Fifth GRADE CURRICULUM MAP 2015 2016€¦ · Fifth Grade Curriculum Map Mathematics To: Fifth Grade Teachers From: Jodi Albers Date: August 21, 2015 Re: FifthGrade Math Expressions

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FIFTH GRADE CURRICULUM MAP MATHEMATICS OFFICE OF CURRICULUM AND INSTRUCTION

Fifth Grade Curriculum Map Mathematics

To: Fifth Grade Teachers

From: Jodi Albers

Date: August 21, 2015

Re: Fifth Grade Math Expressions Curriculum Map

Dear Teachers, This is the first draft of the Math Expressions curriculum map that correlates the Common Core State Standards in Mathematics. Please note: this is a draft. Your suggestions and feedback should be given to your Math Expressions Lead Teacher so appropriate changes can be made. This document is divided into the following sections:

• Instructional Focus • Mathematical Practices • Scope and Sequence • Curriculum Map

Instructional Focus This summary provides a brief description of the critical areas of focus, required fluency for the grade level, major emphasis clusters, and examples of major within-grade dependencies. The Common Core State Standards for Mathematics begin each grade level from kindergarten through eighth grade with a narrative explaining the Critical Areas for that grade level. The Critical Areas are designed to bring focus to the standards by outlining the essential mathematical ideas for each grade level.

Mathematical Practices The Common Core State Standards for Mathematics define what students should understand and be able to do in their study of mathematics. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. The Standards for Mathematical Practice are included first in this document because of their importance and influence in teaching practice.

Scope and Sequence This table provides the unit sequence and pacing for Math Expressions.

Curriculum Map – By Unit The curriculum map provides the alignment of the grade level Math Expressions units with state-adopted standards as well as unit specific key elements such as learning progressions, essential questions learning targets, and formative assessments. A special thank you to the Fifth Grade Math Expressions Trial Teachers who created these documents for the Red Clay Consolidated School District. Sincerely, Jodi Albers Red Clay Consolidated School District Department of Curriculum and Instruction (302) 552-3820 [email protected]


2014 – 2015 Math Expressions Trial Teachers Kindergarten Team

Michelle Finegan, Richardson Park Learning Center Jacqueline Gallagher, Forest Oak Elementary School Jenna Parke, Forest Oak Elementary School Brandi Reardon, Richey Elementary School Kelley Firko, Richardson Park Elementary School

First Grade Team Gilda Gallo, North Star Elementary School Julia Goodrick, Heritage Elementary School Heather Hilgar, Linden Hill Elementary School Christine Saggese, Linden Hill Elementary School

Second Grade Team Gabriele Adiarte, Mote Elementary School Margaret Brady, Richey Elementary School Sherri Brooks, Richey Elementary School Stephanie Fleetwood, Linden Hill Elementary School

Third Grade Team Kristin Becker, North Star Elementary School Karen Cooper, North Star Elementary School Kathleen Gormley, Highlands Elementary School Kathryn Hudson, Baltz Elementary School Sarah Bloom, Brandywine Springs Elementary School Jennifer Greevy, Forest Oak Elementary School

Fourth Grade Team Paula Brown, Warner Elementary School Katherine Cassidy, Brandywine Springs Elementary School Jill League, Brandywine Springs Elementary School John Matthias, Linden Hill Elementary School

Fifth Grade Team Jessica Baker-Chambers, Warner Elementary School Eric Beaman, Shortlidge Academy Sonia Saunders, Brandywine Springs Elementary School Ellen Shackelford, Richey Elementary School Stacie Zdrojewski, Richey Elementary School


Instructional Focus In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume. 1. Students apply their understanding of fractions and fraction models to represent the addition and subtraction of

fractions with unlike denominators as equivalent calculations with like denominators. They develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. Students also use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. (Note: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.)

2. Students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations. They finalize fluency with multi-digit addition, subtraction, multiplication, and division. They apply their understandings of models for decimals, decimal notation, and properties of operations to add and subtract decimals to hundredths. They develop fluency in these computations, and make reasonable estimates of their results. Students use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense. They compute products and quotients of decimals to hundredths efficiently and accurately.

3. Students recognize volume as an attribute of three-dimensional space. They understand that volume can be measured by finding the total number of same-size units of volume required to fill the space without gaps or overlaps. They understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. They select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. They decompose three-dimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes. They measure necessary attributes of shapes in order to determine volumes to solve real world and mathematical problems.

