Year 10 Summer 1 POS
PP
Strategies
Targetted intervention based on weaknesses from assessment.
ActiveLearn to be set for those below target.
PiXL Maths app for use with computers, phones or tablets.
MA
Strategies
For MA, see Pythagoras’ pathway.
ActiveTeach – Higher GCSE
Homework Mathswatch Clips:
Perimeter, Area and Volume:
116 – Circle definitions
117 – Area of a circle
118 – Circumference of a circle
167 – Sectors of a circle
54 – Area of a triangle
55 – Area of a parallelogram
56 – Area of a trapezium
114a – Surface area of a cuboid
114b – Surface area of a triangular prism
115 – Volume of a cuboid
119 – Volume of a prism
Measures:
143 – Distance-time graphs
216 – Velocity-time graphs
142 – Compound units
Oracy
Key words:
Perimeter, Area and Volume: Radius, diameter, circumference, area, semi-circle, sector, segment, cube, cuboid, prism, cylinder, sphere, hemisphere, arc,
perimeter, surface area, volume, formula, parallelogram, trapezium, base, height, length, width, depth, cross-section, compound, dimention.
Measures: Distance, time, speed, compound measure, measure, density, mass, population density, area, population, volume, acceleration, curve,
trapezium, estimate, linear, exponential, velocity,
Literature:
Time
PathwayTeacher and
Learning Activity
Questioning
Challenge
Initial
Lesson
Baseline
Whole class base line assessment on each objective.
Knowledge,
skills and
content
A
X3 Know,
understand and use
the formula for
finding the
circumference of a
circle.
Calculate the circumference of the circle below.
Imogen’s working out for the circumference of the circle is below. Is she correct?
5π = 15.7cm
Paul wants to put a ribbon around the vase below. He has 9cm of pink ribbon, and 13cm of blue ribbon. Which ribbon should he use?
D
X4 Calculate the
perimeter of a
semi-circle;
Calculate the
perimeter of a
quadrant.
Mike is putting a border around a section of his garden as shown below. The panels are sold in 6m packs, for £2.54 each. He has £15. Does he have enough money for the border?
8cm
5cm
D
X5 Calculate the
length of an arc and
hence find the
perimeter of a
sector;
Find the angle of a
sector when given
the length of the
arc.
Calculate the length of the arc below.
Calculate the perimeter of the sector.
Calculate the angle of the sector below:
Jamie works out the angle of the sector below. Is his working out correct?
2.79 ÷ 8 ÷ π x 360 = 40°
David is trying to work out the length of the arc below. Here is his working out. Is he correct?
360
30 x 5π = 94.25cm
Joe is trying to work out the length of the arc. Here is his working out. Is he correct?
30
360 x 10π = 2.62cm
2.62 + 5 + 5 = 12.62cm
Two towns are near a lake. The road between the towns is 3.49km. Calculate the angle from one town to the other in relation to the lake.
A D
X9 Use the formula
to find the area of
any triangle.
Find the area
A D
X10 Calculate the
area of a shape
made from
rectangles, triangles
and parallelograms.
Calculate the area of the compound shape below
Calculate the area of the compound shape below.
Calculate the area of this shape
The compound shape (A) and square (B) below have the same area.
Write an expression in terms of x to show the area of shape A
The diagram shows an area of floor.
The area of the floor is 138m²
Calculate the length of x
The diagram shows the floor of a village hall.
The caretaker needs to polish the floor.
One tin of polish normally costs £19
One tin of polish covers 12 m2 of floor.
There is a discount of 30% off the cost of the polish. The caretaker has £130
Has the caretaker got enough money to buy the polish for the floor?
The diagram shows the floor of a village hall.
The caretaker needs to polish the floor. One tin of polish normally costs £19. One tin of polish covers 12 m2 of floor.
There is a discount of 30% off the cost of the polish. The caretaker has £130.
Has the caretaker got enough money to buy the polish for the floor? You must show all your working.
A D
X11 Know and use
the formula for the
area of a trapezium.
Find the area of a trapezium
Find the missing length of the trapezium below
Here’s a diagram of Jim’s garden
Jim wants to cover his garden with grass seed to make a lawn. Grass seed is sold in bags.
There is enough grass seed in each bag to cover 20 m2 of garden.
Does he have enough money? Explain your answer.
A D
X12 Know and use
the formula for the
area of a circle.
Find the area of the circle
Find the area of the circles. Give your answer in terms of π and to 2 significant figures.
The diagram shows the surface of a pond in the shape of a circle
The circle has a radius of 120 cm. Mark wants to put 20 fish into the pond.
There needs to be a surface area of 1800 cm2 for each fish.
Mr Weaver's garden is in the shape of a rectangle. In the garden
there is a patio in the shape of a rectangle
and two ponds in the shape of circles with diameter 3.8 m. The rest of the garden is grass.
Mr Weaver is going to spread fertiliser over all the grass. One box of fertiliser will cover 25 m2 of grass.
How many boxes of fertiliser does Mr Weaver need? You must show your working.
