Chapter 7 of 7

All 7 chapters
  1. 1Adding in your head, readunderstood
  2. 2Taking away in your head, readunderstood
  3. 3Column adding, readunderstood
  4. 4Column taking away, readunderstood
  5. 5Four digits and more, readunderstood
  6. 6Estimate and check, readunderstood
  7. 7Problems in two steps, readunderstood

M2.2.7 Chapter 7

Problems in two steps

How do I know if a problem needs adding or taking away?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Draw a bar model to decide whether to add or take away
  • Solve a problem that needs two steps
  • Find how many more you need to get from 37 to 50

Some problems do not say add or take away. A picture can help you choose.

A bar model is a picture of a problem. It uses bars for the numbers.

The whole is the long bar on top. It is all of the thing.

A part is one piece of the whole. The parts go side by side under it.

A farmer has 58 hens and 35 ducks. How many birds are there?

Draw it first

Draw the hens and ducks

  1. A bar model. Step 1 draws a long bar on top, shaded with dots and labelled "?", next to the word "whole". Step 2 draws two bars side by side under it, labelled "58" and "35", next to the word "parts". Step 3 writes "58 + 35 = 93".?whole

    1 Draw a long bar for the whole. You do not know it, so write ?.

  2. A bar model. Step 1 draws a long bar on top, shaded with dots and labelled "?", next to the word "whole". Step 2 draws two bars side by side under it, labelled "58" and "35", next to the word "parts". Step 3 writes "58 + 35 = 93".?whole5835parts

    2 Under it, draw the parts side by side. Write 58 and 35.

  3. A bar model. Step 1 draws a long bar on top, shaded with dots and labelled "?", next to the word "whole". Step 2 draws two bars side by side under it, labelled "58" and "35", next to the word "parts". Step 3 writes "58 + 35 = 93".?whole5835parts58 + 35 = 93

    3 You know the parts and want the whole. So add. 58 + 35 = 93.

Now the farmer has 93 birds. 58 are hens. How many are ducks?

A bar model. The long bar on top is labelled "93". Under it are two bars side by side. The first is labelled "58". The second is shaded with dots and labelled "?".9358?
You know the whole and one part. So take away. 93 − 58 = 35.

Worked example

There are 93 birds. 58 are hens. How many are ducks?

  1. The whole is 93. One part is 58.
  2. You want the other part. Take away.
  3. 93 − 58 = 35.

Answer: 35 ducks

See it three ways

With things

Put 12 beans in one pile and 7 beans in another. Push the piles together. Count them.

As a picture

A bar model. The long bar on top is labelled "19". Under it are two bars side by side, labelled "12" and "7".19127

In symbols

12 + 7 = 19. Take away one part to find the other: 19 − 7 = 12.

Some problems need two steps. Do one step, then the next.

A storeroom has 245 books. A van brings 130 more. Then 78 books go to a village. How many are left?

Two bar models, one under the other. The first is for step 1, add. The long bar is shaded with dots and labelled "?". Its parts are labelled "245" and "130". The second is for step 2, take away. The long bar is labelled "375". Its parts are labelled "78" and "?". The words are "Step 1: add" and "Step 2: take away".Step 1: add?245130Step 2: take away37578?
Step 1 finds the whole, 375. Step 2 takes 78 away from it.

Worked example

Work out how many books are left.

  1. Step 1: the parts are 245 and 130. Add. 245 + 130 = 375.
  2. Step 2: the whole is 375. One part is 78. Take away.
  3. 375 − 78 = 297.

Answer: 297 books

Some problems go the other way. Take away first, then add.

A tank has 500 litres of water. Ana takes out 185. Rain adds 130. How much is in it now?

Worked example

Work out how many litres are in the tank now.

  1. Step 1: the whole is 500. One part is 185. Take away.
  2. 500 − 185 = 315.
  3. Step 2: the parts are 315 and 130. Add.
  4. 315 + 130 = 445.

Answer: 445 litres

You need 50 beads for a necklace. You have 37. How many more beads do you need?

The beads you still need are the missing part. Take the 37 you have from the 50 you need.

A bar model. The long bar on top is labelled "50". Under it are two bars side by side. The first is labelled "37". The second is shaded with dots and labelled "?".5037?
You know the whole and one part. The beads you need are the missing part.