Key Areas of Focus for 3 – 5: Multiplication and division of whole numbers and fractions —concepts, skills, and problem solving Required Fluency: 5.NBT.5 Multi-‐digit multiplication Major Emphasis Clusters: Number and Operations in Base Ten

• Understand the place value system. • Perform operations with multi-‐digit whole numbers and with decimals to hundredths.

Number and Operations -‐Fractions • Use equivalent fractions as a strategy to add and subtract fractions. • Apply and extend previous understandings of multiplication and division to multiply and divide

fractions. Measurement and Data

• Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.


Examples of Major Within-‐Grade Dependencies: Understanding that in a multidigit number, a digit in one place represents 1/10 of what it represents in the place to its left (5.NBT.1) is an example of multiplying a quantity by a fraction (5.NF.4).


Standards for Mathematical Practices The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

Connecting the Standards for Mathematical Practice to the Standards for Mathematical Content The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction. The Standards for Mathematical Content are a balanced combination of procedure and understanding. Expectations that begin with the word “understand” are often especially good opportunities to connect the practices to the content. Students who lack understanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices. In this respect, those content standards which set an expectation of understanding are potential “points of intersection” between the Standards for Mathematical Content and the Standards for Mathematical Practice. These points of intersection are intended to be weighted toward central and generative concepts in the school mathematics curriculum that most merit the time, resources, innovative energies, and focus necessary to qualitatively improve the curriculum, instruction, assessment, professional development, and student achievement in mathematics.

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of


important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

2. Reason abstractly and quantitatively Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

3. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

4. Model with mathematics Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

5. Use appropriate tools strategically Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a


spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

6. Attend to precision Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

7. Look for and make use of structure Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well-remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

8. Look for and express regularity in repeated reasoning Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x2 + x + 1), and (x – 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.


Scope and Sequence Date Unit Days August 31 Beginning of the Year Inventory/Assessment September -‐ October Unit 1 25

Big Idea 1: Equivalent Fractions (Lessons 1-‐5) 10 September 21 Quick Quiz 1 Big Idea 2: Addition and Subtraction of Fractions (Lessons 6-‐10) 12 October 12 Quick Quiz 2 Unit Review 2 October 13 Unit 1 Test 1 October -‐ November Unit 2 22

Big Idea 1: Read and Write Whole Numbers and Decimals (Lessons 1-‐3) 6

Big Idea 2: Addition and Subtraction (Lessons 4-‐7) 8 November 2 Quick Quiz 2 Big Idea 3: Round and Estimate with Decimals (Lessons 8-‐10) 5 Unit Review 3 November -‐ December Unit 3 20

Big Idea 1: Multiplication with Fractions (Lessons 1-‐6) 7 Big Idea 2: Multiplication Links (Lessons 7-‐9) 4 December 7 Quick Quiz 2 Big Idea 3: Division with Fractions (Lessons 10-‐14) 6 Unit Review 3 January -‐ February Unit 4 17

Big Idea 1: Multiplication with Whole Numbers (Lessons 1-‐5) 6 Big Idea 2: Multiplication and Decimal Numbers (Lessons 6-‐12) 8 January 25 Quick Quiz 2 Unit Review 3 February -‐ March Unit 5 16 Big Idea 1: Division with Whole Numbers (Lessons 1-‐5) 6 Big Idea 2: Division with Decimal Numbers (Lessons 6-‐11) 7 February 29 Quick Quiz 2 Unit Review 3 March -‐ April Unit 6 17 Big Idea 1: Equations and Problem Solving (Lessons 1-‐4) 5 Big Idea 2: Comparison Word Problems (Lessons 5-‐7) 4 March 14 Quick Quiz 2 Big Idea 3: Problems with More Than One Step (Lessons 8-‐11) 5 Unit Review 3


April -‐ May Unit 7 23 Big Idea 1: Algebraic Reasoning and Expressions (Lessons 1-‐3) 8 *Big Idea 2: Patterns and Graphs (Lessons 4-‐7) 7 Unit Review 3

May June Unit 8 16

Big Idea 1: Measurements and Data (Lessons 1-‐7) 4 Big Idea 2: Area and Volume (Lessons 8-‐13) 4 Big Idea 3: Classify Geometric Figures (Lessons 14-‐17) 5 Unit Review 3 May 26 End of Year Inventory/Assessment Total Days 156


Unit 1: Addition and Subtraction with Fractions

September-October

Learning Progressions: Last year, my students… In my class, students will… Next year, my students will… • represented fractions as

sums of unit fractions. • composed and decomposed

fractions and mixed numbers.

