Multiplying and Dividing: a week of ready-to-teach maths
Five days of lessons for Year 2 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out 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 two card sheets once; they are reused all week.
- Open the free interactive unit on your board. Every plan tells you which picture to show and when.
- 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. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives model answers, so you can walk in and teach it. No times tables are memorised this week; children build, turn and split the pictures instead.
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 lesson can also split into a short warm-up and a main session if your timetable runs small blocks.
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 only | Sort equal groups from a jumble and count them as groups, not one by one | Groups or a jumble |
| 2 | Skip count the rows | Build equal rows and skip count to the total; write it as repeated addition and a times | The Anzac tray |
| 3 | Arrays and the turn-around | Read an array as rows of columns and turn it to see the same total | The array turner |
| 4 | Share it or bag it | Divide by sharing a pile equally and by making equal groups | Share it out or bag it up |
| 5 | Split to multiply | Split a harder times at five and add the two easy pieces | The friendly five |
How the week builds
Day 1 sorts equal groups from a jumble; Day 2 skip counts the rows to a total; Day 3 turns an array to prove the two products match; Day 4 divides the pile two ways; and Day 5 splits a harder times into easy pieces. It builds on counting in equal groups from Year 1, and it opens the way to money problems and the times tables, which arrive next year as old friends.
Materials for the week (one trip)
- From the classroom: scissors, pencils, this pack printed.
- From home or the craft box: a small tub of counters such as dry pasta, buttons or beans, plus a few paper cups or saucers to share onto.
- Cut out once, use all week: the array and group cards, the skip-count strips and the sharing mats in this pack. No maths equipment to buy.
Dear families
This week in maths, Year 2 explores multiplying and dividing. We count equal groups, skip count the rows, turn arrays, share a pile fairly and pack it into equal groups, and split a harder times into easy pieces.
Try this at home
- Lay the cutlery for dinner: how many forks for 4 places, 3 each? Count by threes with your child.
- Find equal rows around the house (an egg carton, a tiled floor, a muffin tray) and read them as rows of columns.
- Share a snack fairly. Ask how many each, then how many bags you would fill if you packed them in equal groups.
- Skip count together while you climb stairs or hop: 2, 4, 6, 8 or 5, 10, 15, 20.
My maths this week
Fill one row a day. Tick when you have counted a group and shared a pile.
| Day | Equal groups I found | I counted a group | I shared a pile | Times I made |
|---|---|---|---|---|
| Monday | □ | □ | ||
| Tuesday | □ | □ | ||
| Wednesday | □ | □ | ||
| Thursday | □ | □ | ||
| Friday | □ | □ |
Printed from the free seegongsik Multiplying and Dividing teaching pack · seegongsik.com/au/y2/number/AC9M2N05/pack
Equal groups only
Multiplication counts equal groups. Today children sort collections into equal groups and jumbles, and meet the one rule that makes a times sentence possible: every group must be the same size.
We are learning to
- spot when a collection is made of equal groups,
- count equal groups as groups instead of one by one,
- write equal groups as a multiplication.
Success criteria
- I can tell an equal-groups collection from a jumble.
- I can write a times sentence for equal groups.
You need
A tub of counters (dry pasta, buttons or beans) and a few paper plates or cups. The array and group cards (cut-out sheet 1), one set per pair. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Equal or a jumble Scatter counters onto a few plates, some plates equal and some not. Children sort them: which plates could we count in equal groups? Ask: “What is the same about the plates we are allowed to multiply?” |
| 30 min | Build and name Pairs build equal groups with counters, say them as groups of, and write the times. Then break one group to feel the times stop working. Ask: “Make 3 groups of 4. Now take one counter away. Can we still say a times? Why not?” |
| 10 min | Show and write Show a built collection; children write a multiplication, or only an addition if it is a jumble. Ask: “Is this a times or only a plus? Convince me on your bench.” |
Two half-sessions instead? End Session A after the sort. Start Session B by rebuilding 3 groups of 4 from memory, then writing its times sentence.
Watch for these ideas
- Trying to write a times for a jumble: unequal groups can only be added, never multiplied.
- Counting the collection one counter at a time instead of by the group.
- Reading 3 groups of 4 as 3 + 4: the two numbers do different jobs, one counts the groups, the other says how big each group is.
Answers
- Draw 3 groups of 4: 4 + 4 + 4 = 12, and 3 × 4 = 12.
- 3 groups of 5 is 3 × 5 = 15. 4 groups of 2 is 4 × 2 = 8. 2 groups of 6 is 2 × 6 = 12.
- Groups of 2, 4 and 3 are not equal, so there is no times: only 2 + 4 + 3 = 9. Own groups vary; check every group is the same size and the times matches.
Equal groups
Equal groups can be multiplied. A jumble can only be added. Show what you know.
