Multiplication and Division

Overview

Students will strengthen multiplication fluency and connect multiplication and division through word problems. They will use multiplication properties, division reasoning, and short multiplication flash-card practice to interpret and solve multiplicative comparison situations.

Learning intentions

• Students will be able to interpret and write multiplication equations to represent multiplicative comparisons.
• Students will be able to solve word problems involving multiplication and division using a letter for the unknown and explain their reasoning.
• Students will use multiplication properties (like 0 and 1, and understanding commutativity) to support fluency and accuracy.
• Students will be able to use division to find unknown quantities when one amount is a known multiple of another.

Success criteria

• I can turn a multiplicative comparison word problem into a multiplication equation with a symbol for the unknown.
• I can use multiplication and division equations to solve for the unknown and interpret the answer in context.
• I can correctly answer most multiplication flash cards (target: 80% or higher in one round) using known facts and properties.

Curriculum links

• Operations and Algebraic Thinking — interpret multiplication equations as comparisons; represent verbal multiplicative comparisons as multiplication equations.
• Operations and Algebraic Thinking — multiply or divide to solve word problems involving multiplicative comparison using drawings/equations with a symbol for the unknown.
• Operations and Algebraic Thinking — solve multistep whole-number word problems using equations with a letter for the unknown; include reasonableness checks.
• Number and Operations in Base Ten — use multiplication/division relationships and explain calculations using equations/area or rectangular-array models (as needed).

Lesson structure (40 minutes)

1. 0–4 min · Warm-up: Quick facts. Teacher displays 4 “Which is greater?” prompts using groups (e.g., “3 groups of 6”). Students give the multiplication sentence or answer silently, then share one with a partner.

2. 4–12 min · Direct teach: Multiplication as comparison. Teacher writes: “If Mia has 4 bags with 7 pencils in each bag…” and models that “4 bags is 4 times as many bags/groups as 1 bag,” focusing on comparison language. Students underline the two quantities being compared and state a multiplication equation (with a symbol if needed), e.g., (7 \times 4 = _).

3. 12–20 min · Properties mini-lesson + modeling. Teacher reviews two properties students can use quickly:

• Identity: any number times 1 equals itself (and dividing by 1 keeps the number).
• Zero: any number times 0 equals 0 (and 0 divided by a nonzero number is 0). Teacher also connects commutativity informally: (6 \times 7) is the same as (7 \times 6). Students complete 3 quick guided examples on mini whiteboards, then connect one multiplication fact to a related division fact (e.g., if (3 \times 8 = 24), then (24 \div 8 = 3)).

4. 20–27 min · Multiplication flash cards (fluency rounds). Teacher runs two 3-minute rounds. Round 1: facts for the current unit set (e.g., 6–9 or all facts through 12 depending on class needs). Round 2: mixed facts including ones linked to properties (0s and 1s, plus reversals). Students respond orally or on mini cards; they record missed facts in a “needs practice” row.

5. 27–36 min · Guided practice: Word problems using multiplication/division. Teacher gives one problem and models thinking, then students solve in pairs: Problem type focus: multiplicative comparison. Example: “A sticker sheet has 5 rows with 6 stickers in each row. How many stickers are in the whole sheet?” (Students write (6 \times 5 = _).) Then a related comparison/division problem: “If there are 30 stickers total and each row has 6 stickers, how many rows are there?” (Students write (_\div 6 = 5) or (6 \times 5 = 30) then identify rows.) Students use equations with a letter for the unknown (e.g., (6 \times r = 30)) and interpret the solution in words.

6. 36–40 min · Exit ticket + reasonableness check. Teacher distributes a 2-question exit ticket:

• Q1: “Ms. Rivera has 3 times as many notebooks as Sam. Sam has 8 notebooks. How many does Ms. Rivera have?” (Students write a multiplication equation and answer.)
• Q2: “You have 42 cookies. If you pack them into bags of 6, how many bags?” (Students write a division or related multiplication equation.) Students also do a quick reasonableness check by estimating (e.g., 42 is about 40, so about (40 \div 6 \approx 7)).

Resources

• Multiplication flash cards (fact sets matched to class scope; include 0s and 1s)
• Mini whiteboards and markers or response cards
• “Needs practice” recording sheet (one per student)
• Word problem task cards (multiplicative comparison and connected division)
• Exit ticket slips
• Optional: simple array/rectangular-area model template for visual support

Assessment

• Formative checks during the warm-up and property mini-lesson (observe accuracy on mini whiteboards)
• Flash-card data (percent correct each round; identify specific missed facts)
• Guided practice monitoring (listen for correct multiplication/division equation writing with an unknown symbol)
• Exit ticket correctness and explanation in context (does the equation match the story?)

Differentiation

• Support:
• Provide sentence frames for translation to equations: “There are ___ groups of ” and “ is ___ times as many as ___.”
• Offer a partially completed equation for students who need a starting point (e.g., (6 \times r = 30)).
• Use arrays/area models for students who benefit from visuals for multiplication and division relationships.
• Extension:
• Challenge students to write two related equations for each problem (one multiplication and one division) and explain how they connect.
• EAL/SEN considerations:
• Pre-teach key language: “times as many,” “per,” “each,” “rows,” “groups,” “total.”
• Allow students to answer with drawings plus equations when language is a barrier, but still require the multiplication/division equation with a letter for the unknown.