Teaching pack: Counting and comparing groups (Foundation) -- a week of maths lessons

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Teaching pack · Foundation Numberseegongsik /au

Counting and comparing groups: a week of ready-to-teach maths

Five days of lessons for Foundation 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.

AC9MFN03

quantify and compare collections to at least 20 using counting and explain or demonstrate reasoning

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 cards and counters 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.

One day, one lesson

The five lessons fill a week of maths, one lesson of about 40 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.

On the board

This pack is the printable half of a free interactive unit. The on-screen half has six interactive pictures (count a bigger group one number at a time, compare which group has more, match two groups one to one, spread a group out to see the amount hold, ask how do you know, and play a which-has-more game) you can run as a class on the board.

seegongsik.com/au/foundation/number/AC9MFN03

Aligned to the Australian Curriculum V9 (AC9MFN03). This pack is original material from seegongsik, independently produced and not endorsed by ACARA. Curriculum content descriptors are (c) ACARA, licensed under CC BY 4.0. Free to print and use in class.

The week at a glance5 lessons

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 a bigger group	Count a group up to 20 carefully, one number for each object	Count a Bigger Group
2	Which group has more?	Count two groups and say which has more, fewer or the same	Which Group Has More?
3	Match one to one	Compare without counting by giving each one a partner	Match Them Up, No Counting
4	Spreading out changes nothing	See that a group spread out is still the same number	Spreading Out Changes Nothing
5	How do you know?	Explain the reasoning, then play the compare game	How Do You Know?

How the week builds

Day 1 counts one bigger group carefully; Day 2 counts two groups and compares them; Day 3 compares by matching, with no counting at all; Day 4 shows the amount does not change when a group is spread out; and Day 5 asks children to explain how they know. It builds on naming numbers and knowing how many at a glance, and it opens the way to adding and taking away.

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 count and move.
Cut out once, use all week: the collection cards and the counters in this pack. No maths equipment to buy.

A note homeHome practice

Dear families

This week in maths, Foundation is learning to count groups up to twenty and to compare two groups. We count carefully, one number for each thing, and we say which group has more, fewer or the same.

Try this at home

Count a group of things together: forks on the table, socks in the wash, steps to the door. Touch each one once and say the numbers in order.
Make two little groups and ask which has more, which has fewer, or if they are the same.
Try it without counting: line the two groups up and give each thing a partner. The group with some left over has more.
Always ask the best question: how do you know?

My counting this week

Fill one row a day. Tick when you have counted it and checked it.

Day	I counted it	I checked it
Monday	□	□
Tuesday	□	□
Wednesday	□	□
Thursday	□	□
Friday	□	□

Printed from the free seegongsik Counting and comparing groups teaching pack · seegongsik.com/au/foundation/number/AC9MFN03/pack

Day 1 · Teacher planDay 1 of 5

Count a bigger group

Children count a group of up to twenty things, one number for each thing. Bigger groups test every counting skill at once, so we count slowly and carefully, and we keep the counted ones apart from the ones still to count.

We are learning to

count a group of up to twenty, saying one number for each thing,
keep the counted things apart from the ones still to count,
know the last number we say is how many there are.

Success criteria

I can count a group of up to twenty and say how many.
I can count without missing one or counting one twice.

You need

A handful of counters (buttons, dry pasta, blocks or bottle tops) for each pair. The collection cards (cut-out sheet 1). The worksheet, one per child.

Lesson flow (about 40 minutes)

10 min	Count together Count a group of classroom things aloud together, touching each one once. Then jumble them and count again. Ask: “Point to each one as we say its number. What was the very last number we said?”
20 min	Count and check Pairs count a pile of counters, then line them up in a row and count again to check. Show them how to slide each counter aside as it is counted. Ask: “You got fifteen, then fourteen. Which is right? Line them up and count once more to be sure.”
10 min	How many? Hold up a collection card; children count the dots and write the number. Ask: “Show me how you kept your place so you did not lose count.”

Two half-sessions instead? End Session A after Count together. Start Session B by counting a fresh pile, then move on to the cards.

