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Cheshire Public Schools | Excellence In Education | Cheshire CT > Curriculum and Instruction > Elementary Math Curriculum

The Connecticut Core Standards provide the foundation for the Cheshire mathematics curriculum. While the mathematical content and skills in each grade level are essential for student success, a good portion of the emphasis in math is related to the eight mathematical practices described in the standards. Those practices help provide a means to ensure the development of strong number sense and robust mathematical thinking throughout all of the grade levels.

The scope and sequence of the curriculum, therefore, is built to have students work through the concrete, representational, and abstract stages for each interconnected concept and skill area. Building a strong conceptual understanding through hands-on manipulatives and a variety of mental math and visual math strategies prior to introducing standard algorithms helps solidify student understanding of concepts. The mental math and visual strategies introduced in the early grades are used throughout the grade levels with increasing complexity and sophistication. The curriculum emphasizes students applying strategies that work for them, communicating and defending their thinking to others, understanding the thinking of others, and increasing computational fluency and efficiency.

Select the grade level below to view the module information.

Grade K
##### Curriculum Module

##### 1 – Numbers to 10

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 2: 2D and 3D Shapes

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 3: Comparisons of Lengths, Width, and Capacity and Number to 10 (condense)

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 4: Number Pairs, Addition and Subtraction to 10

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 5: Numbers to 10 and Counting to 100

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 6: Analyzing, Comparing and Composing Shapes

##### Module Overview

##### CCSS Domain

##### Marking Period

Kindergarten mathematics is about (1) representing, relating, and operating on whole numbers, initially with sets of objects; and (2) describing shapes and space. More learning time in Kindergarten should be devoted to numbers than to other topics.

In Module 1, Kindergarten starts out with solidifying the meaning of numbers to 10 with a focus on embedded numbers and relationships to 5 using fingers, cubes, drawings, 5 groups and the Rekenrek. Students then investigate patterns of “1 more” and “1 less” using models such as the number stairs (see picture). Because fluency with addition and subtraction within 5 is a Kindergarten goal, addition within 5 is begun in Module 1 as another representation of the decomposition of numbers.

- Counting and Cardinality
- Operations and Algebraic Thinking
- Measurement and Data

T1

In Module 2, Students learn to identify and describe squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders and spheres. During this module students also practice their fluency with numbers to 10

- Measurement and Data
- Geometry

T1

In Module 3, students begin to experiment with comparison of length, weight and capacity. Students first learn to identify the attribute being compared, moving away from non-specific language such as “bigger” to “longer than,” “heavier than,” or “more than.” Comparison begins with developing the meaning of the word “than” in the context of “taller than,” “shorter than,” “heavier than,” “longer than,” etc. The terms “more” and “less” become increasingly abstract later in Kindergarten. “7 is 2 more than 5” is more abstract than “Jim is taller than John.”

- Counting and Cardinality
- Measurement and Data

T2

In Module 4, number comparison leads to a further study of embedded numbers (e.g., “3 is less than 7” leads to, “3 and 4 make 7,” and 3 + 4 = 7,). “1 more, 2 more, 3 more” lead into addition (+1, +2, +3). Students now represent stories with blocks, drawings, and equations.

- Operations and Algebraic Thinking

T1, T2

After Module 5, after students have a meaningful experience of addition and subtraction within 10 in Module 4, they progress to exploration of numbers 10-20. They apply their skill with and understanding of numbers within 10 to teen numbers, which are decomposed as “10 ones and some ones.” For example, “12 is 2 more than 10.” The number 10 is special; it is the anchor that will eventually become the “ten” unit in the place value system in Grade 1.

- Counting and Cardinality
- Number in Base Ten

T2

Module 6 rounds out the year with an exploration of shapes. Students build shapes from components, analyze and compare them, and discover that they can be composed of smaller shapes, just as larger numbers are composed of smaller numbers.