Which pizza is the best value for money?
Show that the surface of the pond is large enough for Mark to put 20 fish into the pond.
Anil says ‘the area of a circle with radius 8 is double the area of a circle with radius 4. Is he right? Explain your answer.
D
X13 Calculate the
area of a semi-circle
and a quadrant;
Calculate the area
of composite
shapes including
semi-circles and
quadrants.
The shapes below are part of circles. Given the area, find what the radius would be.
D
X14 Calculate the
area of a sector;
Find the angle of a
sector when given
its area.
Find the value of x.
A D
X16 Calculate the
surface area of a
cube or cuboid.
Work out the Surface Area of these cuboids
Calculate the surface area of the following Cuboid.
A D
X21 Find the
volume of a solid
shape by counting.
Find the volume of the cuboid below.
Find the volume of the shape below.
Heather says that the volume of the cuboid below is 28. Is she correct? Explain your answer.
Mark has counted the cubes on the shape below. He says the volume is 9. Is he correct?
Explain your answer.
A D
X22 Know,
understand and use
the formula for
calculating the
volume of a cube or
cuboid.
Using the formula lwh, find the volume of the cuboid below. The volume of Mr Pilkington’s room is 140m3. Use this information to
find the height of the room.
Jenny has incorrectly calculated the volume of the cuboid below. Correct her working out.
4 x 50 x 7 = 1,400
E P
M11 Interpret
distance-time
graphs;
Create and/or
complete
distance-time graphs.
At 9 am, Bradley began a journey on his bicycle.
From 9 am to 9.36 am, he cycled at an average speed of 15 km/h. From 9.36 am to 10.45 am, he cycled a further 8 km.
(a) Draw a travel graph to show Bradley's journey.
From 10.45 am to 11 am, Bradley cycled at an average speed of 18 km/h.
(b) Work out the distance Bradley cycled from 10.45 am to 11 am.
7cm
50mm
E P
M12 Understand
that the gradient of
a distance-time
graph is its speed
and use this to
calculate the speed
at different points
in the journey.
Each Saturday, Sarah cycles from her house to the gym. The travel graph shows Sarah's journey to the gym.
(b) What time does she leave home? (c) How far is the gym from Sarah's house? Sarah stays at the gym for 1½ hours.
She then cycles back to her house at 18 km/h. (d) Complete the travel graph.
Lisa cycles to work.
The travel graph shows information about her journey to work on Tuesday.
Martin also cycles to work.
On Tuesday his average speed was 16 km per hour. Who has the greater average speed, Lisa or Martin? You must show all your working.
The graph shows information about the distances travelled by a lorry.
The graph is a straight line.
(a) Work out the gradient of the straight line.
(b) Write down a practical interpretation of the value you calculated in part (a).
E P
M13 Interpret
velocity-time
graphs;
Create and/or
complete
velocity-time graphs.
Karol ran in a race.
The graph shows her speed, in metres per second, t seconds after the start of the race.
(a) Write down Karol's speed 3 seconds after the start of the race. (b) Write down Karol's greatest speed.
(c) Write down these two times.
E P
M14 Understand
that the gradient of
a velocity-time
graph is its
acceleration and
use this to calculate
the acceleration at
different points in
the journey;
Understand that
the area under a
velocity-time graph
is the distance
travelled and use
this to calculate the
distance travelled
for different parts
of a journey.
Here is a speed-time graph for a car journey. The journey took 100 seconds.
The car travelled 1.75km in the 100 seconds. (a) Work out the value of V.
(b) Describe the acceleration of the car for each part of this journey.
E P
M15 Interpret the
equations and
graphs of real-life
linear functions,
including the
meaning of the
gradient and
y-intercept in the
given context.
A water company charges customers a fixed standing charge plus an additional cost for the amount of water, in cubic metres, used. The graph shows information about the total cost charged.
(a) Write down the fixed standing charge.
The graph shows the depth, d cm, of water in a tank after t seconds.
(b) Work out the additional cost for each cubic metre of water used.
The graph shows the cost of using a mobile phone for one month for different numbers of
minutes of calls made.
The cost includes a fixed rental charge of £20 and a charge for each minute of calls made.
Work out the charge for each minute of calls made.
E P
M16 Plot and
interpret other
non-linear graphs from
real-life contexts.
The diagram shows a swimming pool in the shape of a prism.
The swimming pool is empty.
The swimming pool is filled with water at a constant rate of 50 litres per minute.
Here are four graphs.
A liquid is cooling.
The graph shows information about the time, in minutes, that the liquid has been cooling and its temperature in °C.
(a) Write down the temperature, in °C, of the liquid when it started to cool.
It takes longer for the liquid to cool from 70°C to 60°C than it does for the liquid to cool from 80°C to 70°C.
(b) How much longer?
Write down the letter of the graph that best shows how the depth of the water in the pool above the line MN changes with time as the pool is filled.
Assessment A D E P
Y10 Summer 1 Assessments
Intervention
