Sharing and grouping: 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 sharing mats and cards, a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Cut out the two card sheets once; the mats and counters are reused all week.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and when.
5. 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 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.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Day 1 shares things out fairly; Day 2 gathers them into equal groups; Day 3 judges whether a share is fair; Day 4 sees the two ways of splitting side by side; and Day 5 puts it all into a party story. It builds on adding and taking away, and it opens the way to division, long before that word or its symbol appears.

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, buttons, blocks or dry pasta to share and group, and a few paper plates or bowls.
• Cut out once, use all week: the sharing mats, the counters and the treat cards in this pack. No maths equipment to buy.

Dear families

This week in maths, Foundation explores sharing and grouping. We deal things out so each share is equal, gather things into equal groups, and decide when a share is fair.

Try this at home

• Share a snack fairly: hand out grapes or crackers one at a time, one for you, one for me, until they are gone.
• Ask which is fair: put a few on two plates and ask, do we each have the same?
• Make equal groups: pop socks into pairs, or sort blocks into groups of the same size, and count the groups.
• Notice the leftover: when a snack will not share evenly, talk about the few left over.

My sharing this week

Fill one row a day. Tick when the share was fair.

Printed from the free seegongsik Sharing and grouping teaching pack · seegongsik.com/au/foundation/number/AC9MFN06/pack

Share fairly

Children share a small pile of things by dealing them out one at a time — one for you, one for me — until each share is the same. Hands come first all week: doing convinces faster than telling.

We are learning to

• share things out one at a time, going round and round,
• keep sharing until each person has the same,
• count how many are in each fair share.

Success criteria

• I can deal things out so each share is the same.
• I can say how many are in each share.

You need

A tub of counters, buttons or blocks to share. The sharing mats and counter cards (cut-out sheets 1 and 2), one set per pair. The worksheet, one per child.

Lesson flow (about 40 minutes)

Two half-sessions instead? End Session A after 6 between 2. Start Session B by dealing 8 between 2, then go on to 9 between 3.

Watch for these ideas

• Piling most on one mat, then handing over a few: sharing must go one at a time to stay fair.
• Stopping before the pile is gone, so the mats do not match.
• Guessing the answer instead of dealing and counting: act it out first.

Answers

• 6 shared between 2 is 3 on each mat. 8 shared between 2 is 4 on each mat.
• 9 shared between 3 is 3 on each mat.
• Own share varies: check each mat holds the same, and none are left in the hand.

One for you, one for me

Deal the counters onto the plates, one at a time, until they are all shared. Draw what lands on each plate, then write how many each plate gets.

Share 6 between 2 plates

Each plate gets ____.

Share 9 between 3 plates

Each plate gets ____.

Just write how many each

Your own fair share

Choose a small pile. Share it onto 2 plates. Draw it, and write how many on each: ____

Make equal groups

Yesterday we shared between people. Today we do the other kind of splitting: we choose how big each group is, gather the things into groups of that size, and count how many groups we get.

We are learning to

• put things into groups of the same size,
• make each group hold the number I chose,
• count how many equal groups there are.

Success criteria

• I can make groups that are all the same size.
• I can count how many groups I made.

You need

A tub of counters, buttons or blocks. The counter cards (cut-out sheet 2), one set per pair. The worksheet, one per child.

Lesson flow (about 40 minutes)

Two half-sessions instead? End Session A after 6 into groups of 2. Start Session B with 9 into groups of 3.

Watch for these ideas

• Making groups of different sizes: equal groups must all hold the same.
• Counting the things instead of the groups: the answer is how many groups.
• Forcing a short last group to count: a group that is not full is not an equal group.

Answers

• 6 in groups of 2 makes 3 groups. 9 in groups of 3 makes 3 groups.
• 10 in groups of 2 makes 5 groups.
• Own grouping varies: check every group is the same size, and count the groups.

Groups of the same size

Ring the counters into equal groups. Then write how many groups you made.

Ring 6 counters into groups of 2

I made ____ groups.

Ring 10 counters into groups of 2

I made ____ groups.

Just write how many groups

Your own groups

Choose a small pile. Ring it into equal groups. Draw it, and write how many groups: ____

Fair or not fair?

Sharing is only fair when each share is equal. Today children become fairness judges: they look at two plates and decide, do these match? The word that holds the week together is equal.

We are learning to

• look at two shares and decide if they are equal,
• say that a share is only fair when each part is the same,
• fix an unfair share by moving one across.

Success criteria

• I can decide if two plates hold the same.
• I can make an unfair share fair.

You need

The sharing mats and counter cards (cut-out sheets 1 and 2), one set per pair. The worksheet, one per child.

Lesson flow (about 40 minutes)

Two half-sessions instead? End Session A after do we match; start Session B with judge and fix.

Watch for these ideas

• Calling a share fair because everyone got some, even when the plates are not equal.
• Looking at the size of the pile, not counting each plate.
• Thinking unfair cannot be fixed: moving one across can make them match.

