Apply Multiplication Word Problems

Overview

Students solve real-world word problems that require multiplication within 100, using drawings and equations with a symbol for the unknown. This lesson builds on previous multiplication facts by focusing on problem meaning and representing the situation mathematically.

Learning intentions

• Students will interpret multiplication as equal groups (e.g., 5 × 7 means 5 groups of 7).
• Students will solve multiplication word problems using drawings and equations.
• Students will use a symbol (like □ or? ) for the unknown in an equation.
• Students will check if their answer makes sense using estimation or mental math.

Success criteria

• I can draw a picture or array to show equal groups in a word problem.
• I can write an equation with a symbol for the unknown number.
• I can solve the problem using multiplication or a related division fact.
• I can explain whether my answer is reasonable.

Curriculum links

• Operations and Algebraic Thinking — multiplication and division within 100 to solve word problems (equal groups, arrays, measurement quantities).
• Operations and Algebraic Thinking — solve two-step and assess reasonableness using estimation/rounding and mental computation.
• Operations and Algebraic Thinking — determine the unknown whole number in a multiplication or division equation.
• Operations and Algebraic Thinking — apply properties of operations as strategies to multiply and divide.

Lesson structure (60 minutes)

1. 0–5 min · Warm-up: equal groups talk. Teacher shows 3 quick scenarios (like “4 boxes with 6 pencils each”) and asks what multiplication could represent; students share their best multiplication sentence.

2. 5–12 min · Guided example: unknown in an equation. Teacher models a problem: “There are 3 bags with the same number of stickers. Each bag has □ stickers. There are 18 stickers total. How many stickers are in each bag?” Teacher draws groups, discusses that 3 equal groups make 18, and writes an equation like 3 × □ = 18; students help complete the unknown and solve.

3. 12–18 min · Checkpoint: representation requirements. Teacher posts a second example (“5 rows with 4 beads in each row. How many beads?”) and asks students to: (a) draw equal groups/array, (b) write an equation with a symbol if needed, and (c) solve; students complete on paper.

4. 18–30 min · Independent work: word problem stations (teacher-led pacing). Teacher runs 2–3 short problem sets (one equal-groups, one array, one measurement quantity) and circulates. Students solve using drawings and equations with a symbol for the unknown, then label final answers with units (stickers, beads, miles, etc.).

• Problem set examples for today:
• Equal groups: “7 packs have 6 trading cards each. How many cards?”
• Array: “A rectangle has 4 rows and 8 columns. How many squares?”
• Measurement quantity: “A rope is cut into 5 equal pieces that are 9 feet each. How long is the rope?”

5. 30–40 min · Reasonableness mini-lesson (estimate). Teacher teaches a quick check: use compatible numbers and rounding/mental math to see if the exact answer is close. Example: if a problem gives 7 × 8 = 56, students estimate 7 × 8 ≈ 8 × 8 = 64 and decide whether 56 is reasonable; students practice on 1–2 solved problems from their page.

6. 40–52 min · Two-step challenge (optional choice within the set). Teacher gives one two-step multiplication word problem, using student-friendly numbers within 100. Example: “There are 3 baskets with 5 apples in each basket. Then put the apples into 2 bowls equally. How many apples are in each bowl?” Teacher reminds students: multiplication first (total apples), then division to find the equal share. Students solve and write an equation using a symbol for the unknown.

7. 52–58 min · Share-out: justify your equation. Teacher selects 2–3 student solutions and asks: “How did your drawing match your equation? Where did the unknown symbol go? How do you know the answer makes sense?” Students respond using sentence frames: “I drew…, so my equation is…, and the answer is…”

8. 58–60 min · Exit ticket (quick check). Teacher collects one final problem: “6 equal groups have a total of 30 items. How many items are in each group? Write an equation with a symbol for the unknown.”

Resources

• Problem set worksheet (3–4 multiplication word problems plus one two-step)
• Chart paper/whiteboard with an example equation template: a × □ = total
• Drawing tools: pencils, crayons/colored pencils (optional)
• Base-ten blocks or counters for representing groups (optional but helpful)
• Arrays/grid paper (dots or blank grids)
• Student mini “reasonableness check” card (estimate method reminders)
• Exit ticket slips

Assessment

• During guided example and independent work: check for correct drawing of equal groups/arrays and correct placement of the unknown symbol in an equation.
• After the reasonableness mini-lesson: listen for whether students use estimation/mental math to judge if answers are plausible.
• Exit ticket: verify the student can write and solve an equation with a symbol for the unknown and explain reasonableness if they finish early.

Differentiation

• Support: provide sentence starters for equations (“□ × 7 = ___”, “There are ___ groups of ___”); offer a pictorial model (pre-drawn equal groups) that students complete with the unknown.
• Support: for students who need it, allow using counters to build equal groups before writing the equation.
• Extension: if a student finishes early, ask them to create their own equal-groups word problem for a given equation (e.g., 4 × □ = 32) and solve it.
• EAL/SEN: allow oral explanation first, then have students copy the key equation and number facts; keep units consistent and read problems aloud once before solving.