Counting in Groups: a week of ready-to-teach maths
Five days of lessons for Year 1 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out cards and strips, 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; the object cards, ten-bundles and array template 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 what young children find tricky, and gives model answers, so you can walk in and teach it.
The big idea of the week
Counting one by one is slow and easy to get wrong. If we make equal groups first, groups of two, five or ten, we can skip count and reach large numbers quickly and safely. By Friday the children bundle tens to count a set to 120, and they always count once more to check.
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 | The pile of pencils | Count one by one is slow; make equal groups of 2 or 5 and skip count | The pile of pencils |
| 2 | Hop along the line | Skip count along a number line in 2s, 5s and 10s to count the groups | Hop along the line |
| 3 | Twelve, four ways | Split twelve into equal groups four ways and count each way | Twelve, four ways |
| 4 | Bundle to 120 | Bundle tens to count a big set to 120: count the tens, then the ones | Bundle to 120 |
| 5 | The egg carton count | Count rows in an array, like an egg carton, by counting each row | The egg carton count |
How the week builds
Day 1 shows why grouping beats counting by ones; Day 2 skip counts along a number line in 2s, 5s and 10s; Day 3 splits twelve into equal groups four ways; Day 4 bundles tens to count a set to 120; and Day 5 counts arrays, like an egg carton, row by row. It builds on knowing numbers to 120 and counts one at a time, and it opens the way to addition and to counting by twos, fives and tens.
Materials for the week (one trip)
- From the classroom: scissors, pencils, this pack printed.
- From home or the craft box: a handful of counters such as buttons, dry pasta, blocks or bottle tops for children to group and count.
- Cut out once, use all week: the object cards, the ten-bundle strips and the array or egg-carton template in this pack. No maths equipment to buy.
Dear families
This week in maths, Year 1 is learning to count large sets faster by making equal groups. Instead of counting one, two, three all the way, we group by twos, fives and tens and skip count, and we can reach 120 this way.
Try this at home
- Pair the socks from the wash. Count them in twos: two, four, six, eight. How many socks?
- Count a bigger set in fives or tens: pegs, blocks, or coins laid in little piles of five.
- Look at an egg carton. It is two rows of six. Count each row: six, then twelve.
- Always count once more a different way to check. Did you get the same number?
My counting this week
Fill one row a day. Tick when you have counted it and checked it a second way.
| Day | What I counted | How many | I grouped it | I checked it |
|---|---|---|---|---|
| Monday | □ | □ | ||
| Tuesday | □ | □ | ||
| Wednesday | □ | □ | ||
| Thursday | □ | □ | ||
| Friday | □ | □ |
Printed from the free seegongsik Counting in Groups teaching pack · seegongsik.com/au/y1/number/AC9M1N03/pack
The pile of pencils
Show the children a big pile of counters and count them one by one. It is slow, and it is easy to lose track and get a different number the second time. The fix is the idea of the whole week: make equal groups first, groups of two or five, then skip count. Grouping turns a slow, risky count into a quick, safe one.
We are learning to
- see that counting a big pile one by one is slow and easy to get wrong,
- make equal groups of two or five from a pile,
- skip count the groups to find how many, and check the count.
Success criteria
- I can make equal groups of two or five from a pile.
- I can skip count the groups to say how many there are.
You need
A handful of counters (buttons, dry pasta, blocks or bottle tops) for each pair. The object cards (cut-out sheet 1). The worksheet, one per child.
Lesson flow (about 40 minutes)
| 10 min | The slow way Count a pile of about eighteen counters one by one, aloud, and get it wrong on purpose by going too fast. Count again and get a different number. Ask: “That took ages and we got two different answers. Is there a faster, safer way to count this pile?” |
| 20 min | Group, then skip count Pairs push their pile into groups of two, then count two, four, six. Then they try groups of five and count five, ten, fifteen and the few left over. Ask: “Make groups of five. Now count them: five, ten, fifteen. How many are left over, and what is the total?” |
| 10 min | Ring the groups On the worksheet children ring the pile into groups of two, then into groups of five, and skip count each way to the same total. Ask: “You grouped by twos and by fives. Did you get the same total both times? Which was quicker?” |
Two half-sessions instead? End Session A after The slow way. Start Session B by grouping a fresh pile, then move on to the worksheet.
