Double-Double 4s Facts

Overview

Students use doubling twice to derive multiplication facts for 4, connecting equal groups, arrays, repeated addition and related division facts. The lesson is designed for 25 Year 3 students and supports mathematical reasoning, fluency and clear communication.

Learning intentions

Students will:

• Use doubling twice to solve 4 × n.
• Represent 4s facts with equal groups, arrays and repeated addition.
• Explain how multiplication and division facts are connected.
• Apply the strategy to a simple real-life problem.

Success criteria

• I can solve a 4s fact by doubling twice.
• I can show a 4s fact using an array, equal groups or repeated addition.
• I can explain my strategy using mathematical language.
• I can use a related division fact to check my answer.

Curriculum links

• Multiplication and division: recall and derive facts using mental strategies and known facts.
• Mathematical modelling: represent problems using equal groups, arrays and number sentences.
• Reasoning: explain strategies, identify errors and justify answers.
• Communication: use mathematical vocabulary, diagrams and equations to share thinking.

This aligns with Tasmanian Year 3 Mathematics expectations for developing multiplication and division fluency, using efficient mental strategies, representing situations and explaining mathematical reasoning.

Vocabulary

• multiply, multiplication, groups of, array, row, column
• double, twice, repeated addition
• divide, division, share equally, fact family

Lesson structure (45 minutes)

1. 0–7 minutes – Learning intentions and warm-up

Open with the hook and learning-intention slides. Display four groups of three counters or dots and ask: “How could we find the total without counting every dot?” Students discuss with a partner, then share strategies such as 3 + 3 + 3 + 3, 4 × 3 or doubling 3 twice.

State: “Today we will use double-double to solve 4s facts.” Briefly rehearse doubles to 10 using hands, counters or mini-whiteboards: double 2, 4, 5, 7 and 10.

2. 7–17 minutes – Teacher modelling

Use the modelling slides and draw each example as an array.

• 4 × 3: “I know double 3 is 6. Double 6 is 12. Therefore, 4 × 3 = 12.” Show four rows of three, 3 + 3 + 3 + 3 and the array.
• 4 × 6: “First double 6 to get 12. Double 12 to get 24. So, 4 × 6 = 24.” Show two groups of 6 becoming four groups of 6.
• 4 × 8: “Double 8 is 16. Double 16 is 32. Therefore, 4 × 8 = 32.”

Model the related division facts: 24 ÷ 4 = 6 and 24 ÷ 6 = 4. Think aloud: “The multiplication fact tells me the total and groups. Division helps me find a missing group size or number of groups.” Emphasise that 4 × 6 and 6 × 4 have the same product, although the rows and columns can be arranged differently.

3. 17–27 minutes – Guided practice

Display the guided-practice prompts in the partner-practice slides. Students work in pairs with mini-whiteboards. Give one fact at a time: 4 × 2, 4 × 5, 4 × 7 and 4 × 9. Partners must show the double-double steps and one representation, then hold up boards.

Invite partner talk using: “First I doubled ___ to get ___. Then I doubled ___ to get ___.” Ask selected students to explain.

Include error analysis: display “4 × 7 = 14 because double 7 is 14.” Partners discuss: “What is correct? What needs changing?” Students correct it to double 14, giving 28, and explain why one doubling is not enough.

4. 27–40 minutes – Independent work

Distribute the graduated double-double worksheet. Students work independently, using drawings where helpful.

• Part A: Build the strategy: complete 4 × 1, 4 × 2, 4 × 3 and 4 × 4 using “double, then double again”.
• Part B: Apply the strategy: solve 4 × 5, 4 × 6, 4 × 7, 4 × 8, 4 × 9 and 4 × 10. Record a matching repeated-addition sentence for two questions.
• Part C: Fact families: complete related division facts for 16, 24 and 32.
• Part D: Word problem: “There are 4 trays with 8 muffins on each tray. How many muffins are there altogether? Show your strategy.”

Students who finish may complete the optional challenge: “A number multiplied by 4 equals 36. What is the number? Explain how division or double-double helps.”

Circulate, check whether students are doubling twice rather than skip-counting without understanding, and provide immediate feedback.

5. 40–45 minutes – Exit check

Use the plenary and exit-check slides. Students answer independently on the back of their worksheet or a small piece of paper:

• Calculation: Solve 4 × 7 using double-double.
• Strategy explanation: Explain how an array or equal groups shows 4 × 6 = 24.
• Transfer: Four children each collect 5 shells. How many shells do they collect altogether? Show a number sentence and explain your strategy.

Collect responses at the door. Ask one or two students to share a clear explanation, then restate the key idea: “For 4 × n, double n, then double the result.”

Resources

• the complete 4s-facts teaching deck
• the graduated double-double worksheet
• Mini-whiteboards and markers
• Counters, linking cubes or small classroom objects
• Prepared arrays or board grid
• Pencils and erasers
• Visual vocabulary displayed on the board

Assessment

• Observe warm-up and partner explanations for correct use of doubling twice.
• Check mini-whiteboards for accurate calculations, representations and error corrections.
• Use the worksheet and exit check to identify students needing further work with doubles, arrays or division connections.

Differentiation

• Support students with counters, a 2s-facts reference, partially completed arrays and sentence frames: “Double ___ is ___. Double ___ is ___.”
• Pair students strategically and allow oral explanations, drawing or concrete materials before recording equations.
• For EAL learners and students requiring adjustments, use gesture, visual arrays, repeated modelling and explicitly rehearse vocabulary such as “groups of”, “total” and “equal”.
• Extend confident students by asking them to solve missing-factor problems, compare 4 × 6 and 6 × 4, or create and solve a 4s-facts word problem.