Doubling and Halving: a week of ready-to-teach maths
Five days of lessons for Year 2 on the twos facts, doubling and halving. 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.
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 | Count by twos | Count pairs by twos and see two times a number as doubling | The pairs machine |
| 2 | The two times table | Read a two-row array both ways and build the two times facts | The egg carton |
| 3 | Halving is doubling backwards | Split even numbers into two equal groups and check by doubling | The halving machine |
| 4 | Fair shares for two | Deal a set into two equal groups and meet the odd one out | Fair share for two |
| 5 | The twos family | Write four facts from one and use a times fact to divide | The twos family |
How the week builds
Day 1 counts pairs by twos; Day 2 turns that count into the two times table; Day 3 runs the machine backwards to halve; Day 4 shares fairly between two and meets odd numbers; and Day 5 ties multiplication and division into one family of facts. It builds on the doubles from Addition Facts to 20, and it opens the way to halves and quarters of real shapes.
Materials for the week (one trip)
- From the classroom: scissors, pencils, this pack printed.
- From home or the craft box: a handful of counters to share and halve, such as dry pasta, buttons or bottle tops, and a few real pairs (socks, shoes, gloves).
- Cut out once, use all week: the pair cards, the number cards, the double and halve cards, and the fact-family triangles in this pack. No maths equipment to buy.
Dear families
This week in maths, Year 2 learns the twos: counting by twos, doubling and halving. We count pairs, build the two times table, split numbers into two equal groups, and see that halving is doubling run backwards.
Try this at home
- Count pairs by twos: socks from the wash, shoes at the door, eggs in the carton. Two, four, six.
- Play double it: say a small number, your child doubles it. Then swap.
- Share fairly between two: split a handful of pasta or grapes into two equal piles. Is any left over?
- Halve and check: halve an even number, then double the answer to check it comes back.
My twos this week
Fill one row a day. Tick when you have said the fact aloud.
| Day | Something I doubled | Something I halved | I said it aloud |
|---|---|---|---|
| Monday | □ | ||
| Tuesday | □ | ||
| Wednesday | □ | ||
| Thursday | □ | ||
| Friday | □ |
Printed from the free seegongsik Doubling and Halving teaching pack · seegongsik.com/au/y2/algebra/AC9M2A03/pack
Count by twos
Children count in twos and see that a pair is one group of two. Two times a number is just doubling it, met today by counting the pairs, not the single things.
We are learning to
- count aloud by twos: two, four, six, eight,
- see a pair as one group of two things,
- say how many things are in a row of pairs.
Success criteria
- I can count a set of pairs by twos.
- I can say how many things some pairs make.
You need
The pair cards (cut-out sheet 1), one set per pair of children. A few real pairs to count: socks, shoes, gloves. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Pair hunt Hunt the room for things that come in twos: shoes, eyes, hands, bike wheels. Count each find by twos. Ask: “How many shoes if four children line up? Count their feet by twos with me.” |
| 30 min | The pairs machine Lay out pair cards one at a time. After each card the class says the running count: two, four, six. Write the count under each pair, then read the whole line back. Ask: “We added one card but the count jumped by two. Why did it not jump by one?” |
| 10 min | Say the double Point to a row of pairs and ask for two times that many. Link it to doubling: two fives is five and five again. |
Two half-sessions instead? End Session A after the pair hunt. Start Session B by rebuilding the pairs machine from four pairs, then grow it.
Watch for these ideas
- Counting every sock by ones instead of counting each pair as two.
- Losing the beat of the skip count and landing on an odd number.
- Thinking two times three means the number twenty-three: it means two threes.
Answers
- Counting row: 8, 10, 12, 14, 16.
- 3 pairs is 6, 5 pairs is 10, 7 pairs is 14, 9 pairs is 18.
- Four pairs of dots is 8. Draw-your-own varies: check each pair is exactly two dots.
Count the pairs
A pair is two. Count each row by twos, and write how many things there are altogether.
Count on by twos
Fill in the counting row.
