1. Task
Draw an array with 5 rows of 7 counters. Split each row into 5 and 2. Label the two part totals and whole total, write both related division facts and explain how the split helps. Use separate paper if your diagram needs more space.
AC9M4A02 • Homework
Multiplication Facts to 10 × 10 and Derived Strategies worksheet
Use this printable homework sheet for written working, application and reflection alongside the online learning activities.
Open practiceEight written homework tasks
Complete each task independently. Show your reasoning and label all drawings. Use separate paper for larger arrays, timelines, timetables and card-game records. An adult should inspect the actual written or practical work using the answer guide.
2. Task
Draw 2 rows of 9. Copy the array to make 4 rows, then double again to make 8 rows. Label all three totals, write the matching multiplication facts and explain what stays the same and what doubles. Use separate paper for the drawings.
3. Task
Find 9 × 6 in two ways: first use 10 × 6, then use 3 × 6 followed by multiplying that result by 3. Write every calculation and explain why both methods count nine groups of 6.
4. Task
Build or draw 4 rows of 8 counters, then turn the array. Record the new row and column counts, write both multiplication facts and both division facts, and explain why the total stays equal.
5. Task
Without a calculator, solve 18 × 6 and 126 ÷ 7. Show useful partitions, name the smaller multiplication facts you use and check each answer with the inverse operation.
6. Task
A student writes 35 × 4 = 125 because 30 × 4 = 120 and 120 + 5 = 125. Explain the mistake, correct the calculation and draw a labelled split model to show the two parts.
7. Task
Solve 25 × 12 mentally by doubling one factor and halving the other. Record two equal-product steps, give the product and explain why the total stays unchanged.
8. Task
Create and play a fact-card game. Choose three multiplication facts with different products and factors 2–10. Make four cards for each: multiplication, product and two related divisions. Write rules requiring a match, mental strategy and inverse check. Play three turns with a partner or adult and write the cards, strategy and check for each turn. Keep your 12 cards and written record for review.
Complete answer guide
Task 1
Answer: The parts are 25 and 10; the whole is 35. 35 ÷ 5 = 7 and 35 ÷ 7 = 5.
5 × 5 + 5 × 2 = 25 + 10 = 35. Require an actual labelled array and an explanation that known fives and twos facts build the sevens fact. Accept an equivalent rotated array with matching labels.
Task 2
Answer: 2 × 9 = 18; 4 × 9 = 36; 8 × 9 = 72.
Each row keeps 9 counters. Each equal copy doubles the number of rows and the total. Require the three arrays or clearly marked stages, all equations and a written explanation; a list of totals alone is incomplete.
Task 3
Answer: 9 × 6 = 54 by both methods.
10 × 6 − 6 = 60 − 6 = 54. Or 3 × 6 = 18, then 3 × 18 = 54. The first removes one group from ten; the second makes three lots of three groups. Require both worked strategies and their group explanations.
Task 4
Answer: 4 × 8 = 8 × 4 = 32; 32 ÷ 4 = 8; 32 ÷ 8 = 4.
The turned array has 8 rows of 4. No counters are added or removed, so both totals are 32. Require the original and turned models or a clearly recorded physical turn, labels, all four facts and explanation.
Task 5
Answer: 18 × 6 = 108 and 126 ÷ 7 = 18.
For example: 10 × 6 + 8 × 6 = 60 + 48 = 108; 108 ÷ 6 = 18 checks. 126 ÷ 7 = 70 ÷ 7 + 56 ÷ 7 = 10 + 8 = 18; 18 × 7 = 126 checks. Accept other efficient mental partitions with correct smaller facts and both checks.
Task 6
Answer: 35 × 4 = 140.
Multiply both parts of 35 by 4. 30 × 4 + 5 × 4 = 120 + 20 = 140. The student added 5 instead of four groups of 5. Require a model for 30 groups of 4 and 5 groups of 4 (or 4 rows split 30+5), with part totals 120 and 20 and whole 140.
Task 7
Answer: 25 × 12 = 50 × 6 = 100 × 3 = 300.
Doubling one factor and halving the other keeps the same total: the larger groups are balanced by half as many groups. Require two valid equal-product steps and an explanation. Accept a different valid sequence with the same relationship.
Task 8
Answer: Answers vary. Example family: 6 × 7, 42, 42 ÷ 6 = 7, 42 ÷ 7 = 6.
For the example, a strategy is 5 × 7 + 1 × 7 = 35 + 7 = 42. Require 12 actual accurate cards from three distinct products, workable written rules and three recorded played turns with matching, reasoning and inverse checks. Accept other correct facts and rules; a proposed game without creation and play is incomplete.