resources-for-grade-level-routines






4.N

BT

.2.5

Topic 14 Multiplication Stretch

Teacher Guide p. 10

Reproducibles p. 3


Pick A Problem #30, 31, 37, 38, 39


Reading Challenge Partial Products Multiplying by Using an Array or Area Model The Produce Shop Resources repeated from Topic 2

www.cpalms.org 2-Digit Array Multiplication [Also in topic 2]

https://www.illustrativemathematics.org/content-standards Thousands and Millions of Fourth Graders [Also in Topics 4, 6, 11]

www.IXL.com/signin/volusia D.5, D.6, D.11, D.18, D.24 Repeated resources


4.N

BT

.2.6

Topic 14 Pack 10 Trading Center Candy Factory

Teacher Guide p. 10

Reproducibles p. 3




Dividing Using an Area Model Book Drive Interpreting Division Dividing Using Place Value Resources repeated from Topic 2

www.cpalms.org Share and Share Alike [Also in topic 2]

https://www.illustrativemathematics.org/content-standards Mental Division Strategy [Also in Topic 2]

www.IXL.com/signin/volusia E.4, E.5, E.8, E.14 Repeated resources

https://learnzillion.com/ Unit 2: Multiplication and division strategies with larger numbers (Lessons 6-10) http://achievethecore.org How Many Teams?

























https://intranet.volusia.k12.fl.us/departments/elementarymath/AIMS%204/CandyFactory.pdf












https://www.illustrativemathematics.org/content-standards/4/NBT/B/6/tasks/1774










Topic 15: Revisiting solving addition and subtraction problems involving fractions and mixed number data present in line plots

Pacing: May 14 – May 18

This is a culminating topic in which students continue their work from topic 9 to strengthen their ability to perform operations with fractions when given data presented in line plots. Work with line plots will be extended in Grade 5 to include more sophisticated fraction operations (adding/subtracting unlike denominators, multiplying whole numbers by fractions/fractions by fractions, and dividing whole numbers by unit fractions/unit fractions by whole numbers).




1

𝑏.

c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. d. Solve word problems involving the addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

MAFS.4.NF.2.3

data set equivalent fraction fraction greater than 1 line plot mixed number unit fraction

• add and subtract mixed numbers with like denominators using equivalent fractions, and/or by using properties of operations and the relationship between addition and subtraction.

• solve word problems involving addition and subtraction of fractions and mixed numbers with like denominators using visual fraction models (i.e., circular models, rectangular models, and number line models) and/or equations.

Make a line plot to display a data set of measurements in fractions of a unit (1

2 ,

1

4 ,

1

8 ). Solve problems involving

addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

MAFS.4.MD.2.4

Students will:

• create a line plot recording measurement data including fraction units of halves, quarters, and eighths.

• use the measurement data on a line plot to solve multistep problems involving the addition and subtraction of fractions and draw conclusions about the data.

2. Reason abstractly and quantitatively. 5. Use appropriate tools strategically.


Topic Comments: 4.NF.1.1 and 4.NF.2.3 are pre-requisite standards for 5.NF.1.1. 4.MD.2.4 is a pre-requisite standard for 5.MD.2.2. Students use line plots and other tools/technology to reason about problem situations (MP.5). Students attend to the underlying meaning of the quantities and operations when solving problems rather than just how to compute answers (MP.2).




4.N

F.2

.3 (

c,d

)

Topic 15 Shady Fractions Cindy's Carpet Emporium Repeated resources




Pick A Problem #46, 47, 48, 49, 50, 55




Anna Marie and the Pizza Fraction Word Problems Adding and Subtracting Mixed Numbers Resources repeated from Topic 9

www.cpalms.org Learning to Love Like Denominators [Also used in Topic 9]

https://www.illustrativemathematics.org/content-standards Cynthia’s Perfect Punch

Peaches


Writing a Mixed Number as an Equivalent Fraction [Also in Topic 9]

www.IXL.com/signin/volusia P.4, P.23, Q.11, Q.12, Q.14 Repeated resources

https://learnzillion.com/ Unit 3: Decomposing and composing fractions for addition and subtraction (lessons 10-12) http://achievethecore.org No aligned resources

