Add and Subtract Within 20: a week of ready-to-teach maths

Five days of lessons for Year 1 Number. Children learn to add and take away within twenty using their part-part-whole knowledge to ten and a handful of dependable strategies: count on from the bigger number, bridge through ten, and find the missing part. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out ten-frames 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; they 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 muddles 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: the bar model on Day 1 is the picture every later day draws on, and each strategy 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 builds on the day before, so run them in order.

How the week builds

Day 1 sees a whole as two parts on a bar and learns the pairs that make ten. Day 2 adds by counting on from the bigger number. Day 3 bridges through ten, splitting the smaller number to make ten first. Day 4 turns the bar around to find a missing part, which is how taking away feels easy. Day 5 puts it all into a birds-on-the-wire story. It builds on part-part- whole to ten from Foundation, and it opens the way to addition and subtraction within a hundred.

Materials for the week (one trip)

• From the classroom: scissors, pencils, this pack printed.
• From home or the craft box: a small handful of counters, buttons or dry pasta, up to twenty per child, in two colours if you can.
• Cut out once, use all week: the ten-frames, counters, the part-part-whole bar mat and the number cards 0 to 20 in this pack. No maths equipment to buy.

Dear families

This week in maths, Year 1 adds and takes away within twenty. We use our fingers, we start at the bigger number and count on, and we make ten first when it helps. No sums to memorise yet: the point is to see how the numbers come apart and go back together.

Try this at home

• Add on your fingers. Hold up 8, then count on 3 more: nine, ten, eleven.
• Start at the bigger number. For 3 and 9, start at nine and count on three; it is quicker.
• Make ten first. For 8 and 5, take 2 to make ten, then add the 3 that is left: thirteen.
• Take away with a story. There are 12 grapes, you eat 5, how many are left? Count back or find the missing part.

My adding this week

Fill one row a day. Tick when you added or took away and said how you worked it out.

Printed from the free seegongsik Add and Subtract Within 20 teaching pack · seegongsik.com/au/y1/number/AC9M1N04/pack

The part-part-whole bar

A bar is one whole. Split it and you have two parts; the two parts always join back to the same whole. This one picture carries the whole week: adding is joining the parts, and taking away is finding a part that is missing. Today we meet the bar and learn the pairs that make ten by heart.

We are learning to

• see a whole as two parts on a bar,
• name the pairs of parts that make ten, such as six and four,
• join two parts to make the whole, and split a whole into two parts.

Success criteria

• I can show a whole as two parts on a bar.
• I can say a pair of parts that makes ten.

You need

A small handful of counters, up to twenty per child, in two colours if you can. The part-part- whole bar mat (cut-out sheet 1), one per pair. The worksheet, one per child.

Lesson flow (about 40 minutes)

Two half-sessions instead? End Session A after filling the bar. Start Session B by rebuilding a whole of ten, then finding a new pair of parts.

Watch for these ideas

• Parts that do not add back to the whole: the two parts must rebuild the bar exactly.
• Thinking the whole grows or shrinks when the divider slides: nothing is added or taken away.
• Counting one part twice, or leaving a counter out, so the pair misses the whole.

Answers

• 10 = 7 and 3. 8 = 5 and 3.
• Parts 6 and 3 make a whole of 9.
• Ten splits many ways: 6 and 4, 7 and 3, 5 and 5, 8 and 2, 9 and 1 (and each turned around). Any pair that makes ten is correct.

Fill the bar

The bar is the whole. It splits into two parts. Use counters on the bar mat, then fill in the missing number so the two parts make the whole.

Find the missing part

Row 3: the two parts are 6 and 3. Write the whole they make.

Pairs that make 10

Write three different pairs of parts that make 10: ____ and ____, ____ and ____, ____ and ____.

Count on, not over

To add, you do not need to count from one every time. Hold the bigger number in your head and count on the rest. For eight and three, start at eight and say nine, ten, eleven: three counts on, and you are there. Counting on is faster and leaves fewer places to slip.

