Patterns and Strategies for 3s

Overview

Lesson 2 of 8 in the unit Multiplication and Division Facts. Students develop fluency with multiplication facts for 3 by building equal groups, recognising patterns, using arrays and explaining efficient strategies.

Learning intentions

Students will:

• build and represent the 3-times facts using equal groups and arrays
• recognise the skip-counting pattern in multiples of 3
• use known facts and efficient strategies to solve facts for 3
• connect related multiplication facts using the commutative property
• explain and record multiplication strategies accurately

Success criteria

• I can build 3-times facts with equal groups.
• I can use skip-counting, arrays and known facts to solve a fact.
• I can explain a strategy, such as doubling and adding one more group.
• I can record multiplication facts accurately.

Curriculum links

• Develop fluency and recall of multiplication facts within the required Year 3 number range, with a focus on multiplying by 3.
• Represent multiplication using equal groups, arrays, repeated addition and number lines.
• Use known facts, patterns, doubling and related facts to solve unknown facts.
• Explain mathematical thinking, use appropriate mathematical language and check whether an answer is reasonable.

Lesson structure (50 minutes)

1. 0–5 minutes – Launch and connect

Display the opening question from the introduction and hook slides: “If one group has 3 objects, how many objects are in 2, 3, 4 and 5 groups?” Students make quick predictions, then build the groups with counters. Introduce the words triple, three-times, multiple and product.

2. 5–17 minutes – Explicit teaching

Use the equal-groups and bead-string slides to build 3 × 1 through 3 × 10 with counters and a bead string. Record the products: 3, 6, 9, 12, 15, 18, 21, 24, 27 and 30. Ask, “What changes each time?” and identify that each next product increases by 3.

Model the same facts on a number line and as arrays. Connect 3 × 4 and 4 × 3, explaining that both have the same product even though the groups are described differently. Model efficient strategies: 3 × 6 as double 6 plus one more 6 (12 + 6), and 3 × 5 as 3 × 4 plus 3 (12 + 3). Emphasise that fluency includes explaining a strategy, not only memorising an answer.

3. 17–32 minutes – Guided practice

As a class, complete the fact-family chart on the 3s facts and strategy worksheet. Invite students to explain how each fact can be linked to the previous fact. Use the multiplication facts strategy mat as a reference for arrays, number lines, related facts and decomposition.

In pairs, students draw or build an array for a selected 3s fact, write the matching equation and explain it to their partner. Partners check that the number of rows, objects in each row and product agree. Prompt with: “What do you know already?” and “How could you solve this without starting at one?”

4. 32–45 minutes – Independent practice and game

Distribute the 3s facts and strategy worksheet. Students complete the mixed 3s grid and missing-factor questions, showing a strategy for at least two answers. Early finishers play “Roll, multiply by 3, explain” using a die and game board: roll, multiply the number by 3, record the product and explain the strategy to a partner. Students may use counters, bead strings or a number line when needed.

5. 45–50 minutes – Fluency check and exit response

Conduct a brief individual or small-group fluency check using selected facts, including one from the beginning, middle and end of the 3s sequence. Listen for accurate recall and strategy language. Students answer the exit question on the worksheet: “Which strategy could solve 3 × 7? Show it.” They also respond orally or in writing: “Why does each next 3s fact increase by 3?”

Resources

• the complete 3s multiplication teaching deck
• the 3s facts and strategy worksheet
• the multiplication facts strategy mat
• Counters, approximately 150 for groups of three
• Bead strings or grouped beads
• Floor or desk number lines
• 3s fact cards
• Mini-whiteboards and markers
• Dice and simple game boards
• Pencils and erasers

Assessment

• Observe representations and explanations during pair work: check equal groups, arrays, correct equations and use of terms such as multiple and product.
• Record results from the fluency check, noting accurate facts, skip-counting errors and whether students can use a known fact.
• Use the exit response to assess whether students can solve 3 × 7 and explain why consecutive 3s facts increase by 3.

Differentiation

• Support students with counters, number lines, bead strings, fact strips and the strategy mat. Begin with 3 × 1 to 3 × 5 before extending to 3 × 10.
• Provide sentence stems: “I know ___, so I can solve ___”; “There are ___ groups of 3”; and “The product increases by 3 because…”.
• For EAL learners and students requiring additional support, model vocabulary with visuals, gestures and repeated oral rehearsal. Pair students strategically and accept drawn arrays alongside written explanations.
• Extend confident students with missing-factor questions such as 3 × __ = 24, and true/false statements such as “3 × 6 = 3 × 5 + 1”. Require them to justify each answer using an array, related fact or another efficient strategy.