RemeliaMaths Year 3 Fractions, decimals & %
Year 3 fractions: six questions and the common mistakes
Under each answer are the wrong answers a child often gives to it, four different mistakes on this page, and what Remelia tells the child who gives one.
Questions written by Remelia for the objectives of the national curriculum for England; not taken from any test paper.
Six questions
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What fraction of the shape is shaded?
Write it as a fraction with a denominator of 4.
Show the answer to question 1
Answer: 3/4
Why:
6 of the 8 equal squares are shaded: 6/8.
8 ÷ 4 = 2, so every 2 parts make 1/4. 6 ÷ 2 = 3.
So 6/8 = 3/4.
Common mistakes:
- 6/2: It looks as if you put the parts not shaded as the denominator. The denominator is how many equal parts there are altogether; the numerator is how many are shaded.
- 1/4: That is the fraction not shaded. The numerator counts the shaded parts.
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3/6 + 1/6 = ?
Write your answer as a fraction, like 5/9.
Show the answer to question 2
Answer: 4/6 (also accept 2/3) · accept equivalent fractions
Why:
The denominators are the same, so add the numerators only: 3 + 1 = 4, giving 4/6. The denominator never changes.
Common mistakes:
- 4/12: It looks as if you added the denominators too. When the denominators are the same, add only the numerators. The denominator stays the same.
-
Elif eats 3/8 of a cake.
What fraction of the cake is left?
Show the answer to question 3
Answer: 5/8 · accept equivalent fractions
Why:
The whole cake is 8/8. 8/8 − 3/8 = 5/8.
Common mistakes:
- 3/8: That is the part given away. The question asks how many are left, so take it away from the whole.
-
What fraction of the shape is shaded?
Write it as a fraction with a denominator of 3.
Show the answer to question 4
Answer: 2/3
Why:
6 of the 9 equal squares are shaded: 6/9.
9 ÷ 3 = 3, so every 3 parts make 1/3. 6 ÷ 3 = 2.
So 6/9 = 2/3.
Common mistakes:
- 6/3: It looks as if you put the parts not shaded as the denominator. The denominator is how many equal parts there are altogether; the numerator is how many are shaded.
- 1/3: That is the fraction not shaded. The numerator counts the shaded parts.
-
6/8 + 2/8 = ?
Write your answer as a fraction, like 3/8.
Show the answer to question 5
Answer: 8/8 (also accept 1/1) · accept equivalent fractions
Why:
The denominators are the same, so add the numerators only: 6 + 2 = 8, giving 8/8. The denominator never changes.
Common mistakes:
- 8/16: It looks as if you added the denominators too. When the denominators are the same, add only the numerators. The denominator stays the same.
-
What fraction of the shape is shaded?
Write it as a fraction with a denominator of 3.
Show the answer to question 6
Answer: 1/3
Why:
3 of the 9 equal squares are shaded: 3/9.
9 ÷ 3 = 3, so every 3 parts make 1/3. 3 ÷ 3 = 1.
So 3/9 = 1/3.
Common mistakes:
- 3/6: It looks as if you put the parts not shaded as the denominator. The denominator is how many equal parts there are altogether; the numerator is how many are shaded.
- 2/3: That is the fraction not shaded. The numerator counts the shaded parts.
Answers
- 1. 3/4
- 2. 4/6 (also accept 2/3) · accept equivalent fractions
- 3. 5/8 · accept equivalent fractions
- 4. 2/3
- 5. 8/8 (also accept 1/1) · accept equivalent fractions
- 6. 1/3
How Remelia uses a mistake
When a wrong answer matches one of these mistakes, the app says what the child seems to have done before they try again, and brings the objective back on a later day.
Remelia practises maths for the child's own year group, in short sessions, and brings back on later days what they got wrong.