CCSS Mathematics Implementation Guide-Grade 4 2014 Web view2. 6. 7. My Math- Chapter 1 . Lesson 1. ... Read and write whole numbers using standard form, word form, ... CCSS Mathematics

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CCSS Mathematics Implementation Guide-Grade 4 2014-2015

First Nine WeeksPacing Big Ideas

Essential QuestionsStandards SMP Suggested Resources Assessment

4 days Big ideas:To increase to the next place value, you must multiply by 10.Essential Question:How are multiplication and division related to place value?

4.NBT.1 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.

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My Math- Chapter 1 Lesson 1 Chapter 10 Lessons 1,2,3

EngageNy- Module 1

**Accelerated Math, Fantastic Five, are ongoing resources for every standard**

Teacher choice for assessment as needed. (chapters tests, quizzes, Check My Progresses, etc)

6 days Big idea:Read and write whole numbers using standard form, word form, and expanded form.Use place value to compare numbers.Essential Questions:What are examples of the different forms of writing numbers?How do you compare two multi-digit numbers using place value and symbols?

4.NBT.2: 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.

4.NF.6 USE decimal notation for fractions with denominators 10 or 100. *Teach decimal place value-tenths and hundredths as you teach place value of whole numbers.

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My Math – Chapter 1 Lessons 2,3,4,5,6 Chapter 10 Lesson 7

Engage NY – Module 6 Topic A,B,C

AssessmentChapter tests and quizzes given throughout. Include vocabulary and a variety of formats.

Standards for Mathematical Practice (SMP’s)1. Make sense of problems and preservers in solving them

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

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4.NBT.3 USE place value understanding to round multi-digit whole numbers to any place.

4.NF.7 Compare two decimal to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole.

7 days 4.NBT.4: Fluently add and subtract multi-digit whole numbers using the standard algorithm

My Math – Chapter 2 Lessons 1-7


5 days Big idea:-You can use adding, subtracting, multiplying, and dividing to solve word problems that have more than one step and unknown numbers.-All answers should be checked to see if it answers the question.-Use mental math and estimation to check answers.

Essential questions:

4.OA.3 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.

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My Math – Chapter 2 Lessons 8, 9

Word Problems are embedded throughout.

Common Assessment 1 (Chapters 1 and 2)









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8 days-How many steps will it take to solve a word problem? How do you know?-What operations will you use to solve a word problem?-How can you check your answers to make sure they make sense?

4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35=5x7 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.

My Math – Chapter 3 Lessons 1,3,2,4,5,6

3 days Big idea:-Two factors multiplied together give you a multiple..-A number can be prime if it has two factors (one and itself).-If a number is not prime, it is composite (more than two factors).Essential question:

-How do multiples and

factors differ?

-What is the difference between a prime and composite number? How do you know?

.4.OA.4 FIND all factor pairs for a whole number 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 whether a given whole number in the range 1-100 is prime or composite.

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My Math – Chapter 3 Lessons 7,8


Second Nine Weeks









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Pacing Big IdeasEssential Questions

Standards SMP Suggested Resources Assessment

Chap. 414 days

Chap. 59-12 days

Big Ideas:You can use different strategies to multiply bigger numbers.

Essential Questions:How would you solve this multiplication problem? Explain your answer.

4.NBT.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.

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My Math- Chapters 4-5

AIMS – Marvelous Multiplication and Dazzling Division

EngageNY-Module 3 Topic A,B,C,D,H


Common Assessment 2 (chapters 3-5)

14-16 days

Big idea:You can use different strategies to divide bigger numbers.

Essential Question:How would you solve this division problem? Explain your answer.

4.NBT.6. 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.

4.MD.3 APPLY the area and perimeter formulas for rectangles in real world and mathematical problems.

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My Math- Chapter 6


EngageNY Module 3 Topic E,F,G


Big Idea: 4.OA2: MULTIPLY or DIVIDE to SOLVE My Math- Chapter 6 Assessment









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-Multiplication and division can be used to solve word problems.-Using drawings and equations can help me solve a problem.-Symbols can be used to represent unknown numbers.

Essential questions:-Multiplication and division can be used to solve word problems.-Using drawings and equations can help me solve a problem.-Symbols can represent unknown numbers.

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.

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Real Life Math Series –Menu Math

Hands-on standardsLessons 11-12

Chapter tests and quizzes given throughout. Include vocabulary and a variety of formats.