- Number in Base Ten
- Counting and Cardinality
- Geometry

T2

Grade 1
##### Curriculum Module

##### 1: Sums and Differences to 10

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 2: Introduction to Place Value Through Addition and Subtraction Within 20

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 3: Ordering and Comparing Length Measurements as Numbers

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 4: Place Value, Comparison, Addition, and Subtraction to 40

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 5: Identifying, Composing, and Partitioning Shapes

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 6: Place Value, Comparison, Addition, and Subtraction to 100

##### Module Overview

##### CCSS Domain

##### Marking Period

First Grade mathematics is about (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes.

In Grade 1, work with numbers to 10 continues to be a major stepping-stone in learning the place value system. In Module 1, students work to further understand the meaning of addition and subtraction begun in Kindergarten, largely within the context of the Grade 1 word problem types. They begin intentionally and energetically building fluency with addition and subtraction facts—a major gateway to later grades.

- Operations and Algebraic Thinking

T1

In Module 2, students add and subtract within 20. Work begins by modeling “adding and subtracting across ten” in word problems and with equations. Solutions involving decomposition and composition like that shown to the right for 8 + 5 reinforce the need to “make 10.” In Module 1, students loosely grouped 10 objects to make a ten. They now transition to conceptualizing that ten as a single unit (using 10 linking cubes stuck together, for example). This is the next major stepping-stone in understanding place value, learning to group “10 ones” as a single unit: 1 ten. Learning to “complete a unit” empowers students in later grades to understand “renaming” in the addition algorithm, to add 298 and 35 mentally (i.e., 298 + 2 + 33), and to add measurements like 4 m, 80 cm, and 50 cm (i.e., 4 m + 80 cm + 20 cm + 30 cm = 4 m + 1 m + 30 cm = 5 m 30 cm).

- Operations and Algebraic Thinking
- Numbers and Operations in Base Ten

T1

Module 3, which focuses on measuring and comparing lengths indirectly and by iterating length units, gives students a few weeks to practice and internalize “making a 10” during daily fluency activities.

- Measurement and Data
- Operations and Algebraic Thinking

T2

Module 4 returns to understanding place value. Addition and subtraction within 40 rest on firmly establishing a “ten” as a unit that can be counted, first introduced at the close of Module 2. Students begin to see a problem like 23 + 6 as an opportunity to separate the “2 tens” in 23 and concentrate on the familiar addition problem 3 + 6. Adding 8 + 5 is related to solving 28 + 5; complete a unit of ten and add 3 more.

- Operations and Algebraic Thinking
- Numbers and Operations in Base Ten

T3

In Module 5, students think about attributes of shapes and practice composing and decomposing geometric shapes. They also practice work with addition and subtraction within 40 during daily fluency activities (from Module 4). Thus, this module provides important “internalization time” for students between two intense number-based modules. The module placement also gives more spatially-oriented students the opportunity to build their confidence before they return to arithmetic.

- Geometry
- Measurement and Data

T3

Although Module 6 focuses on “adding and subtracting within 100,” the learning goal differs from the “within 40” module. Here, the new level of complexity is to build off the place value understanding and mental math strategies that were introduced in earlier modules. Students explore by using simple examples and the familiar units of 10 made out of linking cubes, bundles, and drawings. Students also count to 120 and represent any number within that range with a numeral.

- Numbers and Operations in Base Ten
- Measurement and Data
- Operations and Algebraic Thinking

T3

Grade 2
##### Curriculum Module

##### 1: Sums and Differences to 100

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 2: Addition and Subtraction of Length Units

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 3: Place Value, Counting, and Comparison of Numbers to 1,000

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 4: Addition and Subtraction Within 200 with Word Problems to 100

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 5: Addition and Subtraction Within 1,000 with Word Problems to 100

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 6: Foundations of Multiplication and Division

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 7: Problem Solving with Length, Money, and Data

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 8: Time, Shapes, and Fractions as Equal Parts of Shapes

##### Module Overview

##### CCSS Domain

##### Marking Period

Second Grade mathematics is about (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes.

From Grade 1, students have fluency of addition and subtraction within 10 and extensive experience working with numbers to 100. Module 1 of Grade 2 establishes a motivating, differentiated fluency program in the first few weeks that will provide each student with enough practice to achieve mastery of the new required fluencies (i.e., adding and subtracting within 20 and within 100) by the end of the year. Students learn to represent and solve word problems using addition and subtraction: a practice that will also continue throughout the year.