Watch for these ideas
- Losing track counting by ones: skipping one or counting one twice in a jumbled pile.
- Making groups that are not equal, so skip counting does not work: check each group is the same size.
- Skip counting the groups but forgetting the few left over that are not a full group.
Answers
- Groups of two: nine groups of two make eighteen (two, four, six, eight, ten, twelve, fourteen, sixteen, eighteen).
- Groups of five: three groups of five make fifteen, with three left over, so fifteen and three more is eighteen.
- Both ways give the same total, eighteen. Grouping by fives has fewer groups to count.
Group the pile, then count
Here is a pile of dots. Counting them one by one is slow. Let us make equal groups instead.
Ring groups of two
Draw a ring around each group of two. Then skip count: two, four, six.
How many groups of two? ____ How many dots in all? ____
Ring groups of five
Now ring this same pile into groups of five. Skip count: five, ten, fifteen, and the ones left over.
Groups of five: ____ Left over: ____ How many dots in all? ____
Did you get the same total both ways? Which way had fewer groups to count?
Hop along the line
Yesterday we grouped a pile and skip counted it. Today we skip count along a number line. Each hop is one equal group, so a hop of five moves five along, and we say five, ten, fifteen as we land. The hops must all be the same size, or the count goes wrong. The number line makes the jumps easy to see and to check.
We are learning to
- skip count along a number line in twos, fives and tens,
- see that each hop is one equal group of the same size,
- say the landing numbers and count how many hops it takes.
Success criteria
- I can hop along a number line in fives and read the landings.
- I can count how many hops of ten reach a number.
You need
A large number line on the board or floor. Counters. The worksheet, one per child.
Lesson flow (about 40 minutes)
| 10 min | Hop together Hop a finger or a toy along a class number line in fives, saying each landing. Then try tens. Ask: “Watch me hop in fives: five, ten, fifteen. Every hop is the same size. Where do we land next?” |
| 20 min | Same-size hops Pairs draw hops on a number line, or step them out on the floor, and read the landings for twos, fives and tens. Slip in an uneven hop and let them catch it. Ask: “That hop was too big. Are all our hops the same size? What happens to the count if one is bigger?” |
| 10 min | Read the landings On the worksheet children fill the landings for hops of five, then count the hops of ten to sixty. |
Two half-sessions instead? End Session A after Hop together. Start Session B with same-size hops.
Watch for these ideas
- Uneven hops: making one jump bigger or smaller than the rest breaks the skip count.
- Reading the tick marks instead of the landings, so a hop of five is counted as one.
- Saying the numbers by rote but landing on the wrong marks: match each word to one hop.
Answers
- Hops of five to thirty: 5, 10, 15, 20, 25, 30.
- Hops of ten to sixty: it takes 6 hops (10, 20, 30, 40, 50, 60).
Hop along the line
Hops of five
Start at 0. Each hop is five. Write the number you land on under each hop.
The landings are: 5, ____, ____, ____, ____, ____.
Hops of ten
These hops are ten each. Count the hops it takes to reach 60.
It takes ____ hops of ten to reach 60.
Remember: every hop must be the same size, or the count goes wrong.
Twelve, four ways
Twelve things can be made into equal groups in more than one way: six groups of two, four groups of three, three groups of four, or two groups of six. Every way still adds up to twelve. This shows children that a set has one amount, but many ways to group it, and it lets them choose the grouping that counts fastest.
We are learning to
- make twelve into equal groups four different ways,
- skip count each grouping and get twelve every time,
- see that fewer, bigger groups can be quicker to count.
Success criteria
- I can split twelve into equal groups more than one way.
- I can skip count each way and reach twelve.
You need
Twelve counters for each child or pair. The object cards (cut-out sheet 1). The worksheet, one per child.
