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Working with Even, Odd, and Equal Groups
Students analyze even and odd numbers and work with equal groups to form arrays and partition rectangles into equal-sized squares.
Math
Unit 7
2nd Grade
Unit Summary
In Unit 7, 2nd grade students determine if numbers are even or odd by developing an understanding of equal groups, then a sum of equal addends, and then by skip-counting. Students will further build their understanding of equal groups by working with arrays and later partitioning rectangles to form arrays of smaller equal-sized squares. At the beginning of Topic A, students work with concrete manipulatives to represent numbers and determine whether they can be represented in two equal groups or pairs of two. Students learn that quantities that can be represented in these ways with no leftovers or remainders are considered even numbers. Numbers and quantities that cannot be split into two equal groups are odd. As students explore even and odd numbers, they expand to justifying their even or odd distinctions more abstractly by connecting them to equal addends or doubles facts and later skip-counting by two.
In Topic B, students continue to work with equal groups but this time build and work with arrays. They come to understand that arrays are made up of equal groups of rows and/or columns and identify both as distinct features in an array. They also move beyond counting items in an array by ones to finding the total by recognizing the pattern of equal rows or columns. Instead of seeing an array with 2 rows of 5, counting the first group of five one-by-one, and then counting the next row, students see that since both rows have 5 counters, they can add the two groups of 5 together. They also see that the same array can be seen as 5 columns of 2 and add the 5 groups of 2 to find the total 10.
As their work in Topic B continues, they build arrays with square inch tiles to create rectangles, progress to see that larger rectangles can be partitioned into smaller equal-sized squares that are arranged in rows and columns, and use that structure to find the total.
The work of Topic A and Topic B forms the foundation of multiplication and division that students will develop during their third grade mathematics journey. By being able to identify and manipulate equal groups in concrete and increasingly more abstract ways, they will see that instead of repeated addition, they can use multiplication to find the same totals when arranged in arrays. Similarly, they will make connections between partitioning rectangles and division.
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Assessment
The following assessments accompany Unit 7.
Mid-Unit
Have students complete the Mid-Unit Assessment after Lesson 5.
Post-Unit
Use the resources below to assess student understanding of the unit content and action plan for future units.
Unit Prep
Intellectual Prep
Intellectual Prep for All Units
- Read and annotate the "Unit Summary" and "Essential Understandings" portions of the unit plan.
- Do all the Target Tasks and annotate them with the "Unit Summary" and "Essential Understandings" in mind.
- Take the Post-Unit Assessment.
Unit-Specific Intellectual Prep
- Read pp. 121–123 on Geometry in the Progressions.
Essential Understandings
- Numbers and quantities can be determined to be even based on their ability to be split into two equal groups or pairs of two with no leftovers.
- Numbers and quantities can be determined to be odd based on their ability to not be split into two equal groups or pairs of two with leftovers.
- Arrays can be used to organize and find the total of equal groups of objects in rows and columns.
- The number of objects in an array can be represented with repeated addition equations that represent equal groups of rows or equal groups of columns to find the total.
- When rectangles are partitioned into smaller equal-sized squares, the squares are arranged into equal rows and/or columns.
Vocabulary
Unit Vocabulary
array
column
even
odd
row
To see all the vocabulary for Unit 7, view our 2nd Grade Vocabulary Glossary.
Materials
- Manipulatives (25 per student)
- Groups of Two? Template (1 per student)
- Two Groups? Template (1 per student)
- Two-sided counters (25 per student)
- Square inch tiles (25 per student)
- Square Inch Grid Template (4 per student)
- Ruler (1 per student)
Unit Practice
Lesson Map
Topic A: Even and Odd Numbers
Topic B: Composing and Analyzing Arrays
Common Core Standards
Key
Major Cluster
Supporting Cluster
Additional Cluster
Core Standards
Geometry
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2.G.A.2 — Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
Operations and Algebraic Thinking
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2.OA.C.3 — Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
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2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
Foundational Standards
Operations and Algebraic Thinking
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1.OA.D.7
Future Standards
Measurement and Data
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3.MD.C.6
Operations and Algebraic Thinking
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3.OA.A.1
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3.OA.D.9
Standards for Mathematical Practice
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CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
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CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
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CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
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CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
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CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
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CCSS.MATH.PRACTICE.MP6 — Attend to precision.
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CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
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CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
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