- Operations and Algebraic Thinking
- Number and Operations in Base Ten

T1

In Module 2, students learn to measure and estimate using standard units for length and solve measurement word problems involving addition and subtraction of length. A major objective is for students to use measurement tools with the understanding that linear measure involves an iteration of units and that the smaller a unit, the more iterations are necessary to cover a given length. Students work exclusively with metric units, i.e. centimeters and meters, in this module to support upcoming work with place value concepts in Module 3. Units also play a central role in the addition and subtraction algorithms of Modules 4 and 5. An underlying goal for this module is for students to learn the meaning of a “unit” in a different context, that of length. This understanding serves as the foundation of arithmetic, measurement, and geometry in elementary school.

- Measurement and Data

T1

All arithmetic algorithms are manipulations of place value units: ones, tens, hundreds, etc. In Module 3, students extend their understanding of base-ten notation and apply their understanding of place value to count and compare numbers to 1000. In Grade 2 the place value units move from a proportional model to a non-proportional number disk model (see picture). The place value table with number disks can be used through Grade 5 for modeling very large numbers and decimals, thus providing students greater facility with and understanding of mental math and algorithms.

- Number and Operations in Base Ten

T1

In Module 4, students apply their work with place value units to add and subtract within 200 moving from concrete to pictorial to abstract. This work deepens their understanding of base-ten, place value, and the properties of operations. It also challenges them to apply their knowledge to one-step and two-step word problems. During this module, students also continue to develop one of the required fluencies of the grade: addition and subtraction within 100.

- Operations and Algebraic Thinking
- Numbers and Operations in Base Ten

T2

Module 5 builds upon the work of Module 4. Students again use place value strategies, manipulatives, and math drawings to extend their conceptual understanding of the addition and subtraction algorithms to numbers within 1000. They maintain addition and subtraction fluency within 100 through daily application work to solve one- and two-step word problems of all types. A key component of Modules 4 and 5 is that students use place value reasoning to explain why their addition and subtraction strategies work.

- Number and Operations in Base Ten

T2

In Module 6, students extend their understanding of a unit to build the foundation for multiplication and division wherein any number, not just powers of ten, can be a unit. Making equal groups of “four apples each” establishes the unit “four apples” (or just four) that can then be counted: 1 four, 2 fours, 3 fours, etc. Relating the new unit to the one used to create it lays the foundation for multiplication: 3 groups of 4 apples equal 12 apples (or 3 fours is 12).

- Operations and Algebraic Thinking
- Geometry

T3

Module 7 provides another opportunity for students to practice their algorithms and problem-solving skills with perhaps the most well-known, interesting units of all: dollars, dimes, and pennies. Measuring and estimating length is revisited in this module in the context of units from both the customary system (e.g., inches and feet) and the metric system (e.g., centimeters and meters). As they study money and length, students represent data given by measurement and money data using picture graphs, bar graphs, and line plots.

- Measurement and Data
- Number and Operations in Base Ten

T3

Students finish Grade 2 by describing and analyzing shapes in terms of their sides and angles. In Module 8, students investigate, describe, and reason about the composition and decomposition of shapes to form other shapes. Through building, drawing, and analyzing two- and three-dimensional shapes, students develop a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades.

- Geometry
- Measurement and Data

T3

Grade 3
##### Curriculum Module

##### 1: Properties of Multiplication and Division and Solving Problems with Units of 2-5 and 10

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 2: Place Value and Problem Solving with Units of Measure

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 3: Multiplication and Division with Units of 0, 1, 6-9, and Multiples of 10

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 4: Multiplication and Area

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 5: Fractions as Numbers on the Number Line

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 6: Collecting and Displaying Data

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 7: Geometry and Measurement Word Problems

##### Module Overview

##### CCSS Domain

##### Marking Period

Third Grade mathematics is about (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.