Big idea: 4.OA.5 GENERATE a number or My Math- Chapter 7 Common Assessment 3Standards for Mathematical Practice (SMP’s)

1. Make sense of problems and preservers in solving them








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-Patterns can be made using shapes and numbers. -Patterns follow a rule.

Essential question:-How do you make a pattern using shapes or numbers that follows a specific rule?-How do you find a rule for a specific number or shape pattern?

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.

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MOOB – Signs and SymbolsSafari Montage Videos: Cyberchase: Patterns: The Poddleville Case (29 min.)

Bill Nye: Patterns (23 min.) Number Patterns (15 min.)

(Chapter 6-7)









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Third Nine Weeks









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Pacing Big IdeasEssential Questions

Standards SMP Suggested Resources Assessment

6-7 days Big idea:

Fractions can be equivalent even though they have different numbers.

Multiplication can be used to create equivalent fractions.

Essential Question:

How can you show that two fractions are equivalent? Give an example.

4.NF.1 EXPLAIN why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by USING visual fraction models, with attendion 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.

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My Math- Chapter 8 Lessons 1-5

Fraction Unit Funny & Fabulous Fraction Stories See link at bottom of guide

Safari Montage Videos:Cyberchase: Fractions: Zeus on the Loose (29 min.)

Fractions (10 min.)Equivalent Fractions & Mixed Numbers (15 min.)



4 days Big idea: 4.NF.2 COMPARE two fractions with different numerators and different 2

My Math- Chapter 8 Lessons 6-8

Teacher choice for









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Fractions can be compared by finding common numerators and denominators.

Fractions can be compared using benchmarks.

Fractions can be compared using symbols.

Essential Question:

How can you compare two unlike fractions?

denominators, e.g., by CREATING common denominators or numerators, or by COMPARING to a benchmark fraction such as ½. RECOGNIZE that comparisons 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.

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Fraction Unit

EngageNY Module 5 Topic A-H

assessment as needed. (chapters tests, quizzes, Check My Progresses, etc)

15-17 days

Big Idea: Fractions can be added or subtracted by joining or separating the parts.Essential Question:How can I add or subtract like fractions?

4.NF.3a 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.

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My Math- Chapter 8 Lessons 9-10 Chapter 9

CCSS Fraction Unit given by DO


Big Idea:A fraction can be

4.NF.3b. DECOMPOSE a fraction into a sum of fractions with the same 1

My Math- Chapter 9 Teacher choice for assessment as needed.









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separated into smaller parts.

Essential Question:How do you break apart a fraction?

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 = 8/8 + 8/8 + 1/8.

4.NF.3c . 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.

4.NF.3d. Solve word problems involving 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.

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(chapters tests, quizzes, Check My Progresses, etc)

Big Idea:An improper fraction

4.NF.4a Apply and extend previous understandings of multiplication to 1

My Math- Chapter 9 Teacher choice for assessment as needed.









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can be written as a multiplication equation.

Essential Question:What is another way to represent an improper fraction using multiplication?

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 of 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4).

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Big Idea:Multiply fractions by whole numbers.

Essential Question:Use a fraction model to show how to multiply a whole number time a fraction.

4.NF.4b 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.)

4.NF.4c. Solve word problems involving multiplication of a fraction by a whole number,e.g., by using visual fraction modelsand equations to represent the problem.

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My Math- Chapter 9



7 days Big Idea: Equivalent fractions

4.NF.5 EXPRESS a fraction with denominator 10 as an equivalent 2

My Math – Chapter 10 Lesson 6

Teacher choice for









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from tenths to hundredths can be used to help in adding fractions.

Essential Question:How do you find and add equivalent fractions with denominators of 10 and 100?

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.

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Big Idea:Fractions with denominators of 10 and 100 can be written as decimals.

Essential Question:How do you rewrite a fraction with a denominator of 10 and/or 100?

4.NF.6 USE decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

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My Math-Chapter 10 Lessons 4,5,7,8

EngageNY - Module 6 Topic A-E

Common Assessment 4 (Chapter 8-10)

Fourth Nine WeeksPacing Big Ideas Standards SMP Suggested Resources Assessment









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Essential Questions21 days Big idea:

Use knowledge of the given measurement unit to convert large units to smaller units by multiplying.

Essential question:How do you change large measurement unit into smaller measurement units?

4.MD.1 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), ...

