Math // Number Representation & Place Value

Place Value × 10 Pattern

Recognise that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g. 700 ÷ 70 = 10)

Ages
9 to 10
Type
Concept
Builds on
1 topic
Leads to
6 topics
Standards
1 code

Quick check

Can the learner explain that in 700, the 7 is worth 10 times more than in 70 — because moving one place to the left multiplies the value by 10?

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.
  • Explain that the 3 in 3,000 is ten times the 3 in 300
  • Complete: 700 ÷ 70 = __ and explain using place-value reasoning
  • State how many times greater the value of the 5 in 50,000 is than the 5 in 5,000

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
  • Place value of each digitRequired

    Number Representation & Place Value // Ages 8 to 9

    Four-digit place value is prerequisite to understanding ×10 relationship between places

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Place Value × 10 Pattern

Ages 9 to 10 // Concept

Leads to

6 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

For ages 9-10: pupils recognise that in a multi-digit whole number a digit in one place is worth ten times what the same digit is worth in the place to its right (and one-tenth of the same digit in the place to its left). The 3 in 3,000 is ten times the 3 in 300; 700 ÷ 70 = 10. The aim is to name the multiplicative ×10 structure between adjacent places that has been implicit since 'ten ones make a ten', and to hold it alongside the additive (partition) view. A central scaffold is a place-value / Gattegno chart where moving a digit one column left multiplies its value by 10 and one column right divides it by 10; a static or paper chart with counters can serve the same purpose.

Common misconceptions

  • Seeing place value only additively and missing the ×10 relationship between places.
  • Thinking the 3 in 3,000 is '10 more' than in 300 rather than 10 times.
  • Confusing 'ten times' with 'add a zero' as a meaningless trick (fails for decimals later).
  • Miscounting the factor across non-adjacent places (×10 vs ×100).
  • Not connecting 700÷70=10 to the adjacent-place relationship.

Useful representations

  • Gattegno place-value chart (rows scale ×10 down each column)
  • Place-value chart with a digit sliding between columns
  • Base-ten pieces showing ten-of-one-unit = one-of-next
  • Multiplication/division sentences (×10, ÷10) between places
  • Arrow-card / expanded form as the additive counterpart

Teaching practices

  • Use a Gattegno / place-value chart: sliding a digit left ×10s its value, right ÷10s it — make the multiplicative move physical.
  • Hold the additive (partition) and multiplicative (×10 between places) views together so place value is understood both ways.
  • Expose the relationship with division/multiplication sentences (700 ÷ 70 = 10; 30 = 3 × 10).
  • Compare the same digit across places ('how many times greater is the 5 in 50,000 than in 5,000?').
  • Bridge to multiplying/dividing by 10/100/1000 so the pattern has calculation payoff.

Activities to try

  1. 1

    Slide a digit across the place-value chart

    Why it works: Shifting a digit one place left multiplies its value by 10 and one place right divides it by 10; place value is multiplicative between adjacent columns, not merely 'adding a zero'.

    1. Set up a place-value chart with columns for ones, tens, hundreds, thousands (and more).
    2. Place a single digit — say a 3 — in the hundreds column so it is worth 300.
    3. Move that same 3 one column to the LEFT and state its new value (3,000). Say what happened to the value and by how much: it became ten TIMES as much, not 'ten more'. (For whole numbers the written numeral also gains a zero, but that is a by-product — the reason is the ×10 in value.)
    4. Move the 3 back to the RIGHT (÷10): from 3,000, one column right returns it to 300, and a further column right makes it 30.
    5. Write the matching sentence each time, e.g. 300 × 10 = 3,000 and 3,000 ÷ 10 = 300.
  2. 2

    How many times greater? Counting the place-shifts

    Why it works: The factor between two placements of a digit equals ten raised to the number of column shifts: one shift is ×10, two shifts is ×100. Non-adjacent places are not automatically 'ten times'.

    1. Compare the same digit in two different places, e.g. the 5 in 50,000 and the 5 in 5,000.
    2. Slide one placement of the 5 towards the other, counting the number of column hops.
    3. State the factor: one hop = ×10, so the 5 in 50,000 is ten times the 5 in 5,000.
    4. Repeat for a non-adjacent pair, e.g. the 5 in 50,000 compared with the 5 in 500: count the hops (two), so the factor is ×10×10 = ×100.
    5. Say in words how many times greater, and justify by the number of place-shifts.
  3. 3

    Division and multiplication sentences as the place-value step

    Why it works: Division and multiplication sentences such as 700 ÷ 70 = 10 express the adjacent-place relationship itself: moving one place is ×10 or ÷10.

    1. Complete 700 ÷ 70 = ___ and explain the answer using place names, not just the computed digits.
    2. Explain how 700 ÷ 70 = 10 connects to 70 and 700 sitting in adjacent place-value columns (the 7 in 700 is one place to the left of the 7 in 70, so 700 is ten times as much as 70).
    3. Write a few matched pairs showing both directions, e.g. 30 = 3 × 10 and 3 = 30 ÷ 10.
    4. Point to or highlight the two adjacent columns involved for each sentence so the quotient of 10 is seen as a single left/right place step.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
Common Core State Standards for Mathematics
4.NBT.1

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