The first module builds upon the foundation of multiplicative thinking with units started in Grade 2. First, students concentrate on the meaning of multiplication and division and begin developing fluency for learning products involving factors of 2, 3, 4, 5, and 10 (see key areas of focus and required fluency above). The restricted set of facts keeps learning manageable, and also provides enough examples to do one- and two-step word problems and to start measurement problems involving weight, capacity and time in the second module.

- Operations and Algebraic Thinking

T1

Module 2 focuses on measurement of time and metric weight and capacity. In exploratory lessons, students decompose a kilogram into 100 gram, 10 gram and 1 gram weights and decompose a liter into analogous amounts of milliliters. Metric measurement thereby develops the concept of mixed units, e.g. 3 kilograms 400 grams is clearly related to 3 thousands, 4 hundreds. Students then apply their new understanding of number to place value, comparison and rounding, composing larger units when adding, decomposing into smaller units when subtracting. Students also draw proportional tape diagrams to solve word problems (e.g., “If this tape represents 62 kg, then a tape representing 35 kg needs to be slightly longer than half the 62 kg bar…”). Drawing the relative sizes of the lengths involved in the model prepares students to locate fractions on a number line in Module 5 (where they learn to locate points on the number line relative to each other and relative to the whole unit). Module 2 also provides students with internalization time for learning the 2, 3, 4, 5, and 10 facts as part of their fluency activities.

- Measurement and Data
- Geometry

T1

Students learn the remaining multiplication and division facts in Module 3 as they continue to develop their understanding of multiplication and division strategies within 100 and use those strategies to solve two-step word problems. The “2, 3, 4, 5 and 10 facts” module (Module 1) and the “0, 1, 6, 7, 8, 9 and multiples of 10 facts” module (Module 3) both provide important, sustained time for work in understanding the structure of rectangular arrays to prepare students for area in Module 4. This work is necessary because students initially find it difficult to distinguish the different units in a grid, count them and recognize that the count is related to multiplication. Tiling also supports a correct interpretation of the grid. Modules 1 and 3 slowly build up to the area model using rectangular arrays in the context of learning multiplication and division.

- Operations and Algebraic Thinking
- Numbers and Operations in Base Ten

T2

By Module 4, students are ready to investigate area. They measure the area of a shape by finding the total number of same-size units of area, e.g. tiles, required to cover the shape without gaps or overlaps. When that shape is a rectangle with whole number side lengths, it is easy to partition the rectangle into squares with equal areas.

- Measurement and Data

T2

One goal of Module 5 is for students to transition from thinking of fractions as area or parts of a figure to points on a number line. To make that jump, students think of fractions as being constructed out of unit fractions: “1 fourth” is the length of a segment on the number line such that the length of four concatenated fourth segments on the line equals 1 (the whole). Once the unit “1 fourth” has been established, counting them is as easy as counting whole numbers: 1 fourth, 2 fourths, 3 fourths, 4 fourths, 5 fourths, etc. Students also compare fractions, find equivalent fractions in special cases, and solve problems that involve fractions.

- Numbers and Operations- Fractions
- Geometry

T3

In Module 6, students leave the world of exact measurements behind. By applying their knowledge of fractions from Module 5, they estimate lengths to the nearest halves and fourths of an inch and record that information in bar graphs and line plots. This module also prepares students for the multiplicative comparison problems of Grade 4 by asking students “how many more” and “how many less” questions about scaled bar graphs.

- Measurement and Data

T3

The year rounds out with plenty of time to solve two-step word problems involving the four operations, and to improve fluency for concepts and skills initiated earlier in the year. In Module 7, students also describe, analyze, and compare properties of two-dimensional shapes. By now, students have done enough work with both linear and area measurement models to understand that there is no relationship in general between the area of a figure and perimeter, which is one of the concepts taught in the last module.

- Operations and Algebraic Thinking
- Measurement and Data
- Geometry

T3

Grade 4
##### Curriculum Module

##### 1: Place Value, Rounding, and Algorithms for Addition and Subtraction

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 2: Unit Conversions

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 3: Multi-Digit Multiplication and Division

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 4: Fraction Equivalence, Ordering, and Operations

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 5: Comparisons of Lengths, Width, and Capacity and Number to 10 (condense)

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 6: Analyzing, Comparing and Composing Shapes

##### Module Overview

Module 6 rounds out the year with an exploration of shapes. Students build shapes from components, analyze and compare them, and discover that they can be composed of smaller shapes, just as larger numbers are composed of smaller numbers.

