Fair Share · Answer guide

Lesson 1 · Make fair parts

Recognise a half or quarter only when the whole is divided equally.

1. A whole is cut into 4 unequal pieces. Is every piece a quarter?

   Answer: No. Quarters must be four equal parts of one whole.

2. One of two equal parts is…

   Answer: a half. A half is one of two equal parts.

3. How many quarters make one whole?

   Answer: 4. Four one-quarter parts fill the whole.

Discuss: Fold a paper rectangle to make equal halves, then quarters. Check that the matching pieces cover each other.

Teaching note: Four pieces do not automatically make quarters. They must be equal-sized parts of the same whole. Open responses need discussion; they are not automatically marked.

Lesson 2 · Count equal parts

Read and write fractions of one divided whole.

1. A strip has 4 equal parts and 3 are shaded. Which fraction is shaded?

   Answer: 3/4. There are four equal parts in all and three selected parts.

2. In 2/3, what does the 3 tell us?

   Answer: The whole has 3 equal parts. The denominator tells how the whole is partitioned.

3. If 1/4 is shaded, what fraction is not shaded?

   Answer: 3/4. Three of the four equal parts remain unshaded.

Discuss: Draw five equal boxes as one strip and shade two. Explain what the 2 and the 5 mean.

Teaching note: The denominator counts every equal part, including unshaded parts. It does not count only the shaded pieces. Open responses need discussion; they are not automatically marked.

Lesson 3 · Find a fraction of a group

Find one half or one quarter of an evenly shared collection.

1. What is 1/4 of 8 counters?

   Answer: 2. 8 shared into four equal groups gives two in each group.

2. What is 1/2 of 14?

   Answer: 7. Two equal groups of seven make fourteen.

3. Four equal groups each contain 4 counters. What is the whole collection?

   Answer: 16. 4 + 4 + 4 + 4 = 16.

Discuss: Share 16 counters equally among four imaginary teams. Explain the size of each quarter.

Teaching note: A quarter of 12 is not 4. The 4 tells you how many equal groups to make; then count one group. Open responses need discussion; they are not automatically marked.

Final check · Set 1

Try one set after the lessons. Use the other set after reviewing any errors.

1. How many halves fill one whole?

   2. Two halves make a whole.

2. Which condition makes four pieces quarters?

   Equal size from one whole. Fraction parts must be equal in size.

3. Two of four equal parts are selected. What fraction is selected?

   2/4. The numerator is 2 and denominator is 4.

4. What fraction is unshaded when 3/4 is shaded?

   1/4. One of four parts remains.

5. What is 1/4 of 16?

   4. 16 divided into four equal groups gives 4 in each.

6. What is half of 18?

   9. 9 + 9 = 18.

Final check · Set 2

Try one set after the lessons. Use the other set after reviewing any errors.

1. Two equal pieces from one whole are called…

   halves. Halves are two equal parts.

2. Two quarters cover the same amount as…

   one half. Two out of four equal parts are half of the whole.

3. Three of five equal parts are selected. What fraction is selected?

   3/5. Three selected out of five equal parts is 3/5.

4. In 1/4, the 1 counts…

   selected parts. The numerator counts selected parts.

5. What is 1/4 of 20?

   5. Four groups of five make twenty.

6. What is half of 12?

   6. 6 + 6 = 12.