Math // Fractions

Equivalent fractions

Recognise and show, using diagrams, equivalent fractions with small denominators

Ages
7 to 8
Type
Concept
Builds on
3 topics
Leads to
1 topic
Standards
1 code

Quick check

If the learner sees a bar divided into 4 equal parts with 2 shaded, can they tell you that's the same as 1/2 — and draw a different bar showing the same amount another way?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Show that 1/2 = 2/4 using a diagram of equal parts
  • Use a fraction wall or bar model to find equivalent fractions
  • Explain why two fractions are equivalent by comparing the shaded areas

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

3 topics
  • Understanding fractionsRequired

    Fractions // Ages 6 to 7

    Extends equivalence of 2/4 and 1/2 to broader equivalent fractions

  • Fraction NotationRequired

    Fractions // Ages 6 to 9

    Recognising and showing equivalent fractions requires that vocabulary

  • Fractions on a number lineHelpful

    Fractions // Ages 7 to 8

    Number line supports seeing equivalent fractions as the same point

You are here

Equivalent fractions

Ages 7 to 8 // Concept

Leads to

1 topic

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

Equivalent fractions are different names for the same amount. Holding the whole constant, splitting each part into more (smaller) pieces multiplies both numerator and denominator without changing the quantity, so 2/3 = 4/6 = 6/9. The load-bearing insight, best seen on a fraction wall or bar, is that MORE pieces each SMALLER can total the same amount, which confronts the whole-number bias that '4/6 must be more than 2/3 because 4 > 2'. Teach the multiplicative structure with diagrams before any 'times top and bottom' rule.

Common misconceptions

  • Whole-number bias — 4/6 judged more than 2/3 'because 4 > 2 and there are more pieces'
  • Different numbers must mean different amounts (denies equivalence)
  • Makes 'equivalents' by ADDING the same number to top and bottom (2/3 → 3/4)
  • Compares shaded amounts across different-sized wholes
  • Thinks changing only the numerator or only the denominator keeps the value

Useful representations

  • Fraction wall / stacked equal-length bars (canonical equivalence reference)
  • A single bar re-partitioned by splitting each part (2/3 → 4/6)
  • Number line with dual labelling (thirds above, sixths below) showing the same point
  • Area model (identical rectangles shaded to the same amount)

Teaching practices

  • Build equivalence by SPLITTING each part of a fixed bar (2/3 → split each third in two → 4/6) so the shaded amount visibly never changes
  • Use a fraction wall / stacked bars so equal rows align and equivalents line up
  • Confront the additive error explicitly — show that '+1 to top and bottom' (2/3 → 3/4) shifts the shaded amount
  • Confirm on a number line that equivalent fractions land on the SAME point
  • Compare shaded AREAS of identical wholes, never different-sized wholes, when judging equivalence

Activities to try

  1. 1

    Split each part of a fixed bar (2/3 becomes 4/6)

    Why it works: Splitting each part (multiplying numerator and denominator by the same number) makes more, smaller pieces that cover exactly the same amount; for fractions like 2/3, changing only one of the two numbers, or adding one to each, shifts the amount, so neither is a way to make an equivalent fraction.

    1. Shade two of three equal parts of a bar to show 2/3.
    2. Split every third into two equal pieces by drawing a line through each part; count that four of six parts are now shaded and write 4/6.
    3. Describe what happened to the length of shaded strip: it did not grow or shrink, there are just more lines.
    4. Keep splitting to generate the family: split each part into three for 6/9, into four for 8/12; each time check the shaded strip stays the same length.
    5. Test changing only one number: on an identical bar change only the bottom number (2/3 to 2/6) or only the top number (2/3 to 3/3) and shade it; check that the shaded amount changes, so changing just one part does NOT make an equivalent fraction.
  2. 2

    Fraction wall: which rows line up

    Why it works: A fraction wall is a reliable reference: fractions that cover the same length of the identical whole name the same amount, regardless of how many pieces.

    1. Use a fraction wall of stacked equal-length rows (halves, thirds, quarters, sixths, ninths) and find where rows end at the same vertical line.
    2. Identify equivalents by alignment: 1/2 = 2/4 = 3/6, and 2/3 = 4/6.
    3. Explain in words why two fractions that reach the same line are equal (they cover the same length of the identical whole).
    4. Check a non-example: does 2/3 line up with 3/4? Note it does not, so they are not equivalent.
  3. 3

    Same point on the number line

    Why it works: Equivalent fractions occupy the same magnitude and land on the same point of a number line, independent of how the line is partitioned.

    1. Draw a number line from 0 to 1 and mark thirds above it (1/3, 2/3).
    2. On the same line, mark sixths below it (1/6, 2/6, 3/6, 4/6, 5/6, including 4/6 against 2/3).
    3. Place 2/3 and 4/6 and check whether they land on the same point or different points.
    4. Repeat with 1/2 and 2/4 (marking halves and quarters) to confirm they coincide.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
The national curriculum in England: Key stages 1 and 2 framework document
Ma/KS2/Y3/F/4

Math // Fractions

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