You can also count up from 37 to 50.

A number line from 37 to 50 with a mark at every number. The numbers 37, 40 and 50 are written under it. An arrow from 37 to 40 is labelled "+3". An arrow from 40 to 50 is labelled "+10".+3+10374050
3 makes 40. 10 more makes 50. You need 3 + 10 = 13 more.

Worked example

You need 50 beads and have 37. How many more do you need?

  1. The whole is 50. One part is 37. Take away: 50 − 37.
  2. Count up from 37. 3 more makes 40.
  3. From 40 to 50 is 10 more.
  4. Add the jumps. 3 + 10 = 13.

Answer: 13 beads

Try it

Two steps with beans

You need: 21 beans or small stones, a pencil and paper.

Be safe: Do not eat the beans.

  1. Make a pile of 12 beans and a pile of 9 beans.
  2. Push them together. Count them. Write 12 + 9 = 21.
  3. Take 6 beans away. Count what is left. Write 21 − 6 = 15.
  4. Draw a bar model for each step.

What you will see: Step 1 gave the whole, 21. Step 2 used 21 as the new whole.

If you cannot try it, this is what happens.
Two bar models, one under the other. The first is for step 1. The long bar is labelled "21". Its parts are labelled "12" and "9". The second is for step 2. The long bar is labelled "21". Its parts are labelled "6" and "15". The words are "Step 1" and "Step 2".Step 121129Step 221615

A wrong idea many people have

A word in the story tells you the sum. "More" always means add.

Why it feels right: Many stories say "more" when something is added.

The test that breaks it: Kofi has 50 beans. Ana has 37. How many more has Kofi? Lay 37 beans in a row. Lay 50 under them, one to one. 13 have no partner.

What is true: Draw the bar model, not the words. The whole is 50 and one part is 37. Take away: 50 − 37 = 13.

Key words

bar model
a picture of a problem. The whole is on top. Its parts are under it.
whole
all of the thing. It is the long bar on top.
part
one piece of the whole.
missing part
the part you do not know. You find it by taking away.

Back to your guess

The answer is C: Draw the whole and its parts. See which one is missing.

A picture shows what you know and what is missing. If the whole is missing, add. If a part is missing, take away.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. There are 84 children in a hall. 39 are girls. Which sum finds the boys?

    Tap your answer.

    1. Yes, that is right. The whole is 84. One part is 39. Take away. 84 − 39 = 45 boys, and 45 + 39 = 84.

    2. Not this one. 84 is the whole. 39 is one part. You want the other part, so take away. Try another.

    3. Not this one. You know the whole, 84, and one part, 39. That is enough to find the other part. Try another.

    See the answer

    84 − 39 = 45

    The whole is 84. One part is 39. Take away. 84 − 39 = 45 boys, and 45 + 39 = 84.

    • If you chose B: 84 is the whole. 39 is one part. You want the other part, so take away.
    • If you chose C: You know the whole, 84, and one part, 39. That is enough to find the other part.

  2. One sack holds 376 beans. Another holds 248. Draw a bar model. How many beans in all?

    See the answer

    624

    You know the two parts and want the whole. Add. 376 + 248 = 624.

  3. Kofi picks 468 mangoes in the morning and 259 in the afternoon. He gives away 600. How many are left?

    See the answer

    127

    Step 1: 468 + 259 = 727. Step 2: 727 − 600 = 127.

  4. A water drum holds 50 litres. It has 28 litres in it. How many more litres fill it?

    See the answer

    22 litres

    50 − 28 = 22. Or count up: 2 makes 30, then 20 makes 50. 2 + 20 = 22.

  5. From an earlier chapter

    Mei says 727 − 389 = 348. Add back to check. Is she right?

    Tap your answer.

    1. Not this one. Add 348 + 389. You get 737, not 727. Adding back shows a mistake. Go to M2.2.6. Try another.

    2. Yes, that is right. 348 + 389 = 737, not 727. The right answer is 338, because 338 + 389 = 727.

    3. Not this one. 1 116 is 727 + 389. This is a take away, so the answer is less than 727. Try another.

    See the answer

    No. The answer is 338.