4.M

D.2

.4

Topic 15 Hook, Line, & Sticker Repeated resource

Teacher Guide p. 21

Reproducible p. 3




Race Cars Part One Race Cars Part Two Science Experiment Part One Science Experiment Part Two


www.cpalms.org No aligned resources

https://www.illustrativemathematics.org/content-standards Button Diameters [Also in Topic 9]

www.IXL.com/signin/volusia J.6, J.7, J.8 Repeated resources

https://learnzillion.com/ Unit 9: Lesson 5- Analyzing Line plots with fractions greater than 1. http://achievethecore.org No aligned resources







































https://www.illustrativemathematics.org/content-standards/4/MD/B/4/tasks/1039








Topic 16: Revisiting using conversions to solve measurement problems Pacing: May 21 - May 30 This is a culminating topic in which students continue their work from topic 6 to strengthen their conceptual understanding of the relative sizes of length measures and their ability to make measurement conversions from larger units to smaller units, and move forward with their work from topic 7 applying these conversions to problem solving contexts. Revisiting these concepts will further prepare students for solving multi-step, real world problems in Grade 5 involving conversions from smaller units to larger units. In this final topic, students apply competencies from different domains to solve measurement problems using the four operations, with all of the problem types in the Common Addition and Subtraction and Multiplication and Division Tables (see pg. 67 and 68) being addressed.


Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; L, mL; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …

MAFS.4.MD.1.1

multiplicative comparison

conversions customary units metric units NOTE: Students need to be provided with the Grade 4 FSA Mathematics Reference Sheet in order to practice using the tool.

• know relative size of length units within one system.

• convert larger units of length measure into smaller equivalent units.


MAFS.4.MD.1.2

Students will:

• use the four operations to solve word problems involving distances (i.e., inch, feet, yard, mile; millimeter, centimeter, meter, kilometer), including problems that require expressing measurements given in a larger unit in terms of a smaller unit.

1. Make sense of problems and persevere in solving them. 6. Attend to precision.


Topic Comments: 4.MD.1.1 and 4.MD.1.2 are pre-requisite standards for 5.MD.1.1.

Students use various diagrams and precise language to solve measurement problems and explain their strategies (MP.1, MP.6).




4.M

D.1

.1

Topic 16 Measure for Measure Repeated resource

Reproducible p. 3




Conversions in the Metric System Conversions in the Metric System Part Two Conversions in the Customary System Converting Units of Time Relative Sizes of Measurement Units for Weight Relative Sizes of Measurement Units for Length Resources repeated from Topic 6

www.cpalms.org Lets Think in Small Units [Also used in Topic 6]

https://www.illustrativemathematics.org/content-standards Who is the tallest? [Also used in Topic 6]

www.IXL.com/signin/volusia N.2, N.3, N.4, N.5, N.6, N.7, N.11, N.12, N.13, N.14, N.15, N.16, O.1 Repeated resources

https://learnzillion.com/ Unit 6: Introducing measurement conversions (Lessons 2-10) http://achievethecore.org No aligned resources

4.M

D.1

.2

Topic 16 Step By Step Mix-Ups and Mysteries Repeated resources

Reproducible p. 3


Pick A Problem #56, 57, 58, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72


Shopping List Kesha and Juan Remote Control Motorcycle Piano Lessons Resources repeated from Topics 7, 8, and 12

www.cpalms.org Amazing Race – Elapsed Time [Also used in previous topics]

Money Managers! [Also used in previous topics]


www.IXL.com/signin/volusia M.4, M.6, M.7, O.5, O.6, O.7, Q.11, S.6, S.12, S.15 Repeated resources















































Critical Areas for Mathematics in Grade 4

In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of division to find quotients involving multi-digit dividends; (2) developing understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

(1) Students generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place.

