Adding and Taking Away: 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 story mats and counters, 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 story mats and the 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 mix-ups 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 joins two groups; Day 2 takes some away; Day 3 makes adding quicker by counting on from the bigger group; Day 4 shows that adding and taking away are two sides of one picture; and Day 5 puts it all to work in tuckshop stories. It builds on part-part-whole to 10 from earlier in Foundation, and it opens the way to the number facts and simple sums of Year 1.

Materials for the week (one trip)

• From the classroom: scissors, pencils, this pack printed.
• From home or the craft box: a handful of buttons, dry pasta, bottle tops or blocks to use as counters, in two colours if you can.
• Cut out once, use all week: the story mats and the counters in this pack. No maths equipment to buy.

Dear families

This week in maths, Foundation adds and takes away with real things. We put two groups together to add, take some away to subtract, learn to count on from the bigger group, and see how adding and taking away tell the same story.

Try this at home

• Count out a small handful of pasta or blocks. Add a few more and ask how many altogether.
• Start with a plate of grapes or crackers. Eat some, then ask how many are left.
• To add, say the bigger number first and count on the rest: for 2 and 5, start at 5 and count on two.
• Tell a tiny story at the shops: we had 5 coins, we spent 2, how many are left?

My maths this week

Fill one row a day. Tick when you have shown it with real things.

Printed from the free seegongsik Adding and Taking Away teaching pack · seegongsik.com/au/foundation/number/AC9MFN05/pack

Joining two groups

Children put two groups of counters together and count how many altogether. Adding is not a written trick this week; it is a story acted out with real things, and the number comes after the action, to say how many.

We are learning to

• put two groups together to make one bigger group,
• count how many there are altogether,
• see a small group at a glance, without counting one by one.

Success criteria

• I can join two groups and count them all.
• I can say how many altogether.

You need

A handful of counters (buttons, pasta or blocks) in two colours, one set per pair. The story mats (cut-out sheet 1) and the counters (cut-out sheet 2). The worksheet, one per child.

Lesson flow (about 40 minutes)

Two half-sessions instead? End Session A after the first join. Start Session B by rebuilding 3 and 2 from memory, then go on to 4 and 3.

Watch for these ideas

• Counting only one group and stopping: both groups join to make the total.
• Recounting the first group from one after it has been pushed across, instead of carrying on.
• Writing the two numbers side by side (a 3 and a 2 make 32) instead of joining the amounts.

Answers

• 3 and 2 make 5. 4 and 3 make 7. 5 and 1 make 6. 2 and 4 make 6.
• 2 and 2 make 4 (a group you can see at a glance).
• Build-your-own varies: check the drawing shows both groups and the total matches.

Join the groups

Draw the two groups. Push them together and count how many altogether.

3 and 2

Draw 3 counters, then 2 more. Altogether ____.

Join and count

Your own join

Pick two small groups. Draw them, push them together, and write how many altogether: ____

Taking away

Taking away is the opposite motion to joining. Start with a group, remove some, and count what is left. The same story can be told with anything: birds off a fence, biscuits from a plate, coins spent at the shop.

We are learning to

• start with a group and take some away,
• count what is left,
• keep track of which counters have gone.

Success criteria

• I can take some away from a group.
• I can count how many are left.

You need

The counters (cut-out sheet 2) and the take-away mat (cut-out sheet 1), one set per pair. The worksheet, one per child.

Lesson flow (about 40 minutes)

Two half-sessions instead? End Session A after the first take-away. Start Session B with 6 take away 2.

Watch for these ideas

• Counting the group that went instead of the group that is left.
• Losing track of what has gone, so the same counter is taken twice or skipped.
• Counting the start group again from one after some have gone, rather than the leftovers.

Answers

• 7 take away 3 leaves 4. 6 take away 2 leaves 4. 8 take away 5 leaves 3.
• 5 take away 2 leaves 3 (the quick plate story).
• Take-away-your-own varies: check the crossed-out counters match the number that went.

Take some away

Start with the group. Cross out how many go. Count what is left.

7 take away 3

Draw 7 counters. Cross out 3. How many are left? ____

Take away and count

Your own take-away

Start with a group. Take some away. Draw it and write how many are left: ____

Count on from the bigger

There is a faster way to add than counting a whole group again. Hold the bigger number in your head, then count on the rest one by one. It teaches children to trust a number they already know rather than starting from one every time.

We are learning to

• find the bigger of two groups,
• hold that number in my head,
• count on the smaller group to add.

Success criteria

• I can start at the bigger number.
• I can count on the rest to find the total.

You need

The counters (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 the hidden group. Start Session B with 5 and 3.

Watch for these ideas

• Counting the whole first group again from one before counting on.
• Starting at the smaller number, which means more counting on than needed.
• Counting the starting number as the first jump (saying “five” for the first count on) instead of six.