2, 4, 6, ____, ____, ____, ____, ____
How many in the pairs?
| How many pairs | Of what | How many altogether |
|---|---|---|
| 3 pairs | socks | |
| 5 pairs | shoes | |
| 7 pairs | gloves | |
| 9 pairs | thongs |
Draw and count
Draw 4 pairs of dots. Count them by twos. There are ____ dots.
The two times table
A two-row array is a twos fact you can see. Read it across as two rows, or down as columns of two: the eggs never move, so two times a number equals that number times two.
We are learning to
- read an array as two rows or as columns of two,
- write a two times fact for a two-row array,
- see that two times a number equals that number times two.
Success criteria
- I can write 2 × a number for a two-row array.
- I can show that 2 × 6 and 6 × 2 make the same total.
You need
The pair cards (cut-out sheet 1) to stand side by side as an array, or an egg carton and a drawn grid. Counters. The worksheet, one per child. A board for the class list.
Lesson flow (about 50 minutes)
| 10 min | Two rows Build two rows of five with counters. Count the total down the columns by twos, then along the rows. Ask: “Two rows of five. Count down the columns by twos with me. How many?” |
| 30 min | Turn your head Build the two times table as arrays, from two ones up to two tens. For each, read it the other way too, then write the fact. Ask: “This carton is two rows of six. Turn your head. What is it now, and does the total change?” |
| 10 min | Write the facts Fill the two times table on the worksheet, all the way from two ones to two tens. |
Two half-sessions instead? End Session A after two rows. Start Session B by rebuilding the array, then write the table.
Watch for these ideas
- Believing 2 × 6 and 6 × 2 are different facts because they read differently.
- Miscounting the array by tracing its outline instead of counting the dots.
- Joining the digits, writing 2 × 6 as 26.
Answers
- The two times table: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.
- 2 rows of 5: 2 × 5 = 10 and 5 × 2 = 10.
- 2 rows of 4 is 8, so 2 × 4 = 8.
Two rows, two ways
Finish the two times table. The first two are done for you.
| Two times fact | Answer |
|---|---|
| 2 × 1 | 2 |
| 2 × 2 | 4 |
| 2 × 3 | |
| 2 × 4 | |
| 2 × 5 | |
| 2 × 6 | |
| 2 × 7 | |
| 2 × 8 | |
| 2 × 9 | |
| 2 × 10 |
Read it both ways
Here are 2 rows of 5. Write two facts: 2 × ____ = ____ and ____ × 2 = ____.
Draw the array
Draw 2 rows of 4 dots. How many dots? ____ Write the fact: 2 × 4 = ____.
Halving is doubling backwards
Halving splits a number into two equal groups. It is doubling run backwards: if two nines make eighteen, then eighteen halved gives nine. Even numbers split cleanly, with nothing spare.
We are learning to
- halve an even number into two equal groups,
- see that halving undoes doubling,
- write a halving as a division by two.
Success criteria
- I can halve an even number.
- I can double my answer to check the half.
You need
Counters (dry pasta, buttons or the number cards from cut-out sheet 1). A mat or sheet of paper folded in two. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Double, then undo Double a small number aloud together. Then start from the double and give the half back. Ask: “Two sixes make twelve. So what is half of twelve, and how do you know?” |
| 30 min | The halving machine Take an even number of counters, split them into two equal groups, and write the halving as a division by two. Then check with a doubling fact. Ask: “Split it into two equal groups. If one group has more, what must you do?” |
| 10 min | Check by doubling Swap halves with a partner and double the answer to check it returns to the start. |
Two half-sessions instead? End Session A after double-then-undo. Start Session B at the halving machine.
Watch for these ideas
- Calling two groups a half when the groups are not equal.
- Halving by taking two away, instead of splitting into two equal groups.
- Forgetting to check the half by doubling it back.
Answers
- Halves: 8 is 4, 12 is 6, 16 is 8, 20 is 10, 14 is 7. Doubling each answer returns the start.
