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Pre LearningAssessment

Year 8 Module 1: Prime numbers, Factorisation and Calculating with Fractions

Name: ………………………………………………………………….

Class: ……………………………………………………………………

Teacher: ……………………………………………………………….

What are we learning this half term?Unit 1: Prime Numbers and Factorisation

In this unit you will be introduced to prime numbers and prime factorisation and then use this to determine HCF and LCM of a pair or group of numbers. You will also learn to use prime factorisation to find squares, square roots, cubes and cube roots and to use indices to record repeated multiplication

Unit 2: Calculating with Fractions This unit will refresh your Year 7 fractions knowledge and introduce addition and subtraction of fractions with both

like and unlike denominators. You will also learn to add and subtract mixed numbers and improper fractions.

1) Gina says “9 is a prime number”. Explain why Gina is wrong.

You need: A Pen A Pencil A Ruler

You DO NOT need: A Calculator

Pre-Learning Assessment Mark:

50Teacher Comment:

…………………………………………………………………………………………………………………………………………

…………………………………………………………………………………………………………………………………… (1)

2)

15, 7, 11, 16, 8, 80

From the numbers given above select:

a) A number that is a factor of 40…………………… (1)

b) A square number…………………… (1)

c) The square root of 49………….……..… (1)

3) For each statement decide whether it is true or false. If it is false explain why.

a) The multiples of a number are always bigger than the number.

……………………………………………………………………………………………………......................(1)

b) 63 is a multiple of 9

……………………………………………………………………………………………………......................(1)

c) 20 is a multiple of 120

………………………………………………………………………………………………………...................(1)

4) Write 84 as a product of its prime factors

………………………………………………………………………………………………..…..…….. (2)

5) Put a circle round each of the numbers below that can be written as a product of their

prime factors using only the numbers 3 and 5

45, 225, 105, 230, 135 (3)

6) State the highest common factor of 40 and 100

...............................(1)7) Find the lowest common multiple of 20 and 25

...............................(2)8) Look at these numbers.

a) Which is the largest?

............................... (1)

b) Which is equal to 92?

............................... (1)c) Which two of the numbers below are not square numbers?

...................... and ...................... (2)

9) The highest common factor and lowest common multiple of two numbers are 3 and 126

respectively. If one of the numbers is 21, find the other number.

You may find the diagram below helpful.

……..……..... (2)

10) Give a fraction which is equivalent to each of these:

a)17 =

b)49 =

(2)

11)

a) James is five and seven twelfths feet tall. Write his height in feet as an improper

fraction.

……………….. (2)

b) There are four cookies in a full packet. If a baker has 27 cookies state the number of

packets he can make as a mixed number.

..………………. (2)

12) Complete the following Calculations, simplifying your answers where possible.

a) 45x 1011 b)

56÷2

(2)

13) Sam wrote the calculation:

+ =

Is he correct?

Yes No

Explain your answer.

………………………………………………………………………………………………………………………………..…..

……………………………………………………………………………………………………………………………… (1)14) Find the sums of the following groups of fractions. Simplify your answers where

possible:

a) 37 ,27, 17

…………………… (2)

b) 512 ,312

…………………… (2)

15) Moses had one quarter of a chocolate bar. Lucy had one third of a chocolate bar. What fraction of a chocolate bar did they have altogether?

…………………………..……..…….. (3)

16) Find the sum of

13 and

35 . You may shade the model to help you.

13 +

35 = + =

……..…….. ……..…….. ……..……..

(2)

17) Find the difference between 34 and

16 . You may shade the models to help you.

34 - 16 = - =

……..…….. ……..…….. ……..……..(2)

18) Match each calculation with the correct fraction answer.

The first one is done for you.

15+ 25

1320

38+ 18 3

5

25+ 14

12

78−34

16

12−13

18

(3)

19) Jessica is trying to lose weight. She aims to lose 212 kg in a month. After two weeks she

has lost 1 35 kg. How much more does she have to lose to achieve her goal?

………………. Kg (3)

20) In an international tennis tournament 13 of the players are from Europe,

14 are from the

USA, 16 are from South America and the remainder are from Asia. What fraction of the

players are from Asia?

……………………. (3)

Finishing Task

A farmer wants your help to fence off an area to house a variety of different animals. Each type of animal needs a different quantity of space.

He can only put one type of animal in the area at a time and he does not want any “wasted” space. For example if he fenced off an area of 25 m2 he could fill it exactly with hens or pigs but he could only fit two cows with seven square metres of wasted space.

Investigate which of these fenced areas would be best for housing all the different animals? How many of each one could it hold? Is there any wasted space?

Can you find an area that could house any of the animals above with no wasted space? Is there more than one option?

Deer need 15 m2 each. To make the area also house deer would it change the size of the fenced off area? Why?

Diplodocuses need 99 m2 each. To make the area also house Diplodocuses would it change the size of the fenced off area? Why?

Can you find other quantities of space that fit exactly into this fenced off area?

Hens need1 m2 each

Ducks need3 m2 each

Pigs need5 m2 each

Cows need9 m2 each

Bulls need11 m2 each