Lesson Plan
Divide & Conquer Lesson Plan
Students will solve multiplication and division word problems within 100 using equal groups and arrays, modeling their thinking with manipulatives and drawings.
Understanding equal groups and arrays builds foundational multiplicative reasoning and confidence, promoting fluency in solving real-world problems.
Audience
3rd Grade Students
Time
30 minutes
Approach
Hands-on modeling, guided practice, and independent application with manipulatives.
Materials
- Multiplication & Division Word Problem Cards, - Arrays & Equal Groups Worksheet, - Divide & Conquer Assessment Checklist, - Counters or Manipulatives, - Student Math Journals, - Pencils, and - Whiteboard and Markers
Prep
Material Preparation
5 minutes
- Print and cut Multiplication & Division Word Problem Cards
- Print enough copies of Arrays & Equal Groups Worksheet for pair work
- Gather counters or manipulatives and arrange at each table
- Review Divide & Conquer Assessment Checklist to understand criteria
- Arrange seating for partner collaboration
Step 1
Introduction
5 minutes
- Activate prior knowledge by reviewing arrays and equal groups
- Draw a simple array (e.g., 3 rows of 4) on the whiteboard
- Ask volunteers to describe what they observe and connect to 3 × 4 = 12
- Emphasize how arrays and equal groups represent multiplication and division
Step 2
Model Problems
5 minutes
- Select a card from Multiplication & Division Word Problem Cards and read aloud
- Model solving: draw an array on the whiteboard and use counters to represent the problem
- Think aloud each step: grouping, counting, writing the equation
- Demonstrate how to record work in the math journal
Step 3
Guided Practice
10 minutes
- Students pair up with counters and a copy of Arrays & Equal Groups Worksheet
- Distribute 2–3 different word problem cards to each pair
- Pairs draw arrays or group counters, write equations, and explain reasoning in journals
- Teacher circulates, asks prompting questions, and offers feedback
Step 4
Independent Practice & Discussion
7 minutes
- Students individually solve a new word problem in their math journals
- Draw arrays or equal groups, write the corresponding equation, and add a brief explanation
- Invite 2–3 volunteers to share their solution strategy and answer with the class
Step 5
Closure & Assessment
3 minutes
- Recap key points about arrays and equal groups for solving problems
- Use Divide & Conquer Assessment Checklist to mark student understanding
- Ask students to write a quick thumbs up/down reflection on their confidence in journals
- Collect journals for review and plan any needed next steps
Slide Deck
Divide & Conquer: Multiplication & Division within 100
Learning Target: Solve word problems using arrays and equal groups (2.OA.2)
Materials: Counters, whiteboard, math journals,
Word Problem Cards,
Arrays & Equal Groups Worksheet
Welcome everyone! Introduce today’s goal: solving multiplication and division word problems within 100 using arrays and equal groups. Briefly point out the standard (2.OA.2) and materials students will use.
Introduction: Arrays & Equal Groups
- Review what arrays and equal groups show
- Example: 3 rows of 4 counters = 12 total
- Discuss how the same model can show division
Activate prior knowledge. Draw a 3 × 4 array on the board. Ask volunteers what they notice and how that relates to 3 × 4 = 12. Highlight how arrays visually represent multiplication and division.
Modeling Problem Solving
- Read a problem from Word Problem Cards
- Draw an array and arrange counters
- Write the matching equation in your journal
- Explain your thinking aloud
Model a complete problem. Choose a card from the Word Problem Cards and read it aloud. Demonstrate drawing the array, grouping with counters, and writing the equation. Think aloud each step so students follow your reasoning.
Guided Practice
- Pair up and get counters + Worksheet
- Each pair solves 2–3 word problems
- Draw arrays or equal groups and write equations
- Explain reasoning in your journal
Guide students through practice in pairs. Distribute worksheets and counters. Circulate, ask guiding questions, and reinforce correct reasoning. Provide feedback and clarify misconceptions.
