Year 6 Mathematics · AC9M6N03

Equivalent Fractions on a Common Number Line

Compare halves, thirds, quarters and related fractions and justify their order

Ready to project and teach

Learning goalsSay it simply

Learning goal

Students rename fractions with common denominators, use benchmarks and place proper, improper and mixed forms accurately on one continuous number line.

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: apply knowledge of equivalence to compare, order and represent common fractions including halves, thirds and quarters on the same number line and justify their order
Key conceptTeach from the board

Compare 2/3, 3/4 and 5/6

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

2/3 = 8/12
3/4 = 9/12
5/6 = 10/12

A common denominator creates equal-sized parts, so numerators can be compared meaningfully. Equivalent forms occupy the same point.

Locate fractions greater than one

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

1/23/415/43/21 3/4
02

Partition each whole into equal intervals and preserve the denominator across whole-number boundaries.

Clean visual examplesOne-page board

Clean one-page examples

AC9M6N03 - Equivalent Fractions on a Common Number Line
Example 1

: applying factors and multiples to fraction denominators, such as halves with quarters, eighths and twelfths, and thirds with sixths, ninths and twelfths to determine equivalent representations of fractions in order to make comparisons

Example 2

: representing fractions on the same number line, paying attention to relative position, and using this to explain relationships between denominators

Example 3

: explaining equivalence and order between fractions using number lines, drawings and models

Example 4

: comparing and ordering fractions by placing cards on a string line across the room and referring to benchmark fractions to justify their position; for example, \frac58 is greater than \frac12 can be written as \frac58>\frac12, because half of 8 is 4; \frac16 is less than \frac14, because 6 > 4 and can be written \frac16 < \frac14

Curriculum examplesCopied content

AC9M6N03: apply knowledge of equivalence to compare, order and represent common fractions including halves, thirds and quarters on the same number line and justify their order

  • E1: applying factors and multiples to fraction denominators, such as halves with quarters, eighths and twelfths, and thirds with sixths, ninths and twelfths to determine equivalent representations of fractions in order to make comparisons
  • E2: representing fractions on the same number line, paying attention to relative position, and using this to explain relationships between denominators
  • E3: explaining equivalence and order between fractions using number lines, drawings and models
  • E4: comparing and ordering fractions by placing cards on a string line across the room and referring to benchmark fractions to justify their position; for example, \frac58 is greater than \frac12 can be written as \frac58>\frac12, because half of 8 is 4; \frac16 is less than \frac14, because 6 > 4 and can be written \frac16 < \frac14

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

Questions and answersWith answers

Check understanding

  • Order 2/3, 3/4 and 5/6.
  • Show 3/4 = 9/12.
  • Locate 5/4.
  • Compare 7/8 and 5/6.
  • Use 1/2 as a benchmark.

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
Larger denominator means larger valueFor the same numerator, more parts means smaller parts.
Different wholes comparedFractions must refer to equal-sized wholes.
Improper fraction placed below oneCompare numerator with denominator first.
Number-line intervals drawn unequallyEqual numerical steps require equal spacing.
Curriculum alignmentStart here

Learning goal

Students rename fractions with common denominators, use benchmarks and place proper, improper and mixed forms accurately on one continuous number line.

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: apply knowledge of equivalence to compare, order and represent common fractions including halves, thirds and quarters on the same number line and justify their order
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