Multiplication With Numicon

Overview

In this Year 5 lesson, students revise multiplication as repeated addition, equal groups and arrays using Numicon. They connect multiplication facts with related division facts and extend a growing number pattern to make a brief link with algebraic thinking.

Learning intentions

Students will:

• Represent multiplication using repeated addition, equal groups and arrays.
• Use Numicon to solve and explain facts for the 2s, 3s, 4s, 5s, 8s and 10s.
• Connect multiplication facts with corresponding division facts.
• Continue and describe a growing number pattern based on repeated addition.
• Communicate mathematical thinking using drawings, equations and words.

Success criteria

• I can show a multiplication fact with Numicon, an array and repeated addition.
• I can explain how equal groups help me find a product.
• I can use a multiplication fact to work out a related division fact.
• I can continue a number pattern and explain the rule.

Curriculum links

• Mathematics and Statistics, Phase 2: Number—multiplication and division strategies.
• Mathematics and Statistics, Phase 2: Number—recall and use multiplication and division facts.
• Algebra—Equations and Relationships: recognise, continue and describe growing number patterns.
• Mathematical reasoning, representation and communication through practical investigation and discussion.

Prior knowledge

Students should recognise Numicon shapes and their values, count forwards in 2s, 5s and 10s, and understand addition as combining quantities. Briefly check that students can represent 3 + 3 + 3 and identify it as three equal groups of three.

Vocabulary

factor, product, multiple, equal groups, array, repeated addition, multiplication, division, quotient, fact family, pattern, rule

Lesson structure (60 minutes)

1. 0–7 min · Warm-up. Display a visual of four groups of five Numicon shapes using the hook and warm-up slides and ask, “How many are there altogether, and how could we show it in different ways?” Students think-pair-share, then record 5 + 5 + 5 + 5 and 4 × 5. Invite several representations and address the misconception that the order of the factors changes the total.

2. 7–17 min · Explicit teaching. Use the representation slides to model 3 × 4 as three equal groups of four, 4 + 4 + 4, an array with three rows of four, and the corresponding division facts 12 ÷ 4 = 3 and 12 ÷ 3 = 4. Teacher asks, “What stays the same in each representation?” Students rehearse the sentence frame: “___ groups of ___ equals ___, so ___ × ___ = ___.”

3. 17–30 min · Guided Numicon investigation. In groups of three, students use Numicon pieces, hoops or drawn circles to build teacher-given facts from the 2s, 3s, 4s, 5s, 8s and 10s. They record each as equal groups, repeated addition, an array and a fact family on the Numicon representation worksheet. Pause for formative questions: “How do you know the groups are equal?”, “Which known fact could help?”, and “How could you check using division?”

4. 30–42 min · Partner activity. Display the partner challenge instructions in the investigation and partner-task slides. Partners take turns choosing a target fact, building it with Numicon and giving their partner three clues: the repeated addition, the array dimensions and a related division fact. Partners check one another’s work and explain whether 3 × 8 and 8 × 3 show the same total but different group descriptions. Teacher listens for accurate mathematical language and records students needing further support.

5. 42–53 min · Independent practice. Students complete the individual section of the Numicon representation worksheet: represent 4 × 5, 8 × 3 and 6 × 10; complete related division facts; solve missing-factor equations such as □ × 4 = 20; and continue the pattern 4, 8, 12, 16, __, __, explaining the repeated-addition rule. Students may draw Numicon if practical materials are no longer available.

6. 53–60 min · Plenary and exit ticket. Revisit the key question in the plenary and exit-ticket slides: “How can one multiplication fact help us solve other facts?” Students share one strategy, then complete an exit ticket: (a) show 3 × 4 as repeated addition; (b) write one related division fact; (c) continue 5, 10, 15, __, __ and state the rule. Collect tickets as students leave.

Resources

• Numicon shapes or printed Numicon representations
• Hoops, small trays or paper circles for equal groups
• Mini-whiteboards and pens
• Multiplication with Numicon slide deck
• Numicon representation and practice worksheet
• Pencils, coloured pens and exercise books
• Exit-ticket slips or small pieces of paper
• Optional large Numicon model for teacher demonstration

Assessment

• During the warm-up, check whether students can move between a quantity, repeated addition and a multiplication equation.
• During group and partner work, ask students to justify equal groups, identify factors and use division to check a product.
• Use the independent task and exit ticket to identify students who can represent facts flexibly and those who need further practice with factor order, division or number patterns.

Differentiation

• Support students with pre-selected Numicon pieces, drawn group circles, a multiplication sentence frame and a fact-family triangle. Begin with 2s, 5s and 10s before moving to 3s, 4s and 8s.
• Pair students thoughtfully and allow oral explanations, pointing, drawing or use of a calculator only for checking after representation.
• Provide enlarged, high-contrast Numicon images and tactile access to pieces for students with visual, motor or processing needs. Give instructions one step at a time and check understanding privately.
• For multilingual learners, display the vocabulary with simple diagrams and use gestures for “groups”, “altogether” and “share”. Accept home-language discussion before students explain in English.
• Extend confident students by asking them to find two different arrays for the same product, derive an 8s fact from a 4s fact, or write a general rule for the growing pattern.