Independent Practice & Discussion
- Individually solve a new word problem in your journal
- Draw the array or equal groups and write the equation
- Add a brief explanation of your strategy
- 2–3 volunteers share their solutions
Transition to independent work. Instruct students to tackle a new problem on their own. After a few minutes, invite volunteers to share their strategy and solution. Reinforce clear explanations.
Assessment
- Check work with Divide & Conquer Assessment Checklist
- Collect math journals for review
- Quick thumbs up/down on confidence
Use the assessment checklist to quickly gauge understanding. Collect journals and have students give a confidence signal (thumbs up/down). Note students who need extra support.
Closure
- Recap: Arrays & equal groups model multiplication/division
- Ask: Which strategy helped you the most?
- Preview next practice or upcoming lessons
Wrap up the lesson by reinforcing key takeaways. Ask students which representation (array or groups) helped them most and why. Preview next steps or homework practice.
Worksheet
Arrays & Equal Groups Worksheet
Instructions: For each problem below, draw an array or equal groups to represent the situation. Then write the matching multiplication or division equation and solve.
1. Lucy arranges 4 rows of 5 chairs for an assembly.
Draw the array below:
Write the equation:
Answer: _____ chairs in all.
2. Ramon has 24 candies. He wants to put them into equal groups of 6 candies each.
Draw the equal groups below:
Write the equation:
Answer: _____ candies in each group.
3. A garden has 6 rows with 8 plants in each row.
Draw the array below:
Write the equation:
Answer: _____ plants in all.
Good luck! Use your counters or drawings to help you think through each problem.
Activity
Multiplication & Division Word Problem Cards
Use these cards during modeling and guided practice. Read each problem aloud, then draw arrays or equal groups and write the matching equation.
Card 1:
Sara has 8 boxes of crayons. Each box has 6 crayons. How many crayons does Sara have in all?
Card 2:
A farmer plants 5 rows of 7 corn plants each. How many corn plants are there in the field?
Card 3:
There are 9 shelves with 8 books on each shelf. How many books are on all the shelves?
Card 4:
Dylan has 36 stickers. He wants to share them equally among 4 friends. How many stickers will each friend get?
Card 5:
Maria baked 56 cookies and packed them equally into 7 boxes. How many cookies go into each box?
Card 6:
Mr. Lopez has 48 pencils. He divides them equally into 6 pencil cases. How many pencils are in each case?
Rubric
Divide & Conquer Assessment Checklist
Use this checklist to evaluate students’ work on drawing arrays/equal groups, writing equations, explaining their thinking, and using tools. Score each criterion from 1–4.
| Criterion | 4 – Exemplary | 3 – Proficient | 2 – Developing | 1 – Beginning |
|---|---|---|---|---|
| Representation (Drawing) | • Drawing is clear, neat, and precisely models the entire problem. | • Drawing is accurate with minor omissions; generally represents the problem. | • Drawing is partially accurate; shows some understanding but lacks clarity or completeness. | • Drawing is incorrect, very incomplete, or missing. |
| Equation Accuracy | • Equation exactly matches the drawing and problem context; correct solution. | • Equation matches the problem with one small error; solution nearly correct. | • Equation shows an attempt but has calculation errors or mismatch with the drawing. | • Equation is incorrect or missing. |
| Explanation/Reasoning | • Explanation is thorough, uses mathematical language, and clearly justifies each step. | • Explanation is clear and shows reasoning, though may lack some detail. | • Explanation is vague or incomplete; shows partial reasoning. | • Little or no explanation of reasoning. |
| Use of Tools & Neatness | • Effectively uses counters/journals; work is well organized and easy to follow. | • Uses tools appropriately; work is mostly organized. | • Uses tools inconsistently; work is somewhat disorganized. | • Does not use tools appropriately; work is messy or hard to follow. |
Total Score: _____ / 16
Next Steps/Comments:
Script
Divide & Conquer: Teacher Script
Materials
- Counters or manipulatives
- Whiteboard and markers
- Student math journals and pencils
- Multiplication & Division Word Problem Cards
- Arrays & Equal Groups Worksheet
- Divide & Conquer Assessment Checklist
1. Introduction (5 minutes)
Teacher: “Good morning, mathematicians! Today our learning target is to solve multiplication and division word problems within 100 using arrays and equal groups.”