##### CCSS Domain

##### Marking Period

Fourth-grade mathematics is about (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; and (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.

In Grade 4, students extend their work with whole numbers. They begin with large numbers using familiar units (tens and hundreds) and develop their understanding of thousands by building knowledge of the pattern of times ten in the base ten system on the place value chart (4.NBT.1). In Grades 2 and 3 students focused on developing the concept of composing and decomposing place value units within the addition and subtraction algorithms. Now, in Grade 4, those (de)compositions and are seen through the lens of multiplicative comparison, e.g. 1 thousand is 10 times as much as 1 hundred. They next apply their broadened understanding of patterns on the place value chart to compare, round, add and subtract. The module culminates with solving multi-step word problems involving addition and subtraction modeled with tape diagrams that focus on numerical relationships.

- Operations and Algebraic Thinking
- Numbers and Operations in Base Ten

T1

The algorithms continue to play a part in Module 2 as students relate place value to metric units. This module helps students draw similarities between:

1 ten = 10 ones

1 hundred = 10 tens

1 hundred = 100 ones

1 meter = 100 centimeters

1 thousand = 1,000 ones

1 kilometer = 1,000 meters

1 kilogram = 1,000 grams

1 liter = 1,000 milliliters

Students work with metric measurement in the context of the addition and subtraction algorithms, mental math, place value, and word problems. Customary units are used as a context for fractions in Module 5.

- Measurement and Data

T1

In Module 3, measurements provide the concrete foundation behind the distributive property in the multiplication algorithm: 4 × (1 m 2 cm) can be made physical using ribbon, where it is easy to see the 4 copies of 1 m and the 4 copies of 2 cm. Likewise, 4 × (1 ten 2 ones) = 4 tens 8 ones. Students then turn to the place value table with number disks to develop efficient procedures for multiplying and dividing one-digit whole numbers and use the table with number disks to understand and explain why the procedures work. Students also solve word problems throughout the module where they select and accurately apply appropriate methods to estimate, mentally calculate, or use the procedures they are learning to compute products and quotients.

- Operations and Algebraic Thinking
- Numbers and Operations in Base Ten

T2

Module 5 centers on equivalent fractions and operations with fractions. We use fractions when there is a given unit, the whole unit, but we want to measure using a smaller unit, called the fractional unit. To prepare students to explore the relationship between a fractional unit and its whole unit, examples of such relationships in different contexts were already carefully established earlier in the year:

360 degrees in 1 complete turn

100 centimeters in 1 meter

1000 grams in 1 kilogram

1000 milliliters in 1 liter

The beauty of fractional units, once defined and understood, is that they behave just as all other units do: • “3 fourths + 5 fourths = 8 fourths” just as “3 meters + 5 meters = 8 meters” • “4 x 3 fourths = 12 fourths” just as “4 x 3 meters = 12 meters” Students add and subtract fractions with like units using the area model and the number line. They multiply a fraction by a whole number where the interpretation is as repeated addition e.g. 3 fourths + 3 fourths = 2 x 3 fourths. Through this introduction to fraction arithmetic they gradually come to understand fractions as units they can manipulate, just like whole numbers. Throughout the module, customary units of measurement provide a relevant context for the arithmetic.

- Counting and Cardinality
- Number in Base Ten

T2

In Module 5, students begin to experiment with comparison of length, weight and capacity. Students first learn to identify the attribute being compared, moving away from non-specific language such as “bigger” to “longer than,” “heavier than,” or “more than.” Comparison begins with developing the meaning of the word “than” in the context of “taller than,” “shorter than,” “heavier than,” “longer than,” etc. The terms “more” and “less” become increasingly abstract later in Kindergarten. “7 is 2 more than 5” is more abstract than “Jim is taller than John.”