We are learning to

• start at the bigger number when we add,
• count on the smaller number, one at a time,
• stop on the total and say it.

Success criteria

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

You need

Counters, up to twenty per child, and fingers for counting on. The worksheet, one per child (it carries the number track). A big number track on the board or floor helps.

Lesson flow (about 40 minutes)

Two half-sessions instead? End Session A after hopping the big track; start Session B with the worksheet sums.

Watch for these ideas

• Counting all from one instead of counting on from the bigger number: hold the big number, count the rest.
• Counting the start number as the first hop, so the total lands one short: the first hop is the next number.
• Starting at the smaller number, which makes more hops to slip on: always start at the bigger one.

Answers

• 7 + 2 = 9 (start at 7: eight, nine).
• 9 + 3 = 12 (start at 9: ten, eleven, twelve).
• 6 + 4 = 10 (start at 6: seven, eight, nine, ten).

Start big, count on

Circle the bigger number. Start there and count on the smaller number with hops on the track. Write the total.

Count on to add

For 6 + 4, remember to start at the bigger number, then count on.

Show your hops

For 9 + 3, mark 9 on the track, then draw three hops. Where do you land? ____

Bridge through ten

Ten is the easiest number to add to. So when a sum climbs past ten, make ten first. For eight and five, give two of the five to the eight to make ten, then add the three that is left: ten and three is thirteen. Splitting the smaller number to build a ten is the strategy that carries adding for years to come.

We are learning to

• make ten first when a sum goes past ten,
• split the smaller number into the part that makes ten and the part left over,
• add the leftover part to ten to find the total.

Success criteria

• I can make ten first.
• I can add the part that is left to find the total.

You need

Counters, up to twenty per child, and two ten-frames each (cut-out sheet 1) so ten fills one frame and the rest spills into the next. The worksheet, one per child.

Lesson flow (about 40 minutes)

Two half-sessions instead? End Session A after filling the first ten; start Session B with the worksheet sums.

Watch for these ideas

• Adding straight across without making ten first, so the count spills and slips: build the ten, then add.
• Splitting the smaller number the wrong way, so the ten is not made: take just enough to fill ten.
• Losing the leftover part after making ten: the part left over is what you still add on.

Answers

• 8 + 5 = 13 (8 + 2 = 10, then 10 + 3).
• 7 + 6 = 13 (7 + 3 = 10, then 10 + 3).
• 9 + 4 = 13 (9 + 1 = 10, then 10 + 3).

Make ten first

Use two ten-frames. Fill the ten first, then add the part that is left. Write the total. The make-ten split is shown to help you.

Bridge through ten

Show the split

For 8 + 5: the 5 splits into ____ and ____. Take ____ to make ten, then add ____. The total is ____.

The missing part

Take away is the bar turned around. The whole is on top and one part is shown; the other part is hidden. Ten take away six is really the missing part of a ten made of six and something. Seeing subtraction as a missing part turns a hard-feeling operation into the same part-part-whole picture children already trust.

We are learning to

• see take away as a missing part of a whole,
• find the missing part when the whole and one part are shown,
• write the take away and the missing part as the same story.

Success criteria

• I can find the missing part.
• I can check that my two parts make the whole.

You need

Counters, up to twenty per child, and a cup or hand to hide some. The part-part-whole bar mat (cut-out sheet 1). The worksheet, one per child.

Lesson flow (about 40 minutes)

Two half-sessions instead? End Session A after hiding a part; start Session B with the worksheet.

Watch for these ideas

• Subtracting the wrong way, such as taking the whole from the part: the part is always smaller than the whole.
• Reading the shown part as the answer: the answer is the hidden part.
• Guessing instead of reasoning from the whole: the two parts must make the whole.

Answers

• 9 take away 4: missing part 5. 10 take away 7: missing part 3.
• 6 and 5 make 11, so the missing part is 5.
• Check each: the shown part and the missing part join back to the whole.

What is the missing part?

