Year 6 Mathematics · AC9M6N05

Adding and Subtracting Fractions

Use equivalent fractions, benchmarks and mixed-number interpretation

Ready to project and teach

Learning goalsSay it simply

Learning goal

Students generate common denominators, combine equal-sized parts, bridge whole numbers and interpret improper or mixed results in context.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: solve problems involving addition and subtraction of fractions using knowledge of equivalent fractions
Key conceptTeach from the board

Solve 5/6 − 1/4 using equivalent fractions

Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.

5/6 = 10/12
1/4 = 3/12
difference = 7/12

The denominator remains 12 because the result counts twelfths. Simplify only when numerator and denominator share a factor.

Choose fraction strategies by relationship

Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.

3/4 + 5/8rename 3/4 as 6/8
7/10 + 3/10complete one whole
1 1/3 − 5/6rename whole and thirds as sixths
5/12 + 1/3rename 1/3 as 4/12

Use diagrams or number lines when crossing a whole or interpreting a word problem; use factor knowledge to select the least useful common denominator.

Clean visual examplesOne-page board

Clean one-page examples

AC9M6N05 - Adding and Subtracting Fractions
Example 1

3/4 + 5/8 rename 3/4 as 6/8

Example 2

: representing addition and subtraction of fractions, using an understanding of equivalent fractions and methods such as jumps on a number line, or diagrams of fractions as parts of shapes

Example 3

: determining the lowest common denominator using an understanding of prime and composite numbers to find equivalent representation of fractions when solving addition and subtraction problems

Example 4

: calculating the addition or subtraction of fractions in the context of realistic problems; for example, using part cups or spoons in a recipe; using the understanding of equivalent fractions

Curriculum examplesCopied content

AC9M6N05: solve problems involving addition and subtraction of fractions using knowledge of equivalent fractions

  • E1: representing addition and subtraction of fractions, using an understanding of equivalent fractions and methods such as jumps on a number line, or diagrams of fractions as parts of shapes
  • E2: determining the lowest common denominator using an understanding of prime and composite numbers to find equivalent representation of fractions when solving addition and subtraction problems
  • E3: calculating the addition or subtraction of fractions in the context of realistic problems; for example, using part cups or spoons in a recipe; using the understanding of equivalent fractions
  • E4: understanding the processes for adding and subtracting fractions with related denominators and fractions as an operator, in preparation for calculating with all fractions; for example, using fraction overlays and number lines to give meaning to adding and subtracting fractions with related and unrelated denominators

Use the central and application models above to connect each elaboration to the same underlying concept.

Questions and answersWith answers

Check understanding

  • Solve 5/6 − 1/4.
  • Add 3/4 + 5/8.
  • Subtract 1 1/3 − 5/6.
  • Select a common denominator.
  • Interpret an improper result.

Evidence of mastery

  • Represent or identify the concept
  • Explain the underlying relationship
  • Select an appropriate strategy or feature
  • Apply it in a new context
  • Justify and verify the response

Decision: continue when students can explain the model, apply it to a new example and justify their check. Otherwise return to the central model and reduce the numerical or representational load.

Practice and reviewReady for practice
Numerators and denominators both addedThe common denominator names the unchanged part size.
Fractions combined before renamingDifferent denominators name different-sized parts.
Whole part lost during subtractionRegroup one whole as denominator-sized parts.
Final fraction simplified incorrectlyDivide numerator and denominator by the same factor.
Curriculum alignmentStart here

Learning goal

Students generate common denominators, combine equal-sized parts, bridge whole numbers and interpret improper or mixed results in context.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: solve problems involving addition and subtraction of fractions using knowledge of equivalent fractions
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