Flexible Multiplication Facts

Overview

Students use arrays and area models to partition factors, explain equivalent multiplication equations and solve missing-number problems. They apply these relationships to multiplication and division word problems, building on known facts, place value and equal-group representations.

Learning intentions

• Students will use the distributive property to flexibly partition numbers in multiplication problems.
• Students will use the equals sign to record equivalent number relationships.
• Students will find missing numbers in multiplication and division number sentences.
• Students will represent and solve word problems using appropriate number sentences.

Success criteria

• I can partition a factor and explain how an area model shows the parts.
• I can write equivalent equations and explain why both sides have the same value.
• I can use a related multiplication fact to find a missing number.
• I can choose multiplication or division for a word problem and explain my reasoning.

Curriculum links

• Multiplicative relations: represent and use the structure of multiplication and division to solve problems.
• Multiplicative relations: complete multiplication and division number sentences by finding missing values.
• Place value: use the role of zero and place value to work with multiples of 10.
• Students develop reasoning, problem-solving, communication and fluency through mathematical discussion and representation.

Key vocabulary

Factor, product, multiple, dividend, divisor, quotient, array, area model, partition, distributive property, equivalent, number sentence, missing value, equals sign.

Prerequisite knowledge

Students should recognise multiplication as equal groups and arrays, recall some multiplication facts to 10 × 10, understand division as sharing or grouping, partition two-digit numbers into tens and ones, and know that the equals sign means “has the same value as”.

Lesson structure (60 minutes)

1. 0–7 min · Hook and diagnostic. Open with the hook and diagnostic question and display: “Is 6 × 14 equal to 6 × 10 + 6 × 4? How do you know?” Students sketch or discuss an array, then share explanations. Check whether students see the equals sign as a relationship rather than an instruction to calculate.

2. 7–20 min · Explicit modelling. Use an enlarged array or area model to partition 14 into 10 and 4. Record:

6 × 14 = 6 × (10 + 4) 6 × 14 = (6 × 10) + (6 × 4) 6 × 14 = 60 + 24 = 84

Model a second example, 7 × 13, asking students where the partition line should go and why 7 × 10 + 7 × 3 has the same value. Emphasise that the whole rectangle is unchanged; it is simply split into two smaller rectangles. Use the area-model modelling slides and refer to the multiplication strategy cards as a visual reminder of decomposition strategies.

3. 20–30 min · Guided practice. Complete examples together on the guided practice and problem-solving worksheet: 5 × 16, 8 × 12 and 9 × 15. Students draw an area model, partition one factor and write an equivalent number sentence. Pause after each example for partner explanations. Ask: “Which factor did you partition?”, “What does each smaller rectangle represent?” and “How does the equation prove the answer?”

4. 30–43 min · Collaborative differentiated tasks. In groups of three, students complete the appropriate section of the differentiated multiplication and division tasks. Support groups use arrays and partitioning prompts for facts such as 4 × 13 and 6 × 12. Core groups solve missing-value equations such as 7 × □ = 56, □ × 6 = 42, 48 ÷ □ = 8 and □ ÷ 7 = 6, recording a related fact or model. Extension groups solve equations with a missing factor or dividend, such as □ × 14 = 84 and 96 ÷ □ = 12, then create a different equation with the same answer. Students must agree on and explain each solution before recording it.

5. 43–54 min · Word problems and reasoning. Display the problems on the collaborative word-problem and discussion slides. Pairs solve one multiplication and one division problem, drawing an array, area model or equal-groups representation before writing a number sentence. For example: “There are 6 rows of 14 chairs. How many chairs are there?” and “84 chairs are placed equally into 6 rows. How many chairs are in each row?” Students compare the related equations 6 × 14 = 84 and 84 ÷ 6 = 14. Invite pairs to explain how the context determines the operation.

6. 54–60 min · Plenary and exit ticket. Revisit the hook and ask students to complete: 8 × 13 = 8 × 10 + 8 × □; □ × 7 = 49; and “Explain why 8 × 13 and 8 × 10 + 8 × 3 are equivalent.” Students complete the exit section of the reflection and exit-ticket page independently. Collect responses to identify students needing further support.

Resources

• the complete multiplication and division slide deck
• the modelling, practice, problem-solving and exit-ticket worksheet
• the multiplication strategy cards
• Large array or area-model display
• Mini-whiteboards and markers
• Grid paper
• Counters or square tiles
• Pencils and highlighters

Assessment

• Listen for explanations that connect each partial product to a part of the area model, not simply answers obtained by recall.
• Question individuals during guided and group work: “What does the equals sign tell us?”, “How could division help you check this answer?” and “What related fact do you know?”
• Use the exit ticket to assess partitioning, equivalent equations, missing-value reasoning and the choice of operation in a context.

Differentiation

• Support students with pre-drawn area models, counters, a multiplication chart, sentence starters (“I partitioned ___ into ___ and ___ because…”), and smaller factors such as 3 × 12.
• Provide oral rehearsal, paired reading of word problems and illustrated vocabulary for EAL/D learners. Accept explanations through drawing, speaking or labelled equations before requiring a written explanation.
• For students requiring additional support, work with a teacher-led group using equal groups and fact families, explicitly connecting multiplication and division.
• Extend confident students by asking them to find two different partitions for the same product, create a word problem for a missing-value equation, or prove that reversing the factors gives an equivalent product.
• Address misconceptions: the equals sign does not mean “write the answer”; 6 × 14 is not 6 × 10 + 4; the partitioned parts must recombine to make the original factor; and division equations must match the grouping described in the problem.