Multiply and Divide: a week of ready-to-teach maths
Five days of lessons for Year 3 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus array and fact cards, a mini-check and every answer.
Start here: five minutes to Monday
- Skim the week at a glance on the next page.
- Print the five days. Each day is two A4 sheets: a plan and a worksheet.
- Cut out the array cards and the fact cards once; they are reused all week.
- Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
- Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.
No maths background needed
This pack is written for the busy generalist teacher. Multiplication is equal groups: 4 × 3 means 4 groups of 3. An array shows the groups as rows, and turning it round shows 4 × 3 = 3 × 4. Division runs the other way, either by sharing into a number of groups or by making groups of a size; both give the same answer. No remainders this week.
One day, one lesson
The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.
The week at a glance
One lesson a day for a week. Each day stands on the day before, so run them in order.
| Day | Lesson | Children learn and do | On screen |
|---|---|---|---|
| 1 | Equal groups and arrays | Build equal groups and arrays, write them with the times sign, and turn an array round | Equal groups; The array |
| 2 | Skip count the tables | Skip count by 2, 3, 4, 5 and 10 along a line and read each landing as a times fact | Skip counting |
| 3 | Share or group | Divide by sharing into equal groups and by making groups of a size, and write it with the division sign | Share or group |
| 4 | Fact families | Write the two multiplications and two divisions that one array holds, and find missing numbers | The fact family |
| 5 | Split to multiply | Multiply a two-digit number by splitting it into tens and ones, and solve story problems | Split to multiply |
How the week builds
Day 1 builds multiplication as equal groups and arrays; Day 2 turns skip counting into the times tables; Day 3 meets division as sharing and as grouping; Day 4 joins them in fact families; and Day 5 splits a two-digit number to multiply it. It sits beside Times Tables and Their Division (AC9M3A03), which practises the 3, 4, 5 and 10 facts this week uses.
Materials for the week (one trip)
- From the classroom: scissors, pencils, this pack printed.
- Counters, or any small things to count: bottle tops, pasta, buttons. About 30 per pair.
- Paper plates or circles drawn on paper for the groups, four per pair.
- Cut out once, use all week: the array cards and the fact cards in this pack.
Words for the word wall
equal groups, array, row, column, times, multiply, product, skip count, share, group, divide, fact family, split
Dear families
This week in maths, Year 3 is learning to multiply and divide. We make equal groups and arrays, skip count, share things out fairly, and find quick ways to multiply bigger numbers.
Try this at home
- Spot arrays: eggs in a carton, a muffin tray, windows on a building. How many rows? How many in each row? How many altogether?
- Share out snacks fairly between people. Does everyone get the same? How many each?
- Skip count out loud in 3s, 4s or 5s while you walk or set the table.
- Try a bigger one: 3 packs of 14 stickers is 3 tens and 3 fours, so 30 and 12, which is 42.
Our arrays this week
Fill one row a day with an array you found together.
| Day | What we found | Rows | In each row | Altogether |
|---|---|---|---|---|
| Monday | ||||
| Tuesday | ||||
| Wednesday | ||||
| Thursday | ||||
| Friday |
Printed from the free seegongsik Multiply and Divide teaching pack · seegongsik.com/au/y3/number/AC9M3N04/pack
Equal groups and arrays
Multiplication is equal groups: 4 × 3 means 4 groups of 3. An array lays the groups out in rows, and turning it round shows the same dots as 3 groups of 4.
We are learning to
- make equal groups and write them as a multiplication with the × sign,
- read an array as rows of a number and write its multiplication,
- turn an array round to show that 4 × 3 and 3 × 4 make the same product.
Success criteria
- I can show a multiplication as equal groups and as an array.
- I can write two multiplications for one array.
