# Unit 8 Equal Groups (Family Materials)

In this unit, students develop an understanding of equal groups as the foundation for multiplication and division in grade 3 and beyond. This understanding builds on students’ experiences with skip counting and finding the sums of equal addends.

Near the end of the unit, ask your student to do the following problems:

Write 2 equations to represent the total number of squares.

Questions that may be helpful as they work:

• How many rows?

• How many columns?

• How does each equation match the array?

## Section A Odd and Even

In this section, students build on their personal experiences with sharing equal groups of objects and making pairs to define the terms odd and even. They begin by noticing that some groups of objects can be made into two equal groups without a “leftover” and other groups can be made into two equal groups with “1 leftover.” They notice this same pattern when pairing objects. After the terms even and odd are introduced, students focus on justifying why a group has an even or odd number of members by showing whether the objects can be made into two equal groups, whether the objects can be paired without a leftover, or whether they can skip-count by 2 to count the total number of objects.

## Section B Rectangular Arrays

In this section, students are introduced to rectangular arrays. They learn that rectangular arrays contain objects arranged into rows and columns. They recognize that each row has the same number of objects and each column has the same number of objects. Using this structure, students can skip count by the number in each row or the number in each column to find the total number of objects.

In addition to skip counting, students learn that they can write equations with equal addends to represent the total number of objects in a rectangular array. Students connect these equations to the structure of the array and describe how equations can show the total number of objects as the sum of the objects in each row or the sum of the objects in each column.

Students also connect their work with arrays to their previous work with partitioning shapes into equal-size pieces. Starting with a rectangle, students partition them into equal-sized squares by considering rows and columns. Rectangles in this section have up to 5 rows and 5 columns. Students use the structure of the rows and columns created by the partitions in the rectangle to count the total number of equal-sized squares.