• used bar models to represent equivalent fractions and find sums and differences.

• use number lines to represent equivalent fractions.

• express fractions with unlike denominators in terms of the same unit fraction so they can be added or subtracted.

• use bar models to visualize a sum or difference.

• use equations and models to solve real world problems.

• use estimation to determine whether answers are reasonable.

• use number lines to represent rational numbers.

Common Core State Standards

Content

CC.5.NF.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

CC.5.NF.2: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

CC.5.MD.2: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.


Pract ices

MP.1: Make sense of problems and persevere in solving them. MP.2: Reason abstractly and quantitatively. MP.3: Construct viable arguments and critique the reasoning of others. MP.4: Model with math. MP.5: Use appropriate tools strategically. MP.6: Attend to precision. MP.7: Look for and make use of structure. MP.8: Look for and express regularity in repeated reasoning. Beginning of the Year Inventory (August 31-September 14)

Unit 1: Big Idea 1: Equivalent Fractions (Lessons 1-5) Number of days:10 Quick Practice: (Begins in Lesson 2)

• Practice writing and comparing fractions. • Practice finding like fractions that add to one. • Write equivalent fractions. • Recognize fractions that add to one.

Vocabulary: benchmark, common denominator, common factor, denominator, equivalent fractions, fraction, greater than (>), less than (<), mixed number, multiplier, n-split, numerator, simplify, unit fraction, unsimplify Essential Questions:

• How do I use the math board to discuss fraction ideas? • How can I generate and explain equivalent fractions? • What is the role of the multiplier in equivalent fractions? • What strategies can I use to compare fractions? • How can I convert between fractions and mixed numbers?

Learning Targets: • Use the MathBoard fraction bars to discuss basic fraction ideas. • Generate and explain simple equivalent fractions • Understand the role of the multiplier in equivalent fractions. • Use a variety of strategies to compare fractions • Convert between fractions and mixed numbers.

Assessments: After Lesson 5, give Quick Quiz 1 (September 21 – October 2).

Unit 1: Big Idea 2: Addition and Subtraction of Fractions (Lessons 6-10) Number of days: 12 Quick Practice:

• Change fractions to mixed numbers. • Write equivalent fractions. • Practice finding common denominators.

Vocabulary: add on, benchmark, estimate, line plot, regroup, round, situation equation, solution equation, ungroup Essential Questions:


• What methods can be used to subtract two like mixed numbers when the fraction part of the first number is less than the fraction part of the second?

• Why is it necessary to write fractions with a common denominator before adding them? • What methods can be used to explain a method for subtracting fractions with unlike

Denominators? • In what situations is it necessary to ungroup in order to subtract mixed numbers? In what

situations they need to regroup after adding mixed numbers? • What are the most important ideas to remember when adding and subtracting mixed

numbers? • What is a method for mentally estimating sums and differences of fractions and mixed

numbers? How can these methods be illustrated with examples? • How can estimates be used to determine whether answers to word problems are

reasonable? Learning Targets:

• Add and subtract mixed numbers with like denominators. • Add fractions with different denominators. • Subtract fractions with different denominators. • Add and subtract mixed numbers with unlike denominators. • Estimate sums and differences of fractions and mixed numbers and decide whether answers

are reasonable. • Use estimates to determine whether answers to word problems are reasonable.

Assessments: After Lesson 10, give Quick Quiz 2 (October 12 – October 23). Give Unit 1 Test (October 13- October 27).


Unit 2: Addition and Subtraction with Decimals

October-November Learning Progressions: Last year, my students… In my class, students will… Next year, my students will… • used place-value drawings

to help them conceptualize numbers and understand the relative sizes of place values.

• used different methods to add and subtract whole numbers.

• students expand their understanding of the base-ten system to decimals to the thousandths place.

• observe that the process of composing and decomposing a base-ten unit is the same for decimals as for whole numbers.

• observe that the same methods of recording numerical work can be used with decimals as with whole numbers.

• extend their fluency with the standard algorithms, using these for all four operations with decimals.

• extend the base-ten system to negative numbers.

• extend understanding of number line diagrams and coordinate axes to represent points on the line and in the plane with negative number coordinates.


Content

CC.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. CC.5.NBT.3: Read, write, and compare decimals to thousandths. CC.5.NBT.3a: Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). CC.5.NBT.3b: Read, write, and compare decimals to thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.


