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The Guides for Effective Instruction in Mathematics Revised

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B1.7 Recognize that one half and two fourths of the same whole are equal, in fair-sharing contexts.

Activity 1: Which Game? (Represent Halves and Fourths)

Directions

Give 12 two-coloured tokens to each student or pair of students.

Have students divide the chips into four equal groups of the same colour.

Ask students the following questions:

  • If I divide the chips into four equal groups, what do I call these groups?
  • What does each of these equal groups represent?

Have students divide the chips into four equal groups: two groups of one colour and two groups of another colour.

Ask students the following questions:

  • If I divide the chips into four equal groups, what does each group represent?
  • What fraction of the set represents a group of three chips?
  • What fraction of the whole does each red group represent?
  • What fraction of the whole do the two red groups represent?

Note: To recognize the different groups, write the name of the fraction in words (for example, a fourth). It is important that students associate the name of the fraction (for example, a fourth) with the number of groups or parts.

Source : Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, p. 54.

Activity 2: Making Bracelets and Rings

To create beautiful bracelets and rings, four students share six strings. How many pieces of string will each student get? What do you notice?

Strategy

Use a Length Model (Cuisenaire Rods) to Represent Equivalent Fractions

I choose the rods to represent the 6 strings. Since I have to divide these strings between 4 students, I divide these 6 strings into 4 equal parts using the unit cubes. I can assign a whole purple rod to each student. Each purple rod represents 1 unit or 4 one-fourths.

I have two purple rods left. I divide the two purple rulers equally into 4 equal parts, one part for each student. These equal red parts are each one-half or 2 one-fourths.

Each student is given 1 and a half strings, 1 string and two-fourths or 6 fourths to create bracelets and rings.

Source : En avant, les maths! ML, Nombres, p. 6.