Represent fractions of a whole or set

What you will learn

• Represent fractions of a whole or set

Models used: number sentences, stories, tables.

Before you start

• Add and subtract fractions with denominators up to 12 using at most two different denominators

Find a fraction of a group

Here are 12 counters. We want two thirds of them.

1. Each dot stands for one object. A full row holds five; two full rows make ten.

   Here are 12 counters. We want two thirds of them.

2. There are 3 groups, with 4 objects in each group. Count a group before counting them all.

   Thirds means three equal groups. Each group has 4 counters.

   4 + 4 + 4 = 3 × 4 = 12

3. There are 2 groups, with 4 objects in each group. Count a group before counting them all.

   Keep two of those groups. Two groups of four make eight.

   2/3 of 12 = 8

   4 + 4 = 2 × 4 = 8

Worked example: A new example, together

Find 1/2 of 4.

1. Share into denominator-many parts, then select numerator-many. Read each value with the heading above its column.

   Identify the amount that acts as the whole, then one part, then the selected parts.

   A fraction of a amount scales that quantity by the fraction.

   Share into denominator-many parts, then select numerator-many

   Equal groups	In each group	Parts needed
   2	2	1

2. Share into denominator-many parts, then select numerator-many. Read each value with the heading above its column.

   A fraction of an amount means divide by 2, then take 1 of those parts.

   Share into denominator-many parts, then select numerator-many

   Equal groups	In each group	Parts needed
   2	2	1

   Find 1/2 of 4.

   2

3. Share into denominator-many parts, then select numerator-many. Read each value with the heading above its column.

   4 ÷ 2 × 1.

   Share into denominator-many parts, then select numerator-many

   Equal groups	In each group	Parts needed
   2	2	1

4. Share into denominator-many parts, then select numerator-many. Read each value with the heading above its column.

   The amount is 2.

   Share into denominator-many parts, then select numerator-many

   Equal groups	In each group	Parts needed
   2	2	1

5. Share into denominator-many parts, then select numerator-many. Read each value with the heading above its column.

   Check the result against the question we started with.

   The selected amount divided by 4 equals 1/2.

   We found 2. A fraction of a amount scales that quantity by the fraction.

   Share into denominator-many parts, then select numerator-many

   Equal groups	In each group	Parts needed
   2	2	1

Common mistakes to discuss

• Parts that are not equal. A fraction needs equal-sized parts. Three pieces of a strip only show thirds when the three pieces match exactly.

Check your understanding

• Represent fractions of a whole or set
• explain fraction multiplication as selecting a share of an amount
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.