Math // Fractions

Decimals and fractions (age 10+)

Associate a fraction with division and calculate decimal fraction equivalents for simple fractions (e.g. 3/8 = 0.375); recall and use equivalences between simple fractions, decimals, and percentages in different contexts

Ages
10 to 11
Type
Concept
Builds on
4 topics
Leads to
6 topics
Standards
2 codes

Quick check

If the learner sees 3/8 written on a worksheet, can they convert it to a decimal — and also say roughly what percentage that is?

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.
  • Convert 3/8 to 0.375 by dividing 3 ÷ 8
  • State that 1/5 = 0.2 = 20% from memory
  • Use fraction–decimal–percentage equivalences to compare 30%, 1/3, and 0.35 and put them in order

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

4 topics

You are here

Decimals and fractions (age 10+)

Ages 10 to 11 // Concept

Leads to

6 topics
  • Calculating PercentagesRequired

    Ratio & Proportion // Ages 10 to 11

    Calculating percentages requires fraction-decimal-percentage equivalence

  • One Quantity as a FractionRequired

    Ratio & Proportion // Ages 11 to 12

    Expressing one quantity as a fraction of another requires fluent fraction-decimal equivalence

  • Decimals and fractions (age 11+)Required

    Fractions // Ages 11 to 13

    Fluent fraction-decimal conversion builds on Y6 decimal fraction equivalents

  • Percentages (age 12+)Required

    Ratio & Proportion // Ages 12 to 14

    Using decimal multipliers for percentage change requires fraction-decimal fluency

  • Pie chartsHelpful

    Data & Statistics // Ages 10 to 11

    Understanding fraction-decimal-percentage equivalence deepens pie chart interpretation (e.g. 1/4 = 25% = 90°) but is not strictly required if the child can compute percentages procedurally

  • Order of operations (age 10+)Helpful

    Mathematical Thinking // Ages 10 to 11

    FDP equivalences are key Y6 structural connections

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

For ages 10-11, the goal is fluent, flexible movement between fractions, decimals and percentages as three names for one quantity. The load-bearing insight is that the fraction bar means 'divide the top by the bottom', so 3/8 = 3 ÷ 8 = 0.375. Learners should pick whichever form makes a comparison easiest, converting a mixed set to one common form before ordering (e.g. 30%, 1/3, 0.35 → 0.30, 0.333..., 0.35, so the order is 30% < 1/3 < 0.35). Note that 1/3 landing between 30% and 0.35 is counter-intuitive and is where the surface-digit misconception is confronted.

Common misconceptions

  • Reverses the division: reads 3/8 as 8 ÷ 3 (divides the larger by the smaller out of habit), giving 2.67 instead of 0.375.
  • Compares mixed forms by surface digits — thinks 1/3 is largest of {30%, 1/3, 0.35} because '3 is a big number' or because the numbers look bigger, without converting to a common form.
  • Treats 1/3 as exactly 0.3 (or 0.33) and terminating, not recognising the recurring decimal.
  • Believes every fraction gives a neat terminating decimal, so is thrown when a division doesn't stop.

Useful representations

  • Long/short division laid out for 3 ÷ 8 (with the decimal point and trailing zeros) to show a fraction becoming a decimal
  • A triple-labelled bar or hundred-grid showing the same shaded quantity named as fraction, decimal and percentage at once
  • A number line from 0 to 1 with fractions, decimals and percentages all plotted, so order is visible spatially
  • A double number line / equivalence table of the landmark fractions and their decimal & percentage partners

Teaching practices

  • Establish the fraction-as-division meaning explicitly: 3/8 means 3 shared into 8, and 3 ÷ 8 = 0.375 — connect the bar notation to a division the child can carry out.
  • Teach a small set of recall equivalents as landmarks (1/2, 1/4, 3/4, 1/5, 1/10, 1/3≈0.33) so children convert by memory for common cases and by division for the rest.
  • Make ordering across forms the core task: give mixed sets (30%, 1/3, 0.35) and require conversion to ONE common form before comparing — this is where the equivalence pays off.
  • Use the fact that percentages and decimals are hundredths and tenths to move fluidly (0.35 = 35% = 35/100), reserving division for fractions that aren't already tenths/hundredths.
  • Confront non-terminating cases honestly: 1/3 = 0.333... is NOT 0.3; round only when told to, and show why the division never stops.

Activities to try

  1. 1

    Watch a fraction become a decimal: 3 ÷ 8

    Why it works: The fraction bar means 'divide the numerator by the denominator'; 3/8 is 3 ÷ 8, and some divisions (like 1 ÷ 3) produce recurring, non-terminating decimals.

    1. Before dividing, predict: will 3/8 be more than 1 or less than 1, and roughly what? Say why (3 shared among 8 people is less than one whole).
    2. Carry out the division 3.000 ÷ 8 step by step, keeping the decimal point and trailing zeros, to reach 0.375.
    3. Compare the result against your prediction. If you predicted more than 1, check whether you divided 3 by 8 or 8 by 3.
    4. Try a case that never stops: carry out 1 ÷ 3 far enough to see 0.333... keep repeating, and note it does NOT equal 0.3.
    5. Round only when told to (e.g. 1/3 ≈ 0.333 to three decimal places), and explain why the division never terminates.
  2. 2

    Order a mixed set by converting to a common form

    Why it works: Different forms cannot be reliably compared by surface digits; converting every item to one common form (then plotting on a line) makes the true order visible — and 1/3 sits between 30% and 0.35.

    1. Take the set 30%, 1/3 and 0.35. First predict the order smallest→largest by eye, and say why.
    2. Convert all three to ONE common form (decimals: 0.30, 0.333..., 0.35), using that percentages are hundredths and division for 1/3.
    3. Plot each converted value on a 0-1 number line and read off the order from position, not appearance.
    4. Compare your conversion-based order (30% < 1/3 < 0.35) with your by-eye prediction and note where they differed — especially whether you expected 1/3 to be biggest.
    5. Transfer the method to a new set, e.g. 30%, 2/5, 0.35: convert each (0.30, 0.40, 0.35) and say where 2/5 goes, and why.
  3. 3

    Build a landmark equivalence set

    Why it works: Memorised landmark equivalents let you convert common cases instantly, reserving division for less familiar fractions, while a shared visual shows the three forms name one quantity.

    1. Learn a small recall set as landmarks: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, 1/10 = 0.1 = 10%, and 1/3 ≈ 0.333 ≈ 33.3% (recurring, not exact).
    2. For each landmark, show all three names on one shared bar or hundred-grid so the same shaded quantity is seen as fraction, decimal and percentage at once.
    3. Match a form to its partners from memory (e.g. given 1/5, recall 0.2 and 20%); for fractions that are not landmarks, rewrite them as tenths or hundredths where easy (e.g. 3/20 = 15/100), and otherwise use division.
    4. Note which landmarks are exact and which (like 1/3) are recurring, so you don't record 1/3 as a terminating 0.33.

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
Ma6/2.3fMa6/2.3k

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