You need
Counters and four paper plates per pair. The array cards (cut-out sheet 1). The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Fair plates Put 3 counters on each of 4 plates. Count by threes: 3, 6, 9, 12. Write 4 × 3 = 12 and read it: four groups of three is twelve. Ask: “What if one plate had only 2? Could we still write 4 × 3?” |
| 30 min | Rows of dots Show the two board pictures (see the box). Pairs line the counters up in rows to make arrays, write each one both ways, then do the worksheet. Ask: “Your array is 3 rows of 4. Turn the page. What does it say now? Did the dots change?” |
| 10 min | Array hunt Hand out the array cards. Children write the multiplication for their card both ways and find a partner whose card has the same product. Ask: “2 × 6 and 3 × 4 both make 12. Are they the same array?” |
Two half-sessions instead? Split after Fair plates and the equal-groups picture; start Session B with arrays.
Watch for these ideas
- Unequal groups written as a multiplication. Every group must hold the same number.
- Reading 4 × 3 as 4 + 3 = 7. Times means groups of, not and.
- Thinking 3 × 4 and 4 × 3 are different amounts. Turn the array to check.
Answers
- Equal groups: 3 groups of 4 = 12; 5 groups of 2 = 10.
- Arrays: 2 × 5 = 10 and 5 × 2 = 10; 4 × 3 = 12 and 3 × 4 = 12; 3 × 6 = 18 and 6 × 3 = 18.
- Own array: 4 rows of 5 (or 5 rows of 4), 20 dots.
Groups and arrays
Draw equal groups
3 groups of 4 = ______
5 groups of 2 = ______
Write two multiplications for each array
Draw an array
4 × 5 Draw it as rows of dots. How many dots altogether? ______
Skip count the tables
A times table is skip counting. Each jump along the line is one more equal group, so the number you land on after 6 jumps of 4 is 6 × 4.
We are learning to
- skip count by 2, 3, 4, 5 and 10 forwards and backwards,
- read a skip count as a times fact: the third jump of 5 lands on 3 × 5,
- use a jump we know to find one we do not (6 × 4 is 5 × 4 and one more 4).
Success criteria
- I can skip count to find a times fact.
- I can show a times fact as jumps on a number line.
You need
A long number line from 0 to 30 on the floor or the board. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Count and clap Count by 3s to 30 with a clap on each count. Stop at 18 and ask which jump it is, and write 6 × 3 = 18. Repeat with 4s. Ask: “We stopped on 18. How many jumps of 3 did that take? What times fact is that?” |
| 30 min | Jump and land Jump on the board (see the box), then children draw the jumps for 6 × 4 on the worksheet line and fill in the counts and facts. Ask: “You know 5 × 4 is 20. How can that help you find 6 × 4?” |
| 10 min | Backwards Count back by 5s from 30 and by 4s from 24. Ask how many jumps back to 0. Ask: “24 back to 0 in jumps of 4 took 6 jumps. What division is that?” |
Two half-sessions instead? Split after Count and clap and the board; start Session B with the worksheet.
Watch for these ideas
- Counting the starting 0 as a jump. A jump is the hop, not the mark you start on.
- Losing count of the jumps. Hold up a finger for each jump, then count the fingers.
- Thinking 7 × 5 must be counted from scratch. Count on from a known fact: 5 × 5 = 25, then 30, 35.
Answers
- Counts: 3, 6, 9, 12, 15, 18; 4, 8, 12, 16, 20, 24; 5, 10, 15, 20, 25, 30; 10, 20, 30, 40, 50, 60.
- Facts: 6 × 2 = 12; 4 × 3 = 12; 7 × 5 = 35; 3 × 4 = 12; 8 × 10 = 80; 6 × 4 = 24; 9 × 3 = 27; 5 × 5 = 25.
- Line: six jumps of 4 land on 24. Jumps: 5 jumps of 4 reach 20; 6 jumps of 3 land on 18.
