Math // Fractions

Tenths (age 8+)

Count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 or dividing tenths by 10

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

Quick check

If the learner has £1 and spends 37p, can they say that 37p is 37/100 of a pound — and count up in hundredths from 0/100 to 100/100?

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.
  • Count from 3/100 to 12/100 in hundredths
  • Explain that 1/10 ÷ 10 = 1/100
  • Place several hundredths on a number line between 0 and 1/10

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
  • TenthsRequired

    Fractions // Ages 7 to 8

    Count in tenths is prerequisite to extending to hundredths

You are here

Tenths (age 8+)

Ages 8 to 9 // Concept

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

Build hundredths by subdividing a tenth again by ten, so children feel the recursive tenfold nesting: a hundredth is a tenth of a tenth (1/10 ÷ 10 = 1/100), ten hundredths rebuild one tenth (10/100 = 1/10), and 100 hundredths make one whole. The central obstacle is whole-number bias — believing a hundredth is bigger than a tenth 'because 100 > 10' — so comparing a single tenth against a single hundredth is a strongly recommended way to confront it. Derive hundredths by splitting a tenth, not by cutting the whole into 100 at once.

Common misconceptions

  • Whole-number bias on the denominator: believing a hundredth is bigger than a tenth 'because 100 is bigger than 10'.
  • Not coordinating the nesting — treating 10 hundredths and 1 tenth as different, unrelated amounts.
  • Believing hundredths can only be made by cutting the whole into 100 at once, not by subdividing tenths (missing the recursive ×10 structure).
  • Losing count across the tenth boundary (after 9 hundredths, not seeing 10 hundredths = 1 tenth).
  • Thinking 'hundredths' refers to the large number 100 rather than to tiny parts of a whole.

Useful representations

  • 10×10 hundred grid (whole = 1, column = 1/10, small square = 1/100)
  • Length / number line from 0 to 1/10 subdivided into 10 hundredths
  • A tenth-strip physically cut into ten hundredth-pieces (1/10 ÷ 10 = 1/100)
  • Place-value nesting diagram: whole → tenths → hundredths, each ten-for-one
  • Counting sequence in hundredths crossing 10/100 = 1/10

Teaching practices

  • Derive hundredths by subdividing a tenth, not the whole: take one tenth of a strip and cut it into ten — each piece is a hundredth — so the child sees 1/10 ÷ 10 = 1/100 and that ten hundredths rebuild the tenth.
  • Use the 10×10 (hundred) grid and a length/number-line model together: the whole grid = 1, one column/row = 1/10, one small square = 1/100; shading shows 100 hundredths in the whole and 10 in each tenth.
  • Count in hundredths across the tenth boundary aloud — 8, 9, 10, 11, 12 hundredths — and stop to name 10 hundredths as also 1 tenth, so the 10/100 = 1/10 equivalence is explicit.
  • Confront the whole-number bias directly: put one tenth beside one hundredth and ask which is bigger and why, surfacing the 'but 100 > 10' intuition so it can be overturned.
  • Anchor to prior tenths work — just as tenths come from dividing by 10, hundredths come from dividing again by 10 — making place value a repeatable action, not a new fact per column.

Activities to try

  1. 1

    Split a tenth into ten hundredths

    Why it works: Hundredths come from dividing a tenth again by ten; ten hundredths rebuild one tenth and 100 hundredths make one whole. A hundredth is smaller than a tenth even though 100 is a bigger number than 10, because the same whole is split into more equal parts.

    1. Start with a strip that is one whole, already partitioned into ten equal tenths.
    2. Take a single tenth and cut (or subdivide) it into ten equal pieces; name one piece 'a hundredth' and write 1/10 ÷ 10 = 1/100.
    3. Work out how many of these small pieces would fill the whole strip: each of the ten tenths holds ten hundredths, so 10 × 10 = 100. Connect this to 'a hundredth is one of a hundred equal parts of the whole'.
    4. Count aloud in hundredths across the tenth boundary — 8, 9, 10, 11, 12 hundredths — and pause at 10 hundredths to say it is also 1 tenth.
    5. Lay one hundredth directly beside one tenth and describe how much smaller the hundredth is.
  2. 2

    Count in hundredths across the tenth boundary and place them on a line

    Why it works: Counting in hundredths and placing them between 0 and a tenth reinforces that each tenth holds exactly ten hundredths, so the count crosses cleanly into tenths.

    1. Count up and down in hundredths from 3/100 to 12/100, saying each amount aloud.
    2. When the count reaches 10 hundredths, name the equivalent in tenths (10 hundredths = 1 tenth), and note that the pattern continues (20 hundredths = 2 tenths).
    3. On a number line running from 0 to 1/10, mark the equal gaps needed to show hundredths and place 7/100 in the correct spot.
    4. Explain how many equal gaps lie between 0 and 1 tenth and why.
  3. 3

    Predict and compare: which is bigger, a tenth or a hundredth?

    Why it works: A hundredth is smaller than a tenth; the whole-number intuition that '100 > 10 so a hundredth is bigger' is wrong because splitting the same whole into more equal parts makes each part smaller. The ÷10 action repeats to make even smaller places.

    1. Before any cutting, predict which is bigger — one tenth or one hundredth — and state the reason.
    2. Then split one tenth into ten and lay a single hundredth against a tenth.
    3. Explain whether the result matches the prediction and why a hundredth is smaller despite 100 being larger than 10.
    4. Answer: how many hundredths make one whole, and how do you know?
    5. Consider: if one hundredth were split into ten equal parts again, what would each tiny piece be called?

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/2

Math // Fractions

More in Fractions

All 67 topics