On the board

Open the interactive unit and show “Count a Bigger Group”. Press “Count one more” and say each number out loud together as a dot lights up, laid in rows of five so it is easy to keep track. Press “Start over” to count again from one.

seegongsik.com/au/foundation/number/AC9MFN03

Watch for these ideas

Saying the numbers faster than the finger points, so some things are skipped or counted twice.
Losing track in a jumbled pile: lining the things up or sliding each aside fixes this.
Counting to the last number but not knowing that number is how many there are.

Answers

The three cards on the worksheet have 13, 17 and 20 dots.
Count-your-own varies: check the child counted one number for each counter and said the last number as the total.

Day 1 · Worksheet

How many are there?

NameClassDate

Count the dots in each group. Touch each one once. Write how many.

There are ____ dots.

Count your own

Take a handful of counters. Line them up in a row and count. How many? ____

Draw your counters in a row, then write how many

Day 2 · Teacher planDay 2 of 5

Which group has more?

Yesterday children counted one group. Today they count two and compare them. Count each group, then the bigger number tells you which has more. When the numbers are the same, the groups are the same, and that is a real answer, not a mistake.

We are learning to

count two groups, one at a time,
say which group has more and which has fewer,
know that two groups with the same number are the same.

Success criteria

I can count two groups and say which has more.
I can say when two groups have the same number.

You need

The collection cards (cut-out sheet 1) and counters. The worksheet, one per child.

Lesson flow (about 40 minutes)

10 min	Two piles Make two piles of counters. Guess which has more, then count both to check. Ask: “Which do you think has more? Now let us count. Were you right?”
20 min	Count and compare Pairs turn over two collection cards, count each, and say which has more and which has fewer. Slip in two cards with the same number. Ask: “You counted eight and eight. So which has more? Both the same is allowed.”
10 min	More, fewer, same On the worksheet children count two groups and write more, fewer or same. Say the words aloud as a class.

Two half-sessions instead? End Session A after Two piles. Start Session B with the card compare.

On the board

Show “Which Group Has More?”. Press “7 vs 5”, then “4 vs 6”, counting each side out loud before you press “Show the count”. Stop on “8 vs 8” so children meet two groups that are the same.

seegongsik.com/au/foundation/number/AC9MFN03

Watch for these ideas

Choosing the group that takes up more space rather than the one with more things.
Thinking same is a wrong answer: equal groups are a perfectly good result.
Miscounting one side, so the comparison is off: count each side again to check.

Answers

8 and 6: the group of 8 has more, the group of 6 has fewer.
7 and 9: the group of 9 has more, the group of 7 has fewer.
10 and 10: the same.

Day 2 · Worksheet

Which group has more?

NameClassDate

Count the blue group and the orange group. Write how many. Then write which has more.

____ dots

Which has more? ____________

Which has fewer? ____________

If they are the same, write same.

____ dots

Which has more? ____________

Which has fewer? ____________

If they are the same, write same.

____ dots

Which has more? ____________

Which has fewer? ____________

If they are the same, write same.

Day 3 · Teacher planDay 3 of 5

Match one to one

You do not always need to count to know which group has more. Line two groups up and give each thing a partner. The group with things left over, with no partner, is the bigger one. This gives children a direct feel for more and fewer.

We are learning to

give each thing in one group a partner in the other group,
see that leftover things with no partner mean more,
compare two groups without counting them.

Success criteria

I can match two groups one to one.
I can say which group has more without counting.

You need

Counters in two colours, or the collection cards (cut-out sheet 1). The worksheet, one per child.

Lesson flow (about 40 minutes)

10 min	Give each a partner Lay a row of counters. Under each one, place a counter of another colour. Do any have no partner? Ask: “Every top counter needs one partner below. Which row has some left over?”
20 min	No counting allowed Pairs compare two groups by matching only, not counting. The row with leftovers has more. Then count to check they agree. Ask: “You matched them and two blue ones had no partner. So which has more, and how do you know?”
10 min	Draw the lines On the worksheet children draw a line from each top dot to one below, then say which row has more.

