Math // Fractions

Decimal & Percent Notation

Read, write, and use decimal and percentage notation correctly — decimal, decimal point, tenths, hundredths, thousandths, percentage, per cent, % symbol, convert, terminating decimal — and understand the relationships between fractions, decimals, and percentages as three ways of expressing the same value

Ages
8 to 11
Type
Language
Builds on
0 topics
Leads to
5 topics

Quick check

If the learner saw '0.5' and '50%' written down, could they explain that they both mean the same amount — and write them as a fraction too?

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.
  • Read and write decimal numbers correctly, identifying the value of each digit (ones, tenths, hundredths)
  • Use the % symbol correctly and explain that per cent means 'out of 100'
  • Convert between simple fractions, decimals, and percentages (e.g. 1/2 = 0.5 = 50%) and explain why they are equal

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

0 topics

Nothing in the catalogue comes before this topic, so it is a good place to start.

You are here

Decimal & Percent Notation

Ages 8 to 11 // Language

Leads to

5 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 the shared language of fractions, decimals and percentages: that 1/2, 0.5 and 50% are three notations for ONE value, and that the words (tenths/hundredths/thousandths, per cent, % symbol, convert, terminating decimal) must be USED correctly in context, not just recited. The load-bearing habits are place-value reading of decimals (0.09 can be read 'nine hundredths'; the digit reading 'zero point zero nine' is also conventional, but the place-value name shows what it means) and the 'out of 100' meaning of per cent (writing '9% of £420 = £37.80', never '9% = £37.80', while equivalences such as '9% = 0.09' remain correct). The flagship activity ties one shaded quantity to its fraction, decimal, percentage and number-line position so all forms move together; alternatives (matching/diagnostic practice, explaining to a younger child, a labelled reference display) exercise and check the same vocabulary with different affordances.

Common misconceptions

  • Reading decimals as digit strings ('point oh nine', 'point seven') instead of place-value names ('nine hundredths', 'seven tenths').
  • Treating fraction, decimal and percentage as different, unrelated things rather than three names for one value.
  • Misusing percentage notation — writing '10% = 42' instead of '10% of 420 = 42'.
  • Reading the percentage number as the whole ('50% means 50') rather than as parts per hundred.
  • Confusing per cent (out of 100) with a plain count.

Useful representations

  • Four-way display: shaded hundred square + fraction (n/100) + decimal + point on a 0%–100% number line
  • 0–1 / 0%–100% double number line linking the three forms
  • Place-value chart for reading decimals aloud (ones | tenths | hundredths | thousandths)
  • Real-context cards (50% off, jug 0.5 full, 3/4 of a pizza) matched across notations
  • Matching sets of fraction–decimal–percentage cards for one value

Teaching practices

  • Teach the three forms together as one value using a single quantity shown four ways — a shaded hundred square, the fraction (with denominator 100), the decimal, and a position on a 0%–100% number line — so 1/2, 0.5 and 50% are visibly the same.
  • Insist on place-value reading of decimals: 0.09 is 'nine hundredths', 0.7 is 'seven tenths', never 'point oh nine' or 'point seven', so the digits keep their meaning.
  • Model correct percentage language: per cent means 'out of / for every hundred'; 100% is the whole; write 'X% of N', never the bare 'X% = value'.
  • Use real contexts (sales '50% off', a half-full jug, test scores out of 100) and ask children to state the same fact as a fraction, a decimal and a percentage.
  • Introduce 'terminating decimal' and 'convert' as working vocabulary in the act of converting, so the words are attached to actions rather than defined in isolation.

Activities to try

  1. 1

    One quantity, three names — fill and watch them move together

    Why it works: A fraction, a decimal and a percentage are not three separate topics but one quantity wearing three names; the correct place-value reading and the 'per cent = out of 100' meaning are visible in the same moment the learner acts.

    1. Fill a hundred square (or slide a bar) to show a chosen amount, e.g. drag to fill fifty squares.
    2. Read the linked panel as it updates in lockstep: 50/100, 0.5, 50%, with a marker halfway along a 0%–100% number line.
    3. Say the decimal aloud in place-value language ('five tenths, one half, fifty per cent'); use a 'read it' option to hear the correct reading.
    4. Fill nine squares and confirm the panel reads 9/100, 0.09, 9% and voices the place-value name 'nine hundredths' alongside the digit reading 'zero point zero nine'.
    5. Switch to context skins (a '9% off' price tag, a jug 0.5 full) and state the same fact as a fraction, a decimal and a percentage.
  2. 2

    Match, read and complete — diagnostic usage practice

    Why it works: Correct use of the vocabulary is checkable: the right place-value reading, the right grouping of equivalent forms, and the correct 'X% of N' phrasing distinguish understanding from digit-string reading and base-neglect.

    1. Match cards so that each value's three forms are grouped, e.g. 1/2 ↔ 0.5 ↔ 50%.
    2. Choose the correct place-value reading of a decimal, e.g. 'What is the place-value name for 0.09?' with 'nine tenths' or 'nine' offered as tempting wrong answers.
    3. Complete 'X% of N' statements, e.g. fill the blank in '__% of 420 = 42'.
    4. Sort a mixed set of cards by the single value each one names.
  3. 3

    Explain it to a younger child

    Why it works: Being pressed to explain forces the learner to produce and justify the three forms and the 'parts per hundred of a base' meaning in their own words.

    1. Explain a shop's '9% off' sign or a half-full jug to a younger character who asks 'what does per cent mean?' and 'is that the same as a half?'
    2. Say a single quantity three ways (fraction, decimal, percentage) and read each aloud correctly.
    3. Answer whether '9% off' could ever take off more money than '50% off', and say what it depends on (the base amount).

Math // Fractions

More in Fractions

All 67 topics