Pract ices

MP.1: Make sense of problems and persevere in solving them. MP.2: Reason abstractly and quantitatively. MP.3: Construct viable arguments and critique the reasoning of others. MP.4: Model with math. MP.5: Use appropriate tools strategically. MP.6: Attend to precision. MP.7: Look for and make use of structure. MP.8: Look for and express regularity in repeated reasoning.

Unit 2: Big Idea 1: Read and Write Whole Numbers and Decimals (Lessons 1-3) Number of days: 6 Quick Practice: (Starts in lesson 2)

• Practice naming decimal numbers. • Practice writing fractions as decimals.

Vocabulary: Vocabulary: decimal, equivalent decimal, expanded form, hundredth, notation, power of ten, standard form, tenth, thousandth, word form Essential Questions:

• How are decimals equal divisions of a whole? • How can you read write and model decimals and whole numbers? • How can I model and Identify equivalent decimals?

Learning Targets: • Understand decimals as equal divisions of whole numbers. • Read, write, and model whole and decimal numbers.

Assessments: After Lesson 3, give Quick Quiz 1.

Unit 2: Big Idea 2: Addition and Subtraction (Lessons 4-7) Number of days: 8 Quick Practice:

• Practice naming decimal numbers. Vocabulary: Associative Property of Addition, break apart drawing, centimeter (cm), Commutative Property of Addition, decimeter (dm), Distributive Property of Multiplication Over Addition, grouping, meter (m), millimeter (mm), ungroup/ing Essential Questions:

• How can I add and subtract decimals to the thousands? • How can I use commutative, associative, and distributive properties to compute mentally?

Learning Targets: • Model adding and subtracting decimals • Add whole numbers and decimals to hundredths • Subtract whole and decimal numbers to hundredths • Use the Commutative, Associative, and Distributive Properties to compute mentally

Assessments: After Lesson 7, give Quick Quiz 2 (November 2 – November 14).


Unit 2: Big Idea 3: Round and Estimate with Decimals (Lessons 8-10) Number of days: 5 Quick Practice:

• Practice naming decimal numbers. • Round decimals to the nearest tenth, hundredth, thousandth.

Vocabulary: estimate, round Essential Questions: How can I estimate decimal sums and differences? Learning Targets:

• Estimate decimal sums and differences. • Read graphs with decimal scales and decimal numbers. • Construct graphs with decimal scales and decimal numbers.



Unit 3: Multiplication and Division with Fractions

November-December Learning Progressions: Last year, my students… In my class, students will… Next year, my students will… • represented fractions as

sums of unit fractions. • composed and decomposed

fractions and mixed numbers.

• used bar models to represent equivalent fractions and to find sums and differences.

• use comparison bars to solve multiplication comparative problems involving fractions.

• use number lines to solve problems involving non-unit fractions.

• use area models to solve problems involving fractions.

• use bar models to multiply, compare and divide fractions.

• use bar models to represent equivalent fractions.

• use number lines to multiply and divide fractions.

• use area models to multiply and divide fractions.


Content

CC.5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. CC.5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. CC.5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.


CC.5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

CC.5.NF.4a Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. CC.5.NF.4b Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

CC.5.NF.5 Interpret multiplication as scaling (resizing), by: CC.5.NF.5a Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. CC.5.NF.5b Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

CC.5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. CC.5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

CC.5.NF.7a Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. CC.5.NF.7b Interpret division of a whole number by a unit fraction, and compute such quotients. CC.5.NF.7c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.

CC.5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.

Pract ices


Unit 3: Big Idea 1: Multiplication with Fractions (Lessons 1-6) Number of days: 7 Quick Practice: (Starts at lesson 2)


• Practice writing and saying of statements in equivalent forms. Vocabulary: comparison bars, multiplicative comparison, factor, product, area model for multiplication, fraction-bar model for multiplication, Multiply and Simplify Method, Simplify and Multiply Method, Unit Fraction Method Essential Questions:

• How is multiplying by a unit fraction equivalent to dividing by a whole number? • How can we multiply a whole number by a non-unit fraction? • How can we multiply a whole number by a fraction to produce a fraction? • How can we multiply two fractions? • How can we tell if it is possible to simplify in fraction multiplication before multiplying? • How is multiplying mixed numbers similar to multiplying fractions? How is it different?

Learning Targets: • Connect multiplying by 1/n to dividing by n, and use this idea to make multiplicative

comparisons. • Interpret a/b times a quantity as a of b equal parts of that quantity. • Multiply a whole number by a fraction to produce a fraction. • Multiply any two fractions. • Compare and apply strategies for multiplying fractions. • Multiply mixed numbers.


