StonelawMathematics Department
Blue Course – Block B
Revision Sheets
BB0Decimals
BB0.1I have revised and understood that digits after the decimal point represent tenths, hundredths and thousandths respectively.
2 ∙ 3 4 5
2 units3 tenths 4 hundredths 5 thousandths
Read the following then write as a number.
a)3 units, 4 tenths, 3 hundredths and 8 thousandths.
b)4 tens, 1 unit, 6 tenths, 8 hundredths and 9 thousandths.
c)I am a number with 8 thousandths, 1 tenth, 7 hundredths and no units.
(Be careful!).
d)I am a number with 9 hundredths, 4 units, 3 tenths and no thousandths.
BB0.2I can read scales to the nearest graduation where the value of an intermediate graduation may need to be deduced (to 2 decimal places).
What numbers are located at a) to h) on these number lines
BB0.3I can add or subtract any decimal I meet in the context of a problem without using a calculator.
Try the following questions without using a calculator:
a) 5∙1 + 3∙8b) 3∙6 + 5∙7c) 8∙9 – 5∙2d) 15∙5 – 10∙6
e) 10∙39 – 5∙21f) 6∙89 + 5∙1g) 7∙67 – 1∙89h) 64∙53 + 49∙08
i) 47∙5 – 17∙56j) 92∙4 + 33∙307k) 13∙425 – 11∙313
l) 109∙56 + 289∙385
BB0.4I can multiply or divide any decimal by a single digit whole number without a calculator.
a) 2 ×0∙3 b) 1∙4 × 3 c) 7∙8 ÷ 2d) 29∙6 ÷ 4
e) 6∙8 × 4 f) 78∙5 ÷ 5 g) 19∙8 ÷ 6h) 17∙9 × 9
i) 108∙9 ÷ 9 j) 234∙7 × 7 k) 182∙4 ÷ 8 l) 638∙7 × 6
BB0.5I can round decimals to a given number of decimal places.
1.Round each number to one decimal place.
a) 0∙345 b) 1∙463 c) 7∙819d) 29∙654
e) 6∙833 f) 78∙552 g) 19∙833h) 17∙915
2.Round each number to two decimal places.
a) 18∙912 b) 4∙7376 c) 2∙455 d) 0∙7245
e) 0∙9776 f) 0∙077 g) 18∙488 h) 19∙999
BB1Length and Area
BB1.1I am aware of the different metric units in which length is measured and can decide which unit is most appropriate in a given context.
1. / Convert into millimetres(a) / 7 cm / (b) / 12 cm / (c) / 8.6 cm
(d) / 3 cm 4 mm / (e) / 59·1 cm / (f) / 702 cm
2. / Convert into centimetres
(a) / 60 mm / (b) / 400 mm / (c) / 250 mm
(d) / 3 mm / (e) / 4 m / (f) / 0·5 m
(g) / 17 m / (h) / 8 m 90 cm / (i) / 9 m 8 cm
(j) / 3·6 m / (k) / 0.02 m / (l) / 1.75 m
3. / Convert into metres
(a) / 300 cm / (b) / 5000 cm / (c) / 1400 cm
(d) / 590 cm / (e) / 60 cm / (f) / 71 cm
(g) / 2 km / (h) / 52 km / (i) / quarter of a km
(j) / 4 ½ km / (k) / 3·8 km / (l) / 1 km 80 m
(m) / 9·44 km / (n) / 0·6 km / (o) / 57 km 200 m
(p) / 5000 mm / (q) / 670 mm
4. / Convert into kilometres
(a) / 4000 m / (b) / 71000 m / (c) / 200 m
(d) / 19300 m / (e) / 8650 m / (f) / 470 m
(g) / 900000 cm / (h) / 200000 mm / (i) / 13000 cm
BB1.2I can calculate the perimeter of a shape.
1. / Calculate the perimeter of each shape. Show your working clearly./ (a) / (b) / / (c)
2. / Calculate the length of the missing side in these shapes
(a) / (b) / (c)
Perimeter = 13·9 cm / Perimeter = 21 m / Perimeter = 424 mm
3. / The diagram shows the floor plan of Mrs Andrew’s
dining room.
The room is 3·65 metres long and 2·8 metres wide.
The door is 0.8 metres wide and the window is 1·3 metres wide.
A wallpaper border is to be fixed around the walls. It will not cross the door or window.
If the border costs £1·50 per metre, how much will it costMrs Andrew altogether?
BB1.3I can use a formula to find the area of a rectangle.
1. / Calculate the area of these rectangles. Make sure you show a formula & working.Remember to provide appropriate units with your answers.
(a) / / (b) / / (c)
BB1.4I can use the formula to calculate the area of a triangle.
1. / Calculate the area of these triangles. Make sure you show a formula & working.Remember to provide appropriate units with your answers.