Draw 3 groups of 4
Adding: 4 + 4 + 4 = ____. Multiplying: 3 × 4 = ____.
Equal groups or a jumble?
Write yes or no for equal groups. If yes, write the times and the total.
| The groups | Equal groups? | Sentence and total |
|---|---|---|
| 3 groups of 5 | ||
| groups of 2, 4 and 3 | ||
| 4 groups of 2 | ||
| 2 groups of 6 |
Your own equal groups
Draw your own equal groups, then write the multiplication.
My groups: ____ × ____ = ____
Skip count the rows
Nobody counts a full tray one biscuit at a time. Today children build equal rows and skip count the running total, then write the same fact two ways: the long way with plus signs and the short way with a times.
We are learning to
- skip count to find the total of equal rows,
- write equal rows as a repeated addition,
- write the same equal rows as a multiplication.
Success criteria
- I can skip count to a total.
- I can match a repeated addition to a times.
You need
The array cards and the skip-count strips (cut-out sheets 1 and 2). Counters and a tray or grid to lay rows on. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Skip count warm-up Chant up the skip-count strips together: twos, then fives, then threes, pointing to each number as you say it. Ask: “Start at 6 and count on by threes. Where do we land after three more jumps?” |
| 30 min | Bake the rows Pairs lay equal rows of counters, one row at a time, skip counting aloud as each row lands. They write each tray as a repeated addition and as a times. Ask: “You added a row of 4. What is the new total, and how did you get it without counting them all again?” |
| 10 min | Two ways to write it Children write a tray both ways on the worksheet. Ask: “Show me the long way with plus signs and the short way with a times. Which is quicker?” |
Two half-sessions instead? End Session A after the skip-count warm-up and the first tray. Start Session B by rebuilding that tray and writing it both ways.
Watch for these ideas
- Skip counting by the wrong number: count by the size of each row, not by how many rows there are.
- Losing the running total and starting the count from one again for each row.
- Gluing the digits together, reading 4 rows of 6 as forty-six instead of counting 6, 12, 18, 24.
Answers
- 5 rows of 2: 2, 4, 6, 8, 10, so 5 × 2 = 10. 3 rows of 4: 4, 8, 12, so 3 × 4 = 12. 4 rows of 3: 3, 6, 9, 12, so 4 × 3 = 12.
- 5 + 5 + 5 + 5 = 20, so 4 × 5 = 20. 6 + 6 + 6 = 18, so 3 × 6 = 18. 2 + 2 + 2 + 2 + 2 + 2 = 12, so 6 × 2 = 12.
- Draw 3 rows of 5: skip count 5, 10, 15, so 3 × 5 = 15.
Skip count to multiply
Skip count each row of equal groups, then write it as a times.
Skip count the rows
5 rows of 2. Skip count: 2, ____, ____, ____, ____. So 5 × 2 = ____.
3 rows of 4. Skip count: 4, ____, ____. So 3 × 4 = ____.
4 rows of 3. Skip count: 3, ____, ____, ____. So 4 × 3 = ____.
Two ways to write it
Write the multiplication and the total for each repeated addition.
| Repeated addition | Multiplication | Total |
|---|---|---|
| 5 + 5 + 5 + 5 | ||
| 6 + 6 + 6 | ||
| 2 + 2 + 2 + 2 + 2 + 2 |
Draw and skip count
Draw 3 rows of 5. Skip count them, then write the times.
Skip count: 5, ____, ____. So 3 × 5 = ____.
Arrays and the turn-around
An array is equal rows lined up in columns, and it is the central picture of this whole topic. Today children build arrays, read them as rows of columns, and turn them to discover that a times and its turn-around give the same total.
We are learning to
- read an array as rows of columns,
- write an array as a multiplication,
- turn an array and see the total stays the same.
Success criteria
- I can write an array as rows times columns.
- I can write its turn-around with the same total.
You need
The array cards (cut-out sheet 1), one set per pair. Counters to build arrays with. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Read the array Hold up array cards; the class reads each one as rows of columns and says the times. Ask: “How many rows? How many in each row? Now say the times.” |
| 30 min | Turn the tray Pairs build an array with counters and write its times, then turn the card a quarter turn and write the new times, checking the total did not change. Ask: “You turned 3 rows of 4 into 4 rows of 3. Did any counter leave the tray? So what must be true about the two totals?” |
| 10 min | Prove it Children record a turned pair on the worksheet and explain why the totals match. Ask: “Why is 3 times 4 the same as 4 times 3?” |
Two half-sessions instead? End Session A after reading the cards. Start Session B by building one array and turning it.
Watch for these ideas
- Thinking the turn-around makes a bigger number: turning moves no counters, so the total cannot change.
- Counting the whole array by ones instead of reading it as rows of columns.