Unit 3: Big Idea 2: Multiplication Links (Lessons 7-9) Number of days: 4 Quick Practice:

• Relate multiplication equations to equivalent division equations. Vocabulary: Associative Property, Commutative Property, Distributive Property Essential Questions:

• Will the product of two fractions less than one be greater than or less than their sum? • How can a fraction box be used to find a common denominator? • When multiplying one number by another, how can we tell if the product will be greater

than, less than, or equal to the number? Learning Targets:

• Relate operations with fractions and whole numbers and discuss properties of arithmetic. • Add, subtract, compare and multiply fractions to solve word problems. • Predict the size of a product relative to the size of one factor based on the size of the

other factor. Assessments: After Lesson 9, give Quick Quiz 2 (December 7 – December 18)

Unit 3: Big Idea 3: Division with Fractions (Lessons 10-14) Number of days: 6 Quick Practice:

• Relate multiplication equations to equivalent division equations. • Divide a whole number by a unit fraction.


Vocabulary: decimal fraction, dividend, divisor, quotient Essential Questions:

• How can we divide a whole number by a unit fraction and a unit fraction by a whole number?

• How is dividing a whole number by a unit fraction different from dividing a unit fraction by a whole number?

• Why does multiplying a number n by a unit fraction give a number less than n, but dividing n by a unit fraction gives a number less than n?

• How can we solve real world problems involving mixed operations? Learning Targets:

• Relate division by a unit fraction or a whole number to multiplication. • Write and solve division word problems. • Determine whether solving a word problem requires multiplication or division. • Solve numerical and word problems involving all four operations with fractions. • Use the Common Core Content Standards and Practices in a variety of real world problem

solving situations. Assessments: After Lesson 14, give Quick Quiz 3.


Unit 4: Multiplication with Whole Numbers and Decimals

January-February Learning Progressions: Last year, my students… In my class, students will… Next year, my students will… • use strategies based on

place value and properties to multiply whole numbers.

• represented multiplying multi-digit numbers with array and area numbers.

• wrote equations to represent multiplication situations.

• represent multiplying decimals with money and drawings.

• use strategies based on place value and properties to multiply decimal numbers.

• write equations to represent multiplication situations.

• use strategies based on place value and properties to multiply decimal numbers.

• write equations to represent multiplication situations.


Content

CC.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. CC.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. CC.5.NBT.3: Read, write, and compare decimals to thousandths. CC.5.NBT.3b: Read, write, and compare decimals to thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. CC.5.NBT.4: Use place value understanding to round decimals to any place. Perform operations with multi-digit whole numbers and with decimals to hundredths. CC.5.NBT.5: Fluently multiply multi-digit whole numbers using the standard algorithm. CC.5.NBT.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.


CC.5.NF.5: Interpret multiplication as scaling (resizing). CC.5.NF.5a: Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. CC.5.NF.5b: Interpret multiplication as scaling (resizing), by: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.

Pract ices


Unit 4: Big Idea 1: Multiplication with Whole Numbers (Lessons 1-5) Number of days: 6 Quick Practice: (Starts in lesson 2)

• Practice multiplying with tens, hundreds and thousands. • Practice multiplying fives and tens.

Vocabulary: shift, base, exponent, exponential form, power of ten, even, odd, partial products, Place Value Sections, Expanded Notation, New Groups Below, Place Value Rows, Short Cut Essential Questions:

• What happens when a number is multiplied by 10, 100 or 1,000? • Why do multiples of 5 need extra attention in the zeros pattern? • How can a place value model be used to solve multi-digit multiplication problems? • What methods can be used to solve two-digit multiplication problems? • What is the difference between multiplication of a 2-digit number by a 2-digit number and

by a 1-digit number? Learning Targets:

• Understand the shift pattern when multiplying by 10, 100, 1000. • Understand that multiples of 5 need extra attention in the zeros pattern. • Understand how a place value model can be used to solve multi-digit multiplication

problems. • Solve two-digit multiplication problems using various methods. • Practice multiplying multi-digit numbers.

Assessments: After Lesson 5, give Quick Quiz 1 and Fluency Check 1.


Unit 4: Big Idea 2: Multiplication and Decimal Numbers (Lessons 6-12) Number of days: 8 Quick Practice:

• Use zero patterns to multiply and divide. • Place the decimal point in multiplication problems. • Use zero patterns to multiply.

Vocabulary: Commutative Property of Multiplication, Associative Property of Multiplication, Distributive Property of Multiplication over Addition Essential Questions:

• How do we decide where to place the decimal point in the product in a problem with decimal and whole number factors?

