Mathematics classroom notes
Year 6 - Add, subtract, and multiply fractions and mixed numbers
Strand / topic: Number and Algebra / Add, subtract, and multiply fractions and mixed numbers
Based on Pi Leo Academy's Victorian Curriculum F-10 Mathematics year-level guide and aligned to NAPLAN-style mathematical reasoning. Official curriculum code: Not stated in the provided curriculum source.
By the end of this note, students should be able to explain add, subtract, and multiply fractions and mixed numbers, use a clear method, solve simple and test-style questions, and check their answers for Year 6 Number and Algebra work.
It builds number sense, reasoning and confidence for classwork, quizzes and problem solving. This topic builds the reasoning, fluency and confidence students need for future NAPLAN-style questions and everyday mathematics.
1 What this means
Fractions show equal parts of a whole or equal parts of a collection.
Fractions make sense when students keep asking, 'What is the whole, and are the parts equal?' In Year 6, students should connect the words in the question to a model such as a diagram, table, number line, grid, formula or equation. They then work in small steps and check whether the answer matches the question, the units and the size of the numbers.
- Start by identifying the mathematical structure, then choose the most efficient representation.
- A fraction only describes the amount correctly when the parts are equal.
- The denominator names the size of the parts; the numerator counts how many parts are used.
- Use fraction bars or number lines before relying on rules.
2 Important rules / ideas
Fractions only work when the whole is split into equal parts.
Only compare fractions fairly when they refer to the same whole.
A larger denominator means smaller parts when the whole is the same.
Important vocabulary
The top number in a fraction.
The bottom number showing equal parts.
Equal in value, even if written differently.
A fraction with 1 as the numerator.
3 Step-by-step method
- Check that parts are equal.
- Look at the denominator first.
- Use a diagram or common denominator if needed.
- Simplify or explain the answer in context.
4 Worked examples
Shade 3/4 of a rectangle.
- Split the rectangle into 4 equal parts.
- Shade 3 equal parts.
- One part remains unshaded.
Which is larger: 2/3 or 2/5?
- The numerators are the same.
- Thirds are larger pieces than fifths.
- 2/3 is larger.
Find 3/5 of 40.
- Divide 40 by 5 to find one fifth: 8.
- Multiply by 3: 8 x 3 = 24.
- 3/5 of 40 is 24.
A ribbon is cut into 8 equal pieces. Mia uses 3 pieces. What fraction is used?
- There are 8 equal pieces altogether.
- 3 pieces are used.
- The fraction used is 3/8.
5 More examples
Put 3/4 between 0 and 1.
Split the space from 0 to 1 into 4 equal jumps. Land on the third jump.
Find 1/3 of 18 counters.
Share 18 into 3 equal groups. Each group has 6 counters.
NAPLAN-style thinking
In NAPLAN-style questions, add, subtract, and multiply fractions and mixed numbers may appear as a short calculation, a word problem, a diagram, a table or a multi-step reasoning question. Students should slow down and decide what the question is really asking before calculating.
Estimate first and eliminate answers that are too small, too large or use the wrong unit.
Write only the answer required, but use working on paper to avoid mental slips.
Circle the numbers, underline the action words and decide whether all numbers are needed.
Do one step at a time and label intermediate answers so the final step is clear.
6 Common mistakes
A fraction only works when the parts are equal.
Think about the size of each part, or use a diagram.
Always identify what one whole represents.
- Choosing the first operation seen in the wording.
- Forgetting units, labels or place value.
- Stopping after the first step when the question asks for a final comparison.
7 Tips to remember
Fractions only compare fairly when the whole is the same size.
Fraction bars make equivalent fractions and ordering easier.
Read 3/5 as 'three fifths' to remember the denominator names the parts.
Parent teaching tips
- Ask your child to explain the method aloud before writing the answer.
- Use a real-life context at home, such as shopping, cooking, sport scores, maps or timetables.
- Praise clear working and checking, not only speed.
- Encourage a quick diagram or table for word problems before calculating.
Remember
Fractions must be equal parts. Always identify the whole first.
8 Quick practice
- Shade 3/4 of a rectangle.
- Which is larger: 2/3 or 2/5?
- Find 3/5 of 40.
- A ribbon is cut into 8 equal pieces. Mia uses 3 pieces. What fraction is used?
9 Answers / explanation
Question 1
Answer: One part remains unshaded.
Split the rectangle into 4 equal parts. Shade 3 equal parts. One part remains unshaded.
Question 2
Answer: 2/3 is larger.
The numerators are the same. Thirds are larger pieces than fifths. 2/3 is larger.
Question 3
Answer: 3/5 of 40 is 24.
Divide 40 by 5 to find one fifth: 8. Multiply by 3: 8 x 3 = 24. 3/5 of 40 is 24.
Question 4
Answer: The fraction used is 3/8.
There are 8 equal pieces altogether. 3 pieces are used. The fraction used is 3/8.
Extension challenge
Create your own multi-step question for this topic using an Australian context, then solve it and explain each step.
Hint: Use shopping, sport, maps, timetables, weather, school events or measurement at home.
Answer guide
Answers will vary. A strong answer includes clear working, correct units and a final sentence.
Quick revision
- Know what add, subtract, and multiply fractions and mixed numbers is asking you to find.
- Choose a diagram, table, formula, number line or equation before calculating.
- Show enough working that you can find and fix mistakes.
- Check the final answer, units and reasonableness.