Math / 2nd Grade / Unit 7: 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
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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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The following assessments accompany Unit 7.
Have students complete the Mid-Unit Assessment .
Use the resources below to assess student understanding of the unit content and action plan for future units.
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Suggestions for how to prepare to teach this unit
The central mathematical concepts that students will come to understand in this unit
The materials, representations, and tools teachers and students will need for this unit
Terms and notation that students learn or use in the unit
array
column
even
odd
row
To see all the vocabulary for Unit 7 , view our 2nd Grade Vocabulary Glossary.
Topic A: Even and Odd Numbers
Determine if a set of objects can be arranged into two equal groups.
Standards
2.OA.C.3
Determine if a set of objects can be arranged into groups of two.
Determine if the number of objects in a group is even or odd.
Represent even numbers as a total of two equal addends.
Determine if numbers are even or odd and explain thinking.
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Topic B: Composing and Analyzing Arrays
Build and describe arrays as rows of equal groups.
2.OA.C.4
Build and describe arrays as columns of equal groups.
Build and represent various arrays with the same total.
Use concrete squares to build rectangles.
2.G.A.2
Draw rectangles to model equal groups of rows or columns.
Partition rectangles into rows and columns of equal-sized squares using square inch tiles, and find the total number of squares.
Partition rectangles into rows and columns of equal-sized squares, not drawn to scale, and find the total.
Key
Major Cluster
Supporting Cluster
Additional Cluster
The content standards covered in this unit
2.G.A.2 — Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
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.
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.
Standards covered in previous units or grades that are important background for the current unit
1.OA.D.7 — Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
Standards in future grades or units that connect to the content in this unit
3.MD.C.6 — Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
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