Lesson flow (about 40 minutes)
| 10 min | Twelve counters Give each pair twelve counters. Make groups of two together and count two, four, six up to twelve. Ask: “We made groups of two and counted to twelve. Could we group these same twelve a different way?” |
| 20 min | Four ways Pairs regroup the same twelve into threes, then fours, then sixes, skip counting each time. Keep checking the groups are equal, with none left over. Ask: “Groups of three: three, six, nine, twelve. How many groups did you make? Is it still twelve?” |
| 10 min | Ring four ways On the worksheet children ring twelve into groups of two, three, four and six, and write how many groups each way. |
Two half-sessions instead? End Session A after Twelve counters. Start Session B with the four ways.
Watch for these ideas
- Making groups that are not equal, so one group has more: every group must be the same size.
- Thinking a different grouping changes the total: twelve is twelve however it is grouped.
- Counting the groups instead of the things, or the things instead of the groups: be clear which you are counting.
Answers
- Groups of two: 6 groups (2, 4, 6, 8, 10, 12).
- Groups of three: 4 groups (3, 6, 9, 12).
- Groups of four: 3 groups (4, 8, 12).
- Groups of six: 2 groups (6, 12). Sixes is fastest here, only two groups to count.
Twelve, four ways
Each row has twelve dots. Ring them into equal groups. Then write how many groups you made.
Ring groups of 2
12 = ____ groups of 2. Skip count: it comes to ____.
Ring groups of 3
12 = ____ groups of 3. Skip count: it comes to ____.
Ring groups of 4
12 = ____ groups of 4. Skip count: it comes to ____.
Ring groups of 6
12 = ____ groups of 6. Skip count: it comes to ____.
Which way had the fewest groups to count? Which way was quickest for you?
Bundle to 120
To count a really big set, we bundle ten sticks together and treat each bundle as one ten. Then we count the tens, ten, twenty, thirty, and add on the single sticks at the end. Eight bundles of ten and six single sticks is eighty-six. This is how children reach numbers all the way to 120 without counting every stick one by one.
We are learning to
- bundle ten single things into one ten,
- count the tens first, then the ones left over,
- read a big set of bundles and sticks as a number to 120.
Success criteria
- I can count the tens, then the ones, to name a number.
- I know a bundle of ten counts as ten, not as one.
You need
Sticks, straws or pasta and elastic bands or string to bundle tens. The ten-bundle strips (cut-out sheet 1). The worksheet, one per child.
Lesson flow (about 40 minutes)
| 10 min | Make a ten Count ten sticks and bundle them with a band. Now the bundle is one ten. Make a few bundles together. Ask: “This bundle has ten sticks. When I count it, do I say one, or do I say ten?” |
| 20 min | Count the tens Pairs build a big number with bundles and loose sticks, then count the tens first and the ones last: ten, twenty, thirty, and then the ones. Ask: “Count your bundles: ten, twenty, thirty. Now the loose sticks. What is the whole number?” |
| 10 min | Read the bundles On the worksheet children count the tens then the ones and write the number for each set. |
Two half-sessions instead? End Session A after Make a ten. Start Session B with Count the tens.
Watch for these ideas
- Counting each bundle as one instead of ten, so seven tens is read as seven.
- Counting the ones first and losing them, or mixing them in with the tens.
- Forgetting to say the tens in order: ten, twenty, thirty, before adding the ones.
Answers
- 7 bundles of ten and 3 sticks: 7 tens and 3 ones is 73.
- 10 bundles of ten and 5 sticks: 10 tens and 5 ones is 105.
- Always count the tens first, then add the ones.
Count the tens, then the ones
Each bundle is a ten. The loose ones are on the right of the line. Count the tens first, then the ones.
Tens: ____ Ones: ____ The number is ____.
Tens: ____ Ones: ____ The number is ____.
Ten bundles of ten is one hundred. Ten tens and five ones is one hundred and five.
The egg carton count
Some groups are already made for us. An egg carton is two rows of six, so it holds twelve, and we can count it by rows: six, then twelve. Rows are equal groups laid in a neat array, and they are everywhere, from egg cartons to muffin trays to garden beds. Today we count arrays by rows and gather the whole week: equal groups, skip counting and bundling.
We are learning to
- see a row in an array as one equal group,
- count an array by rows using skip counting,
- count every row, not just the first one.
Success criteria
- I can count an array by rows.
- I can say how many rows and how many in each row, and find the total.
