Math // Multiplication & Division

Multiplying by Tens

Multiply one-digit whole numbers by multiples of 10 in the range 10–90 using strategies based on place value and properties of operations

Ages
8 to 9
Type
Method
Builds on
2 topics
Leads to
0 topics
Standards
1 code

Quick check

Can the learner quickly work out '7 × 40' or '6 × 80' by first doing the single-digit multiplication and then placing the zero — getting 280 and 480?

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.
  • Calculate 7 × 30 = 210 by reasoning 7 × 3 tens = 21 tens = 210
  • Explain why multiplying by a multiple of 10 adds a zero to the product
  • Use this skill to estimate products of larger numbers

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

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Multiplying by Tens

Ages 8 to 9 // Method

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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 8–9: multiply a one-digit number by a multiple of 10 (10–90) by reasoning from a known fact scaled by ten — 7×30 = 7×(3×10) = (7×3)×10 = 21 tens = 210 — using place value and the associative property. The objective is the reasoning, not the 'add a zero' trick: learners should understand multiplying by 10 as making a number ten times larger so its digits shift one place left, which is why 210 ends in a zero (the ones place empties). This understanding survives the later move to decimals, where 'add a zero' fails (0.7×10 = 7, not 0.70), and powers estimation (234×5 ≈ 200×5) and multiplication by multiples of 100/1000.

Common misconceptions

  • Over-relying on 'add a zero' as a rule without understanding, which later misfires with decimals (0.7×30).
  • Multiplying the wrong part (7×30 as 21 rather than 210) — losing the place-value scaling.
  • Adding an extra or too few zeros through miscounting places.
  • Not connecting 7×30 to the known fact 7×3, so it's computed from scratch.
  • Confusing multiplying by a multiple of ten with adding tens.

Useful representations

  • Place-value counters / columns — 21 tens regrouped to 210
  • Known-fact-×-ten chain (7×3=21 → 7×30=210)
  • Gattegno/place-value chart — the leftward digit shift for ×10
  • Number line in tens — skip counting by 30

Teaching practices

  • Reason from the known fact scaled by ten: 7×30 = (7×3) tens = 21 tens = 210, using associativity and place value explicitly.
  • Teach 'ten times larger → digits shift one place left', NOT 'add a zero', so the idea survives the move to decimals.
  • Use place-value counters and columns so 21 tens visibly becomes 210 (regrouping ten tens into a hundred).
  • Connect immediately to estimation — rounding a factor to a multiple of ten to bound a larger product.
  • Extend the same reasoning to multiples of 100/1000 once secure, keeping the place-value story constant.

Activities to try

  1. 1

    Scaling a known fact by ten with place-value counters

    Why it works: Multiplying by a multiple of 10 is multiplying by the single-digit fact and then by ten; the extra zero in the product is the result of every digit shifting one place left as the amount becomes ten times larger, not a zero 'stuck on the end'.

    1. Build the known fact 7×3 as an array of 21 single counters (or draw them).
    2. Replace each single counter with a rod of ten, stating aloud 'now there are 21 tens'.
    3. Regroup the 21 tens: exchange ten tens for one hundred, repeat, ending with 2 hundreds and 1 ten.
    4. Record the result on a place-value chart (hundreds | tens | ones) and read it as 210.
    5. Say the full reasoning chain: '7×3 = 21, so 7×30 = 21 tens = 210, because 30 is 3 tens.'
  2. 2

    Why 'add a zero' is not the real rule

    Why it works: Multiplying by ten always shifts digits one place to the left; for whole numbers this shows up as a trailing zero, but the shift — not the zero itself — is the real rule, which is why it still works for decimals.

    1. On a place-value chart, place 7 in the ones column, then slide it one column left to make 70; describe what happened to the digit.
    2. Do the same with 21: slide it one column left so the ones place becomes empty and a 0 fills it, giving 210.
    3. Now try 0.7×10 on the same chart: slide 0.7 one column left to get 7 — notice no zero was added.
    4. State in your own words why '×10 shifts digits one place left' is safer than 'add a zero'.
    5. (Optional extension, once the tens pattern feels secure) Predict and check 7×300 using the same idea: 7×3 = 21, shifted two places = 2100.
  3. 3

    Using tens facts to estimate

    Why it works: Multiplying by a multiple of ten (and, by the same reasoning, a multiple of a hundred) lets you quickly bound or approximate a larger product, which checks whether an exact answer is reasonable.

    1. Estimate 6×43 by rounding 43 to 40 and computing 6×40 = 240 (6×4 = 24, so 6×40 = 24 tens = 240), explaining the reasoning.
    2. (Optional extension, once the tens case is secure) Estimate 234×5 by rounding 234 to 200 and computing 200×5 = 1000 (2×5 = 10, so 200×5 = 10 hundreds = 1000), using the same known-fact-then-scale reasoning.
    3. Compare each estimate to the exact answer (6×43 = 258; 234×5 = 1170) and say whether the estimate is high or low and roughly by how much.
    4. Make up one estimation of your own using a multiple of ten and justify it.

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
3.NBT.3

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