Big Idea(s):

Exploring multiplication of numbers to 10 × 10 and division to 100 ÷ 10

Expectations:

B2. Operations: use knowledge of numbers and operations to solve mathematical problems encountered in everyday life

• Math Facts: 2.2 recall and demonstrate multiplication facts of 2, 5, and 10, and related division facts

• Multiplication and Division: B2.6 represent multiplication of numbers up to 10 × 10 and division up to 100 ÷ 10, using a variety of tools and drawings, including arrays

teacher background

Students may benefit from prior experience with:

• using arrays to multiply and divide

• skip-counting forward and backward

• multiplying and dividing using equal grouping and equal sharing

• using repeated addition and subtraction

• representing multiplication of numbers up to 5 × 5 and division up to 25 ÷ 5

• using the distributive property of multiplication

Find the total number of zucchinis, then record the related multiplication sentence (2 × 6 = 12).

Provide a situation that involves division; for example, “A garden has 32 pumpkins arranged in rows of 8. How many rows are there?”

Have students use Colour Tiles to model the problem, then record the related division sentence (32 ÷ 8 = 4).

Students can use Colour Tiles to make arrays or draw on grid paper. Ensure students understand the idea of a community garden (see pages 3 and 4 of Planting Seeds).

LOOK-FORS:

• What strategies are students using to find the number of carrots (e.g., using equal groups of tiles, skip-counting, repeated addition, known facts, the distributive property)?

• Do students realize that the two smaller arrays can be “joined” to make the larger array?

• How do students find the different ways the tomato plants might have been planted (e.g., using tiles, using an array, using known multiplication/division facts)?

• Are students able to record a multiplication/division sentence to represent each situation?

Ask: “Is 7 × 8 equal to 8 × 7? Why? Is this relationship true for all arrays? Explain.”

Discuss the strategies students used to find the different ways the tomato plants may have been arranged. Have volunteers arrange 40 tiles to make as many different arrays as they can (i.e., 1 row of 40; 2 rows of 20, 4 rows of 10, 5 rows of 8, then rotated to show 8 rows of 5, 10 rows of 4, 20 rows of 2, and 40 rows of 1).

Record a division sentence and a related multiplication sentence for each array (e.g., 40 ÷ 8 = 5 and 5 × 8 = 40). Make connections between the array and the multiplication sentence. For example, ask: “Where do you see 5 groups in the array? What does 5 tell us in the multiplication sentence?”

To allow students to show what they have learned in this lesson, go to the Exit Ticket and/or Practice. (Log into your Mathology account to access the Exit Ticket/Practice pages as a PDF or editable Word document)

Highlight for Students

• Multiplication combines equal groups and division separates into equal groups.

• We can decompose an array into smaller arrays to help us multiply larger numbers.

How to Differentiate:

Accommodation: Provide problems with fewer gardens and smaller numbers and encourage the use of arrays; for example: Karen planted 2 rows of 3 carrots. Aimee planted 5 rows of 3 carrots. Renee planted 12 tomato plants. You might also have students build their arrays on Math Mat 23: Colour Tile Grid, then trace around the arrays to create pictorial representations of them.

Extension: Have students compare gardens where the carrots are planted in rows of different lengths; for example: Karen planted 7 rows of 8 carrots. Lindsey planted 6 rows of 9 carrots. Aimee planted 5 rows of 10 carrots. James planted 56 potatoes.

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SEL Self-Assessments (English) and Teacher Rubric

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