Autumn 1- Study Book (20-29)
Study Period
Maths
Booklet.
Name:
Tutor Group:
Maths Class:
1
Autumn 1- Study Book (20-29)
Confidence Rating
Rate how confident you are at each topic.
Topic:
Objective:
Place Value
and
calculations
 Recall multiplication facts to 12 x 12 and
use them to derive quickly the
corresponding division facts;
 Order integers and use the symbols <, >
and understand the ≠ symbol;
 Add and subtract integers and decimals
efficiently;
 Multiply and divide by powers of 10
mentally;
 Begin to use efficient methods for
multiplication and division;
 Calculate with negative numbers;
Area and
Perimeter
 Find the perimeter of compound shapes;
 Calculate areas and perimeters of
compound shapes made from triangles
and rectangles;
 Find the area of a parallelogram;
Probability
 Write probabilities in words or fractions,
decimals and percentages;
 Find the probability of an event happening
using theoretical probability;
 Find and justify probabilities based on
equally likely outcomes in simple contexts
and use theoretical models to include
outcomes using dice, spinners, coins;
2
Autumn 1- Study Book (20-29)
Place Vale and Calculations.
Recall multiplication facts to 12 x 12 and use them to derive quickly the corresponding
division facts;
1. Circle two numbers that multiply together to give an answer of 21.
6
3
2
7
11
2. Circle all the multiples of 9 in this list:
27
19
36
54
43
3. Complete the multiplication grid:
4. Vera writes down the multiplication 7 x 4 = 28
Use the same three numbers to write another multiplication and a division.
X
=
÷
=
5. Calculate: a) eleven multiplied by eight
b) nine lots of seven.
3
Autumn 1- Study Book (20-29)
Order integers and use the symbols <, > and understand the ≠ symbol;
1. Write the correct sign, < less than or > greater than, between each pair of numbers
a) 5
7
b) 3
-1
c) 12
-11
2. Write the correct symbol, < or >, between each pair of numbers.
a) 97.74
100
b) £0.25
5p
c) -0.1
-5.0
3. Write the correct symbol, = equal to or ≠ not equal to, in the boxes below:
a) 5 + 3
8
b) 35 ÷ 7
6
c) 12 x 11
121
4. Order the following integers from smallest to largest:
a) 12, 7, 11, 13, 2, 6, 10, 5
b) -7, -5, -10, -13, -6, -4,
c) 12, -5, 0, -2, 3, 7, -1, 9
5. Order the following integers from largest to smallest:
a) 44, 67, 35, 74, 42, 62, 33
b) -44, -67, -35, -74, -42, -33
c) 77, -63, 46, -24, -25, 34
6. Raul has tried to put these decimal numbers in order, starting with the smallest.
8.2 8.07 8.35 8.77 9.0
a) Which numbers has Raul put in the wrong place?
b) Rewrite the numbers in the correct order.
7. The table shows how many people followed different religions in Britain in 1989.
Religion
Followers
Religion
Presbyterians
1 346 000
Baptists
Anglicans
1 928 000
Roman Catholics
Followers
25 000
2 059 000
Jews
108 000
Hindus
150 000
Orthodox
231 070
Sikhs
200 000
Buddhists
241 000
Muslims
900 000
Methodists
2 059 000
Rearrange in size order:
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Autumn 1- Study Book (20-29)
Add and subtract integers and decimals efficiently;
1. Use the column method to add the following:
a) 5 6 3
b) 4 3 9
c) 5 6 4
+ 354
+236
+378
e) 436 + 162 + 35
d) 5 8 7
+165
f) 786 + 547 + 694
2. Use the column method to add the following:
a) 6 7 5
b) 5 3 4
c) 6 5 7
- 342
-217
-284
d) 8 3 3
-241
3. Use the column method to add and subtract the following:
a) 1 6 . 3
b) 4 7 . 4
c) 4 3 . 4
d) 6 1 2 . 3 5
+ 31.6
+18.35
- 2.6
-231.51
4. The table shows part of the records of an antique dealer.
Antique
Bought for
Sold for
Clock
£87
£215
Mirror
£58
£136
Chest
£435
£821
Table
£394
£760
Chair
£168
£225
Profit
a) How much profit did she make on each item?
b) At an auction she bought a pair of bookcases for a total of £437. She later sold one
of them for £350 and the other for £364. What was her total profit?
c) At the same auction she bought a desk for £363 and a swivel chair for £85. She
later sold them together for £734. How much profit did she make?