Two half-sessions instead? End Session A after Give each a partner. Start Session B with the no-counting compare.

On the board

Show “Match Them Up, No Counting”. Press “Match one to one” to draw a line between each pair; the dots with no partner show which group has more. Press “Reset” and let a child predict before you match again.

seegongsik.com/au/foundation/number/AC9MFN03

Watch for these ideas

Giving one thing two partners, or leaving a gap, so the match is not fair.
Thinking the longer-looking row must win, even when the rows pair up exactly.
Forgetting that when every thing has a partner, the groups are the same.

Answers

Top row 6, bottom row 8: the bottom row has more, with two left over.
Top row 5, bottom row 5: they match exactly, so the groups are the same.

Day 3 · Worksheet

Give each one a partner

NameClassDate

Draw a line from each top dot to one dot below it. Then answer without counting.

Which row has more? ____________

How do you know? ____________________________________

Which row has more? ____________

How do you know? ____________________________________

Day 4 · Teacher planDay 4 of 5

Spreading out changes nothing

Here is an idea that trips up many young children. The number of things does not change when you spread them out or push them together. Seven counters in a tight bunch and the same seven spread across the table are still seven. Many children think the spread-out group has more, because it looks bigger. This is famous and completely normal. The cure is gentle: count both ways, and let the child discover the amount did not change.

We are learning to

see that the amount stays the same when a group is spread out,
count a group both close together and spread wide,
trust the count, not how much space the group takes up.

Success criteria

I can say the amount is the same when a group is spread out.
I can check by counting both ways.

You need

A handful of counters for each pair. The worksheet, one per child.

Lesson flow (about 40 minutes)

10 min	Push and spread Count a group of counters together. Push them into a bunch, then spread them wide. Ask before counting each time. Ask: “I have spread them out. Do you think there are more now? Let us count and see.”
20 min	Still the same Pairs take a set number of counters, spread and squash them, and count each time. They record that the number never changed. Ask: “It looked bigger when it was spread out. But when we counted, how many were there?”
10 min	Same or not? On the worksheet children count the same group close together and spread wide, then tick that the number is the same.

Two half-sessions instead? End Session A after Push and spread. Start Session B with Still the same.

On the board

Show “Spreading Out Changes Nothing”. Press “Spread wide” and “Close together” to move the same five dots apart and back. The label stays the same both ways, so children can see the amount never changed.

seegongsik.com/au/foundation/number/AC9MFN03

Watch for these ideas

Saying the spread-out group has more because it takes up a longer space.
Guessing instead of counting: the fix is always to count both arrangements.
Believing the number changed even after counting the same total twice.

Answers

The first group is 7 close together and 7 spread wide: the same, 7.
The second group is 9 close together and 9 spread wide: the same, 9.
Spreading a group out never changes how many there are.

Day 4 · Worksheet

Is it still the same?

NameClassDate

These are the same counters, close together and spread wide. Count both. Are they the same?

Close together

How many? ____

Spread wide

How many? ____

Are there the same number? Yes □ No □

Close together

How many? ____

Spread wide

How many? ____

Are there the same number? Yes □ No □

When you spread a group out, the number stays the ____________.

Day 5 · Teacher planDay 5 of 5

How do you know?

The most important question in this whole topic is not which group has more, but how do you know. A child might say “I counted them and got nine and six”, or “I matched them up and these had no partner”. Both are excellent. Asking for the reason shows whether a child truly understands, and builds the habit of explaining, right from the start.

We are learning to

say which group has more,
explain how we know, by counting or by matching,
check a friend’s answer and its reason.

Success criteria

I can say which group has more and explain how I know.
I can compare two groups by counting or by matching.

You need

Counters and the collection cards (cut-out sheet 1). The worksheet, one per child.

Lesson flow (about 40 minutes)

10 min	Two good reasons Compare two groups. Take two answers: one child who counted, one who matched. Praise both ways. Ask: “You both said blue has more. Tell me how you know. Did you count, or did you match?”
20 min	The compare game Partners each make a group, then say which has more and how they know. Swap the job of checking the reason. Ask: “Your partner says theirs has more. Ask them: how do you know? Do you agree?”
10 min	Write how you know On the worksheet children compare two groups and write which has more and how they know.