/ (a) / / (b) / / (c)
(d) / (e) / (f)
BB1.5I can find the area of composite shapes made up from rectangles and triangles.
Find the area of these composite shapes.
a)b)
c)
d)
e)
BB2More Calculations
BB2.1I can carry out Long Multiplications without a calculator.
A calculator can not be used for this exercise and you must show all working.
1.Completethe long multiplication below:
(a) 336 × 17(b) 705 × 46(c) 59 × 645
(d) 83 × 1011(e) 9632 × 29(f) 4444 × 74
(g) 11 × 2345(h) 18 × 9678(i) 7328 × 469
(j) 7147 × 463(k) 52396 × 3927
2.A ticket to the Scottish cup final is £29.
How much would 155 tickets cost?
3.Louise earns £113 per day as a Mobile Phone salesperson.
How much will she earn for 275 days work?
4.Challenge Question:
How many seconds are in a year?
(Assume year is a non-leap year)
BB2.2I can carry out Long divisions without a calculator.
A calculator can not be used for this exercise and you must show all working.
1.Completethe long division below:
(a) 396 ÷ 12(b) 1552 ÷ 16(c) 5177 ÷ 31
(d) 17353 ÷ 67(e) 470 ÷ 18(f) 895 ÷ 17
(g) 6983 ÷ 29(h)43234 ÷ 92(i) 88615 ÷ 112
(j) 43516 ÷ 152(k) 15171 ÷ 205
2.A farmer has 624 eggs.
They are to be placed in trays which hold 48 eggs.
How many trays can be filled?
3.£608778 is to be shared equally between 93 lottery winners.
How much will each person receive?
4.Challenge Question:
Each year in Scotland 1,173,840 Mars Bars are produced.
How many are made a day?
(Assume year is a non-leap year)
BB2.3I can multiply or divide any whole number or decimal by a multiple of 10,100 and 1000.
a) 5∙6 x 30b) 1∙94 x 400c) 721 x 5000d) 69∙35 ÷ 500
e) 6000 x 987∙63f) 82925 ÷ 50g) 0∙00563 x 700h) 0∙02 ÷ 200
i) 846∙81 ÷ 9000j) 43 x 800k) 74635∙095 ÷ 50l) 0∙864 ÷ 4000
BB2.4I can add, subtract, multiply or divide any decimal I meet in the context of a problem with a calculator.
1) John went to the shop with £8∙96.
He bought a packet of crisps for £0∙56, a chocolate bar for £0∙78 and a bottle of juice for £1∙05.
How much will John now have left?
2) A baby was born with a weight of 3∙75kg, after a month the baby’s weight had increased by 0∙88kg.
What is the new weight of the baby?
3) A plank of wood weighs 1∙3kg.
A builder needs 58 of these planks of wood to build a small bridge.
What will the weight of the bridge be?
4) The height of a tower block is 51∙36m, if there are 15 floors in the tower block, what is the height of one of the floors?
5) A group of 5 friends had lunch together at a local cafe. James spent £5∙33, Elle spent £6∙85, Graham spent £4∙66, Jemma spent £7∙62 and Jackie spent £5∙39.
a)How much did they spend altogether?
b)Elle complained about the lengthy wait for her food and the manager took the price of her food off the bill.
All friends, including Elle decide to split the remainder of the bill.
How much will they each have to pay?
BB3Circles 1
BB3.3I can use my approximation for pi to calculate the circumference given the diameter and vice versa
1.Calculate the circumference of these circles. Make sure you set down all the working. Remember to provide units in your answers
2.Calculate the circumference of the semi-circle and quarter-circle. Make sure you set down all the working and provide units in your answers.
3.Calculate the perimeter of the semi-circle and quarter-circle. Make sure you set down all the working and provide units in your answers.
4.A circle has a circumference of 22∙86 centimetres.Calculate the size of the diameter ofthis circle.
BB4Volume and Surface Area
BB4.1I can calculate the volume of a variety of 3D shapes including prism by applying a formula
1.Calculate the volume of each of the shapes below:
(a)(b)(c)
(d)(e)(f)
2.Calculate the volumes of the cuboids measuring:
(a)12cm by 8cm by 9cm(b)18mm by 12mm by 3mm
(c)50cm by 20cm by 5cm(d)15m by 7m by 8m
(e)11mm by 9mm by 2mm(f)
3.Calculate the volumes of a cube withsides of:
(a)6cm(b)4mm(c)14cm
4.Calculate the volume of the prisms below:
(a) (b)
For Q5,Q6 & Q7
5.Calculate the volume of each cylinder below:
(a)(b)(c)
6.The drinks can opposite is cylindrical in shape.
Calculate its volume if it has a diameter of 6cm and alength
of 11.68cm. Give your answer to the nearest cm3.
7.Six cola-cans each with a diameter of 6.8cm and a height of
9.183cm are sold together in an economy pack.
