Arrays for 3s and 4s

Overview

In this lesson, students build understanding of multiplication as equal groups and develop fluency with 3s and 4s through arrays, repeated reasoning about division, and brief practice. This is Lesson 3 of 12 in the unit “Mastering Multiplication Basics,” building on prior work with multiplication as counting groups.

Learning intentions

• Students will interpret multiplication as “equal groups” (e.g., 3 × 4 means 3 groups of 4).
• Students will solve multiplication and related division facts for 3s and 4s within 100 using models and strategies.
• Students will use arrays to describe products and recognize patterns.
• Students will explain how multiplication and division are related for 3s and 4s.

Success criteria

• I can draw or use an array to show 3 × 4 and explain what each row and column means.
• I can write an equation for a multiplication story and find the product.
• I can use what I know about multiplication to solve a division fact (and vice versa).
• I can fluently multiply and divide within 100 using strategies for 3s and 4s.

Curriculum links

• Operations and Algebraic Thinking: interpret products of whole numbers as equal groups.
• Operations and Algebraic Thinking: apply properties of operations as strategies to multiply and divide (including commutative and distributive reasoning).
• Operations and Algebraic Thinking: determine unknown whole numbers in multiplication/division equations.
• Operations and Algebraic Thinking: use multiplication and division within 100 to solve word problems involving equal groups and arrays.
• Operations and Algebraic Thinking: fluently multiply and divide within 100, including using the relationship between multiplication and division; know products of two one-digit numbers from memory by the end of Grade 3.

Lesson structure (60 minutes)

1. 0–5 min · Warm-up (Fact Review). Teacher displays a quick “3s and 4s” slide with 6 blanks (e.g., 3×□=12, □×4=20) and students write answers on boards. Students share one strategy for how they knew each answer.

2. 5–15 min · Direct teach (Arrays as Equal Groups). Teacher models a 3×4 array using square tiles on a grid and labels rows and columns (3 rows, 4 columns). Teacher narrates: “There are 3 groups, and each group has 4.” Students build the same array with manipulatives and use the array to say the product aloud.

3. 15–25 min · Guided practice (From array to equations). Teacher points to the array and asks students to write the matching multiplication equation and then a related division equation (example: for a 3×4 array, 3×4=12, and 12÷4=3 and 12÷3=4). Students complete a short worksheet page with three arrays: one for 3×3, one for 3×4, one for 4×3. For each, they write:

• the multiplication equation
• one division equation that matches the array

4. 25–35 min · Hands-on rotation (Stations with turn-and-talk). Teacher sets up two stations (timer on the board) and one whole-class check-in.

• Station A (Array Builder): students use grid paper or tiles to make a specified product (e.g., 4×4, 3×5 not exceeding grade range for this unit), then record the multiplication and one division fact.
• Station B (Match & Explain Cards): students match “3×4,” “12 objects,” and “12÷3” cards, then explain which cards connect and why. Students rotate every 5 minutes; teacher circulates with prompts: “What does each row show?” “How do you know your division answer?”

5. 35–45 min · Strategy talk (Properties to compute efficiently). Teacher reviews two quick facts from memory (e.g., 3×4=12, 4×3=12) and asks students to explain why reversing factors keeps the product the same. Teacher models using distributive thinking only as a support strategy: “To find 4×6, I can think 4×(3+3)=4×3+4×3.” Students complete a “Strategy Choice” mini-sheet for 3s and 4s where they choose a strategy and solve 4 problems (two multiplication, two division). Prompts include: “Use the relationship between multiplication and division” or “Use known facts to make a new one.”

6. 45–55 min · Word problems with symbols (Unknowns). Teacher reads two brief word problems with drawings suggested:

• Problem 1 (equal groups): “There are 3 rows with 4 chairs in each row. How many chairs?” Students draw and write 3×4=__.
• Problem 2 (related division/unknown): “There are 12 stickers in equal groups of 3. How many groups?” Students write 12÷3=__ or __×3=12. Teacher reminds students to use a box or symbol for the unknown. Students work independently, then check with a partner using the arrays/representations.

7. 55–60 min · Exit ticket (Quick assessment). Students complete 4 items:

• Two multiplication facts for 3s and 4s (e.g., 3×5, 4×4)
• One related division fact (e.g., 12÷4)
• One unknown equation (e.g., 4×?=16 or?×3=15)

Resources

• Base-ten or square tiles and grid mats
• Array templates (3×3, 3×4, 4×3) on paper
• Grid paper
• Fact cards and match cards for 3s and 4s
• Station task sheets (one per station)
• Whiteboards/markers for warm-up
• Worksheet with arrays and equation writing prompts
• Mini “Strategy Choice” sheet
• Exit ticket slips

Assessment

• Formative during warm-up: listen for correct answers and reasoning language (“groups,” “rows,” “columns”).
• Formative during stations and guided practice: teacher checks that students can connect an array to both multiplication and at least one related division equation.
• Exit ticket: verify fluency with 3s and 4s and accuracy using multiplication-division relationships and unknowns.

Differentiation

• Support: provide sentence frames for explanation (“In 3×4, ___ groups of ____. That makes ___ total.”; “Because 3×4=12, 12÷4=__.”).
• Support: allow using an array template so students focus on equations rather than drawing complexity.
• Extension: for students ready early, add one challenge item: write two division equations that match a given array (e.g., for 3×4=12, write 12÷3 and 12÷4).
• EAL/SEN: offer a word bank (row, column, group, total, equation) and encourage pointing to the array while speaking answers.