GCSE Maths Starter 18

1. Write down the reciprocal of ¼

2. A small pot costs 20 pence. A large pot costs 150% more, how much does the large pot cost?

3. Copy the pattern into your book, add one more square so the pattern has one line of symmetry

4. Write these numbers in order of size, smallest first:1.8, 3.71, 0.5, 12.4

5.

Lesson 18 Estimation and using a calculator

Mathswatch clip (14/101/63).

• To round numbers to a given degree of accuracy (Grade E )

• To use your calculator to solve numerical problems (Grade E/D)

EXTN: To calculate an estimate for a given sum (Grade C)

4 . 3 3 2 5

Significant Figures (Rounding)

Numbers can be rounded to 1,2, 3 or more significant figures. We count the number of figures from the first non-zero digit.

Rounding to 1 s.f

5 or bigger ?

4

5. 7 4 2 5

5 or bigger ?

6

0. 0 4 2 5

5 or bigger ?

0.04

No Yes No

First non-zero

digit.

Rounding to 1 s.f

0 . 0 7 6

5 or bigger ?

0.08

0. 0 0 1 5

5 or bigger ?

0.002

Yes Yes

First non-zero

digit.

First non-zero

digit.

Significant Figures (Rounding)

1 . 4 7 2 9

5 or bigger ?

1.5

0. 0 5 3 5

5 or bigger ?

0.054

Yes Yes

First non-zero

digit.

Significant Figures (Rounding)

Rounding to 2 s.f

2 . 0 7 5 9

5 or bigger ?

2.08

0. 0 2 0 4 6 3

5 or bigger ?

0.0205

Yes Yes

First non-zero

digit.

Significant Figures (Rounding)

Rounding to 3 s.f

The following number could be the population of a country at a particular instant in time.Write this number to 1, 2, 3, 4, 5, 6 and 7 significant figures.

56 345 67860 000 000 56 000 000 56 300 000

56 350 000 56 346 000 56 345 700

56 345 680

Lesson 18 Estimation and using a calculator

Mathswatch clip (14/101/63).

Martin uses his calculator to work out 39 × 72.

The display shows an answer of 1053.

How do you know this answer must be wrong?

“is approximately equal to”

39 × 72 40 × 70 = 2800

The product of 39 and 72 must therefore end in an 8.

9 × 2 = 18.9 × 2 = 18.

Estimation

Also, if we multiply together the last digits of 39 and 72 we have

3.5 × 17.5 can be approximated to:

4 × 20 = 80

3 × 18 = 54

4 × 17 = 68

or between 3 × 17 = 51 and 4 × 18 = 72

How could we estimate the answer to 3.5 × 17.5?

Estimation

4948 ÷ 58 can be approximated to:

5000 ÷ 60 = ?

5000 ÷ 50 = 100

4950 ÷ 50 = 99

or 4800 ÷ 60 = 80

How could we estimate the answer to 4948 ÷ 58?

Estimation

(60 does not divide into 5000)

Estimate the following. (Clearly show your rounded values)

1) 29 × 51 2) 431 × 48 3) 2184 × 3962

4) 17.41 × 8.73 5) 4.372 × 1.821 6) 5.32 × 0.236

7) 0.731 × 0.489 8) 0.0813 × 0.27 9) 1.043 × 4.21

10) 2.73 × 4.1 × 6.2 11) 2.43 × 0.045 × 3 12) 0.23 × 2.74 × 3.05 × 0.97

1500

20,000

8,000,000

180

8 1

0.35

0.024

4

72

0.3

1.8

Lesson 18 Estimation and using a calculator

Mathswatch clip (14/101/63).

Solving complex calculations mentally

What is ?3.2 + 6.8

7.4 – 2.4

3.2 + 6.8

7.4 – 2.4=

10

5= 2

We could also write this calculation as: (3.2 + 6.8) ÷ (7.4 – 2.4).

How could we work this out using a calculator?

Using bracket keys on the calculator

What is ?3.7 + 2.1

3.7 – 2.1

We start by estimating the answer:

3.7 + 2.1

3.7 – 2.1 3

6

2=

Using brackets we key in:

(3.7 + 2.1) ÷ (3.7 – 2.1) = 3.625

Lesson 18 Estimation and using a calculatorMathswatch clip (14/101/63).

Some for you to try..

Four people used their calculators to work out .9 + 30

15 – 7

Tracy gets the answer 4.

Fiona gets the answer 4.875.

Andrew gets the answer –4.4.

Sam gets the answer 12.75.

Who is correct?

What did the others do wrong?

Lesson 18 Estimation and using a calculatorMathswatch clip (14/101/63).

Some for you to try..

Lesson 18 Estimation and using a calculatorMathswatch clip (14/101/63).

Exam questions