Solve problems involving addition and subtraction of fractions with the same or related denominators, using different strategies

Students rename fractions with common denominators, combine or separate equal-sized parts and interpret results that may cross a whole, using diagrams, number lines and equations.

Fractions can be added or subtracted only after the parts have been expressed with a common size.

Six eighths plus five eighths equals eleven eighths. The denominator remains 8 because the parts are still eighths.

Choose a strategy based on the relationship between denominators and benchmarks. Simplify or rename the final result where useful.

Learning routine: Represent → Reason → Calculate → Interpret → Verify

Success looks like

• Represent the concept accurately
• Explain the place-value or number relationship
• Select an efficient strategy
• Apply it to a new context
• Verify and justify the result

Content description: solve problems involving addition and subtraction of fractions with the same or related denominators, using different strategies.

• E1: using different ways to add and subtract fractional amounts by subdividing different models of measurement attributes; for example, adding half an hour and three-quarters of an hour using a clock face, adding a \frac34 cup of flour and a \frac14 cup of flour, subtracting \frac34 of a metre from 2\frac14 metres
• E2: representing and solving addition and subtraction problems involving fractions by using jumps on a number line, bar models or making diagrams of fractions as parts of shapes
• E3: using materials, diagrams, number lines or arrays to show and explain that fraction number sentences can be rewritten in equivalent forms without changing the quantity; for example, \frac12 + \frac14 is the same as \frac24 + \frac14

Core idea: Fractions can be added or subtracted only after the parts have been expressed with a common size.

Remember

• Represent the concept accurately
• Explain the place-value or number relationship
• Select an efficient strategy
• Apply it to a new context
• Verify and justify the result

Important questions

• Solve 3/4 + 5/8. Explain using the model or evidence above.
• Solve 2/3 − 1/6. Explain using the model or evidence above.
• Find complement of 7/10. Explain using the model or evidence above.
• Rename 13/6. Explain using the model or evidence above.
• Choose a strategy for 5/12 + 1/3. Explain using the model or evidence above.

• Numerators and denominators both added — Keep the common denominator because part size does not change.
• Fractions combined before renaming — Different denominators name different-sized parts.
• Whole crossed but not interpreted — Rename an improper result as a mixed numeral when context benefits.
• Same denominator assumed from appearance — Check actual denominator relationship and the same whole.

Learn from the Topic Guide and fixed Teacher Slides, complete the Practice Sheet, use Practice for supported feedback, then take the Test when ready.

Students rename fractions with common denominators, combine or separate equal-sized parts and interpret results that may cross a whole, using diagrams, number lines and equations.

Fractions can be added or subtracted only after the parts have been expressed with a common size.

Six eighths plus five eighths equals eleven eighths. The denominator remains 8 because the parts are still eighths.

Choose a strategy based on the relationship between denominators and benchmarks. Simplify or rename the final result where useful.

Learning routine: Represent → Reason → Calculate → Interpret → Verify

Success looks like

• Represent the concept accurately
• Explain the place-value or number relationship
• Select an efficient strategy
• Apply it to a new context
• Verify and justify the result

Australian Curriculum Version 9.0

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