Answers

• 4 and 4 is fair. 5 and 3 is not fair. 3 and 3 is fair. 6 and 2 is not fair.
• To make 5 and 3 fair, move one across to make 4 and 4.
• To make 6 and 2 fair, move two across to make 4 and 4.

Is it a fair share?

Count each plate. If they hold the same, it is fair. Tick Yes or No for each one.

Make it fair

One plate has 5 and the other has 1. Move some across so both plates are the same. Draw both plates.

Two ways to split

The same pile can be split two ways. You can share it between people, or you can make groups of a set size. Today children see both ways side by side and notice they can land on the same number.

We are learning to

• share a pile between people to find how many each,
• group the same pile into a set size to find how many groups,
• see that sharing and grouping are two ways of splitting.

Success criteria

• I can split a pile by sharing it out.
• I can split the same pile by making equal groups.

You need

A tub of counters. The sharing mats and counter cards (cut-out sheets 1 and 2), one set per pair. The worksheet, one per child.

Lesson flow (about 40 minutes)

Two half-sessions instead? End Session A after the pile of 6; start Session B with the pile of 8.

Watch for these ideas

• Thinking sharing and grouping are the same action: one deals out, the other bundles up.
• Mixing up the answer: sharing tells how many each, grouping tells how many groups.
• Expecting a different pile for each way: it is the same pile, split two ways.

Answers

• 6 shared between 2 is 3 each. 6 grouped by 2 is 3 groups.
• 8 shared between 2 is 4 each. 8 grouped by 2 is 4 groups.
• Each pile splits the same way both times because it is the same amount of counters.

Split it two ways

Take the same pile twice. First share it between 2 plates. Then make groups of 2. Fill in both answers.

Share 6, then group 6

Share 6 between 2 plates: ____ on each plate.

Make groups of 2 from 6: ____ groups.

Do both for each pile

Real problems (the party bags)

It is party day. Filling party bags is exactly this week’s maths: share the treats so each bag is the same, or pack them in equal groups. Today the week comes together, and sometimes there are a few left over.

We are learning to

• share treats so each party bag holds the same,
• pack treats into equal groups,
• notice when a few are left over.

Success criteria

• I can share treats equally into party bags.
• I can say how many are left over.

You need

The treat cards (cut-out sheet 2) and a few paper bags or drawn bags. The worksheet, one per child.

Lesson flow (about 40 minutes)

Two half-sessions instead? End Session A after the party problems; start Session B with the mini-check.

Watch for these ideas

• Putting more in one bag to use up the leftover: a fair share keeps the bags equal.
• Thinking a leftover is a mistake: it is simply what is left when a pile will not share evenly.
• Guessing instead of dealing: pack the treats out and count each bag.

Answers

• 8 shared into 2 bags is 4 in each bag. 6 packed in groups of 3 is 2 bags.
• 10 shared into 2 bags is 5 in each bag.
• 7 shared into 2 bags is 3 in each bag, with 1 left over.

The party bags

It is party day. Pack the treats fairly. Deal them out, draw them, and write the answer.

Share 8 treats into 2 party bags

Each bag gets ____.

Party problems

The leftover one

Share 7 treats into 2 party bags. Each bag gets ____, and ____ is left over.

Sharing mats

Cut out the mats. To share, deal counters onto the mats one at a time until each mat holds the same. Use the plates to share onto plates, or the people mats to give one to each person. One set per pair is plenty.

Plates to share onto

People to share to

Teacher note: the mats are the plates from the on-screen pictures, so the floor sharing and the screen match. Share onto two mats, or three, or four.

Counters and treat cards

Cut out the counters and treat cards. Use the counters to share and to make equal groups (Days 1, 2, 3 and 4). Use the treat cards to fill the party bags (Day 5).

Counters

Treat cards

Teacher note: all the counters are the same, so a fair share means each mat holds the same number of them.

What we know: sharing and grouping

Work on your own. Draw the counters if it helps.

1. Share 4 apples between 2 plates. How many on each plate? ____
2. Share 6 grapes between 3 children. How many each? ____
3. Put 8 blocks into groups of 2. How many groups? ____
4. Put 4 pencils into groups of 2. How many groups? ____
5. One plate has 2 lollies, the other has 2. Is this a fair share? Circle: fair / not fair
6. One plate has 4 lollies, the other has 1. Is this a fair share? Circle: fair / not fair
7. Share 8 treats into 4 party bags. How many in each bag? ____
8. Draw 8 counters. Ring them into groups of 4. How many groups? ____

Answers and marking guide

Answers

1. 2 on each plate.
2. 2 each.
3. 4 groups.
4. 2 groups.
5. Fair (2 and 2 are equal).
6. Not fair (4 and 1 are not equal).
7. 2 in each bag.
8. 2 groups.

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say why a share is fair.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: share fairly, make equal groups, judge fair or not, split two ways, and solve party problems.