Chapter 4 of 8

All 8 chapters
  1. 1Ratio: comparing parts, readunderstood
  2. 2Ratios and fractions, readunderstood
  3. 3Sharing in a ratio, readunderstood
  4. 4Finding one first, readunderstood
  5. 5Direct proportion, readunderstood
  6. 6Rates and speed, readunderstood
  7. 7Maps and scale drawings, readunderstood
  8. 8Inverse proportion, readunderstood

M3.4.4 Chapter 4

Finding one first

A recipe makes 4 flat breads with 240 g of flour. How much flour do I need for 10 flat breads?

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

  • Find the amount for one, then for any number
  • Scale a recipe for 4 flat breads up to 10 flat breads

A recipe says how much of each thing you need for a number of servings. To change the number of servings, find the amount for one first. We call this the unit amount. Then multiply.

Making more is called to scale up. Making less is called to scale down. The same two steps work for both.

Draw it first

Find one first on a double number line

  1. Step 1: two number lines, flat breads above and flour (g) below. 0 flat breads match 0 g, and 4 flat breads match 240 g. Step 2: an arrow marked ÷ 4 goes to 1 flat bread and 60 g. Step 3: an arrow marked × 10 goes to 10 flat breads and 600 g.flat breadsflour (g)004240

    1 4 flat breads need 240 g of flour. Mark both on the number lines.

  2. Step 1: two number lines, flat breads above and flour (g) below. 0 flat breads match 0 g, and 4 flat breads match 240 g. Step 2: an arrow marked ÷ 4 goes to 1 flat bread and 60 g. Step 3: an arrow marked × 10 goes to 10 flat breads and 600 g.flat breadsflour (g)004240160÷ 4

    2 Divide by 4 to find 1 flat bread: 240 ÷ 4 = 60 g.

  3. Step 1: two number lines, flat breads above and flour (g) below. 0 flat breads match 0 g, and 4 flat breads match 240 g. Step 2: an arrow marked ÷ 4 goes to 1 flat bread and 60 g. Step 3: an arrow marked × 10 goes to 10 flat breads and 600 g.flat breadsflour (g)00424016010600× 10

    3 Multiply by 10 to find 10 flat breads: 60 × 10 = 600 g.

Worked example

Four flat breads need 240 g of flour. How much flour do 10 flat breads need?

  1. 1 flat bread needs 240 ÷ 4 = 60 g.
  2. 10 flat breads need 10 × 60 = 600 g.

Answer: 600 g

A table with two columns, flat breads and flour (g). The rows are 1 and 60, 4 and 240, 10 and 600.flat breadsflour (g)160424010600
Every row has 60 g of flour for each flat bread.

You can also find one first when the question asks for time or for how many. Work out how much one unit gives, then see how many units you need.

Worked example

A tap fills 12 litres in 3 minutes. How long does it take to fill 20 litres?

  1. 1 minute fills 12 ÷ 3 = 4 litres.
  2. 20 litres need 20 ÷ 4 = 5 minutes.
  3. The tap takes 5 minutes.

Answer: 5 minutes

Two number lines, minutes above and litres below. 0 minutes match 0 litres, 1 minute matches 4 litres, 3 minutes match 12 litres, and 5 minutes match 20 litres.minuteslitres0014312520
The tap adds 4 litres every minute. 20 litres is 5 lots of 4 litres.

See it three ways

With things

Put the 240 g of flour into 4 equal bowls. One bowl holds the flour for 1 flat bread. Then count out 10 bowls.

As a picture

A bar cut into 4 equal parts, labelled 240 g in 4 equal parts.240 g in 4 equal parts

In symbols

240 ÷ 4 = 60. Then 60 × 10 = 600.

Try it

Find the beans in a spoon

You need: a spoon, dry beans or seeds, a bowl.

  1. Fill the spoon level with beans. Tip them out and count them. This is the amount for 1 spoon.
  2. Now count the beans in 3 level spoons. Check that it is 3 times the first count.
  3. Use your count for 1 spoon to guess how many beans are in 8 spoons.
  4. Count 8 spoons to test your guess.

What you will see: For example, if 1 spoon holds 12 beans, then 3 spoons hold 36 and 8 spoons hold 96. Your numbers will differ, but the steps are the same.

If you cannot try it, this is what happens.
Two number lines, spoons above and beans below. 0 spoons match 0 beans, 1 spoon matches 12 beans, 3 spoons match 36 beans and 8 spoons match 96 beans.spoonsbeans00112336896

A wrong idea many people have

If 4 flat breads need 240 g of flour, then 10 flat breads need 240 + 6 = 246 g.