• How is multiplying a decimal number by a decimal number similar to multiplying a whole number by a decimal number? How is it different?

• What method can be used to multiply two decimal numbers that are both greater than one? How do we decide where the decimal should be placed in the product?

• What happens to the product when a decimal number is multiplied by 10, by 100, and by 1,000?

• What methods can be used for estimating the product of two decimal numbers? • What methods can be used to solve multi-digit multiplication with decimal numbers?

Learning Targets: • Solve multiplication problems in which one factor is a decimal number. • Solve multiplication problems in which at least one factor is a decimal number. • Multiply with decimal numbers greater than 1. • Understand and apply shift patterns when multiplying by 10, 100, 1000, 0.1, or 0.01. • Round whole numbers and decimal numbers to estimate the product in a multiplication

problem. • Perform multi-digit multiplication with decimal numbers.

Assessments: After Lesson 12, give Quick Quiz 2 (January 25 – February 5) and Fluency Check 2.


Unit 5: Division with Whole Numbers and Decimals February-March

Learning Progressions: Last year, my students… In my class, students will… Next year, my students will… • drew visual arrays and

rectangle diagrams to represent multiplication.

• reasoned repeatedly about the connection between math drawings and written numerical work.

• saw that division algorithms are summaries of their reasoning about quantities.

• connect the methods for whole numbers to computing with decimals.

• explain patterns in the number of zeros of the product when dividing by powers of ten.

• decompose factors into base-ten units and apply the Distributive Property.

• use 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.

• use strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.

• use the standard algorithm for computation with whole numbers and decimals.


Content

CC.5.NBT.A.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. CC.5.NBT.A.3.B Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. CC.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm. CC.5.NBT.B.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.


CC.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. CC.5.NF.B.5 Interpret multiplication as scaling (resizing), by:

CC.5.NF.B.5.A Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

Pract ices


Unit 5: Big Idea 1: Division with Whole Numbers (Lessons 1-5) Number of days: 6 Quick Practice:

• Determine the place value of the first digit in a quotient. Vocabulary: Digit-by-Digit method, dividend, divisor, Expanded Notation method, Place Value Sections method, quotient, remainder, over estimate, under estimate Essential Questions:

• How can multi-digit numbers be divided by single-digit divisors? • How can we solve division problems that have two-digit divisors? • How can we adjust our estimate of the first digit of a quotient if it is too low? • How do we decide what to do with the remainder in division problems? • What are the steps for dividing whole numbers?

Learning Targets:

• Divide multi-digit numbers by single-digit divisors. • Solve division problems with two-digit divisors. • Understand several ways to adjust the estimated divisor when it is too small. • Express and interpret remainders for a variety of problem types. • Practice dividing whole numbers.


Unit 5: Big Idea 2: Division with Decimal Numbers (Lessons 6-11) Number of days: 7 Quick Practice:

• Determine the place value of the first digit in a quotient. Vocabulary: none Essential Questions:


• How can decimal numbers be divided by one and two digit whole numbers? • How can we solve division problems that have decimal divisors? • How can we solve division problems in which both numbers are decimals? • How can we solve division problems involving whole numbers and decimal numbers? • What strategies can be used to solve problems that involve multiplying or dividing whole

numbers and decimal numbers? • How can the Common Core Content Standards and Practices be used to solve a variety of

real world problems? Learning Targets:

• Divide decimal numbers by one and two digit whole numbers. • Solve division problems that have decimal divisors. • Solve division problems in which both numbers are decimals. • Solve division problems involving whole numbers and decimal numbers. • Solve problems that involve multiplying or dividing whole numbers and decimal numbers. • Use the Common Core Content Standards and Practices in a variety of real world problem

solving situations. Assessments: After Lesson 11, give Quick Quiz 2 (February 29 – March 11) and Fluency Check 4.


Unit 6: Operations and Word Problems March-April

Learning Progressions: Last year, my students… In my class, students will… Next year, my students will… • used drawings and equations

with a symbol for the unknown number to represent the problem.

• represented verbal statements of multiplicative comparisons as multiplication equations.

• wrote equations to represent problems with more than one step.

• draw a model to solve comparison problems.

• draw visual fraction models or write equations to represent the problem.

• use benchmark fractions and number sense of fractions to estimate mentally and assess reasonableness of answers.

• use strategies based on the relationship between addition and subtraction.

• use visual models and equations to represent the problems.

• use the standard algorithm for each operation for whole numbers and decimals.

• write and solve equations to solve real world problems.