5
Autumn 1- Study Book (20-29)
Multiply and divide by powers of 10 mentally;
1. Work out:
a) 53 x 10 =
d) 87 x 10 =
b) 38 x 10 =
e) 10 x 62 =
c) 49 x 100 =
f) 100 x 32 =
g) 254 x 10 =
h) 132 x 100 =
i) 10 x 187 =
j) 100 x 76 =
k) 97 x 100 =
l) 100 x 10 =
2. Calculate:
a) 34 x 10 x 10 =
b) 87 x 10 x 100 =
c) 4 x 8 x 100 =
d) 456 x 100 x 10 =
e) 9 x 7 x 10 x 10 =
f) 100 x 100 =
g) 10 x 100 x 10 =
h) 100 x 34 x 10 =
i) 10 x 628 x 100 =
j) 4 x 100 x 8 =
3. a) 360 ÷ 10 =
b) 780 ÷ 10 =
c) 9800 ÷ 100 =
d) 6500 ÷ 100 =
e) 7800 ÷ 10 =
f) 8400 ÷ 10 =
g) 65 000 ÷ 100 =
h) 8000 ÷ 100 =
i) 65 000 ÷ 10 =
j) 506 000 ÷ 100 =
4. Split the following calculations up to make it easier when calculating:
a) 23 x 30 = 23 x 3 x 10 =
b) 47 x 20 =
c) 38 x 30 =
d) 63 x 40 =
e) 90 x 63 =
f) 400 x 85 =
g) 74 x 600 =
h) 962 x 60 =
6
Autumn 1- Study Book (20-29)
Begin to use efficient methods for multiplication and division;
1. Using method of your choosing calculate the following:
a) 43 x 21 =
b) 76 x 32
c) 89 x 43
d) 388 x 65
e) 306 x 84
f) 464 x 71
2. Use the following example to help you divide the following numbers:
a) 95 ÷ 4 =
b) 85 ÷ 6 =
c) 97 ÷ 4 =
d) 798 ÷ 7 =
e) 944 ÷ 8 =
f) 753 ÷ 9 =
7
Autumn 1- Study Book (20-29)
Calculate with negative numbers;
1. Calculate the new temperature if the temperature now is
a) 12oC and warms up by 4oC
b) -4oC and rises by 12oC
c) -11oC and warms up by 6oC
2. Calculate the new temperature if the temperature is now
a) 10oC and it cools by 9oC
(b) 5oC and it falls by 7oC
c) -5oC and it cools down by 5oC
(d) -2oC and it cools down by 11oC
3. Write these changes to bank accounts as number sentences. Calculate the final bank
balance. Example
a) Current balance £12, withdrawal £20.
b) Current balance -£9, deposit £15.
c) Current balance -£15, deposit £12.
d) What does it mean if your bank balance is -£50?
4. Find each missing number by adding the two numbers in the two bricks below it.
5. Calculate:
a) -5 x -7
e) -45 ÷ 9
(b) -6 x 8
(f) -8 ÷ -2
(c) 5 x -4
(g) 100 ÷ -25
(d) -1 x -1 x -1
(h) -8 ÷ -4 ÷ -1
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Autumn 1- Study Book (20-29)
Area and Perimeter
Find the perimeter of compound shapes;
1. Calculate the perimeters of:
2. Find the perimeter of Mrs Akhtars’ lounge floor from this plan:
3. What is the missing length if the perimeter is 24cm ?
4. Work out the perimeter of this rectangular sports field.
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Autumn 1- Study Book (20-29)
5. The Murphy family have a patio in the shape of a T. Work out the perimeter:
6. Calculate the area and perimeter of the following shapes which are all measured in
centimetres:
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Autumn 1- Study Book (20-29)
Calculate areas and perimeters of compound shapes made from triangles and rectangles;
1. Work out the areas of these triangles:
2. Which of these shapes has the larger area and by how much?
3. Calculate the area of the shaded region
4. Calculate the areas of each of these compound shapes:
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Autumn 1- Study Book (20-29)
Find the area of a parallelogram;
1. Make an accurate drawing of this rectangle from the measurements given. Cut it
along the red line. Make and sketch the following shapes from the rectangle’s pieces.