Why it feels right: You want 6 more flat breads, so it seems you should add 6 to the flour as well.

The test that breaks it: 1 flat bread needs 60 g. Six more flat breads need 6 × 60 = 360 g more, not 6 g more. And 240 + 360 = 600.

What is true: Do not add the same number to both amounts. Find the amount for one, then multiply or divide.

Key words

unit amount
the amount for one, such as the flour for 1 flat bread.
scale up
to make more of a recipe, by multiplying.
scale down
to make less of a recipe, by dividing.

Back to your guess

The answer is C: Find the flour for 1 flat bread, then take 10 of those: 600 g.

One flat bread needs 240 ÷ 4 = 60 g of flour. Ten flat breads need 10 × 60 = 600 g. Adding 6 g is far too little. Six more flat breads need much more flour than that.

Check yourself

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

  1. A soup for 6 people uses 18 carrots. How many carrots does the same soup need for 10 people?

    Two number lines, people above and carrots below. 0 people match 0 carrots, 6 people match 18 carrots, and 10 people match a question mark.peoplecarrots0061810?
    Tap your answer.

    1. Not this one. You added 4 because 10 is 4 more than 6. But each extra person needs 3 carrots, so 4 more people need 12 more carrots. Go to M3.4.4. Try another.

    2. Not this one. That is the carrots for 1 person, which is the first step. Now multiply by 10 people. Go to M3.4.4. Try another.

    3. Yes, that is right. 1 person needs 18 ÷ 6 = 3 carrots. 10 people need 10 × 3 = 30 carrots.

    4. Not this one. You multiplied 18 by 10. But 18 carrots are for 6 people, not for 1. Find the carrots for 1 person first. Go to M3.4.4. Try another.

    See the answer

    30 carrots

    1 person needs 18 ÷ 6 = 3 carrots. 10 people need 10 × 3 = 30 carrots.

    • If you chose A: You added 4 because 10 is 4 more than 6. But each extra person needs 3 carrots, so 4 more people need 12 more carrots. Go to M3.4.4.
    • If you chose B: That is the carrots for 1 person, which is the first step. Now multiply by 10 people. Go to M3.4.4.
    • If you chose D: You multiplied 18 by 10. But 18 carrots are for 6 people, not for 1. Find the carrots for 1 person first. Go to M3.4.4.

  2. 5 shelves hold 120 books. Every shelf holds the same number. How many books fit on 8 shelves?

    Tap your answer.

    1. Not this one. You added 3 because 8 is 3 more than 5. But each shelf holds 24 books, so 3 more shelves hold 72 more. Go to M3.4.4. Try another.

    2. Not this one. That is the books on 1 shelf. You still need to multiply by 8 shelves. Go to M3.4.4. Try another.

    3. Not this one. You multiplied 120 by 8. But 120 books are on 5 shelves, not 1. Find the books on 1 shelf first. Go to M3.4.4. Try another.

    4. Yes, that is right. 1 shelf holds 120 ÷ 5 = 24 books. 8 shelves hold 8 × 24 = 192 books.

    See the answer

    192 books

    1 shelf holds 120 ÷ 5 = 24 books. 8 shelves hold 8 × 24 = 192 books.

    • If you chose A: You added 3 because 8 is 3 more than 5. But each shelf holds 24 books, so 3 more shelves hold 72 more. Go to M3.4.4.
    • If you chose B: That is the books on 1 shelf. You still need to multiply by 8 shelves. Go to M3.4.4.
    • If you chose C: You multiplied 120 by 8. But 120 books are on 5 shelves, not 1. Find the books on 1 shelf first. Go to M3.4.4.

  3. A recipe for 12 flat breads uses 1 800 g of flour. How much flour is needed for 3 flat breads?

    Two number lines, flat breads above and flour (g) below. 0 flat breads match 0 g, 3 flat breads match a question mark, and 12 flat breads match 1 800 g.flat breadsflour (g)003?121 800
    Tap your answer.

    1. Not this one. You took away 9 because 3 is 9 fewer than 12. But 9 fewer flat breads need far more than 9 g less flour. Go to M3.4.4. Try another.

    2. Not this one. That is the flour for 1 flat bread. You want 3 flat breads, so multiply by 3. Go to M3.4.4. Try another.

    3. Not this one. You divided by 3, the number of flat breads you want. Divide by 12 first, the number the recipe is for. Go to M3.4.4. Try another.

    4. Yes, that is right. 1 flat bread needs 1 800 ÷ 12 = 150 g. 3 flat breads need 3 × 150 = 450 g. This time you scale down.

