Year 4 Mathematics · AC9M4N03
Equivalent fractions name the same point or amount even though they use different-sized parts. Multiplying or dividing the numerator and denominator by the same factor…
Ready to project and teach
Equivalent fractions name the same point or amount even though they use different-sized parts. Multiplying or dividing the numerator and denominator by the same factor preserves value.
Learning routine: Identify equal whole → Scale numerator and denominator → Verify model → Connect to tenths/hundredths → Compare
Each model covers the same proportion of an equal-sized whole. The number of parts changes, but the shaded amount does not.
Fractions with denominators 10 or 100 connect directly to decimal place value. For the common fractions in this table, the denominators can be multiplied to make 10 or 100. Do not assume every fraction can be written exactly using only tenths or hundredths.
Worked example: 3/5 = 6/10 = 60/100 = 0.6 = 0.60. Splitting fifths into tenths doubles both counts; splitting tenths into hundredths multiplies both counts by 10. The value stays the same.
Quick check: Is 0.04 the same as 4/10? No: 0.04 is four hundredths. Four tenths are 0.4 or 0.40.
Example: 2/3 = ?/12. Each third is divided into four smaller parts. Multiply both numbers by 4: 2/3 = 8/12. In reverse, grouping 8 selected twelfths and all 12 twelfths in fours gives 2/3.
Teacher asks: Why must both numbers change by the same factor? Student explains: The number of selected parts and the total number of parts change together; the same amount of the same whole is represented.
The blue point is 2/4 on the upper line and 3/6 on the lower line. Both points are halfway from 0 to 1, so 2/4 = 3/6 = 1/2.
Build a fraction wall and identify aligned endpoints for halves, quarters, fifths, tenths and hundredths.
Start from 2/5 each time and multiply both numerator and denominator by the same number.
These are separate equivalent representations of 2/5; each calculation starts from the original fraction.
Match common fractions to decimal representations and justify using hundredths.
Content description: find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation.
The following teaching examples cover the curriculum elaborations.
Arrange 20 counters in four equal rows of five. Colour three rows. Fifteen of twenty counters are coloured, and three of four equal rows are coloured: 15/20 = 3/4. Regroup the same collection into ten pairs and identify 2/5 = 4/10 in a separate selection of eight counters.
Look for: The whole collection stays fixed while students change the equal groups. Ask students to show the selected counters, rather than only recite a rule.
Use the same cup as one whole. Half a cup can be measured as two quarter-cups or four eighth-cups: 1/2 = 2/4 = 4/8. Use water or dry counters to model the amounts without needing to read a curved water surface.
Check: How many eighth-cup measures match three quarter-cups? Six, because each quarter contains two eighths.
Fold equal paper rectangles into halves, quarters and eighths. Unfold and shade the same half: 1/2 = 2/4 = 4/8. For a second model, mark a strip into five equal parts, colour two parts, then halve every fifth. Record 2/5 = 4/10 = 0.4.
Check: The outside size and coloured region must remain unchanged; every part within one partition must be equal.
One metre is 100 centimetres. Divide a metre strip into four equal lengths: 100 ÷ 4 = 25, so 1/4 m = 25/100 m = 0.25 m = 25 cm. One tenth of a metre is 10 cm, so 1/10 m = 0.10 m = 10 cm.
Check: Three fifths of a metre are 60 cm or 0.60 m because one fifth is 20 cm.
The array shows 3 × 4 = 12. One of three equal rows contains 4 counters: 12 ÷ 3 = 4 and 1/3 of 12 is 4. One of the four columns contains 3 counters: 12 ÷ 4 = 3 and 1/4 of 12 is 3.
Teacher asks: Why can one third and one quarter of the same collection be different counts? Expected answer: Three equal groups are larger than four equal groups when the total collection is unchanged.
Core idea: Equivalent fractions name the same point or amount even though they use different-sized parts. Multiplying or dividing the numerator and denominator by the same factor preserves value.
Before this lesson: Students recognise equal parts, unit fractions and multiplication/division facts. Support: Use two identical strips and match halves with quarters before using number sentences. Core: Connect a model, related-denominator fraction and decimal for halves, quarters, fifths, tenths and hundredths. Extend within this code: Explain a missing numerator or denominator and justify a fraction such as 9/20 = 45/100 = 0.45.
Boundary: Use models and related denominators. General fraction algorithms, recurring decimals and formal fraction arithmetic are not the target here.
Use the Topic Guide, then project the Classroom View. Complete the written worksheet tasks before Practice and Test. Drawing tasks need an adult to inspect the actual work; a completion tick alone does not establish mastery.
AC9M4N03
Content description: find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation.
The following teaching examples cover the curriculum elaborations.
Mastery evidence: Students keep the whole constant and can prove equivalence with a model, a related denominator or decimal place value.
Explore optional teaching slide packs for classroom lessons and explanations at home.
Browse Teach & Explain · Browse Print & Go
Teachers: follow SkillrHub on TPT, then email us to request a free sample before buying. Include the year, subject and topic or curriculum code.
After trying the sample, honest feedback is welcome. A TPT review is optional, where available, and does not need to be positive.