They apply their understanding of models for multiplication (e.g., equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products. They develop fluency with efficient procedures for multiplying whole numbers; understand and explain why the procedures work based on place value and properties of operations; and use them to solve problems. Students apply their understanding of models for division, place value, properties of operations, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multi-digit dividends. They select and accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remainders based upon the context.

(2) Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizing equivalent fractions. Students extend previous understandings about how fractions are built from unit fractions, composing fractions from unit fractions, decomposing fractions into unit fractions, and using the meaning of fractions and the meaning of multiplication to multiply a fraction by a whole number.

(3) Students describe, analyze, compare, and classify two-dimensional shapes. Through building, drawing, and analyzing two-

dimensional shapes, students deepen their understanding of properties of two-dimensional objects and the use of them to solve problems involving symmetry.


Grade 4 Major, Supporting, and Additional Work

Topic Title Major Work Supporting Work Additional Work

1 Exploring multiples and factors

4.OA.2.4 4.OA.3.5

2 Using multiplication and division strategies with larger numbers

4.OA.1.3, 4.NBT.2.5, 4.NBT.2.6, 4.OA.1.a, 4.OA.1.b

4.MD.1.3

3 Decomposing and composing fractions for addition and subtraction

4.NF.2.3 (a,b)

4 Applying place value concepts in whole number addition and subtraction

4.NBT.1.1, 4.NBT.1.2, 4.NBT.1.3, 4.NBT.2.4

5 Understanding fraction equivalence and comparison

4.NF.1.1, 4.NF.1.2

6 Introducing measurement conversions 4.OA.1.1, 4.NBT.1.1

4.MD.1.1

7 Solving problems using multiplicative comparison 4.OA.1.2, 4.NBT.1.3,

4.OA.1.a , 4.OA.1.b 4.MD.1.2

8 Solving measurement problems using the four operations 4.OA.1.3, 4.NBT.2.4,

4.OA.1.a, 4.OA.1.b 4.MD.1.2

9 Solving addition and subtraction problems involving fractions and mixed numbers

4.NF.2.3 (c,d) 4.MD.2.4

10 Angle measurement

4.G.1.1 4.MD.3.5 (a,b), 4.MD.3.6

11 Multiplying fractions by whole numbers

4.OA.1.1, 4.NF.2.4

12 Comparing decimal fractions and understanding notation 4.NF.3.5, 4.NF.3.6,

4.NF.3.7 4.MD.1.2

13 Recognizing and analyzing attributes of 2-dimensional shapes 4.G.1.1, 4.G.1.2, 4.G.1.3,

4.OA.3.5, 4.MD.3.7

14 Problem solving with whole numbers 4.OA.1.2, 4.OA.1.3,

4.NBT.2.4, 4.NBT.2.5, 4.NBT.2.6

15 Revisiting solving addition and subtraction problems involving fractions and mixed number data present in line plots

4.NF.2.3 (c,d)

4.MD.2.4

16 Revisiting using conversions to solve measurement problems

4.MD.1.1, 4.MD.1.2


Standards for Mathematical Practice Grade 4 students will:

1. Make sense of problems and persevere in solving them. (SMP.1) Mathematically proficient students in Grade 4 know that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the

meaning of a problem and look for ways to solve it. Fourth graders may use concrete objects or pictures to help them conceptualize and solve problems. They may check their

thinking by asking themselves, “Does this make sense?” They listen to the strategies of others and will try different approaches. They often will use another method to check their

answers.

2. Reason abstractly and quantitatively. (SMP.2)

Mathematically proficient students in Grade 4 recognize that a number represents a specific quantity. They extend this understanding from whole numbers to their work with fractions

and decimals. This involves two processes- decontexualizing and contextualizing. Grade 4 students decontextualize by taking a real-world problem and writing and solving equations

based on the word problem. For example, consider the task, “If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds

of roast beef will be needed? Students will decontextualize by writing the equation 3/8 × 5 or repeatedly add 3/8 5 times. While students are working they will contextualize their work-

knowing that the answer 15/8 or 1 7/8 represents the total number of pounds of roast beef that will be needed. Further, Grade 4 students write simple expressions, record calculations

with numbers, and represent or round numbers using place value concepts.