- Mixing up which number is the rows and which is the columns when writing the times.
Answers
- 3 rows of 4 is 3 × 4 = 12; turned it is 4 × 3 = 12. Same total.
- 2 rows of 5: 2 × 5 = 10 and 5 × 2 = 10. 3 rows of 4: 3 × 4 = 12 and 4 × 3 = 12. 4 rows of 5: 4 × 5 = 20 and 5 × 4 = 20.
- 2 × 8 = 16, so 8 × 2 = 16. 5 × 3 = 15, so 3 × 5 = 15.
Turn the array
Read each array as rows of columns. Turn it and the total stays the same.
Draw 3 rows of 4
Write it: 3 × 4 = ____. Turn it: 4 × 3 = ____.
Write each array two ways
| The array | Write it | Turn it | Total |
|---|---|---|---|
| 2 rows of 5 | |||
| 3 rows of 4 | |||
| 4 rows of 5 |
Fill the turn-around
2 × 8 = 16, so 8 × 2 = ____.
5 × 3 = 15, so 3 × 5 = ____.
Share it or bag it
One pile of counters can be divided two ways. Sharing deals the pile out equally and asks how many each; grouping packs it into equal bags and asks how many bags. Today children do both, and meet the division sign.
We are learning to
- share a pile equally and say how many each,
- pack a pile into equal groups and say how many groups,
- write both as a division.
Success criteria
- I can share a pile fairly and write the division.
- I can pack a pile into equal groups and write the division.
You need
The sharing mats (cut-out sheet 2) and counters. Small cups, envelopes or paper bags for grouping. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Deal one each Play a quick dealing game: hand counters round the group one each until the pile is gone, then count each hand. Ask: “We dealt them one each. How many did everybody end up holding?” |
| 30 min | Share it or bag it Pairs take a pile of 12. First they share it onto a mat of 3 or 4 and record how many each. Then they pack the same pile into equal bags and record how many bags. Ask: “Same 12 counters. When did we ask how many each, and when did we ask how many bags?” |
| 10 min | Write the division Children record one share and one group on the worksheet using the division sign. Ask: “Where is the pile, where is the group size, and where is the answer in your sentence?” |
Two half-sessions instead? End Session A after sharing the pile. Start Session B by packing the same pile into equal bags.
Watch for these ideas
- Sharing unfairly, so some plates hold more than others; every share must be equal.
- Confusing the two questions: how many each is sharing, how many groups is grouping.
- Writing the numbers the wrong way round: the whole pile comes first in the division sentence.
Answers
- 15 cherries on 3 plates: 5 each, so 15 ÷ 3 = 5. 15 cherries in bags of 5: 3 bags, so 15 ÷ 5 = 3.
- 12 shells among 4 children is sharing: 12 ÷ 4 = 3 each. 12 shells in bags of 3 is grouping: 12 ÷ 3 = 4 bags.
- 18 stickers among 3 is sharing: 18 ÷ 3 = 6 each. 16 pegs in bags of 4 is grouping: 16 ÷ 4 = 4 bags.
Two kinds of dividing
Sharing asks how many each. Grouping asks how many bags. The pile always comes first.
Share it out
15 cherries shared onto 3 plates. Draw them dealt out fairly.
Each plate has ____. So 15 ÷ 3 = ____.
Bag it up
15 cherries packed into bags of 5. Draw the bags.
There are ____ bags. So 15 ÷ 5 = ____.
Share or group?
Write share or group, then the number sentence and the answer.
| The story | Share or group? | Number sentence | Answer |
|---|---|---|---|
| 12 shells shared among 4 children | |||
| 12 shells packed in bags of 3 | |||
| 18 stickers shared among 3 | |||
| 16 pegs packed in bags of 4 |
Split to multiply
A harder times does not have to be memorised. Split one factor at the friendly five and it becomes two easy pieces that add back together. This is partitioning, the strategy half of the unit, and it turns unknown facts into known ones.
We are learning to
- split a harder times at five,
- work out the two easy pieces and add them,
- choose a sensible strategy for a times.
Success criteria
- I can split a times at five and add the pieces.
- I can choose a strategy that suits the numbers.
You need
The array cards (cut-out sheet 1) and counters, to build an array and split it after the fifth row. A ruler or a strip of paper to mark the split. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Fives are friendly Warm up on the fives with the skip-count strip: 5, 10, 15, 20. Fives are the easiest big count. Ask: “How many fives make 20? How might the fives help us with a bigger times?” |
| 30 min | Split at five Pairs build a harder array, say 6 rows of 4, then lay a strip after the fifth row. They work the top piece and the bottom piece and add them. Ask: “The top is 5 fours, which is 20. What is the small piece below the line, and what is the whole thing?” |
| 10 min | Choose a way Give three times and ask which strategy fits each: double, count by fives, or split at five. Ask: “Which of these would you double, and which would you split at five? Why?” |
Two half-sessions instead? End Session A after the fives warm-up and one split. Start Session B with a fresh split, then the strategy choice.