Jump the tables
Skip count
3, 6, ____, ____, ____, ____ (six jumps of 3)
4, 8, ____, ____, ____, ____ (six jumps of 4)
5, 10, ____, ____, ____, ____ (six jumps of 5)
10, 20, ____, ____, ____, ____ (six jumps of 10)
Draw the jumps
Draw six jumps of 4 on the line. Where do you land? 6 × 4 = ______
Times facts
| 6 × 2 = ______ | 4 × 3 = ______ | 7 × 5 = ______ | 3 × 4 = ______ |
| 8 × 10 = ______ | 6 × 4 = ______ | 9 × 3 = ______ | 5 × 5 = ______ |
Think in jumps
| Question | Answer |
|---|---|
| How many jumps of 4 reach 20? | |
| Where do 6 jumps of 3 land? |
Share or group
Division has two readings. Share 12 into 3 equal groups and each gets 4; or make groups of 3 from 12 and you get 4 groups. Both are 12 ÷ 3 = 4.
We are learning to
- divide by sharing a total into a number of equal groups,
- divide by making groups of a size and counting the groups,
- write a division with the ÷ sign and say which reading a story uses.
Success criteria
- I can share or group counters to divide.
- I can write a division sentence for a story.
You need
Counters and four paper plates per pair. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Deal them out Deal 12 counters one at a time onto 3 plates, like cards. Each plate gets 4. Write 12 ÷ 3 = 4. Ask: “How do we know the share is fair? What would we do with one left over?” |
| 30 min | Two ways to divide Now make groups of 3 from 12: 4 groups, the same answer. Switch the board picture between its two readings (see the box), then children do the worksheet with counters. Ask: “Sharing asked how many in each group. Grouping asked how many groups. Why is the answer the same?” |
| 10 min | Which reading? Read the two worksheet stories aloud. Children vote share or group, then solve. Ask: “Which words in the story told you it was sharing?” |
Two half-sessions instead? Split after Deal them out and the sharing picture; start Session B with grouping.
Watch for these ideas
- Unfair shares: one plate gets more. Deal one at a time until the counters run out.
- Writing 3 ÷ 12. The total comes first: 12 ÷ 3.
- Thinking sharing and grouping give different answers. They answer different questions with the same number.
Answers
- Share: 12 between 3 is 4 each (12 ÷ 3 = 4); 20 among 4 is 5 each (20 ÷ 4 = 5).
- Group: 15 in groups of 5 is 3 groups (15 ÷ 5 = 3); 18 in groups of 3 is 6 groups (18 ÷ 3 = 6).
- Stories: 24 ÷ 4 = 6 bags (grouping); 30 ÷ 5 = 6 stickers each (sharing).
Share it, group it
Share it
12 shared between 3: each gets ______
12 ÷ 3 = ______
20 shared among 4: each gets ______
20 ÷ 4 = ______
Group it
15 in groups of 5: ______ groups
15 ÷ 5 = ______
18 in groups of 3: ______ groups
18 ÷ 3 = ______
Story problems
1. 24 oranges are packed into bags of 4. How many bags are needed? Division: ____ ÷ ____ = ____ (share or group?)
2. 30 stickers are shared equally among 5 friends. How many stickers does each friend get? Division: ____ ÷ ____ = ____ (share or group?)
Fact families
One array holds four facts. A 3 by 4 array gives 3 × 4 = 12, 4 × 3 = 12, 12 ÷ 3 = 4 and 12 ÷ 4 = 3. Division undoes multiplication, so a times fact solves a division.
We are learning to
- write the two multiplications and two divisions that one array holds,
- use a multiplication fact to solve a division,
- find the missing number in a multiplication or division sentence.
Success criteria
- I can write all four facts in a fact family.
- I can use a times fact to find a missing number.
You need
The array cards and fact cards (cut-out sheets 1 and 2), one set per pair. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | One array, four facts Draw a 3 by 4 array. Children call out every fact they can see; write all four. Ask: “Which three numbers turn up in every fact? Can you find a fifth fact?” |
| 30 min | Match and fill Step through the board families (see the box). Pairs match each array card with its two fact cards, then do the worksheet. Ask: “24 ÷ 6 = ? Which times fact helps? How?” |
| 10 min | Missing-number race Call a sentence with a gap (4 × ? = 32). Children write the missing number and the fact that helped. Ask: “Did you think of a times fact or a division fact? Both are fine.” |
Two half-sessions instead? Split after the card match; start Session B with the worksheet.