- 2 × 6 = 12, so 12 ÷ 2 = 6.
- Half of 10 is 5.
Halve it, then check
Halve each number by splitting it into two equal groups. Then double your answer to check.
| Number | Half | Check: double the half |
|---|---|---|
| 8 | ||
| 12 | ||
| 16 | ||
| 20 | ||
| 14 |
Use a doubling fact
2 × 6 = 12. So 12 ÷ 2 = ____.
Draw and halve
Draw 10 dots. Circle them in two equal groups. Half of 10 is ____.
Fair shares for two
Sharing between two is halving by dealing: one for you, one for me, until the bag is empty. Even numbers share with nothing left. Odd numbers leave one with no partner, and that leftover is how we spot an odd number.
We are learning to
- share a set fairly between two,
- find half by dealing one at a time,
- tell whether a number shares fairly between two.
Success criteria
- I can deal a set into two equal groups.
- I can say if a number is even or odd by sharing it.
You need
Counters (dry pasta, buttons or bottle tops). Two plates or mats to share onto. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | One for you, one for me Deal a small even set between two children, one at a time. Check the two piles match. Ask: “Deal them out one at a time. Do both plates have the same amount now?” |
| 30 min | The odd one out Deal several bags. Sort each number into shares fairly or leaves one over, and record the half each time. Ask: “This bag left one with no partner. What does that tell you about the number?” |
| 10 min | Even or odd List the numbers that shared fairly (even) and the ones that left one over (odd). |
Two half-sessions instead? End Session A after one-for-you-one-for-me. Start Session B with the odd one out.
Watch for these ideas
- Sharing by eye in two grabs instead of dealing one at a time.
- Thinking an odd number cannot be shared at all, rather than leaving one over.
- Calling two groups equal when one has an extra.
Answers
- 10 shares as 5 and 5 (even); 16 as 8 and 8 (even); 12 as 6 and 6 (even).
- 11 gives 5 each with 1 left over (odd); 9 gives 4 each with 1 over (odd); 15 gives 7 each with 1 over (odd).
- 14 dots share as 7 and 7 with none left over. 8 shares fairly; 7 does not.
Deal it out
Deal each bag between two children, one at a time. Write how many each gets, how many are left over, and whether the number is even or odd.
| Bag of | Each child gets | Left over | Even or odd |
|---|---|---|---|
| 10 | |||
| 11 | |||
| 16 | |||
| 9 | |||
| 12 | |||
| 15 |
Draw and share
Draw 14 dots. Share them onto two plates. Each plate gets ____, and ____ are left over.
Quick check
Can 8 be shared fairly between two? Yes □ No □
Can 7 be shared fairly between two? Yes □ No □
The twos family
One twos fact carries a whole family. From two times eight makes sixteen come four sentences: two times eight, eight times two, sixteen shared into twos, sixteen shared into eights. Knowing the times fact hands you the division for free.
We are learning to
- write the four facts in a twos family,
- use a times fact to answer a division,
- solve a problem by doubling or halving.
Success criteria
- I can write four facts from one twos fact.
- I can use two times what to divide by two.
You need
The fact-family triangles (cut-out sheet 2), one set per pair of children. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Cover a corner Hold a triangle and cover one corner. The partner names the hidden number and says how they know. Ask: “I have covered the top. Two and seven are showing. What is hidden, and how do you know?” |
| 30 min | Four from one For each triangle write the two multiplication facts and the two division facts. Then apply them: double a recipe for two, share a snack between two. Ask: “Sixteen divided by two. Do not count one by one. Ask: two times what makes sixteen?” |
| 10 min | Use it Answer a short mix of doubling and halving problems, then run the on-screen quiz as a class game. |
Two half-sessions instead? End Session A after cover a corner. Start Session B with four from one.
Watch for these ideas
- Writing the division the wrong way round, such as 2 ÷ 16 for 16 ÷ 2.
- Not seeing that all four facts use the same three numbers.
- Counting up to divide instead of recalling the times fact.
