Math // Fractions

Adding Fractions (Same Denominator)

Add and subtract fractions with the same denominator, including results greater than one whole (e.g. 5/8 + 6/8 = 11/8)

Ages
8 to 9
Type
Method
Builds on
1 topic
Leads to
3 topics
Standards
1 code

Quick check

If a recipe uses 5/8 of a bag of flour and then another 6/8, can the learner work out the total and explain what the answer means as a mixed number?

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 3/5 + 4/5 = 7/5 and explain it equals 1 2/5
  • Subtract 2/6 from 5/6
  • Solve addition problems where the sum exceeds the whole: 7/8 + 3/8

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

1 topic
  • Simple Fraction SumsRequired

    Fractions // Ages 7 to 8

    Add/sub within one whole is prerequisite to extending beyond one whole

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Adding Fractions (Same Denominator)

Ages 8 to 9 // 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

Teaches adding and subtracting same-denominator fractions where the result can pass one whole (e.g. 3/5 + 4/5 = 7/5 = 1 2/5). Extends the counting-like-units idea by one step: when the combined count passes the denominator, the extra unit fractions re-group into a whole. Core aims are making children comfortable that a fraction can legitimately exceed one, and fluent at re-unitising an improper result into a mixed number. Addresses the add-across error (3/5 + 4/5 = 7/10), the belief that fractions cannot exceed one, and miscounting the re-group when converting. Covers subtraction too, both within one whole and crossing it from a mixed/improper start.

Common misconceptions

  • Adds the denominators as well: 3/5 + 4/5 = 7/10 (add-across; on harder items this error spreads into middle-achieving pupils, NFER).
  • Believes a fraction cannot exceed one whole, so forces the result — stops at 5/5 = 1, or flips 7/5 to 5/7 — rather than accepting an improper fraction.
  • Miscounts the re-grouping when converting improper to mixed (e.g. 7/5 = 2 2/5 or 1 3/5), losing track of how many wholes the denominator makes.

Useful representations

  • Two (or more) partitioned whole-bars side by side, pieces spilling from one into the next
  • Number line extending past 1, counting on in the unit fraction (fifths past 5/5)
  • Ten-frame-style grouping where a full set of denominator-many pieces fuses into one whole
  • Improper↔mixed toggle on the same shaded quantity (10/8 ↔ 1 2/8)

Teaching practices

  • Keep the counting-like-units foundation ('seven one-fifths') and simply let the count exceed the denominator, so the improper fraction arises naturally from adding.
  • Use two adjacent whole-bars so pieces spilling past the first whole are visibly re-grouped into 1 and a remainder — making 7/5 = 1 2/5 something the child sees, not a trick.
  • Name the improper fraction as legitimate ('7/5 is a real number, more than one') to head off the belief that fractions must be less than a whole.
  • Teach improper↔mixed conversion as counting how many whole-groups of the denominator fit, using the model before the numeric rule.
  • Do subtraction across the whole too (from a mixed/improper start) as separating like units.

Activities to try

  1. 1

    Spilling into the next whole: an adding model across two bars

    Why it works: A fraction can exceed one whole; when the running count of unit fractions reaches the denominator those pieces re-group into one whole, which is how an improper fraction becomes a mixed number — seen, not memorised. Subtraction reverses the same re-grouping when a whole must be broken back into unit fractions.

    1. Set up two identical bars side by side, each partitioned into the SAME fixed unit (e.g. eighths), with the denominator kept locked so only the count of pieces changes.
    2. Add 7/8 + 3/8 by placing eighth-pieces: fill the first bar with eight eighths, then let the remaining two eighths land in the second bar.
    3. When a full set of denominator-many pieces (eight eighths) completes the first bar, group that full set into a single 'one whole' tile, so the child watches the whole form from the count.
    4. Read the quantity both ways on the same shaded amount: as an improper fraction 10/8 and as a mixed number 1 2/8.
    5. Repeat with 3/5 + 4/5: count fifths past 5/5 and re-group 7/5 as 1 2/5.
  2. 2

    Counting on past one whole on a number line

    Why it works: Adding same-denominator fractions is counting on in the unit fraction; passing the '1' mark shows concretely that the result is more than one whole and where the mixed-number remainder comes from.

    1. Mark a number line from 0 extending past 1, with tick marks at each unit fraction (fifths past 5/5).
    2. Place 3/5, then count on four more fifth-steps (4/5 in total), landing at 7/5 and noting where the count crossed the 1 mark.
    3. State how many unit steps are before 1 and how many are after, reading off the mixed number 1 2/5.
    4. Repeat for 7/8 + 3/8, identifying the point where the total passes one whole.
  3. 3

    Check and explain: improper and mixed forms

    Why it works: Requiring both the improper and mixed form, plus a magnitude check, reveals whether the child can re-group the whole or is only manipulating symbols; adding two positive same-denominator fractions cannot shrink the total below either addend.

    1. Work out 3/5 + 4/5 and 7/8 + 3/8, writing each answer first as an improper fraction and then as a mixed number, showing each step.
    2. Match improper fractions to their mixed-number equivalents on the same shaded quantity (e.g. 10/8 ↔ 1 2/8).
    3. Explain in words why the denominator stays fixed while the count grows.
    4. Respond to a friend's claim that 7/8 + 3/8 = 10/16: simplify 10/16, compare its size with 7/8, and judge whether adding could make the total smaller.

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/Y4/F/4

Math // Fractions

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