Math // Number Representation & Place Value

Place Value to 1000

Solve number problems and practical problems involving place value of numbers up to 1000

Ages
7 to 8
Type
Thinking skill
Builds on
2 topics
Leads to
0 topics
Standards
1 code

Quick check

If the learner is told 'I have 4 hundreds, 3 tens, and 7 ones — what number is that?', can they put it together and tell you 437?

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.
  • Solve a problem that requires identifying how many hundreds, tens, or ones are in a number
  • Apply place-value knowledge to a practical context (e.g. counting money in pounds)
  • Explain the strategy used to solve a place-value problem

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

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Place Value to 1000

Ages 7 to 8 // Thinking skill

Leads to

0 topics

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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 7-8, solve number and practical problems using three-digit place value to 1000, applying it flexibly rather than first learning it. The central objective is flexible re-unitising: seeing that the SAME number can be decomposed many equivalent ways (340 = 3 hundreds 4 tens = 34 tens = 300 + 40) and choosing the view that fits the problem. Children work 'how many tens/hundreds' questions, missing-digit clues (4 hundreds, 0 tens, 7 ones give 407), and money/measure contexts, explaining and checking their reasoning.

Common misconceptions

  • Only seeing canonical partition (340 = 300 + 40) and missing '34 tens'.
  • Counting in ones instead of using place-value structure.
  • Mishandling internal zeros in problem numbers (407).
  • Inverse-blindness on missing-digit/missing-number clues.
  • Not mapping money/measure contexts onto place-value columns.

Useful representations

  • Part-whole and bar models for problem structure
  • Place-value counters and H|T|O chart
  • Money (pounds/tens of pence/pence) as a place-value context
  • 0-1000 number line for jump/benchmark reasoning
  • Arrow cards for flexible partitioning

Teaching practices

  • Pose genuine problems (how-many-tens, missing-digit clues, money/measures) that reward place-value reasoning, not routine recall.
  • Model with part-whole / bar models and place-value counters, thinking aloud, then transfer the explaining to the child.
  • Stress flexible partitioning: 340 is 3 hundreds 4 tens AND 34 tens AND 300 + 40 — choose the useful view.
  • Use money as a natural place-value context (£/10p/1p mirror hundreds/tens/ones).
  • Include missing-value / inverse problems to build reasoning beyond direct calculation.

Activities to try

  1. 1

    Place-value problem workbench: re-unitise to answer

    Why it works: The same number can be re-unitised into equivalent decompositions; you pick the view that answers the question, and you can check by rebuilding the original number.

    1. Read a problem card such as 'How many tens are in 340?'
    2. Build 340 with place-value pieces (three hundred-flats, four tens-rods) or arrow cards.
    3. Exchange each hundred-flat for ten tens-rods on an exchange pad and watch 340 reassemble as 34 tens-rods, then read off the answer: 34 tens.
    4. Repeat for another number (e.g. how many tens in 350? how many hundreds in 680?) and say which decomposition you used.
    5. Name the strategy you used each time ('I re-unitised the hundreds into tens').
  2. 2

    Money and measures as place-value columns

    Why it works: Money (pounds / 10p / 1p) mirrors the hundreds/tens/ones structure, so a shopping total is solved with the identical place-value reasoning.

    1. Solve a money problem such as '£4.07 = how many pence?' using a money tray (pounds, 10p, 1p).
    2. Counting the amount in pence, map pounds onto hundreds (£1 = 100p), 10p onto tens, and 1p onto ones, lining them up in place-value columns.
    3. Work a small shopping total using the same columns you used for whole numbers.
    4. State how the money columns mirror hundreds/tens/ones.
  3. 3

    Missing-digit and missing-value clues

    Why it works: Place value is a two-way tool: you can reason backwards from a description to the number, and internal zeros act as placeholders that must be honoured.

    1. Read a clue such as 'I have 4 hundreds, 0 tens and 7 ones — what number am I?' and build the number (407).
    2. Honour the placeholder: put no tens pieces in the tens column but keep the column, and write a 0 digit there when recording, so the number is written correctly as 407, not 47.
    3. Work an inverse/missing-value problem, e.g. '__ tens make 340' or 'a number has 34 tens and no ones — what is it?'
    4. Explain how you knew where each digit belonged.

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/NPV/6

Math // Number Representation & Place Value

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