Watch for these ideas
- Writing 3 ÷ 12 = 4. In a division the product, the biggest number, comes first.
- Thinking 3 × 4 and 12 ÷ 3 are unrelated facts. They come from the same array.
- Guessing missing numbers. Say the fact aloud with the gap: four times what is twenty?
Answers
- 2 and 7: 2 × 7 = 14, 7 × 2 = 14, 14 ÷ 2 = 7, 14 ÷ 7 = 2. 4 and 6: 4 × 6 = 24, 6 × 4 = 24, 24 ÷ 4 = 6, 24 ÷ 6 = 4.
- 3 and 5: 3 × 5 = 15, 5 × 3 = 15, 15 ÷ 3 = 5, 15 ÷ 5 = 3.
- Missing numbers: 5; 6; 4; 7; 60; 9.
- Check it: 28 ÷ 4 = 7 because 4 × 7 = 28.
Fact families
Four facts from one array
| ____ × ____ = ____ | ____ × ____ = ____ |
| ____ ÷ ____ = ____ | ____ ÷ ____ = ____ |
| ____ × ____ = ____ | ____ × ____ = ____ |
| ____ ÷ ____ = ____ | ____ ÷ ____ = ____ |
| ____ × ____ = ____ | ____ × ____ = ____ |
| ____ ÷ ____ = ____ | ____ ÷ ____ = ____ |
Find the missing number
| 4 × ____ = 20 | ____ × 3 = 18 | 24 ÷ ____ = 6 |
| 35 ÷ 5 = ____ | ____ ÷ 10 = 6 | 3 × ____ = 27 |
Check it
| Division | The times fact that proves it |
|---|---|
| 28 ÷ 4 = ______ |
Split to multiply
To multiply a two-digit number, split it into tens and ones, multiply each part, then add: 4 × 13 is 4 × 10 and 4 × 3, which is 40 + 12 = 52.
We are learning to
- split a two-digit number into tens and ones to multiply it,
- multiply each part and add the products,
- choose multiplication or division for a story problem and write the number sentence.
Success criteria
- I can multiply a two-digit number by splitting it.
- I can write and solve a number sentence for a story.
You need
Counters or base-ten blocks. The worksheet, one per child. The unit’s self-check quiz.
Lesson flow (about 50 minutes)
| 10 min | Too big to count Ask for 4 groups of 13. Build it as 4 tens and 4 threes, then add: 40 + 12 = 52. Ask: “Counting 52 dots one by one is slow. What made it quick?” |
| 25 min | Split and solve Split on the board (see the box), then children do the worksheet splits and the three stories, writing a number sentence for each. Ask: “Is this story asking for groups altogether, or a share? Multiply or divide?” |
| 15 min | Class quiz Run the self-check quiz as a team game: teams hold up one, two or three fingers for their choice. Ask: “Which picture from this week would prove that answer?” |
Two half-sessions instead? Split after the worksheet splits; start Session B with the stories and the quiz.
Watch for these ideas
- Multiplying only the tens (4 × 13 = 40) or only the ones. Both parts need multiplying.
- Writing 4 × 13 = 4 × 1 and 4 × 3. The 1 in 13 is a ten, worth 10.
- Choosing the operation from a key word alone. Picture the story: groups to join, or a total to share?
Answers
- Splits: 3 × 14 = 30 + 12 = 42; 4 × 16 = 40 + 24 = 64; 5 × 13 = 50 + 15 = 65; 2 × 38 = 60 + 16 = 76; 3 × 25 = 60 + 15 = 75.
- Stories: 6 × 14 = 60 + 24 = 84 chairs; 13 × 4 = 40 + 12 = $52; 32 ÷ 4 = 8 pencils.
