Math // Fractions

Simple Fraction Sums

Add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7)

Ages
7 to 8
Type
Method
Builds on
2 topics
Leads to
3 topics
Standards
1 code

Quick check

If a recipe calls for 2/8 of a cup of milk and then another 3/8 of a cup, can the learner work out the total without a calculator?

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.
  • Calculate 2/5 + 2/5 = 4/5
  • Calculate 6/8 − 3/8 = 3/8
  • Explain that when denominators are the same, you add/subtract the numerators

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

2 topics

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Simple Fraction Sums

Ages 7 to 8 // Method

Leads to

3 topics

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

Adding and subtracting fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7, 6/8 − 3/8 = 3/8). The core idea: the denominator NAMES the unit being counted (sevenths, eighths) and stays fixed, while the numerators COUNT how many of that unit and are combined like whole numbers — 'two fifths and two fifths make four fifths' just as two apples and two apples make four apples, where the 'apple' is the fifth. Teaching targets two misconceptions: adding the denominators too (2/5 + 2/5 → 4/10) and dropping the unit to give a bare whole number (6/8 − 3/8 → 3). For ages 7–8.

Common misconceptions

  • Adds (or subtracts) the denominators as well as the numerators: 2/5 + 2/5 = 4/10, misapplying whole-number addition (IES; ~10% of lower-achieving Y6 on an easy same-denominator item, NFER).
  • Drops the unit and answers a bare whole number: 6/8 − 3/8 = 3, operating only on the numerators as if the denominator weren't there.
  • Treats the denominator as a quantity to be operated on rather than the name of the unit being counted.

Useful representations

  • Fraction strip / bar partitioned into the fixed unit (sevenths, eighths) where pieces are combined or removed
  • Number line marked in the unit fraction, counting on/back in that unit
  • Discrete 'like objects' framing (each piece = one unit fraction) to make combining feel like counting
  • Paper folded/cut into equal parts (NFER's cut-a-strip-into-sevenths)

Teaching practices

  • Present it as counting like units — use 'dual naming' ('three one-fifths and one one-fifth make four one-fifths' alongside '3/5 + 1/5 = 4/5') so the denominator is heard as the unit being counted, not a second number.
  • Hold the whole and the unit constant with a single partitioned bar or fraction strip so pieces are visibly the same size and only the count changes.
  • Keep to same denominators and results within one whole first; establish which of a pair is bigger before adding, per NFER.
  • Confront the add-across error early and directly (2/5 + 2/5 is not 4/10) using a model where the denominator cannot change.
  • Do subtraction alongside addition as separating the same units (6/8 − 3/8 = 3/8), keeping the eighth as the fixed unit.

Activities to try

  1. 1

    Locked-unit bar combiner (fixed-denominator model)

    Why it works: When denominators are the same, you are counting same-size pieces, so only the count (numerator) changes and the unit (denominator) stays fixed.

    1. Work with a bar already partitioned into a fixed unit, e.g. fifths, with the label 'fifths' shown on the bar.
    2. Combine 2/5 and another 2/5 by placing the pieces onto the bar; watch a running count read '4/5' as each piece is read aloud as 'one fifth'.
    3. Test the answer '4/10' by laying four tenth-sized pieces next to the 4/5 you built. Notice that they cover only as much as two fifths, which is less than the four fifths on the bar, so 4/10 is the wrong amount. The pieces you are counting are all fifths.
    4. Switch to subtraction on an eighths bar and remove pieces: start with 6/8 and take away 3/8, reading off 3/8 left.
    5. Try adding one 2/5 too many and watch it run past the end of the bar, foreshadowing sums beyond one whole.
  2. 2

    Dual naming — read fractions as repeated unit fractions

    Why it works: A non-unit fraction is a repeated sum of unit fractions, so adding/subtracting is counting those units up or down — the denominator is the label, not a quantity to operate on.

    1. Say each fraction two ways: 'three one-fifths' alongside '3/5', and 'one one-fifth' alongside '1/5'.
    2. State the sum both ways: 'three one-fifths and one one-fifth make four one-fifths' alongside '3/5 + 1/5 = 4/5'.
    3. Do the same for subtraction: 'six one-eighths take away three one-eighths leaves three one-eighths', alongside '6/8 − 3/8 = 3/8'.
    4. Point to the denominator each time and name it as the unit being counted.
  3. 3

    Number line counting in the unit fraction

    Why it works: Fractions are quantities/points measured in the unit; combining them is counting on or back in that unit, and the answer is still a count of eighths (6/8 − 3/8 = 3/8, not 3).

    1. Mark a number line in the unit fraction (e.g. eighths) from 0 to 1.
    2. For 6/8 − 3/8, land on 6/8, count back 3 eighths, and read where you stop (3/8).
    3. For a sum, start at one fraction and count on in the unit, reading each step.
    4. State whether the answer is bigger or smaller than one of the pieces and check your result against that expectation.

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/5

Math // Fractions

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