    See the answer

    450 g

    1 flat bread needs 1 800 ÷ 12 = 150 g. 3 flat breads need 3 × 150 = 450 g. This time you scale down.

    • If you chose A: You took away 9 because 3 is 9 fewer than 12. But 9 fewer flat breads need far more than 9 g less flour. Go to M3.4.4.
    • If you chose B: That is the flour for 1 flat bread. You want 3 flat breads, so multiply by 3. Go to M3.4.4.
    • If you chose C: You divided by 3, the number of flat breads you want. Divide by 12 first, the number the recipe is for. Go to M3.4.4.

  4. 9 bottles hold 27 litres in all. All the bottles are the same. How many litres do 12 bottles hold?

    Two number lines, bottles above and litres below. 0 bottles match 0 litres, 9 bottles match 27 litres, and 12 bottles match a question mark.bottleslitres0092712?
    Tap your answer.

    1. Yes, that is right. 1 bottle holds 27 ÷ 9 = 3 litres. 12 bottles hold 12 × 3 = 36 litres.

    2. Not this one. You added 3 because 12 is 3 more than 9. But 3 more bottles hold 3 × 3 = 9 litres more, not 3. Go to M3.4.4. Try another.

    3. Not this one. You multiplied 27 by 12. But 27 litres is for 9 bottles. Find the litres for 1 bottle first. Go to M3.4.4. Try another.

    See the answer

    36 litres

    1 bottle holds 27 ÷ 9 = 3 litres. 12 bottles hold 12 × 3 = 36 litres.

    • If you chose B: You added 3 because 12 is 3 more than 9. But 3 more bottles hold 3 × 3 = 9 litres more, not 3. Go to M3.4.4.
    • If you chose C: You multiplied 27 by 12. But 27 litres is for 9 bottles. Find the litres for 1 bottle first. Go to M3.4.4.

  5. 3 spoons hold 36 beans. How many beans do 5 spoons hold?

    Two number lines, spoons above and beans below. 0 spoons match 0 beans, 3 spoons match 36 beans, and 5 spoons match a question mark.spoonsbeans003365?
    Tap your answer.

    1. Not this one. You added 5 to 36. But beans are not added to spoons. Each spoon holds 12 beans, so find that first. Go to M3.4.4. Try another.

    2. Not this one. That is the beans in 1 spoon. The question asks about 5 spoons, so multiply by 5. Go to M3.4.4. Try another.

    3. Yes, that is right. 1 spoon holds 36 ÷ 3 = 12 beans. 5 spoons hold 5 × 12 = 60 beans.

    4. Not this one. You multiplied 36 by 5. But 36 beans are for 3 spoons. Divide by 3 first to find the beans in 1 spoon. Go to M3.4.4. Try another.

    See the answer

    60 beans

    1 spoon holds 36 ÷ 3 = 12 beans. 5 spoons hold 5 × 12 = 60 beans.

    • If you chose A: You added 5 to 36. But beans are not added to spoons. Each spoon holds 12 beans, so find that first. Go to M3.4.4.
    • If you chose B: That is the beans in 1 spoon. The question asks about 5 spoons, so multiply by 5. Go to M3.4.4.
    • If you chose D: You multiplied 36 by 5. But 36 beans are for 3 spoons. Divide by 3 first to find the beans in 1 spoon. Go to M3.4.4.

  6. A soup for 4 people uses 12 carrots. How many carrots does the same soup need for 9 people?

    See the answer

    27 carrots

    1 person needs 12 ÷ 4 = 3 carrots. 9 people need 9 × 3 = 27 carrots.

  7. 4 flat breads need 240 g of flour. How much flour do 7 flat breads need?

    See the answer

    420 g

    1 flat bread needs 240 ÷ 4 = 60 g. 7 flat breads need 7 × 60 = 420 g.

  8. From an earlier chapter

    Share 45 seeds between Mei and Yusuf in the ratio 2 : 3. How many seeds does each get?

    See the answer

    18 and 27

    2 + 3 = 5 parts. 45 ÷ 5 = 9 seeds a part. Mei gets 2 × 9 = 18 and Yusuf gets 3 × 9 = 27.

Keep it

Copy this into your exercise book.

Find the amount for one by dividing. Then multiply to get the amount you want. Do not add the same number to both amounts. Check with one more example.

Draw: Draw two number lines. Mark 4 and 240 g. Draw an arrow to 1 and 60 g, then an arrow to 10 and 600 g.

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 (710 KB). It opens on any phone.