- Counting and Cardinality
- Measurement and Data

T2

- Number in Base Ten
- Counting and Cardinality
- Geometry

T2

Grade 5
##### Curriculum Module

##### 1: Place Value and Decimal Fractions

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 2: Multi-Digit Whole Number and Decimal Fraction Operations

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 3: Addition and Subtraction of Fractions

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 4: Multiplication and Division of Fractions and Decimal Fractions

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 5: Addition and Multiplication with Volume and Area

##### Module Overview

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### 6: Problem Solving with the Coordinate Plane

##### Module Overview

##### CCSS Domain

##### Marking Period

Fifth grade mathematics is about (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 two-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.

Students’ experiences with the algorithms as ways to manipulate place value units in Grades 2-4 really begin to pay dividends in Grade 5. In Module 1, whole number patterns with number disks on the place value table are easily generalized to decimal numbers. As students work word problems with measurements in the metric system, where the same patterns occur, they begin to appreciate the value and the meaning of decimals. Students apply their work with place value to adding, subtracting, multiplying and dividing decimal numbers with tenths and hundredths.

- Numbers in Base Ten
- Measurement and Data

T1

Module 2 begins by using place value patterns and the distributive and associative properties to multiply multi-digit numbers by multiples of 10 and leads to fluency with multi-digit whole number multiplication.79 For multiplication, students must grapple with and fully understand the distributive property (one of the key reasons for teaching the multi-digit algorithm). While the multi-digit multiplication algorithm is a straightforward generalization of the one-digit multiplication algorithm, the division algorithm with two-digit divisors requires far more care to teach because students have to also learn estimation strategies, error correction strategies, and the idea of successive approximation (all of which are central concepts in math, science, and engineering).

- Operations and Algebraic Thinking
- Numbers in Base Ten
- Measurement and Data

T1

Work with place value units paves the path toward fraction arithmetic in Module 3 as elementary math’s place value emphasis shifts to the larger set of fractional units for algebra. Like units are added to and subtracted from like units. The new complexity is that when units are not equivalent, they must be changed for smaller equal units so that they can be added or subtracted. Probably the best model for showing this is the rectangular fraction model pictured below. The equivalence is then represented symbolically as students engage in active meaning-making rather than obeying the perhaps mysterious command to “multiply the top and bottom by the same number.”

- Numbers and Operations – Fractions

T2

Relating different fractional units to one another requires extensive work with area and number line diagrams. Tape diagrams are used often in word problems. Tape diagrams, which students began using in the early grades and which become increasingly useful as students applied them to a greater variety of word problems, hit their full strength as a model when applied to fraction word problems. At the heart of a tape diagram is the now familiar idea of forming units. In fact, forming units to solve word problems is one of the most powerful examples of the unit theme and is particularly helpful for understanding fraction arithmetic. Near the end of Module 4 students know enough about fractions and whole number operations to begin to explore multi-digit decimal multiplication and division. In multiplying 2.1 × 3.8, for example, students now have multiple skills and strategies that they can use to locate the decimal point in the final answer, including:

Unit awareness: 2.1 × 3.8 = 21 tenths × 38 tenths = 798 hundredths

Estimation (through rounding): 2.1 × 3.8 ≈ 2 × 4 = 8, so 2.1 × 3.8 = 7.98

Fraction multiplication: 21/10 × 38/10 = (21 × 38)/(10 × 10)

Similar strategies enrich students’ understanding of division and help them to see multi-digit decimal division as whole number division in a different unit. For example, we divide to find, “How many groups of 3 apples are there in 45 apples?” and write 45 apples ÷ 3 apples = 15. Similarly, 4.5 ÷ 0.3 can be written as “45 tenths ÷ 3 tenths” with the same answer: There are 15 groups of 0.3 in 4.5. This idea was used to introduce fraction division earlier in the module, thus gluing division to whole numbers, fractions and decimals together through an understanding of units.