Watch for these ideas
- Adding the two factors instead of the two pieces: split the array, not the numbers being multiplied.
- Forgetting the small piece and giving only the five rows.
- Splitting at five but then miscounting the leftover rows below the line.
Answers
- 6 × 4: 5 × 4 = 20, 1 × 4 = 4, and 20 + 4 = 24.
- 7 × 4: 20 + 8 = 28. 8 × 3: 15 + 9 = 24. 6 × 6: 30 + 6 = 36.
- Choose a strategy: 2 × 9 = 18 (double 9), 5 × 6 = 30 (count by fives), 7 × 3 = 21 (split at five: 15 + 6). Any sound strategy that reaches the right answer is fine.
Split the hard ones
Split the first number at five. Work the two easy pieces, then add them.
Worked together: 6 × 4
Split the 6 into 5 and 1. 5 × 4 = ____. 1 × 4 = ____. Add: ____ + ____ = ____.
Your turn
| Times | Five rows | The rest | Total |
|---|---|---|---|
| 7 × 4 | 5 × 4 = ______ | 2 × 4 = ______ | |
| 8 × 3 | 5 × 3 = ______ | 3 × 3 = ______ | |
| 6 × 6 | 5 × 6 = ______ | 1 × 6 = ______ |
Choose a way
Work each one out your own way, then write the answer.
2 × 9 = ____
5 × 6 = ____
7 × 3 = ____
Tell a friend which way you chose for each: doubling, counting by fives, or splitting at five.
Array and group cards
Cut out the cards. Read an array as rows of columns, and turn a card a quarter turn to see its turn-around. Each plate card is one equal group; lay out equal plates to build groups of the same size.
Array cards
Group cards
Teacher note: these are the trays and groups from Groups or a jumble and The array turner on screen. Turning an array card is the same move as the Turn the tray button. Add counters to build bigger groups.
Skip-count strips and sharing mats
Cut out the strips and mats. Point along a strip to skip count to a total (Day 2). Deal counters one at a time onto a mat to share a pile fairly (Day 4).
Skip-count strips
Sharing mats
Teacher note: the strips are the running totals from The Anzac tray, and the mats are the plates from Share it out or bag it up. One set per pair is plenty.
What we know: Multiplying and Dividing
Work on your own. Show your thinking if you can.
- 4 jars each hold 3 marbles. Write the multiplication: ____ × ____ = ____
- Skip count on: 3, 6, 9, ____, ____. How many threes make 15? ____
- Write 4 + 4 + 4 + 4 as a multiplication and total: ____ × ____ = ____
- An array has 2 rows of 7. Write it two ways: ____ × ____ and ____ × ____. Total: ____
- 18 stickers shared equally among 3 children. Each child gets ____. Number sentence: ____ ÷ ____ = ____
- 24 pencils packed into bags of 4. How many bags? ____ Number sentence: ____ ÷ ____ = ____
- Work out 8 × 4 by splitting the 8 at five: 5 × 4 = ____, 3 × 4 = ____, total ____
- There are 5 nests with 4 eggs in each. How many eggs altogether? ____ Show your thinking.
Answers and marking guide
Answers
- 4 × 3 = 12.
- 12, 15; five threes make 15.
- 4 × 4 = 16.
- 2 × 7 = 14 and 7 × 2 = 14; total 14.
- 6 each; 18 ÷ 3 = 6.
- 6 bags; 24 ÷ 4 = 6.
- 5 × 4 = 20, 3 × 4 = 12, total 32 (so 8 × 4 = 32).
- 20 eggs; 5 × 4 = 20.
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Equal groups (Q1) | counts the objects one by one | writes a multiplication for equal groups | explains why unequal groups cannot be a multiplication |
| Skip counting (Q2, Q3) | skip counts along a strip with support | skip counts to a total and matches a repeated addition to a times | skip counts on from any point without starting again |
| Arrays and turning (Q4) | counts an array by ones | writes an array two ways and sees the total is the same | uses a known fact to write its turn-around without recounting |
| Division (Q5, Q6) | shares or groups with counters | writes a division sentence for sharing and for grouping | links the division back to a multiplication fact |
| Partitioning (Q7, Q8) | works a times with counters or a drawing | splits a times at five and adds the two easy pieces | chooses a strategy to suit the numbers and explains the choice |
Eight questions, five ideas. A child at standard answers most questions and can explain their thinking, groups first.
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 | Equal groups | Skip counting | Arrays | Division | Partitioning |
|---|---|---|---|---|---|
The five columns are the five days: equal groups, skip counting, arrays and turning, sharing and grouping, and splitting to multiply.