Content

CC.5.OA.A.1Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. CC.5.NBT.A.4 Use place value understanding to round decimals to any place. CC.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm. CC.5.NBT.B.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. CC.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. CC.5.NF.A.1Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.


CC.5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. CC.5.NF.B.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. CC.5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

CC.5.NF.B.4.A Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. CC.5.NF.B.4.B Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

CC.5.NF.B.5 Interpret multiplication as scaling (resizing), by: CC.5.NF.B.5.A Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. CC.5.NF.B.5.B Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

CC.5.NF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1

CC.5.NF.B.7.A Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. CC.5.NF.B.7.B Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. CC.5.NF.B.7.C Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.

Pract ices

MP.1: Make sense of problems and persevere in solving them. MP.2: Reason abstractly and quantitatively. MP.3: Construct viable arguments and critique the reasoning of others. MP.4: Model with math. MP.5: Use appropriate tools strategically. MP.6: Attend to precision. MP.7: Look for and make use of structure.


MP.8: Look for and express regularity in repeated reasoning.

Unit 6: Big Idea 1: Equations and Problem Solving (Lessons 1-4) Number of days: 5 Quick Practice:

• Name solution equations. • Naming solution equations given a situation equation.

Vocabulary: situation equation, solution equation, break apart drawing, rectangle model, benchmark Essential Questions:

• What are situation and solution equations and what is the relationship between them? • How can situation and solution equations be used to solve multiplication and division

problems? • How can we write word problems involving fractions and decimals and model the product? • What are some strategies that can be used to determine if an answer is reasonable?

Learning Targets: • Write situation and solution equations to solve addition and subtraction problems. • Write situation and solution equations to solve multiplication and division problems. • Write word problems for equations involving fractions and decimals and model the product. • Use a variety of methods to determine reasonable answers.


Unit 6: Big Idea 2: Comparison Word Problems (Lessons 5-7) Number of days: 4 Quick Practice:

• Naming solution equations. • Generalize the size of products.

Vocabulary: comparison, leading language, misleading language, scaling Essential Questions:

• What is the difference between leading and misleading language? • What is scaling? • What is the difference between an additive and a multiplicative comparison problem?

Learning Targets: • Understand and apply comparison language. • Model and solve multiplicative comparison problems. • Solve comparison problems.

Formative Assessments: After Lesson 7, give Quick Quiz 2 (March 14 – March 24) and Fluency Check 6.

Unit 6: Big Idea 3: Problems with More Than One Step (Lessons 8-11) Number of days: 5 Quick Practice:

• Generalize the size of products. Vocabulary: parentheses, equation


Essential Questions: • What strategies can be used to solve two-step problems? • What strategies can be used to solve multi-step problems? • How can the Common Core Content Standards and Practices be used to solve a variety of

real world problems? Learning Targets:

• Solve two- step problems. • Solve multi-step problems. • Practice solving multi-step problems. • Use the Common Core Content Standards and Practices in a variety of real world problem

solving situations. Assessments: After Lesson 11, give Quick Quiz 3 and Fluency Check 7.


Unit 7: Algebra, Patterns and Coordinate Graphs

April-May Learning Progressions: Last year, my students… In my class, students will… Next year, my students will… • represented multiplicative

comparison problems using drawings and equations with ha symbol for the unknown number.

• represented problems using equations with a letter standing for the unknown quantity.

• identified apparent features of a pattern that are not explicit in the rule itself.

• simplify an expression using the Order of Operations.

• interpret expressions without simplifying them.

• identify relationships between corresponding terms in two patterns.

• represent points in a coordinate plane.

• identify parts of an expression using mathematical terms.

• use the Order of Operations.

• use the properties of operations to generate equivalent expressions.

• write an equation to express one quantity, the dependent variable, in terms of the quantity thought of as the independent variable.


Content

CC.5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. CC.5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. CC.5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. CC.5.G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). CC.5.G.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.


Pract ices


Unit 7: Big Idea 1: Algebraic Reasoning and Expressions (Lessons 1-3) Number of days: 4 Quick Practice: (Starts in lesson 2)

• Practice the Order of Operations. Vocabulary: expression, Order of Operations, simplify, evaluate, variable Essential Questions:

• How do we read and write expressions? • How do we simplify numerical expressions? • How do we write and evaluate expressions with variables?

Learning Targets: • Read and write expressions. • Simplify numerical expressions. • Write and evaluate expressions with certain variables.