You need
An empty egg carton or a picture of one. The array template (cut-out sheet 1) and counters. The worksheet, one per child.
Lesson flow (about 40 minutes)
| 10 min | The egg carton Show an egg carton: two rows of six. Count one row, then the next, to reach twelve. Ask: “This row has six. If both rows are the same, how many eggs fit in the carton?” |
| 20 min | Count by rows Pairs fill the array template with counters and count by rows, five, ten, fifteen, or ten, twenty. Remind them to count every row. Ask: “You counted the top row and stopped. How many rows are there? Keep going, count them all.” |
| 10 min | Row by row On the worksheet children count arrays by rows: three rows of five, then four rows of ten. |
Two half-sessions instead? End Session A after The egg carton. Start Session B with Count by rows.
Watch for these ideas
- Counting only the first row and forgetting the rest of the array.
- Counting around the edge and missing the middle, or counting a dot twice.
- Not noticing the rows are equal, so skip counting by the row size does not click.
Answers
- Three rows of five: count by fives, 5, 10, 15, so 15 in all.
- Four rows of ten: count by tens, 10, 20, 30, 40, so 40 in all.
- An egg carton is two rows of six, which is 12.
Count the array by rows
An egg carton is rows of the same amount. Count each row and skip count to the total.
Three rows of five
Each row has ____. There are ____ rows. Count by fives: 5, ____, ____. Total ____.
Four rows of ten
Each row has ____. There are ____ rows. Count by tens: 10, ____, ____, ____. Total ____.
An egg carton is two rows of six. Count the rows: six, then twelve. Remember to count every row.
Object cards and ten-bundle strips
Cut out the object cards. Each card is a set of dots. Ring or push them into equal groups of two, three, four, five or six, then skip count to check. One set per pair is plenty.
Teacher note: the cards show 10, 12, 15, 18, 20 and 24 dots, laid in rows of five. The numbers are not printed, so children count for themselves.
Ten-bundle strips
Cut out the ten-strips. Each strip is one ten. Line up strips to count in tens, then add single counters for the ones, to build numbers to 120 (Day 4).
Teacher note: twelve strips make one hundred and twenty. Ten strips is one hundred.
Array and egg-carton template
These are empty rows, like an egg carton. Place a counter in each circle, then count the array by rows (Day 5). Cut out either template, or use both together for a bigger count.
Egg carton: two rows of six
Two rows of six is twelve. Count each row: six, then twelve.
A bigger array: four rows of ten
Teacher note: fill the rows with counters and count by tens: ten, twenty, thirty, forty. Four rows of ten is forty.
What we know: counting in groups
Work on your own. Make groups, skip count, and check your answer a second way.
- Ring these dots into groups of five. How many groups of five? ____
- Skip count in tens. Write the missing number: 10, 20, ____, 40.
- Here are twelve dots in three equal rows. Twelve is 3 groups of ____.
- Count the tens, then the ones. The number is ____.
- This array has two rows of six, like an egg carton. How many in all? ____
Answers and marking guide
Answers
- 4 groups of five (twenty dots, five in each group, makes four groups).
- 30 (the count is 10, 20, 30, 40).
- 4 (three groups of four make twelve).
- 64 (6 tens and 4 ones).
- 12 (two rows of six, counted six then twelve).
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Make equal groups (Q1, Q3) | makes groups that are not all equal | partitions a set into equal groups of a given size and counts them | chooses a helpful group size and explains why |
| Skip count (Q2) | counts by ones only | skip counts in tens (and fives) and fills a missing number | skip counts on from any number in the pattern |
| Bundle tens (Q4) | counts each bundle as one | counts the tens then the ones to name a number to 120 | renames the tens and ones fluently either way |
| Count arrays (Q5) | counts one row only | counts an array by rows using skip counting | sees the array as rows and columns and counts either way |
Five questions, four ideas. A child at standard makes equal groups, skip counts, bundles tens and counts an array by rows.
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 | Group a pile | Skip count on a line | Twelve, four ways | Bundle to 120 | Count by rows |
|---|---|---|---|---|---|
The five columns are the five days: group a pile, skip count on a line, twelve four ways, bundle to 120, and count an array by rows.