Show length and height dimensions clearly.
a) Triangle.
(b) parallelogram.
(c) trapezium.
2. Find the area of each parallelogram.
3. Find the area of each shape.
4. Accurately draw a rectangle and three different parallelograms, each with an area of
30cm2.
12
Autumn 1- Study Book (20-29)
Probability.
Write probabilities in words or fractions, decimals and percentages;
1. Choose words to describe the probability of the following events:
a) I will pick a red card from an ordinary pack of cards.
b) A human can run at 100mph.
c) I will win the national lottery.
d) The day after Monday will be Tuesday.
2. Nigella is completing her maths homework. So far she has written If this spinner is
spun, there are two possible outcomes.
a) Is she right?
b) List all the different possible outcomes.
3. Use the words to complete the following sentences:
4. Katie throws a fair die with numbers 1,2,3,4,5 & 6 on it:
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Autumn 1- Study Book (20-29)
Find the probability of an event happening using theoretical probability;
1. Here is a fairground wheel of fortune. When it is spun, the pointer can land on any
one section. You win the amount the pointer stops at.
a) List all the different amounts you could win with one spin.
b) Work out the probability of winning:
(i)
50p
(ii) £1
(iii) £2
(iv) £5
2. Here is a spinner. Work out the probability of getting:
a) 5
(b) 3 or 4
(c) an odd number
(d) 9
(e) a prime number
(f) a multiple of 2
3.
Five different bulbs have been placed in a bag. One bulb is a yellow daffodil, one is a
purple crocus, one is a white snowdrop, one is a white lily and one is a red tulip.
a) A bulb is picked from the bag without looking. What is the probability that a tulip is
picked from the bag?
b) What is the probability that a bulb picked from the bag will grow into a white
flower?
c) What is the probability that a bulb picked from the bag will produce a flower that
is not yellow?
d) What is the probability that a bulb picked from the bag will produce a flower that
is not white?
14
Autumn 1- Study Book (20-29)
Find and justify probabilities based on equally likely outcomes in simple contexts and Use
theoretical models to include outcomes using dice, spinners, coins;
1. Joan does not like coffee so she chooses a hot drink from tea or hot chocolate. There
3
is a probability of that she chooses tea.
5
a) What is the probability that she will choose coffee?
b) What is the probability that she will choose hot chocolate?
c) Explain your answers.
2. Jim owns a greyhound called Spot. He says Spot has a probability of
3
15
of winning a
race. What is the probability that Spot will not win the race?
3. There are five horses in a race with equal chances of winning. Four horses are grey and
one is black.
a) What is the probability that the black horse will win?
b) What is the probability that the black horse will not win?
4. When a card is chosen at random from a set of cards numbered 1 to 25.
What is the probability of choosing:
a) An odd number
(b) an even number
(c) a prime number
d) a non-prime number
(e) a number from 5 to 9?
5. Two scratch cards, A and B, offer exactly the same prizes.
1
The probability of winning a prize on scratch card A is .
3
2
The probability of winning a prize on scratch card B is .
5
Which one would you advise someone to buy? Explain why.
6. A fair dice is rolled 600 times. How many times would you expect it to land on a 6?
15
Autumn 1- Study Book (20-29)
Confidence Rating
Rate how confident you are at each topic.
Topic:
Objective:
Place Value
and
calculations
 Recall multiplication facts to 12 x 12 and
use them to derive quickly the
corresponding division facts;
 Order integers and use the symbols <, >
and understand the ≠ symbol;
 Add and subtract integers and decimals
efficiently;
 Multiply and divide by powers of 10
mentally;
 Begin to use efficient methods for
multiplication and division;
 Calculate with negative numbers.
Area and
Perimeter
 Find the perimeter of compound shapes;
 Calculate areas and perimeters of
compound shapes made from triangles
and rectangles;
 Find the area of a parallelogram;
Probability
 Write probabilities in words or fractions,
decimals and percentages;
 Find the probability of an event happening
using theoretical probability;
 Find and justify probabilities based on
equally likely outcomes in simple contexts
and use theoretical models to include
outcomes using dice, spinners, coins
16