Unit 7: Big Idea 2: Patterns and Graphs (Lessons 4-7) Number of days: 4 Quick Practice:

• Practice the Order of Operations. Vocabulary: numerical pattern, term, coordinate plane, ordered pair, origin, x-coordinate, y-coordinate, x-axis, y-axis Essential Questions:

• How do we generate and extend numerical patterns and identify relationships of corresponding terms?

• How do we locate and plot points in the first quadrant of the coordinate plane? • How do we use ordered pairs and use them to represent and solve real world problems?

Learning Targets: • Generate and extend numerical patterns and identify relationships of corresponding terms. • Locate and plot points in the first quadrant of the coordinate plane. • Use ordered pairs and use them to represent and solve real world problems.



Unit 8: Measurement and Geometry May-June

Learning Progressions: Last year, my students… In my class, students will… Next year, my students will… • recorded measurement

equivalents in a two-column table.

• represented measurement quantities using diagrams such as number lines that feature a measurement scale.

• understand the concepts of volume

• use unit cubes to pack a right rectangular prism.

• relate volume to the operations of multiplication and division.

• classify two-dimensional figures in a hierarchy.

• compose polygons into rectangles and decompose polygons into triangles.

• use nets made from rectangles and triangles.

• apply volume formulas to rectangular prisms with fractional edge lengths.


Content

CC.5.MD.1Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems CC.5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. CC.5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. CC.5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. CC.5.MD.C.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

CC.5.MD.5a Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. CC.5.MD.5b Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. CC.5.MD.5c Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.


CC.f.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. CC.5.G.4 Classify two-dimensional figures in a hierarchy based on properties.

Pract ices


Unit 8: Big Idea 1: Measurements and Data (Lessons 1-7) Number of days: 10 Quick Practice: (Starts in lesson 2)

• Practice converting metric units of length. • Practice converting metric units of liquid volume. • Practice converting metric units of mass.

Vocabulary: meter, millimeter, centimeter, decimeter, dekameter, hectometer, kilometer, liter, milliliter, centiliter deciliter, dekaliter, hectoliter, kiloliter, mass, gram, milligram, centigram, decigram, dekagram, hectogram, kilogram, mile (mi), ton, frequency table, line plot Essential Questions:

• How do you convert metric units? • How do you convert customary units? • How do you read and make line plots?

Learning Targets: • Convert metric and customary units. • Read and make line plots.


*Unit 8: Big Idea 2: Area and Volume (Lessons 8-13) Number of days: 7 *Unit 8: Big Idea 2 is important. Be sure to get to it before SBAC. It can be taught before Unit 7 and Unit 8 Big Ideas 1 and 3.) Quick Practice:

• Practice converting customary units of length. • Practice converting customary units of liquid volume. • Practice converting customary units of weight.

Vocabulary: perimeter, area, square centimeter, square unit, face, edge, rectangular prism,


cube, unit cube, volume, cubic unit, one-dimensional, two-dimensional, three-dimensional, composite Essential Questions:

• How do you calculate the perimeter and area of rectangles? • How do you calculate volume of a rectangular prism? • How do you calculate the volume of a composite solid figure? • How do you use formulas to calculate volume?

Learning Targets: • Calculate area and perimeter of rectangles. • Calculate the volume of rectangular prisms by counting blocks or using a formula. • Calculate the volume of composite solid figures.


Unit 8: Big Idea 3: Classify Geometric Figures (Lessons 14-17) Number of days: 5 (17 optional) Quick Practice:

• Review geometric figures. Vocabulary: acute angle, adjacent angles, adjacent sides, congruent, counterexample, line of symmetry, opposite angles, opposite sides, parallel, parallelogram, perpendicular, quadrilateral, rectangle, rhombus, right angle, square, trapezoid, congruent angles, congruent sides, equilateral, triangle, isosceles triangle, obtuse angle, obtuse triangle, perpendicular sides, right angle, right triangle, scalene triangle, closed, concave, convex, open, reflex angle, regular polygon Essential Questions:

• How do I describe quadrilaterals with attributes? • How do I describe triangles with attributes? • How do I describe two-dimensional shapes with attributes?

Learning Targets: • Describe the attributes of quadrilaterals, triangles, and two-dimensional shapes.

Assessments: After Lesson 17, give Quick Quiz 3 and Fluency Check 12. End of Year Inventory (May 26 – June 9)

Documents

Fifth GRADE CURRICULUM MAP 2015 2016€¦ · Fifth Grade Curriculum Map Mathematics To: Fifth Grade Teachers From: Jodi Albers Date: August 21, 2015 Re: FifthGrade Math Expressions