3. Construct viable arguments and critique the reasoning of others. (SMP.3) Mathematically proficient students in Grade 4 construct arguments using concrete representations, such as objects, pictures, and drawings. They explain their thinking and make

connections between models and equations. Students refine their mathematical communication skills as they participate in mathematical discussions involving questions like “How did

you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking through discussions and written responses.

4. Model with mathematics. (SMP.4)

Mathematically proficient students in Grade 4 represent problem situations in various ways, including writing an equation to describe the problem. Students need opportunities to

connect the different representations and explain the connections. They should be able to use all of these representations as needed. Grade 4 students should evaluate their results in

the context of the situation and reflect on whether the results make sense.

5. Use appropriate tools strategically. (SMP.5)

Mathematically proficient students in Grade 4 consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful.

For instance, they may use graph paper or a number line to represent and compare decimals and protractors to measure angles. They use other measurement tools to understand the

relative size of units within a system and express measurements given in larger units in terms of smaller units.

6. Attend to precision. (SMP.6)

Mathematically proficient students in Grade 4 develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and in their

own reasoning. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, they use appropriate labels when creating a line

plot.

7. Look for and make use of structure. (SMP.7)

Mathematically proficient students in Grade 4 closely examine numbers to discover a pattern or structure. For instance, students use properties of operations to explain calculations

(area model). They relate representations of counting problems such as arrays to the multiplication principal of counting. They generate number and shape patterns that follow a given

rule.

8. Look for and express regularity in repeated reasoning. (SMP.8)

Mathematically proficient students in Grade 4 notice repetitive actions in computation to make generalizations. Students use models to explain calculations and understand

how algorithms work. They also use models to examine patterns and generate their own algorithms. For example, students use visual fraction models to write equivalent

fractions.


Common Addition and Subtraction Situations Table

Result Unknown Change Unknown Start Unknown

Add to

Two bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now?

2 + 3 = ?

Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to the first two?

2 + ? = 5

Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass before?

? + 3 = 5

Take from

Five apples were on the table. I ate two apples. How many apples are on the table now?

5 – 2 = ?

Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat?

5 - ? = 3

Some apples were on the table. I ate two apples. Then there were three apples. How many apples were on the table before?

? – 2 = 3

Total Unknown Both Addends Unknown1 Addend Unknown2

Put Together/

Take Apart

Three red apples and two green apples are on the table. How many apples are on the table?

3 + 2 = ?

Grandma has five flowers. How many can she put in her red vase and how many in her blue vase?

5 = ? + ? 5 = 0 + 5, 5 = 5 + 0 5 = 1 + 4, 5 + 4 + 1 5 = 2 + 3, 5 = 3 + 2

Five apples are on the table. Three are red and the rest are green. How many apples are green?

3 + ? = 5 5 – 3 = ?

Difference Unknown Bigger Unknown Smaller Unknown

Compare

“How many more?” version:

Lucy has two apples. Julie has five apples. How many more apples does Julie have than Lucy?

“How many fewer?” version:

Lucy has two apples. Julie has five apples. How may fewer apples does Lucy have than Julie?

2 + ? = 5 5 – 2 = ?

“More” version suggests operation:

Julie has 3 more apples than Lucy. Lucy has two apples. How many apples does Julie have?

“Fewer” version suggests operation:

Julie has three more apples than Lucy. Julie has five apples. How many apples does Lucy have?

“Fewer” version suggests wrong operation:

Lucy has three fewer apples than Julie. Lucy has two apples. How many apples does Julie have?

2 + 3 = ? 3 + 2 = ?

“More” version suggests wrong operation: Lucy has three fewer apples than Julie. Julie has five apples. How many apples does Lucy have?

5 – 3 = ? ? + 3 = 5

Darker shading indicates the four Kindergarten problem subtypes. Grade 1 and 2 students work with all subtypes and variants. Unshaded (white) problems are the four difficult subtypes or variants that students should work with in Grade 1 but need not master until Grade 2. Adapted from CCSS, p. 88, which is based on Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity, National Research Council, 2009, pp. 32–33.