Two half-sessions instead? End Session A after Two good reasons. Start Session B with the compare game.

On the board

Show “How Do You Know?” and press “I counted” then “I matched them” to see both reasons written out. Then open “Which Has More? A Game”, press “Blue (left)”, “Same” or “Orange (right)” as a class, and press “New round” for a fresh pair.

seegongsik.com/au/foundation/number/AC9MFN03

Watch for these ideas

Giving the answer but no reason: gently ask how do you know every time.
Thinking there is only one right way: counting and matching are both good.
Accepting a friend’s answer without checking the reason makes sense.

Answers

9 and 6: blue has more. A good reason: I counted nine and six, and nine is more; or I matched them and three blue had no partner.
7 and 7: the same. A good reason: I matched them and every one had a partner; or I counted seven and seven.
Own game varies: check the child gives an answer and a reason.

Day 5 · Worksheet

How do you know?

NameClassDate

Compare the two groups. Write which has more. Then write how you know.

Blue

Orange

Which has more? ____________

How do you know?

Blue

Orange

Which has more? ____________

How do you know?

Play the compare game

Make a group of counters. Your partner makes one too. Say which has more, and how you know. Then swap.

Cut-out cards 1 of 2Collection cards

Collection cards

Cut out the cards. Each card is a group of dots. Count a card to say how many, or hold up two cards and ask which group has more. One set per pair is plenty.

Teacher note: the cards show 6, 9, 11, 13, 15, 17, 18 and 20 dots, laid in rows of five so they are easy to count. The numbers are not printed, so children count for themselves.

Cut-out cards 2 of 2Counters

Counters

Cut out the counters. Use them to build a group and count it (Day 1), to match two groups one to one (Day 3), and to spread a group out and count again (Day 4). Keep them in a bag or a cup between lessons.

Teacher note: thirty counters is enough for one child to build and compare groups to twenty all week.

Mini-check · End of the weekCounting and comparing

What we know: counting and comparing groups

NameClassDate

Work on your own. Count carefully. Show your thinking if you can.

Count this group. How many? ____
Count this group. How many? ____
Count each group. Which has more? ____________
Blue
Orange
Count each group. Which has fewer? ____________
Blue
Orange
Count each group. Are they the same? Write yes or no: ____
Blue
Orange
Fifteen counters are spread out across the table. Now there are ____ counters.
You matched two rows one to one. Three dots in the top row had no partner. Which row has more? ____________
Look at the two groups in question 3. How do you know which one has more? Write or draw how you know. ____________________________________

Mini-check · Answers and markingFor the teacher

Answers and marking guide

Answers

12.
16.
The orange group has more (14 is more than 10).
The group of 8 has fewer.
Yes, they are the same (13 and 13).
Still 15: spreading a group out does not change how many there are.
The top row has more, by three (the three with no partner).
A good reason is either: I counted them and got ten and fourteen, and fourteen is more; or I matched them and the orange group had some left over. Accept any clear count or match.

A quick three-level guide

Idea	Working towards	At standard	Beyond
Quantify (Q1, Q2)	counts a small group with help	counts a group to 20, one number each, and says the last number is how many	counts on and checks by counting again
Compare (Q3, Q4, Q5)	compares by looking	counts both groups and says more, fewer or the same	compares by matching as well as by counting
Amount holds (Q6, Q7)	thinks spreading out changes the amount	knows the amount holds when spread out, and reads the leftovers in a match	explains why the amount did not change
Explain (Q8)	gives an answer with no reason	gives a reason: I counted, or I matched them	checks whether a friend has given a reason that makes sense

Eight questions, four ideas. A child at standard answers most questions and can say how they know.

Weekly recordClass checklist

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	Counts to 20	Compares groups	Matches one to one	Amount stays the same	Explains how

The five columns are the five days: count to twenty, compare groups, match one to one, see the amount hold, and explain how you know.