Big Idea(s):

Creating and solving problems that involve multiplication and division

Building fluency with multiplication and division

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

• Multiplication and Division: B2.7 represent and solve problems involving multiplication and division, including problems that involve groups of one half, one fourth, and one third, using tools and drawings

C4. Mathematical Modelling: apply the process of mathematical modelling to:

• represent, analyse, make predictions, and provide insight into real‐life situations

teacher background

Students may benefit from prior experience with:

• skip-counting forward and backward

• multiplying and dividing using models (e.g., arrays and number lines)

• making equal groups

• using repeated addition and subtraction

Sammy the squirrel went to the park with his family for a picnic. There were 20 legs at their picnic table. How many squirrels were at the table?

Four geese came along and sat at another picnic table. How many legs were at that table?

Discuss which operation students would use to solve each problem and why (e.g., division when we know the total number of legs and multiplication when we want to find the total number of legs). Point out that squirrels have 4 legs and geese have 2 legs.

Work together to solve the problems in different ways. Write the number sentences (e.g., 20 ÷ 4 = 5, 4 × 2= 8).

Possible strategies:

– using arrays:

Have counters, Colour Tiles, number lines, and grids available. To make arrays, students can use counters, place Colour Tiles on the grid, or draw on the grid.

Post a list of possible problem contexts (e.g., 5: points on a star, eyes on a Praying Mantis; 6: faces on a cube, legs on an insect; 7: days in a week, colours in a rainbow; 8: arms on an octopus, sides on a stop sign; 9: squares on a tic-tac-toe board, players on a baseball team; 10: legs on a crab, fingers on both hands).

Write some multiplication and division sentences on the board for students to choose from; for example:

3 × 5 = 15, 8 × 4 = 32, 6 × 7 = 42, 25 ÷ 5 = 5, 72 ÷ 8 = 9, 100 ÷ 10 = 10.

LOOK-FORS:

• Are students able to create a story problem to match a given multiplication/division sentence?

• Are students able to choose the correct operation to solve a problem?

• How do students solve the problems (e.g., using counters, skip-counting, using repeated addition/subtraction, taking jumps on a number line, using arrays, using distributive property)?

• Can students use the information in a story problem to write a number sentence?

Post the number sentences around the room and have students post their word problems with the matching number sentence.

Go on a gallery walk. Select one number sentence. Look at a couple of the posted problems. Do the chosen contexts make sense in terms of the numbers?

Talk about how students decided which operation to use, then have volunteers model some of the strategies they used to solve the problems.

Choose a multiplication story problem. Work together to rewrite it as a division story problem.

For example, “A horse has 4 legs. How many legs do 8 horses have?” (32)

This could be written as, “A horse has 4 legs. I see 32 legs. How many horses do I see?” (8)

Point out that we can rewrite story problems in this way because multiplication and division are related.

To allow students to show what they have learned in this lesson, go to the Exit Ticket and/or Practice Page.

Highlight for Students

• Many different strategies can be used to solve the same story problem.

• Real-life problems that involve equal groups or sharing equally can be solved using multiplication or division.

How to Differentiate:

Accommodation: Focus on one operation and provide a context (e.g., 4 × 3 = 12; wheels on tricycles).

Extension: After solving the other pair’s multiplication/division problem and writing a matching number sentence, have students write a problem that can be solved using the related division/multiplication sentence.

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