1 This can be used to show all decompositions of a given number, especially important for numbers within 10. Equations with totals on the left help children understand that = does not always mean “makes” or “results in” but always means “is the same number as.” Such problems are not a problem subtype with one unknown, as is the Addend Unknown subtype to the right. These problems are a productive variation with two unknowns that give experience with finding all the decompositions of a number and reflecting on the patterns involved.

2 Either addend can be unknown; both variations should be included.


Common Multiplication and Division Situations Table1

1 The first examples in each cell are examples of discrete things. These are easier for students and should be given before the measurement examples. 2 The language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in the grocery window are in 3 rows and 6 columns. How many apples are in there? Both forms are valuable. 3 Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially important measurement situations. 4 Multiplicative Compare problems appear first in Grade 4, with whole-number values for A, B, and C, and with the “times as much” language in the table. In Grade 5, unit fractions language such as “one third as much” may be used. Multiplying and unit fraction language change the subject of the comparing sentence, e.g., “A red hat costs A times as much as the blue hat” results in the same comparison as “A blue hat

costs 1

𝑎 times as much as the red hat,” but has a different subject.

Unknown Product

Group Size Unknown (“How many in each group?” Division)

Number of Groups Unknown (“How many groups?” Division)

3 × 6 = ? 3 × ? = 18 and 18 ÷ 3 = ? ? × 6 = 18 and 18 ÷ 6 = ?

Equal Groups

There are 3 bags with 6 plums in each bag. How many plums are there in all? Measurement example. You need 3 lengths of string, each 6 inches long. How much string will you need altogether?

If 18 plums are shared equally into 3 bags, then how many plums will be in each bag? Measurement example. You have 18 inches of string, which you will cut into 3 equal pieces. How long will each piece of string be?

If 18 plums are to be packed 6 to a bag, then how many bags are needed? Measurement example. You have 18 inches of string, which you will cut into pieces that are 6 inches long. How many pieces of string will you have?

Arrays2, Area3

Unknown Product Unknown Factor Unknown Factor There are 3 rows of apples with 6 apples in each row. How many apples are there? Area example. What is the area of a 3 cm by 6 cm rectangle?

If 18 apples are arranged into 3 equal rows, how many apples will be in each row? Area example. A rectangle has area 18 square centimeters. If one side is 3 cm long, how long is a side next to it?

If 18 apples are arranged into equal rows of 6 apples, how many rows will there be? Area example. A rectangle has area 18 square centimeters. If one side is 6 cm long, how long is a side next to it?

Compare4

Larger Unknown Smaller Unknown Multiplier Unknown A blue hat costs $6. A red hat cost 3 times as much as the blue hat. How much does the red hat cost? Measurement example. A rubber band is 6 cm long. How long will the rubber band be when it is stretched to be 3 times as long?

A red hat costs $18 and that is 3 times as much as a blue hat costs. How much does the blue hat cost? Measurement example. A rubber band is stretched to be 18 cm long and that is 3 times as long as it was at first. How long was the rubber band at first?

A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat? Measurement example. A rubber band was 6 cm long at first. Now it is stretched to be 18 cm long. How many times as long is the rubber band now as it was at first?

Smaller Unknown 1

3 x 18 = ?

Larger Unknown 1

3 x ? = 6

Multiplier Unknown ? x 18 = 6

A red hat costs $18. A blue hat costs 1

3 as

much as the red hat. How much does the blue hat cost?

A blue hat costs $6 and that is 1

3 of the cost of a

red hat. How much does a red hat cost?

A red hat costs $18 and a blue hat costs $6. What fraction of the cost of the red hat is the cost of the blue hat?

General a × b = ? a × ? = p and p ÷ a = ? ? × b = p and p ÷ b = ?


Grade 4 Math Curriculum Map July 2017

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Fourth Grade MATHEMATICSmyvolusiaschools.org/K12-Curriculum/Curriculum Maps and Guides/Ma… · Fourth Grade MATHEMATICS ... Topic 12: Comparing decimal ... multiplication of 2‐digit