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My Math- Chapters11-12

EngageNY - Module 2



Big idea:-To solve word

4.MD.2 USE the four operations to solve word problems involving 1

My Math- Chapters 11-12Common Assessment 5









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problems involving measurement using addition, subtraction, multiplication, or division.-Use diagrams to represent measurement quantities.

Essential questions:-How can you use a diagram to show the answer to a measurement word problem?

distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. REPRESENT measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

4.MD.4 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.

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EngageNY- Module 7

MOOB – Inside and Outside

Ch.11 Lesson 8

(Chapter 11 – Test 2A)

Common Assessment 6 (Chapter 12 – Test 2A)

7 days 4.MD.3 APPLY the area and perimeter formulas for rectangles in real world and mathematical problems.

My Math – Chapter 13 Teacher choice for assessment as needed. (chapters tests, quizzes, Check My Progresses, etc)

14 days Big idea:You can measure an

4.MD.5 RECOGNIZE angles as geometric shapes that are formed 6

My Math- Chapter 14 Teacher choice for









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angle in reference to a circle as a whole and the angles as a part.

Essential question:How do you measure an angle in reference to a circle?

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 though n one-degree angles is said to have an angle measure of n degrees.

7MOOB – Corners and Containers

EngageNY Module 4 Topics A-D

Hands-on Standards Lessons 6-7


Big Idea:You can draw and

4.G.1 DRAW points, lines, line segments, rays, angles (right, acute, 5

My Math- Chapters 14 Teacher choice for assessment as needed.









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identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines.Essential Question:Draw an example of each: points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines.

Big idea:Angles can be measured and drawn using a protractor.

Essential question:What mathematical tool is used to measure and draw angles? Draw a 30 ̊angle.

obtuse), and perpendicular and parallel lines. IDENTIFY these in two-dimensional figures.

4.MD.6 MEASURE angles in whole-number degrees USING a protractor. SKETCH angles of specified measure.

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My Math- Chapter 14

MOOB – Corners and Containers


Big idea:-You can find an

4.MD.7 RECOGNIZE angle measure as additive. When an angle is 1

My Math- Chapter 14 AssessmentChapter tests and quizzes









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unknown angle measurement by adding or subtracting angle parts.-You can write an equation for the unknown angle measure (symbol).

Essential question:-How can you find an unknown angle measurement when two other related angle measurements are given? Write your answer as an equation. (80 is ̊decomposed as a 30 ̊ + ? ) ̊

decomposed into non-overlapping 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.

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MOOB – Corners and Containers

given throughout. Include vocabulary and a variety of formats.

Big Idea: -Two-dimensional

4.G.2 CLASSIFY two-dimensional figures based on the presence or 5

My Math – Chapter 14 Teacher choice for assessment as needed.









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shapes can be classified by lines and/or angles.-A right triangle has one 90° angle.

Essential Question:Observe the shapes, classify them according to their lines and angles.

Define and identify a right triangle.

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.

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Big Idea: A line of symmetry will split a figure into two equal parts.Essential question: How many lines of symmetry can a square have?

4.G.3 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.

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My Math – Chapter 14 Common Assessment 7 (Chapter 13- 14)

After State TestingPacing Big Ideas Standards SMP Suggested Resources Assessment









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Essential QuestionsBig idea:Read and write whole numbers using standard form, word form, and expanded form.Use place value to compare numbers.

Essential Questions:What are examples of the different forms of writing numbers?How do you compare two multi-digit numbers using place value and symbols?

5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

5. NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

5.NBT.3 Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form

b. Compare two decimals to thousandths based on meanings of

See 5th Grade textbook and Engage NY Modules










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the digits in each place, using >, =, and < symbols to record the results of comparisons.

5.NBT. 4 Use place value understanding to round decimals to any place5.NBT. 5 Fluently multiply multi-digit whole numbers using the standard algorithm.

5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-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. Review 4th Grade Fractions

See 4.NF.1 – 4.NF.4

http://msdiazclass.wikispaces.com/file/view/Fractions+Funny+Stories.pdf Funny and Fabulous Fraction Stories link









http://msdiazclass.wikispaces.com/file/view/Fractions+Funny+Stories.pdf

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CCSS Mathematics Implementation Guide-Grade 4 2014 Web view2. 6. 7. My Math- Chapter 1 . Lesson 1. ... Read and write whole numbers using standard form, word form, ... CCSS Mathematics