Answers
- Family 2, 5, 10: 2 × 5 = 10, 5 × 2 = 10, 10 ÷ 2 = 5, 10 ÷ 5 = 2.
- Family 2, 4, 8: 2 × 4 = 8, 4 × 2 = 8, 8 ÷ 2 = 4, 8 ÷ 4 = 2.
- Use it: 2 rows of 6 is 12; 12 shared between two is 6 each; 18 ÷ 2 = 9.
Four facts from one
Each family has three numbers. Write the two times facts, then the two division facts.
Family one: 2, 5 and 10
- 2 × 5 = ____
- 5 × 2 = ____
- 10 ÷ 2 = ____
- 10 ÷ 5 = ____
Family two: 2, 4 and 8
- 2 × 4 = ____
- 4 × 2 = ____
- 8 ÷ 2 = ____
- 8 ÷ 4 = ____
Use it
- A snack pack has 2 rows of 6. How many pieces? ____
- 12 stickers shared between 2 friends. Each friend gets ____.
- Use 2 × 9 = 18 to help. 18 ÷ 2 = ____.
Your own family
Choose a twos fact. Draw its triangle and write the four facts around it.
Pair cards and number cards
Cut out the cards. Each pair card holds two dots. Lay pair cards in a line and count by twos, or stand them side by side to make a two-row array. The number cards say how many pairs, or the number to double or halve.
Pair cards (each one is two)
Number cards 1 to 10
Teacher note: a line of pair cards is the pairs machine from the screen; a block of them two rows deep is the egg carton. Same dots, two jobs.
Double, halve and family cards
Cut out the cards. Turn a double or halve card face up, pick a number card from sheet 1, and do what it says. The triangles are the twos families: cover one corner and the other two numbers tell you the one that is hidden.
Double and halve cards
Twos family triangles
Teacher note: these triangles are the factor triangle from the twos family on the screen. The top number is two times the corner number; two multiplications read across the top two corners, and two divisions read down from the top.
What we know: Doubling and Halving
Work on your own. Show your thinking if you can.
- Count on by twos: 2, 4, 6, ____, ____, ____.
- 4 pairs of gloves. How many gloves altogether? ____
- An egg carton has 2 rows of 5. Write a two times fact: 2 × ____ = ____.
- 2 × 3 = 6. So 3 × 2 = ____.
- Half of 20 is ____. Check by doubling: ____.
- 9 stickers shared between 2 children: ____ each and ____ left over.
- Use 2 × 6 = 12 to help. What is 12 ÷ 2? ____
- Write all four facts in the twos family for 2 × 4 = 8: ____
Answers and marking guide
Answers
- 8, 10, 12.
- 8 gloves (four twos: 2, 4, 6, 8).
- 2 × 5 = 10.
- 6 (the same total read the other way).
- Half of 20 is 10; doubling 10 gives 20 back.
- 4 each and 1 left over (9 is odd).
- 6.
- 2 × 4 = 8, 4 × 2 = 8, 8 ÷ 2 = 4, 8 ÷ 4 = 2.
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Count by twos (Q1, Q2) | counts a set by ones | counts on by twos and finds how many things some pairs make | explains why each pair adds two to the count |
| Two times facts (Q3, Q4) | counts an array one at a time | writes a two times fact for an array and knows two times a number equals that number times two | uses a known fact to reach a new one |
| Halving (Q5) | halves with counters and help | halves an even number and checks it by doubling | explains why doubling checks the half |
| Fair shares (Q6) | shares a small even set | deals a set into two and names the leftover from an odd number | predicts even or odd before dealing |
| The twos family (Q7, Q8) | writes one fact | uses a times fact to divide by two and writes the four family facts | writes a family for a fact of their own |
Eight questions, five ideas. A child at standard answers most questions and can say how, leaning on a doubling or halving fact.
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 | Count by twos | Two times facts | Halving | Fair shares | Twos family |
|---|---|---|---|---|---|
The five columns are the five days: count by twos, the two times facts, halving, fair shares, and the twos family.