Calculate the total volume of cola in the six-pack.
Answer to the nearest cm3.
BB4.2Having investigated different routes to a solution, I can find volume of compound 3D objects (cuboids only), applying my knowledge to solve practical problems.
1. Calculate the volume of the shape below:
BB4.3I can comfortably convert between litres, millilitres and cubic centimetres.
1.Convert each of the following volumes in cubic centimetresinto litres:
(a)3000 cm3(b)2400 cm3(c)12600 cm3(d)600 cm3
(e)1460 cm3(f)480 cm3(g)320000 cm3(h)2565 cm3
2. Calculate the volume of water in each tank below, giving your answer in litres:
(a)(b)
3. Brian gets a fish tank for his birthday. It measures 30 cm by 60cm by 30 cm.
(a) Calculate the volume of the fish tank in litres.
(b) If Brian pours 36 litres of water into the empty tank, what will be the depth of the water in the tank?
BB4.4Working with others I have accurately made the net of a cube, cuboid and triangular prism and I can calculate surface area of a cube, cuboid and triangular prism.
1. Construct the net of the shapes below:
(a) (b)(c)
2.Calculate the surface area of this cuboid.
3.Calculate the surface area of the carton shown below:
BB4.5Working with others I have investigated nets that work and nets that don’t work.
1.Draw three different nets of a cube.
2.Which of the following nets below represent a net of a cube:
(a)(b)(c)
(d)(e)(f)
(g)(h)(i)
BB4.6I can solve practical problems by applying my knowledge of measure, choosing the appropriate units and degree of accuracy for the task.
1. A wheelie bin is in the shape of a cuboid.
The dimensions of the bin are:
- Length 70 centimetres
- Breadth 60 centimetres
- Height 95 centimetres
(a) Calculate the volume of the bin.
(b) The council is considering a new design of wheelie bin. The new bin will have the same volume as the old one.
The base of the new bin is to be a square of side 55cm.
Calculate the height of the new wheelie bin.
2.Mr Kane is moving house and decides to pack his collection of Maths books into cardboard boxes measuring 60cm by 45cm by 35cm.
All his books are the same size and measure 15cm by 20cm by 5cm
(a)What is the maximum number of books he can pack into a box?
(b) If each book weighs 800g and the empty box weighs 300g, what is the total weight of the box, in kilograms, when it is full of books?
3.Rosie turns on a tap in order to fill this cuboid paddling pool with water.
The water pours at a rate of 5 litres per minute.
She thinks she can fill the paddling pool in
under an hour.
Is this claim justified?
Explain your answer.
Mixed Examples
1.Mr Dodds can run 175 metres in 1 minute
How many metres could he run in 35 minutes?
2.A box holds 36 tins of beans.
Each tin weighs 228g.
What is the total weight of the tins in the box?
3.The height of Mount Everest is 8840 metres.
What would the height of 172 Mount Everest’s be?
4.15 Eiffel towers have a combined height of 4860ft.
What would the height of 1 Eiffel Tower be?
5.Thomas earns £23452 a year as a plumber.
How much does he earn per week?
6.The income from the Kings of Leon concert ticket sales was £37310.
If 455 people attended the concert then how much did one ticket cost?
7.A box of chocolates is in the shape of a triangular prism.
Calculate its volume.
8.The diagram shows a triangular prism.
The dimensions are given on the diagram.
A net of this triangular prism is shown below.
Calculate the length and breadth of this net.
9.The diagram below shows the net of a cube.
The total surface area of the cube is 150cm2.
Calculate the length of the side of the cube.
10.The end face of a grain hopper is shown below in the diagram.
(a) Calculate the area of the end face.
The grain hopper is in the shape of a prism with a length of 3.5 metres as shown below:
(b) Find the volume of the hopper.
BB5Fractions
BB5.1I can display a fraction and equivalent fractions visually using divided shapes.
- For each of the following, say what fraction has been shaded:-
a) b) c)
d) e) f)
g) h) i)
BB5.2I can find a number of equivalent fractions to any given fraction and can simplify fractions to their simplest form.
1. / Write four more fractions equivalent to the fraction given.(a) / / (b) / / (c) /
2. / Give each fraction in its simplest form.
(a) / / (b) / / (c) /
BB5.3I can calculate the fraction (unitary and non unitary) of a quantity involving at most 4 digits without a calculator.
1. / Carry out the following calculations(a) / of 1404 / (b) / of 248 / (c) / of 430
2. / Carry out the following calculations
(a) / of 1956 / (b) / of 476 / (c) / of 3528
BB6Bearings
BB6.1I understand that bearings are angles measured clockwise from North and that they are always given in 3 figures.
What bearing would you be on if you were travelling(a) / due South / (b) / due East / (c) / due North East
BB6.2I am aware of some real life context in which bearings are used.
Estimate the bearing of the following journeys(a) / (b)