Objective
Students will be able to interpret multiplication as equal groups and represent multiplication facts using arrays, repeated addition, and the multiplication symbol. Students will solve at least 8 out of 10 multiplication problems involving facts up to 5 x 5 on an exit ticket.
Standards
- CCSS.MATH.CONTENT.3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each.
- CCSS.MATH.CONTENT.3.OA.A.3 — Use multiplication within 100 to solve word problems.
Materials
- Counters or unifix cubes (30 per student)
- Grid paper for drawing arrays
- Multiplication anchor chart (equal groups, arrays, repeated addition)
- Whiteboard and marker per student
- Word problem task cards (10 cards)
- Exit ticket worksheet
Warm-Up (5 minutes)
Display the following on the board: "There are 4 bags. Each bag has 3 apples. How many apples are there in all?" Ask students to solve it any way they can — drawing pictures, counting, adding. After 2 minutes, invite volunteers to share strategies. Most will use repeated addition (3 + 3 + 3 + 3 = 12). Introduce the idea: "There is a faster way to write this. Today we are going to learn about multiplication."
Direct Instruction (12 minutes)
Introduce multiplication as a shortcut for adding equal groups. Write on the board: 4 groups of 3 = 4 x 3 = 12. Explain each part: 4 tells us how many groups, 3 tells us how many in each group, and the x means "groups of." Model three representations side by side:
- Equal groups: Draw 4 circles with 3 dots inside each.
- Array: Draw 4 rows of 3 dots arranged in a rectangle. Point out rows and columns.
- Repeated addition: Write 3 + 3 + 3 + 3 = 12.
Show that all three represent the same problem: 4 x 3 = 12. Do two more examples (2 x 5 and 3 x 4) using all three representations. For each, have students follow along at their desks using counters to build the groups and arrays physically. Emphasize that the order of the factors can switch (3 x 4 = 4 x 3) — this is the commutative property. Show this with arrays: rotate a 3 x 4 array to become a 4 x 3 array.
Guided Practice (10 minutes)
Write 4 problems on the board. Students solve each one at their desks and represent it two ways (their choice of equal groups, array, or repeated addition):
- 2 x 6 (2 groups of 6)
- 5 x 3 (5 groups of 3)
- 4 x 4 (4 groups of 4)
- 3 x 5 (3 groups of 5)
After each problem, have a student share their work under the document camera. Ask: "Who used a different representation? Did you get the same answer?" Reinforce that different strategies lead to the same product. Address common errors: students who confuse the number of groups with the number in each group.
Independent Practice (10 minutes)
Students work through word problem task cards at their desks. Each card presents a real-world scenario:
- "There are 3 fish tanks. Each tank has 5 fish. How many fish are there altogether?" (3 x 5 = 15)
- "A baker made 4 trays of cookies. Each tray has 6 cookies. How many cookies did the baker make?" (4 x 6 = 24)
Students write the multiplication equation and draw an array or equal groups to show their work. They complete at least 6 of 10 cards. Early finishers create their own word problem on the back of their recording sheet for a partner to solve.
Assessment
- Formative: Circulate during guided practice. Check that students can build arrays with the correct dimensions and write the matching equation.
- Summative: Exit ticket with 10 problems — 5 equation-only (e.g., 3 x 4 = ___) and 5 word problems requiring a drawing and an equation. Target: 8 out of 10 correct.
Differentiation
- Struggling learners: Limit facts to 2s and 5s. Provide pre-drawn array templates where students just fill in the dots. Use manipulatives for every problem. Offer a multiplication chart for reference after attempting each problem independently.
- ELL students: Pre-teach "groups of," "rows," "columns," "each," "altogether," and "in all" with picture cards. Simplify word problem language and include illustrations. Allow students to explain their thinking using drawings and gestures.
- Advanced learners: Extend to facts through 10 x 10. Introduce the concept of division as the inverse of multiplication. Challenge them to find all the arrays that make 24 (1x24, 2x12, 3x8, 4x6).
- Students with IEPs: Provide graph paper for drawing arrays (keeps dots organized). Allow use of a multiplication chart after the first attempt. Reduce exit ticket to 5 problems. Pair with a supportive partner during task cards.
Closure (3 minutes)
Play "Quick Flash" — hold up a card showing an array (e.g., 3 rows of 4) and students write the multiplication equation on their whiteboards as fast as they can. Do 5 rounds. Then ask: "How is multiplication connected to addition? Could you use addition to solve any multiplication problem?" Help students articulate that multiplication is a shortcut for repeated addition. Preview tomorrow's lesson on multiplying by 2s and 5s using skip counting.