The whole and one part are shown. Find the missing part. Use counters or the bar mat to help, then write it.

Row 1 is 9 take away 4. Row 2 is 10 take away 7. Row 3 is 6 and ____ make 11.

Say it two ways

The whole is 10 and one part is 6. The missing part is ____. Write it as a take away: 10 take away 6 is ____.

Birds on the wire

Birds land on a wire and birds fly away. Landing adds; flying away takes away. It is the same bar all week: the birds already there are one part, the birds that land are the other part, and together they make the whole flock. Today the week’s strategies walk into a story, then the class meets the mini-check.

We are learning to

• tell an add or take away story from birds on a wire,
• draw the bar and write the number sentence,
• choose a strategy: count on, bridge through ten, or find the missing part.

Success criteria

• I can write the number sentence for a story.
• I can find the answer and check it on the bar.

You need

Counters as pretend birds, up to twenty per child. The part-part-whole bar mat (cut-out sheet 1). The worksheet and the mini-check, one each per child.

Lesson flow (about 40 minutes)

Two half-sessions instead? End Session A after the bird stories; run the mini-check as Session B.

Watch for these ideas

• Adding when the story says fly away, or taking away when it says land: match the action to the number sentence.
• Counting all from one when counting on or making ten would be quicker: choose the strategy that fits.
• Losing track of the whole flock while parts change: the two parts still make the whole.

Answers

• Story 1: 5 + 4 = 9 birds.
• Story 2: 12 - 5 = 7 birds.
• Story 3: 6 + 7 = 13 birds (make ten: 6 + 4 = 10, then 10 + 3).

Birds on the wire

Read each story. Draw the bar with two parts. Write the number sentence, then the answer. Use counters as birds if it helps.

Story 1: birds land

5 birds are on the wire. 4 more land. How many birds now?

Number sentence: ____ + ____ = ____. Answer: ____ birds.

Story 2: birds fly away

12 birds are on the wire. 5 fly away. How many birds are left?

Number sentence: ____ - ____ = ____. Answer: ____ birds.

Story 3: birds land

6 birds are on the wire. 7 more land. How many birds now?

Number sentence: ____ + ____ = ____. Answer: ____ birds.

Ten-frames, counters and the bar mat

Cut out the ten-frames, a sheet of counters and the part-part-whole bar mat. Fill a ten-frame to make ten, then spill the rest into the next frame to bridge through ten. Lay the whole along the top of the bar mat, then push the counters down into the two parts. One set per pair is plenty, and it is used every day this week.

Two ten-frames

Counters (two colours)

Part-part-whole bar mat

Teacher note: the whole bar sits above its two parts, so a child can see the whole come apart and join back. This is the same picture the bar and the birds use on screen.

Number cards (0 to 20)

Cut out the cards. Use them to name a part or a whole, to build a sum, and to play the missing-part game: show the whole and one part, and turn a card face down for the part that is hidden.

Teacher note: the cards reach to twenty, so children can build any sum within twenty and show the whole and its two parts side by side.

What we know: add and subtract within 20

Work on your own. Use counters, a ten-frame or a drawing if it helps.

1. 10 = 6 + ____.
2. 8 + 3 by counting on. Start at 8: ____.
3. 7 + 6 = ____. Make ten first if it helps.
4. 14 - 5 = ____.
5. There are 8 birds on the wire. 5 more land. How many birds now? ____

Answers and marking guide

Answers

1. 4 (6 and 4 make ten).
2. 11 (start at 8: nine, ten, eleven).
3. 13 (make ten: 7 + 3 = 10, then 10 + 3).
4. 9 (14 take away 5: the missing part of 14 that leaves 5 is 9).
5. 13 birds (8 + 5 = 13; make ten: 8 + 2 = 10, then 10 + 3).

A quick three-level guide

Five questions, five ideas. A child at standard answers most questions and can say the whole story: two parts make the whole, whether they add or take away.

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: bonds to ten, count on, bridge through ten, find the missing part, and solve a problem.