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Multiplication and Division Problems

A 45-minute Grade 3 lesson on word problems where the pupil must decide between multiplying and dividing, using what is known and what is missing rather than a keyword.

Multiplication and Division Problems is a free 45-minute Grade 3 maths lesson plan for Common Core standard 3.OA.A.3 — solve story problems using multiplication and division. 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.OA.A.3

Grade 3 · Operations & Algebraic Thinking

3.OA.A.3

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.

Objective

Students will be able to solve multiplication and division word problems within 100 by identifying which quantity is unknown.

Students are successful when they can

  • Identifies the number of groups, the size of each group, and the total in a problem.
  • Multiplies when the total is unknown and divides when it is not.
  • States the answer with its unit.

What you need

  • Counters and squared paper for arrays
  • Blank three-box templates: groups, size of group, total
  • Word problem cards of both types
  • The printable practice sheet linked at the end of this plan

The lesson

Warm-up — find the three numbers

5 min
  1. Read three problems. For each, ask only which of the three quantities is missing.
  2. Number of groups, size of group, total. Do not solve anything.

Teach — the missing box decides the operation

14 min
  1. Draw three boxes labelled groups, size, total. Read a problem and fill in the two you are given.
  2. 'Six bags with four apples in each' — groups 6, size 4, total missing. Multiply.
  3. 'Twenty-four apples in six bags' — groups 6, total 24, size missing. Divide.
  4. 'Twenty-four apples in bags of four' — size 4, total 24, groups missing. Divide again, but a different question.
  5. Say the rule plainly: if the total is missing you multiply; if the total is known you divide.
  6. Do one measurement problem — 'a ribbon 32 cm long cut into 4 equal pieces' — to show the boxes work when nothing is in groups at all.
“Do not look for words like 'each' or 'altogether'. Find the three numbers, see which one is missing, and the operation is decided for you.”

Guided practice — fill the boxes first

12 min
  1. Pairs take a problem card and fill the three boxes before calculating.
  2. The rule is no arithmetic until all three boxes are labelled.
  3. Circulate and ask which box is empty. A pair who can point at it will choose correctly.

Independent practice

11 min
  1. Students complete a mixed multiplication and division problems page.
  2. Where both numbers were multiplied on a division problem, the total was already there and got used as a factor. That is the error to name.

Close

3 min
  1. Read one problem and ask only which box is missing.
  2. Stopping before the calculation keeps the attention on the structure.

What goes wrong, and why

Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.

Multiplies the two numbers in every problem.

Why: Multiplication is the operation currently being taught, and a problem in a multiplication unit is assumed to need it. This is a reasonable inference about the lesson rather than about the problem.

Fix: Mix division problems in from the first day. If the operation can be guessed from the page heading, the page is not teaching the choice.

Divides the smaller number by the larger.

Why: The numbers have been placed in the order they appear in the problem, without checking which is the total.

Fix: The three boxes. The total is always the biggest of the three and always goes first in a division — checking that is quicker than remembering a rule.

Gets the right number and cannot say what it counts.

Why: The problem has been processed as arithmetic, with the context dropped once the numbers were extracted.

Fix: Require a unit in every answer. Four bags and four apples are different answers to different questions, and the unit is what distinguishes them.

If they are not there yet

  • Use facts from the 2, 5 and 10 tables so the arithmetic is automatic and the structure gets the attention.
  • Provide the three-box template pre-printed, so labelling is a matter of filling in rather than remembering the categories.

If they finish early

  • Give a problem where the answer has a remainder and ask what to do with it.
  • Give a two-step problem needing a multiplication then a division.
  • Write a division problem whose answer is 7 bags.

Exit ticket

There are 35 chairs arranged in rows of 5. How many rows? Say which quantity was missing.

What to look for: 7 rows, with the number of groups identified as missing. An answer of 175 means the total was used as a factor — the three boxes would have caught it.

Printable practice for 3.OA.A.3

Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.

Questions about Multiplication and Division Problems

How long does the Multiplication and Division Problems 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 Multiplication and Division Problems teach?

CCSS.MATH.CONTENT.3.OA.A.3 — 3.OA.A.3, Operations & Algebraic Thinking for Grade 3: “Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.” In plain terms, solve story problems using multiplication and division.

What do I need to teach this lesson?

Counters and squared paper for arrays, blank three-box templates: groups, size of group, total, word problem cards of both types 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: multiplies the two numbers in every problem; divides the smaller number by the larger and gets the right number and cannot say what it counts. 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: “There are 35 chairs arranged in rows of 5. How many rows? Say which quantity was missing.” 7 rows, with the number of groups identified as missing. An answer of 175 means the total was used as a factor — the three boxes would have caught it. 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 Multiplication and Division Problems?

Yes — 2 printable 3.OA.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 Multiplication and Division Problems 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.OA.A.3 of the Common Core State Standards for mathematics.