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
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.
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
Topic B: Composing and Analyzing Arrays
Key
Major Cluster
Supporting Cluster
Additional Cluster
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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Determine if a set of objects can be arranged into two equal groups.
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