Math // Fractions

Tenths

Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and from dividing one-digit numbers or quantities by 10

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

Quick check

If the learner splits a chocolate bar with 10 equal pieces, can they tell you each piece is one tenth — and count up from 1/10 to 10/10 in order?

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: one tenth, two tenths, three tenths … up to ten tenths (one whole)
  • Show that dividing a shape into 10 equal parts gives tenths
  • Explain that 3 ÷ 10 = 3/10

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

2 topics
  • Fractions of amountsRequired

    Fractions // Ages 6 to 7

    Tenths extend fraction understanding from halves, thirds, quarters

  • Counting in 2sHelpful

    Counting & Cardinality // Ages 5 to 7

    Skip counting supports counting in tenths

You are here

Tenths

Ages 7 to 8 // Concept

Leads to

2 topics
  • Tenths (age 8+)Required

    Fractions // Ages 8 to 9

    Count in tenths is prerequisite to extending to hundredths

  • Fractions on a number lineHelpful

    Fractions // Ages 7 to 8

    Counting in tenths supports placing fractions on a number line

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

Tenths build on earlier work with fractions such as halves and quarters: dividing ONE whole into ten equal parts, and the bridge toward decimal place value. The load-bearing ideas are that ten equal tenths recompose exactly one whole (10/10 = 1), that each tenth is small because it takes ten of them to rebuild the whole, and that 3/10 is the same as 3÷10 (three wholes shared among ten). Partitioned strips, length-based number lines, and sharing models let counting in tenths land cleanly at one whole rather than drifting into 'ten'.

Common misconceptions

  • Whole-number bias — reads ten-tenths as 'ten', or thinks a tenth is big 'because 10 is a big number'
  • Larger denominator = larger part (a tenth 'bigger than a half because 10 > 2')
  • Accepts any ten pieces as tenths, ignoring that the parts must be equal
  • Sees no connection between 3/10 and 3÷10 ('3 ÷ 10 can't be done, 3 is smaller than 10')
  • Thinks a tenth of a large whole and a tenth of a small whole are the same size

Useful representations

  • Whole strip partitioned into ten equal tenths (recomposes to one whole)
  • 0-to-1 number line marked in tenths
  • Sharing model: three wholes shared among ten to show 3/10 = 3÷10
  • Overlay of tenths against a half (5/10 = 1/2)

Teaching practices

  • Count up and down in tenths on a number line and a strip, stopping deliberately at 10/10 = one whole to break the 'ten-tenths is ten' bias
  • Insist on ten EQUAL parts of one whole (not any ten pieces) using a partitioned strip
  • Connect 3/10 to 3÷10 by sharing three whole strips across ten places
  • Compare a tenth with a half (5/10 = 1/2) so children feel a tenth is far smaller than a half
  • Keep the whole visible and constant so a tenth of a bigger whole is seen to be a bigger piece with the same name

Activities to try

  1. 1

    Collect the tenths back into one whole

    Why it works: Ten equal tenths put back together remake exactly one whole, so 10/10 = 1 (not 'ten'), and each tenth is small because it takes ten of them to rebuild the whole — far smaller than a half.

    1. Start with a single whole bar or strip and partition it into ten equal segments.
    2. Collect the segments one at a time while counting aloud: one-tenth, two-tenths, three-tenths … up to ten-tenths.
    3. At the tenth count, reassemble the ten segments end-to-end against the original whole and check that they match exactly, labelling the result '10/10 = 1 whole'.
    4. Lay a piece covering exactly five tenths over one half of the whole and confirm that 5/10 = 1/2, so a single tenth is plainly far smaller than a half.
  2. 2

    Share three wholes among ten to see 3/10 = 3÷10

    Why it works: A fraction such as 3/10 is the result of sharing three wholes equally among ten, so 3/10 = 3÷10; dividing by a number larger than the dividend is possible and gives a fraction less than one.

    1. Set out three identical whole bars and ten plates (or ten places) to share them among.
    2. Partition each whole into tenths and deal the tenths out equally, one at a time, until each of the ten places has received the same amount.
    3. State how much each place received (three tenths) and write the sharing as 3 ÷ 10 = 3/10.
    4. Discuss why this works even though 3 is smaller than 10: you share the three wholes into smaller pieces rather than giving whole bars each.
  3. 3

    Equal parts only, and the same whole

    Why it works: Only ten EQUAL parts of one whole count as tenths; and because a tenth is defined relative to its whole, the physical piece that is a tenth of a larger whole is larger than a tenth of a smaller whole when both wholes are shown, though both pieces share the name 'a tenth' and name the same fraction of their own whole.

    1. Compare a whole split into ten EQUAL pieces with a whole split into ten UNEQUAL pieces.
    2. Decide which one shows tenths and explain why (the ten parts must be the same size).
    3. Check by trying to recompose each set back into the whole and noticing which one tiles the whole with matching equal pieces.
    4. Then compare a tenth of a small whole bar with a tenth of a larger whole bar, keeping both wholes visible, and describe how the two tenths differ in physical size even though both are called 'a tenth'.

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/1

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