Multiplying by Multiples of Ten
A 45-minute Grade 3 lesson on multiplying a one-digit number by a multiple of ten, taught as a known fact plus a unit change rather than as a rule about adding a zero.
Multiplying by Multiples of Ten is a free 45-minute Grade 3 maths lesson plan for Common Core standard 3.NBT.A.3 — multiply by tens. It is timed across 5 sections, gives the exact wording to use where the wording carries the mathematics, names 3 misconceptions with the teaching move that addresses each, and ends with an exit ticket and a printable worksheet with its answer key.
- Grade:
- Grade 3
- Length:
- 45 minutes
- Standard:
- 3.NBT.A.3
Grade 3 · Number & Operations in Base Ten
3.NBT.A.3
Multiply one-digit whole numbers by multiples of 10 in the range 10-90.
Objective
Students will be able to multiply a one-digit number by a multiple of ten using a known fact and place value reasoning.
Students are successful when they can
- Works out 6 × 40 from 6 × 4.
- Explains why the answer is ten times as large.
- Uses the strategy in a word problem.
What you need
- Base ten rods
- Place value charts
- Squared paper for arrays
- The printable practice sheet linked at the end of this plan
The lesson
Warm-up — the facts underneath
5 min- Rapid round of one-digit facts: 6 × 4, 7 × 3, 8 × 5.
- These are the facts the whole lesson rests on, and they need to be instant.
Teach — same fact, bigger units
14 min- Build 6 × 4 with counters: 24. Now build 6 × 4 with rods instead of counters.
- Six groups of four rods is twenty-four rods. Twenty-four tens is 240.
- Write 6 × 40 = 240 beside it. The fact did not change; the unit did.
- Ask why a zero appears. Not because zeros get added, but because twenty-four tens is two hundred and forty.
- Test the difference: ask for 6 × 400 and let them reason it as twenty-four hundreds rather than by adding another zero.
- Do a word problem — six boxes of forty pencils — so the strategy meets a context.
“Six fours is twenty-four. Six forties is twenty-four tens. You already knew the fact — the only change is what you were counting.”
Guided practice — fact first, then units
12 min- Pairs take a card like 7 × 60 and write the underlying fact first, then the answer.
- The partner checks the fact is right before the answer is accepted.
- Then they build one of them with rods to confirm.
Independent practice
11 min- Students complete a multiplying by tens page.
- Answers with too many or too few zeros are the diagnostic. Ask what unit they were counting.
Close
3 min- Give 8 × 70 and ask for the fact underneath before the answer.
- Fifty-six tens is 560, and hearing it said that way is the point.
What goes wrong, and why
Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.
Answers 6 × 40 as 24 by ignoring the zero.
Why: The zero has been treated as decoration rather than as the thing that changes the unit, so the known fact was used unchanged.
Fix: Build it with rods. Twenty-four rods is visibly not twenty-four counters, and the difference is exactly ten times.
Adds a zero to 5 × 40 to get 200 but then writes 5 × 400 as 2000 without checking.
Why: The zero-adding rule happens to give the right answer here, so it is reinforced rather than examined. It will fail on 50 × 40.
Fix: Ask for the unit every time. Twenty hundreds is two thousand, and reasoning through the unit survives cases the rule does not.
Answers 6 × 40 as 2400 by adding the zero twice.
Why: The rule has been applied without a check on the size of the answer, and no estimate exists to contradict it.
Fix: Estimate first: six lots of forty is somewhere near six lots of fifty, about 300. Two thousand four hundred is obviously wrong before it is calculated.
If they are not there yet
- Work only with facts the pupil knows instantly, so the multiplication is not competing with the place value.
- Build every calculation with rods for the first session. The unit change has to be seen before it can be reasoned about.
If they finish early
- Multiply a multiple of ten by a multiple of ten: 30 × 40.
- Divide a multiple of ten by a one-digit number and explain the unit.
- Estimate 38 × 6 by rounding to 40 × 6 and say whether the estimate is high or low.
Exit ticket
Work out 7 × 80. Write the fact you used first.
What to look for: 7 × 8 = 56, so 560. An answer of 5600 is the zero rule misapplied; 56 means the zero was ignored entirely.
Printable practice for 3.NBT.A.3
Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.
- Multiply by TenWork out each answer.
- Multiply by Multiples of TenWork out each answer.
Questions about Multiplying by Multiples of Ten
How long does the Multiplying by Multiples of Ten lesson take?
45 minutes, split across 5 timed sections: warm-up 5 min, teach 14 min, guided practice 12 min, independent practice 11 min, close 3 min. The minutes are stated per section and add up to the stated length, so the plan can be cut or extended at a section boundary rather than abandoned halfway.
Which standard does Multiplying by Multiples of Ten teach?
CCSS.MATH.CONTENT.3.NBT.A.3 — 3.NBT.A.3, Number & Operations in Base Ten for Grade 3: “Multiply one-digit whole numbers by multiples of 10 in the range 10-90.” In plain terms, multiply by tens.
What do I need to teach this lesson?
Base ten rods, place value charts, squared paper for arrays and the printable practice sheet linked at the end of this plan. Everything listed is either ordinary classroom equipment or a free printable from this site — there is nothing to buy and nothing to prepare beyond photocopying.
What mistakes should I expect in this lesson?
Three, each a reasoning error rather than carelessness: answers 6 × 40 as 24 by ignoring the zero; adds a zero to 5 × 40 to get 200 but then writes 5 × 400 as 2000 without checking and answers 6 × 40 as 2400 by adding the zero twice. The plan gives the thinking behind each one and the teaching move that addresses the thinking rather than the symptom.
How do I know whether the lesson worked?
The exit ticket asks: “Work out 7 × 80. Write the fact you used first.” 7 × 8 = 56, so 560. An answer of 5600 is the zero rule misapplied; 56 means the zero was ignored entirely. That tells you whether the class needs a reteach or a thirty-second conversation before you plan tomorrow.
Is there a worksheet to go with Multiplying by Multiples of Ten?
Yes — 2 printable 3.NBT.A.3 worksheets, linked at the end of the plan and free like the rest of the site. Each one comes with an answer key and 25 versions, so the practice after the lesson can be a different paper on every desk.
Is Multiplying by Multiples of Ten free to use?
Yes. The plan, its printables and their answer keys are free to read, print and photocopy for your own class, with no account and no email capture. It was last reviewed on 5 September 2026. Please do not resell it or republish it as your own.
Last reviewed 2026-09-05. Aligned to 3.NBT.A.3 of the Common Core State Standards for mathematics.