Multiples Patterns

Overview

In this 4th lesson of 10 for “Mastering Times Tables”, you will identify and explain patterns in the 5 and 10 times tables. You will use the patterns to strengthen recall, justify answers, and check for mistakes.

Learning intentions

WALT: Recognize and use patterns to learn multiplication, focusing on the 5 and 10 times tables.

Success criteria

• I can state the pattern for multiplying by 5.
• I can state the pattern for multiplying by 10.
• I can use a pattern to quickly find a product in the 5 or 10 times table.
• I can explain how the pattern helps me check whether an answer makes sense.

Curriculum links

• Mathematics (Number, Year 10): Use known multiplication facts to solve problems and explain reasoning using patterns and structure.
• Mathematics (Number, Year 10): Represent and apply multiplication in ways that support efficient calculation and checking.
• Mathematics (Number, Year 10): Communicate mathematical reasoning clearly, including how patterns justify results.

Lesson structure (30 minutes)

1. 0–3 min · Quick warm-up. Teacher says one multiplication fact at a time (e.g., 5×6, 10×7) and asks the student for the answer and a one-sentence reason. Student answers quickly and gives a short reason (e.g., “5×6 is half of 10×6” if they know it, or “I used the pattern”).

2. 3–10 min · Direct teaching: pattern discovery. Teacher writes a small table:

• For 5×: 5×1=5, 5×2=10, 5×3=15, 5×4=20, 5×5=25, 5×6=30
• For 10×: 10×1=10, 10×2=20, 10×3=30, 10×4=40, 10×5=50, 10×6=60 Teacher asks guiding questions: “What changes each time you increase the multiplier by 1?” and “What do you notice about the last digit?” Student identifies and states the patterns in their own words; teacher prompts with sentence starters if needed.

Key points to aim for (teacher models, then student repeats):

• Multiplying by 10: the result ends with 0, and each step increases by 10.
• Multiplying by 5: results end in 0 or 5, and each step increases by 5 (you add 5 each time you go up one in the times table).

3. 10–17 min · Pattern practice: “Find without counting from scratch”. Teacher calls out products to compute using pattern thinking, not repeated addition. Student writes the answer and explains the method using the pattern (e.g., “If I know 5×6=30, then 5×7=35 because I add 5.”).

Suggested prompts (choose those your student needs most):

• 5×8, 5×9, 10×8, 10×9
• 5×12 (discuss “12” as continuing the pattern), 10×12
• 5×0 (confirm the rule: 5×0=0) and 10×0=0 Teacher checks explanations: the student must reference the pattern (add 5 each step for 5×, add 10 each step for 10×, and the end-digit rule).

4. 17–23 min · Error-checking and “spot the pattern break”. Teacher gives a few incorrect statements for the student to evaluate: Examples:

• “5×6=25” (Is the answer correct? What should it be?)
• “10×4=60”
• “5×9=40” Student corrects each one and justifies the correction using the pattern (increment and last digit).

Teacher prompts:

• “How did the last digit help you?”
• “What would you expect the next answer to be, based on adding 5 or 10?”

5. 23–28 min · Mixed recall: mini-quiz with explanation. Teacher runs a 5-question mixed set alternating between 5× and 10× facts. Student answers and for each question provides one short reason linked to pattern rules.

Example set (keep it short for a 1-student setting):

• 5×7, 10×3, 5×10, 10×6, 5×4

6. 28–30 min · Exit ticket (quick check). Teacher asks two final questions:

• “Write the pattern rule for 5 times table.”
• “Write the pattern rule for 10 times table, and use it to find 10×9.” Student completes on paper or a notebook page.

Resources

• Notebook and pencil
• Printed “5 and 10 times table” strip (1–12 if possible)
• Whiteboard or scrap paper for teacher and student working
• Optional: counters or base-ten blocks to visualise “×10 ends in 0”

Assessment

• During warm-up: observe whether the student can give a reasoning sentence, not only an answer.
• During practice and error-checking: check that explanations reference a pattern (add 5/add 10 and end-digit).
• Exit ticket: ensure the student can state both pattern rules and apply one to calculate 10×9.

Differentiation

• Support: provide sentence starters such as “When I go up one in the times table, I add…”, “The last digit is…”, and allow the student to use a table strip.
• Support: if needed, start with smaller multipliers (1–6) and extend only after the student confidently states the pattern.
• Extension: ask the student to predict further products (e.g., “What is 5×13?”) and to explain the end-digit rule for 5×.
• EAL/SEN consideration: encourage oral explanations first, then convert to short written sentences; accept intuitive reasoning if it accurately uses the pattern.