- Operations and Algebraic Thinking
- Numbers in Base Ten
- Numbers and Operations – Fractions
- Measurement and Data

T2

Frequent use of the area model in Modules 3 and 4 prepares students for an in-depth discussion of area and volume in Module 5. But the module on area and volume also reinforces work done in the fraction module: Now, questions about how the area changes when a rectangle is scaled by a whole or fractional scale factor may be asked and missing fractional sides may be found. Measuring volume once again highlights the unit theme, as a unit cube is chosen to represent a volume unit and used to measure the volume of simple shapes composed out of rectangular prisms.

- Numbers and Operations – Fractions
- Measurement and Data
- Geometry

T3

Scaling is revisited in the last module on the coordinate plane. Since Kindergarten where growth and shrinking patterns were first introduced, students have been using bar graphs to display data and patterns. Extensive bar-graph work has set the stage for line plots, which are both the natural extension of bar graphs and the precursor to linear functions. It is in this final module of K-5 that a simple line plot of a straight line is presented on a coordinate plane and students are asked about the scaling relationship between the increase in the units of the vertical axis for 1 unit of increase in the horizontal axis. This is the first hint of slope and marks the beginning of the major theme of middle school: ratios and proportions.

- Operations and Algebraic Thinking
- Geometry

T2

Grade 6
##### Curriculum Module

##### Unit 1: Numerical Expressions and Factors

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### Unit 2: Fractions and Decimals

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### Unit 3: Algebraic Expressions

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### Unit 5: Ratios and Rates

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### Unit 6: Integers on the coordinate plane

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### Unit 7: Equalities and inequalities

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### Unit 4: Area of Polygons

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### Unit 8: Surface Area and Volume

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### Unit 9: Statistical Measures

##### CCSS Domain

##### Marking Period

##### Curriculum Module

##### Unit 10: Data Displays

##### CCSS Domain

##### Marking Period

The curriculum guide that follows provides an overview of the 6th-grade curriculum units, and their related domains, and report card term.

- Number Systems
- Expressions and Equations

T1

- Number Systems

T1

- Number Systems
- Expressions and Equations

T1

- Ratios and Proportional Relationships

T2

- Number Systems

T2

- Expressions and Equations

T2

- Geometry

T3

- Geometry

T3

- Statistics and Probability

T3

- Statistics and Probability

T3

Select the video icon to play the math strategy.

In this video, you will learn about number bonds: A number bond is a visual strategy that helps students to represent their thinking. It helps students to recognize the relationship between numbers, particularly with part-part-total.

In this video, you will learn about: Problem solving strategies for Grades K-1. How students learn to represent their thinking in meaningful ways as a key foundation to problem

In this video, you will learn: More about the “Make Ten” or “Make a Friendly Number” strategy. How this strategy helps students to better develop mental math skills.

In this video, you will learn: More about the “Take From Ten” or “Take From a Friendly Number” strategy. How this strategy helps students to better develop mental math skills.

In this video, you will learn: How students use the place value “chip” model to develop their understanding of addition using place value strategies.

In this video, you will learn: How students use the place value “chip” model to develop their understanding of subtraction using place value strategies.

In this video, you will learn about: The Read-Draw-Write process for problem solving. How the tape diagram can be used as a great visual model to help students represent their thinking

In this video, you will learn about: The Read-Draw-Write process for problem solving. How the tape diagram can be used as a great visual model to help students represent their thinking

In this video, you will learn about: The Read-Draw-Write process for problem solving. How the tape diagram can be used as a great visual model to help students represent their thinking

In this video, you will learn: How students use the area model to develop their understanding of multiplication using place value strategies.

In this video, you will learn: How students use the area model to develop their understanding of multiplication using place value strategies.

In this video, you will learn: How students use the place value “chip” model to develop their understanding of division using place value strategies. The place value “chip” model helps students to visually conceptualize division and helps them to understand why the standard algorithm for division works.

In this video you will learn: How area models can be used to help students understand and create equivalent fractions. How area models are a great visual strategy to help students to create equal size pieces, so that they are able to add, subtract, or compare fractions.

In this video, you will learn: How area models can be used to help students understand how to multiply fractions by fractions. How area models are a great visual strategy to help students understand conceptually what happens when you multiply a fraction by a fraction.

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