    348 + 389 = 737, not 727. The right answer is 338, because 338 + 389 = 727.

    • If you chose A: Add 348 + 389. You get 737, not 727. Adding back shows a mistake. Go to M2.2.6.
    • If you chose C: 1 116 is 727 + 389. This is a take away, so the answer is less than 727.

  6. A rope is 120 m long. Sipho cuts off 75 m. How long is the rest?

    A bar model. The long bar on top is labelled "120 m". Under it are two bars side by side. The first is labelled "75 m". The second is shaded with dots and labelled "?".120 m75 m?
    Tap your answer.

    1. Not this one. 120 m is the whole rope before the cut. The rest is a part, so take away. Try another.

    2. Yes, that is right. The whole is 120 m. One part is 75 m. Take away. 120 − 75 = 45. Check: 45 + 75 = 120.

    3. Not this one. You took the smaller digit from the bigger one in each column. Add back: 155 + 75 = 230, not 120. Try another.

    See the answer

    45 m

    The whole is 120 m. One part is 75 m. Take away. 120 − 75 = 45. Check: 45 + 75 = 120.

    • If you chose A: 120 m is the whole rope before the cut. The rest is a part, so take away.
    • If you chose C: You took the smaller digit from the bigger one in each column. Add back: 155 + 75 = 230, not 120.

  7. A tank has 250 litres of water. Ana adds 135 litres. Then she uses 180 litres. How many litres are left?

    Tap your answer.

    1. Not this one. You added all three numbers. Ana uses 180 litres, so take them away at step 2. Try another.

    2. Not this one. You left out the 135 litres Ana added. Add first: 250 + 135 = 385. Then take away 180. Try another.

    3. Yes, that is right. Step 1: 250 + 135 = 385. Step 2: 385 − 180 = 205.

    See the answer

    205 litres

    Step 1: 250 + 135 = 385. Step 2: 385 − 180 = 205.

    • If you chose A: You added all three numbers. Ana uses 180 litres, so take them away at step 2.
    • If you chose B: You left out the 135 litres Ana added. Add first: 250 + 135 = 385. Then take away 180.

  8. Priya has a book of 400 pages. She has read 156 pages. Then she reads 85 more. How many pages are left?

    Tap your answer.

    1. Yes, that is right. Step 1: 156 + 85 = 241 pages read. Step 2: 400 − 241 = 159 pages left.

    2. Not this one. You forgot the 85 pages. Step 1: she has read 156 + 85 = 241. Step 2: 400 − 241. Try another.

    3. Not this one. 241 is how many pages she has read. The question asks how many are left. Take 241 from 400. Try another.

    See the answer

    159 pages

    Step 1: 156 + 85 = 241 pages read. Step 2: 400 − 241 = 159 pages left.

    • If you chose B: You forgot the 85 pages. Step 1: she has read 156 + 85 = 241. Step 2: 400 − 241.
    • If you chose C: 241 is how many pages she has read. The question asks how many are left. Take 241 from 400.

  9. A minibus has 62 seats. 48 are taken. Hana counts up from 48 to 62. Her first hop is 2, to 50. How long is the next hop?

    A number line from 48 to 62. A short hop labelled +2 goes from 48 to 50. The numbers 48, 50 and 62 are written under the line.+2485062
    Tap your answer.

    1. Not this one. 14 is the whole gap, both hops together. The next hop goes from 50 to 62. Try another.

    2. Not this one. 62 is where the hop ends. The hop is how far it goes, from 50 to 62. Try another.

    3. Yes, that is right. The next hop goes from 50 to 62. 62 − 50 = 12. The two hops make 2 + 12 = 14 free seats.

    See the answer

    12

    The next hop goes from 50 to 62. 62 − 50 = 12. The two hops make 2 + 12 = 14 free seats.

    • If you chose A: 14 is the whole gap, both hops together. The next hop goes from 50 to 62.
    • If you chose B: 62 is where the hop ends. The hop is how far it goes, from 50 to 62.

Keep it

Copy this into your exercise book.

Draw the whole on top and its parts under it. Know the parts? Add. Know the whole and one part? Take away. Missing part: 50 − 37 = 13.

Draw: A long bar labelled 50. Under it, two bars: 37 and ?.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (699 KB). It opens on any phone.