Section B: Practice Problems Rectangular Arrays

Section Summary

Details

In this section, we learned that arrays are groups of objects that are organized into rows and columns. Arrays have the same number of objects in each row and the same number of objects in each column. We practiced different ways to count the objects in an array and used expressions with equal addends to show that you can find the total objects in an array by adding the sum of each row or the sum of each column. We also learned that rectangles can be composed of an array of equal-size squares. We practiced partitioning rectangles into rows and columns of equal-size squares.

Array.
Tray of waffles.
Rectangle. Partitioned into 4 rows of 5.

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Problem 1 (Lesson 7)

3 rows of 5 counters

  1. How many counters are in each row?

  2. How many rows are there?

  3. How many counters are there in all?

Problem 2 (Lesson 8)

  1. Clare described an array that she built with 16 counters. “It has only 2 columns and it’s really tall.”

    How many counters are in each of Clare’s columns?

  2. Build a different array using 16 counters. How would you describe your array?

Problem 3 (Lesson 9)

  1. Circle the 2 expressions that represent the array.

    Array. 7 rows of 2. 7 red, 7 yellow.

  2. How many counters are there in the array?

Problem 4 (Lesson 10)

  1. Make an array with 15 counters.

  2. Write 2 equations with equal addends to show how many counters there are.

Problem 5 (Lesson 11)

  1. Draw lines so the rectangle is completely partitioned into equal-size squares.

    Rectangle partially partitioned to show 5 rows of 3 same sized squares.

  2. How many columns of squares are there?

    How many squares are in each column?

  3. How many rows of squares are there?

    How many squares are in each row?

  4. Write 2 equations that represent the number of squares in the array.

Problem 6 (Lesson 12)

  1. Split the rectangle into equal-size squares.

    Rectangle. Length, 5. Width, 2.

  2. Write 2 equations that represent the number of squares in the array.

Problem 7 (Exploration)

This large solar panel collects energy from the sun. There are different arrays of equal-size rectangles in the panel.

Solar panels.

  1. Describe some arrays of equal sized rectangles that you see in the panel. How many equal-size rectangles are there in each array?

  2. Write an equation for the number of equal-size rectangles in each array.

Problem 8 (Exploration)

  1. What are some things in the classroom or at home that come in arrays?

  2. Choose one of the arrays and find the number of rows, the number of columns, and the total number of objects.