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GCSE Maths · Higher · Chapter 1: Basic number · Lesson 1

Calculating with decimals and estimates

Grades 4–7About 45 minutesNo calculator40 marks
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NameClassDate
A

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

  1. A1
    Needed today

    Work out .

    [1 mark]
    Answer
  2. A2
    Key Stage 3

    Work out .

    [1 mark]
    Answer
  3. A3
    Key Stage 3

    Work out .

    [1 mark]
    Answer
  4. A4
    Key Stage 3

    Write in its simplest form.

    [1 mark]
    Answer
B

Example, then your turn

Grades 4–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

Work out .

Hint Work out , then count the decimal places in the question.
  1. B1

    Work out .

    [2 marks]
    Answer
Example 2

Estimate .

Hint Round each number to 1 significant figure first.
  1. B2

    Estimate .

    [3 marks]
    Answer
C

Practice

Grades 5–6
  1. C1

    Work out .

    [2 marks]
    Answer
  2. C2

    Round to 3 significant figures.

    [1 mark]
    Answer
  1. C3

    You are told that . Write down the value of and of .

    [2 marks]
    Answer and
  2. C4

    Grapes cost £3.40 per kilogram. Work out the cost of 0.65 kg of grapes.

    [2 marks]
    Answer
  3. C5

    427 students and 38 teachers go on a trip. Each coach holds 52 people. How many coaches are needed? You must show your working.

    [2 marks]
    Answer
  4. C6

    A box holds 46 tiles. Work out the number of tiles in 378 boxes. You must show your working.

    [2 marks]
    Answer
  5. C7

    Estimate the value of .

    [2 marks]
    Answer
  6. C8

    Max works out and gets . Without working out the exact answer, explain why he must be wrong.

    [2 marks]
D

Exam-style questions

Grades 6–7
  1. D1

    Tom says, ", because dividing always makes a number smaller."

    Explain why Tom is wrong, and give the correct answer.

    [2 marks]
  1. D2

    Fabric costs £6.80 per metre. Priya buys 2.75 m of fabric and pays with a £20 note.

    (a)

    Work out her change.

    [3 marks]
    Answer
    (b)

    She cuts the fabric into strips 0.25 m long. How many strips does she get?

    [2 marks]
    Answer
    (c)

    She makes one bookmark from each strip and sells every bookmark for £1.45. Does she get back what she paid for the fabric? Show how you decide.

    [2 marks]
    Total for D2: 7 marks
  2. D3

    Lena's garden is a rectangle m long and m wide. One box of grass seed covers .

    38.7 m19.6 m
    Not drawn accurately
    (a)

    Estimate the area of the garden.

    [2 marks]
    Answer
    (b)

    Use your estimate to work out how many boxes of seed she needs.

    [1 mark]
    Answer
    (c)

    Is your estimate of the area an overestimate or an underestimate? Give a reason.

    [1 mark]
    Total for D3: 4 marks
E

Extension

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

  1. E1

    Without a calculator, find the value of .

    [3 marks]
    Hint 1 · What to try

    Write every number as a whole number times a power of 10.

    Hint 2 · The first line

    and .

    Hint 3 · The full method

    Multiply both by : .

    Answer
F

How did it go?

Colour one circle on each line.
Not yetNearlyYes
I can multiply and divide by a decimal without a calculator.
I can round to significant figures and estimate an answer.
I can use an estimate to check an answer.

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