Answers

• 5 and 3 make 8 (start at 5, count on three).
• 2 and 6 make 8 (start at the bigger, 6, count on two).
• 4 and 4 make 8 (start at 4, count on four).
• Count-on-your-own varies: check they started at the bigger number.

Start at the bigger, then count on

Write which number you start at, then count on the rest and write the answer.

Your own

Choose two numbers. Start at the bigger and count on: ____ and ____ make ____

Add and take away are linked

The deepest idea of the week: adding and taking away are two sides of one picture. If 3 and 2 make 5, then 5 take away 2 leaves 3. The same three numbers make a little family of facts, so knowing one fact hands you the others.

We are learning to

• see that the same three numbers make adding and taking-away facts,
• use an add fact to find a take-away fact,
• tell the four facts in one number family.

Success criteria

• I can find a take-away from an add I know.
• I can say the facts that go with three numbers.

You need

The counters (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 turning it around. Start Session B with the whole family.

Watch for these ideas

• Thinking a take-away needs a fresh count when a known add already gives the answer.
• Mixing up the whole and a part, so the take-away starts from the wrong number.
• Believing 4 and 3 is a different sum from 3 and 4: the order of the parts does not change the whole.

Answers

• 4, 3, 7: 4 + 3 = 7, 3 + 4 = 7, 7 take away 4 = 3, 7 take away 3 = 4.
• 5, 4, 9: 5 + 4 = 9, 4 + 5 = 9, 9 take away 5 = 4, 9 take away 4 = 5.
• 2, 6, 8: 2 + 6 = 8, 6 + 2 = 8, 8 take away 2 = 6, 8 take away 6 = 2.

One story, four facts

The same three numbers make four facts. Fill in each family. Use counters to check.

Finish the sentence

If I know 4 and 3 make 7, then 7 take away 3 leaves ____.

Real problems: the tuckshop

A story does not say “add” or “take away”; the child has to hear which one is happening. Today the week comes together at the tuckshop, where groups grow when you buy more and shrink when you spend.

We are learning to

• listen to a story and decide whether to add or take away,
• act it out with counters or coins,
• say how many altogether or how many are left.

Success criteria

• I can tell whether a story adds or takes away.
• I can find the answer with counters.

You need

The counters (cut-out sheet 2) as coins, one set per pair. The worksheet, one per child. The mini-check is ready when you are.

Lesson flow (about 40 minutes)

Two half-sessions instead? End Session A after the tuckshop stories. Start Session B with the mini-check.

Watch for these ideas

• Adding when the story takes away, or taking away when it adds: the words tell you which.
• Answering with the number that changed (how many spent) instead of what is left.
• Reaching for a written sum before acting the story out with real things.

Answers

• 6 coins spend 4 leaves 2 (take away).
• 3 pies buy 4 more make 7 (add).
• 8 grapes eat 3 leaves 5 (take away).
• Own story varies: check it clearly adds or takes away and the answer matches.

At the tuckshop

Read each story. Do you add or take away? Use counters, then write the answer.

1. You have 6 coins. You spend 4 on a muffin. How many coins are left? ____
2. You buy 3 party pies, then 4 more for a friend. How many pies now? ____
3. There are 8 grapes on your plate. You eat 3. How many are left? ____

Your own tuckshop story

Write a story for a partner. Make it add or take away, and know the answer.

Story mats

Cut out the two mats. Use the joining mat to add: put a group in each side, push them together, and count the altogether space. Use the take-away mat to subtract: fill the start space, slide some into the gone space, and count what is left. One mat per pair is plenty.

Teacher note: the mats hold the same story the screen tells. The joining mat is the two groups from “Joining Two Groups”; the take-away mat is the crossing-out from “Taking Away”.

Counters

Cut out the counters. Use them on the mats every day: as counters to join and take away, and as coins at the tuckshop on Day 5. Colour half in one colour and half in another if you like, so a joining story shows two groups.

Counters (colour them in)

Teacher note: two dozen counters is enough for the small numbers this week. Print a second sheet if a pair needs more.

What we know: Adding and Taking Away

Work on your own. Use counters if you need them.

1. 4 red counters and 2 blue counters. How many altogether? ____
2. 3 and 3 make ____
3. 9 take away 2 leaves ____
4. 8 take away 4 leaves ____
5. To add 6 and 3, start at the bigger number and count on. 6 and 3 make ____
6. You know 5 and 2 make 7. So 7 take away 2 leaves ____
7. You have 3 marbles and win 5 more. How many now? ____
8. You have 10 stickers and give 4 to a friend. How many are left? ____

Answers and marking guide

Answers

1. 6 altogether.
2. 6.
3. 7 left.
4. 4 left.
5. 9 (start at 6, count on three).
6. 5 (the same three numbers, 5, 2 and 7, make both facts).
7. 8 marbles.
8. 6 stickers left.

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can act out why with counters.

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: join, take away, count on, link add and take away, and solve story problems.