- Own story: any story of 5 groups of 12 (or 12 groups of 5); 5 × 12 = 50 + 10 = 60.
Split to multiply
Split it
Example: 4 × 13 = 4 × 10 + 4 × 3 = 40 + 12 = 52.
3 × 14 = ____ × ____ + ____ × ____ = ____ + ____ = ______
4 × 16 = ____ × ____ + ____ × ____ = ____ + ____ = ______
5 × 13 = ____ × ____ + ____ × ____ = ____ + ____ = ______
2 × 38 = ____ × ____ + ____ × ____ = ____ + ____ = ______
3 × 25 = ____ × ____ + ____ × ____ = ____ + ____ = ______
Story problems
1. The hall has 6 rows of chairs with 14 chairs in each row. How many chairs? Number sentence: ______________ Answer: ______
2. Footy tickets cost $4 each. How much do 13 tickets cost? Number sentence: ______________ Answer: ______
3. A teacher shares 32 pencils equally among 4 tables. How many pencils does each table get? Number sentence: ______________ Answer: ______
Your own story
Write a story for 5 × 12 and solve it.
Array cards
Cut out the eight cards. Each card is an array: rows of dots. Use them for the array hunt on Day 1 and the fact-family match on Day 4.
Teacher note: every array can be read two ways, so each card matches two multiplications and two divisions.
Fact cards
Cut out the sixteen cards. Each array card has one multiplication card and one division card. Lay the arrays out, then place the two facts that belong to each one.
Teacher note: the pairs are 2 by 3 (2 × 3, 6 ÷ 2), 3 by 4, 2 by 5, 4 by 5, 3 by 5, 4 by 6, 3 by 6 and 5 by 5. Ask for the two missing facts of each family out loud.
What we know: Multiply and Divide
Work on your own. Draw a picture if it helps.
- 5 groups of 3 = ______ Write it with ×: ______________
- Write two multiplications for this array: ______________ ______________
- 6 × 4 = ______ 9 × 5 = ______ 7 × 10 = ______
- Share 18 equally among 3 children. Each child gets ______.
- 20 counters in groups of 5 make ______ groups. Write it with ÷: ______________
- Write the fact family for 4, 8 and 32: ______________________________________________
- 3 × 16 = ______ Show how you split it: ______________________
- Chairs are set out in 5 rows of 12. How many chairs are there? ______
Answers and marking guide
Answers
- 15; 5 × 3 = 15.
- 3 × 7 = 21 and 7 × 3 = 21.
- 24; 45; 70.
- 6 (18 ÷ 3 = 6).
- 4 groups; 20 ÷ 5 = 4.
- 4 × 8 = 32, 8 × 4 = 32, 32 ÷ 4 = 8, 32 ÷ 8 = 4.
- 48 (3 × 10 = 30 and 3 × 6 = 18, so 30 + 18).
- 60 (5 × 12 = 50 + 10).
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Represent (Q1, Q2) | builds equal groups with counters | writes a multiplication for equal groups and both multiplications for an array | explains why turning an array keeps the product |
| Facts and division (Q3, Q4, Q5, Q6) | skip counts from the start each time | recalls or derives 2, 3, 4, 5 and 10 facts, divides by sharing and grouping, writes a fact family | uses a known fact to reach a new one (6 × 4 from 5 × 4) |
| Two-digit and stories (Q7, Q8) | multiplies only the tens or only the ones | splits a two-digit number to multiply and writes a number sentence for a story | chooses between multiplying and dividing and explains the choice |
Eight questions, three ideas. A child at standard answers most questions and can show an answer as groups, an array or jumps.
Weekly class record
Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.
| Name | Groups, arrays | Skip counts | Shares, groups | Fact families | Splits |
|---|---|---|---|---|---|
The five columns are the five days: equal groups and arrays, skip counting, sharing and grouping, fact families, and splitting to multiply.