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The Guides for Effective Instruction in Mathematics Revised

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C2.1 Describe how variables are used, and use them in various contexts as appropriate.

Activity 1: Commutative Property (Array)

Present students with the following situation:

Jacob arranged 21 shells in three rows.

21 seashells placed into three rows.

Ask them to write the corresponding a number sentence.

(3 × 7 = 21)

Then continue to describe the situation:

Gabrielle wants to arrange the same shells in seven rows.

Ask students to write the equation that will allow Gabrielle to determine the number of shells per row.

Open parenthesis, 7, multiply, by an unknown, equals, 21, closed parenthesis.

Ask them to illustrate the arrangement of Gabrielle's shells and solve the equation by comparing the two math sentences.

Then ask the following questions:

  • What do you notice about the quantities of shells arranged by Jacob and Gabrielle?
  • If you compare the number of rows in Jacob's arrangement with Gabrielle's, what do you notice?
  • Will you get the same result with two more amounts? Try it out.

Source : Guide d’enseignement efficace des mathématiques de la maternelle à la 3e année, p. 92.

Activity 2: Commutative Properties

Project or write the equations below on the board or on a large sheet of paper one at a time.

6 + 9 = 9 + ❖

56 + 78 = 78 + ▲

✣ + 90 = 90 + 23

5 × 7 = 7 × ✹

5 × 3 = 3 × ✤

a × 7 = 7 × 6

For each equation, have students determine the value of the variable, then ask the following questions:

  • How did you determine the value of the variable in this equation?
  • Could you use the same strategy with larger numbers, as in the equation 160 + 195 = 195 + ▲?
  • Does this strategy work if the addition sign is replaced by the subtraction sign or if the multiplication sign is replaced by the division sign?

Source : Guide d’enseignement efficace des mathématiques de la maternelle à la 3e année, p. 93.

Activity 3: Stamp Collection

Summary

In this activity, students represent equality situations in different ways and check if they are true.

Material

  • large sheets (one per team)
  • markers (one per team)
  • sheets of graph paper (one per team)
  • coins (enough for each team)
  • centicubes (enough for each team)

Action

Present the following situation:

Kaya and her friend go to the Philaterium store to buy stamps to add to their collection. They want to buy stamps from Colombia, Denmark, Ukraine and Venezuela. Here are the values of the stamps.

Colombia = Cinq cents

Danemark = Dix cents

Venezuela = Vingt-five cents

Ukraine = Un dollar

Present the following problem:

In the store, Kaya and her friend look at a poster that shows the following ties:

5 C = 1 V

9 D + 2 C = 1 U

4 V + 3 D = 1 U + 6 C

V + 5 C = 1 U

  • What do numeric symbols and literal symbols represent?
  • How can Kaya and her friend check if the equations are true? Explain your reasoning.
  • Ask students to represent each equality situation in several ways (e.g., with centicubes, on a double open number line, on sheets of graph paper, with drawings of stamps, with coins). Then ask them to find and represent other equalities related to the data in the problem.

Source : Guide d’enseignement efficace des mathématiques de la maternelle à la 3e année, p. 181.