Teacher: “First, let’s review arrays. Watch me draw 3 rows of 4 dots on the board.”
[Teacher draws a 3×4 array]
Teacher: “Who can tell me how many dots there are in total? Turn and tell your partner.”
Wait 20 seconds.
Teacher: “Okay, Mia, what did you and your partner say?”
Student: “Twelve.”
Teacher: “Right! We can say 3 × 4 = 12. Arrays help us see multiplication.”
Teacher: “Now, notice we can also use that same drawing to show division. If someone asked, ‘How many dots in each of 3 rows if there are 12 dots total?’ we could ask, 12 ÷ 3 = ?”
Teacher: “Arrays and equal groups are two ways to represent multiplication and division. Let’s see this in a word problem!”
2. Model Problems (5 minutes)
Teacher: “I’ll pick Card 1 from our Word Problem Cards.”
[Teacher reads aloud]
“Sara has 8 boxes of crayons. Each box has 6 crayons. How many crayons does Sara have in all?”
Teacher: “Sara has 8 equal groups, each of 6 crayons. I’ll draw 8 rows of 6 dots.”
[Teacher draws an 8×6 array and places counters if available]
Teacher (thinking aloud): “I see 8 rows. In each row I count 6. So the equation is 8 × 6 = ?”
[Teacher writes 8 × 6 = 48]
Teacher: “Sara has 48 crayons. I’ll record this in my journal: 8 × 6 = 48 and explain, ‘I drew 8 rows of 6 to find the total.’”
Teacher: “Notice how I grouped and drew before writing my equation. That helps me avoid mistakes.”
3. Guided Practice (10 minutes)
Teacher: “Now, at your tables, please grab counters and an Arrays & Equal Groups Worksheet. I’m going to give each pair two different Word Problem Cards.”
Teacher: “With your partner, follow these steps for each card:
- Read the problem aloud.
- Choose array or equal-groups drawing.
- Draw on your worksheet.
- Write the matching equation and solve.
- Explain your thinking to each other.”
Teacher (circulating): “Alejandro, show me how you decided to draw your groups. Which equation did you write?”
Prompting Questions:
- “What does each row or group represent?”
- “How did you know how many rows (or groups) to draw?”
- “Can you count to check your total?”
Teacher: “Great! I see you and Priya explained your reasoning clearly.”
4. Independent Practice & Discussion (7 minutes)
Teacher: “Now, please open your math journals. I’ll read one more problem for you to solve alone.”
Teacher (reading): “A school auditorium has 7 sections of seats. Each section has 9 seats. How many seats are in the auditorium?”
Teacher: “In your journal, draw an array or equal groups, write the equation, solve it, and add one sentence about how you solved it.”
Wait 2–3 minutes as students work.
Teacher: “Who would like to share? Jonas, can you show us your drawing and explain your steps?”
Volunteer shares. Teacher reinforces the clear parts of their explanation and asks a follow-up: “Why did you choose an array instead of equal groups?”
Invite one more volunteer.
5. Closure & Assessment (3 minutes)
Teacher: “Let’s recap. How do arrays help us solve multiplication problems?”
Students respond.
Teacher: “And how do equal groups help us with division?”
Students respond.
Teacher: “Thank you! Now, give me a quick thumbs up if you feel confident or thumbs down if you need more practice.”
[Students show their thumbs]
Teacher: “I’ll collect your journals and use the Divide & Conquer Assessment Checklist to see who needs extra support. Great work today—see you tomorrow for more practice!”