Patterns for Fives and Tens

Overview

This is lesson 4 of 8 in the unit Multiplication and Division Facts. Students investigate patterns in the 5 and 10 multiplication facts, using equal groups, skip-counting and place value to explain why the patterns work.

Learning intentions

Students will:

• Model 5 and 10 equal groups using materials and diagrams.
• Notice and describe patterns in multiples of 5 and 10.
• Use known 10s facts to support recall of 5s facts.
• Explain the relationship between factors, products and place value.

Success criteria

• I can model 5 and 10 equal groups.
• I can use skip-counting and place value to find products.
• I can recall multiplication facts for 5 and 10 up to 10 groups.
• I can explain why multiples of 5 end in 0 or 5.

Curriculum links

• Recall and demonstrate proficiency with multiplication facts involving 5 and 10.
• Represent multiplication using equal groups, arrays, number lines and materials.
• Recognise and explain number patterns using place-value knowledge.
• Communicate mathematical reasoning using appropriate vocabulary and representations.

Lesson structure (50 minutes)

1. 0–5 minutes – Hook and readiness

Display the question, “Why do multiples of 5 end in 0 or 5?” using the opening pattern question. Students count aloud in 5s and 10s while the teacher records the sequence on the board. Briefly introduce the words multiple, product, factor, place value, ones digit, tens and half.

2. 5–17 minutes – Explicit teaching

Use the worked examples for 5s and 10s to model 5 × n with counters arranged in five-frames and jumps on a number line. Ask students to predict each product before revealing it, then highlight that products in the 5s sequence alternate between a ones digit of 5 and 0.

Connect 10 × n to place value using bundles of ten: 10 × 4 is four tens, or 40. Emphasise that multiplication by 10 means making equal groups of ten, not simply “adding a zero”. Demonstrate that 5 × n is half of 10 × n when n is even, such as 5 × 6 = half of 10 × 6. Model how known 10s facts can support 5s facts.

3. 17–32 minutes – Guided investigation

Place students in groups of three or four. Distribute the 5s and 10s pattern investigation and provide hundred charts, counters, ten-frames and bundles of ten. Students shade or mark multiples of 5 and 10, predict missing products and check their predictions with materials.

Pause for a class discussion using the hundred-chart investigation prompts. Ask:

• What do you notice about the ones digits?
• How are the 5s and 10s patterns connected?
• Why is every second multiple of 5 also a multiple of 10?

Connect the patterns to familiar Australian contexts. Display clocks and Australian coin images and discuss groups of five minutes, 5-cent coins and 10-cent coins. Students explain one context to a partner using a multiplication sentence.

4. 32–45 minutes – Independent practice

Students complete the remaining sections of the 5s and 10s pattern investigation independently. Include fact cards, pattern statements and two short problems, such as:

• Mia has 7 groups of 5-cent coins. How many cents does she have?
• There are 6 bundles of 10 counters. How many counters are there?

Students must show a model, skip-counting sequence or place-value explanation for at least one answer. Ask early finishers to prove or disprove statements such as “All multiples of 5 end in 0” and “5 × 10 means 5 + 10”.

5. 45–50 minutes – Formative assessment and exit ticket

Hand out the multiplication facts exit ticket slips. Students answer and explain: “How are 5 × 7 and 10 × 7 connected? What are their products? Why do multiples of 5 alternate between 5 and 0?”

Use the final reflection prompts to invite two or three students to share their reasoning. Collect the slips to identify students who need further work with equal groups, place value or fact recall.

Resources

• the complete 5s and 10s teaching deck
• the 5s and 10s pattern investigation
• Multiplication Facts Exit Ticket Slips
• Bundles of ten
• Counters and five-frames
• Ten-frames
• Hundred charts
• Number lines
• Clocks and Australian 5-cent and 10-cent coin images
• Fact cards and mini-whiteboards

Assessment

• Listen during modelling and group discussion for accurate use of factor, product, multiple, ones digit and tens.
• Observe whether students represent 5 and 10 equal groups accurately and connect 10 × n with tens place value.
• Review the worksheet and exit ticket for correct facts and explanations, particularly the relationship between 5 × 7 and 10 × 7.

Differentiation

• Support students with concrete bundles, counters and ten-frames. Rehearse skip-counting orally with a partner and provide sentence stems: “I know ___ because ___.”
• Reduce the initial task to products up to 5 × 5 and 10 × 5, then build towards facts to 10.
• Provide visual number lines, highlighted ones digits and partially completed pattern statements for students requiring additional support, including EAL and students with learning difficulties.
• Extend confident students by asking them to derive 5s facts from 10s facts, explain when “half of” is useful, and prove or disprove additional pattern statements.