Download Y8 Autumn Term Units Document

YEAR 8: AUTUMN TERM
Teaching objectives for the oral and mental activities
a.
b.
c.
d.
e.
Order, add, subtract, multiply and divide integers.
Multiply and divide decimals by 10, 100, 1000.
Count on and back in steps of 0.4, 0.75, 3/4…
Round numbers, including to one or two decimal places.
Know and use squares, positive and negative square
roots, cubes of numbers 1 to 5 and corresponding roots.
f. Convert between fractions, decimals and percentages.
g. Find fractions and percentages of quantities.
h. Know or derive complements of 0.1, 1, 10, 50, 100, 1000.
i. Add and subtract several small numbers or several
multiples of 10, e.g. 250 + 120 – 190.
j. Use jottings to support addition and subtraction of whole
numbers and decimals.
k. Calculate using knowledge of multiplication and division
facts and place value,
e.g. 432  0.01, 37  0.01.
l. Recall multiplication and division facts to 10  10.
m. Use factors to multiply and divide mentally, e.g. 22  0.02,
420  15.
n. Multiply and divide a two-digit number by a one-digit
number.
o. Use partitioning to multiply, e.g. 13  1.4.
p. Use approximations to estimate the answers to
calculations, e.g. 39  2.8.
q. Solve equations, e.g. 3a – 2 = 31.
r. Visualise, describe and sketch 2-D shapes.
s. Estimate and order acute, obtuse and reflex angles.
t. Use metric units (length, mass, capacity) and units of time
for calculations.
u. Use metric units for estimation (length, mass, capacity).
v. Convert between m, cm and mm, km and m, kg and g,
litres and ml, cm2 and mm2.
w. Discuss and interpret graphs.
x. Apply mental skills to solve simple problems.
YEAR 8
AUTUMN TERM
Number/algebra 1
Number of lessons: 6 one-hour lessons
Integers, powers and roots (48 – 59)
Sequences and functions (144 – 157)
Teaching objectives:A.
Add, subtract, multiply and divide integers.
B.
Recognise and use multiples, factors (divisors), common factor, highest common factor, lowest common
multiple and primes; find the prime factor decomposition of a number (e.g. 8000 = 26 x 53).
C.
Use squares, positive and negative square roots, cubes and cube roots, and index notation for small positive
integer powers.
D.
Generate and describe integer sequences.
E.
Generate terms of a linear sequence using term-to-term and position-to term definitions of the sequence, on
paper and using a spreadsheet or graphical calculator.
F.
Begin to use linear expressions to describe the nth term of an arithmetic sequence, justifying its form by
referring to the activity or practical context from which it was generated.
Oral and Mental
Objective l, x
Arithmegon on page 54
(last bullet point)
Main Teaching
1/2 lessons
Objective B
Notes
Key vocab.
Plenary
multiple,
prime,
factor,
common factor,
lowest common
multiple,
powers
Repeat arithmegon idea
and recall key words.
Recap Highest Common Factor of
two numbers.
Objective x
Group work e.g. Find factors of 36,
60.
Write 3 digits on board and What are the common factors?
ask pupils to find a
What is the Highest Common Factor?
multiple of 3 or 4 or 5 etc
Could use number cards/whiteboards Continue factors
or prime number e.g. 5, 1, etc.
with lower
4
attaining groups
Recap Lowest Common Multiple.
Multiple of 3 is 51
Use multiple cards in small groups.
Include talk of Prime Numbers in
Recaps.
Ask for factor pairs of a number e.g.
200
200 = 25 x 8
200 = 2 x 100
continue factorising until prime
factors are found. Discuss more
examples if necessary.
Worksheets/text for exercises.
Why are prime factors
useful?
What is the difference
between a factor and a
multiple?
Recall key words and
investigate problems page
54. Model solutions.
Oral and mental
Objectives e, l
Target Board 4 in ‘10 min
starters’.
Ask for types of numbers.
Extend to questions such
as those in framework.
(Page 59)
Main Teaching
1/2 lessons
Objectives C, A
Put nos:
{1, 2, 3, 4, 5 …………
{1, 4, 9 ……….
{1, 3, 6 ……….
{1, 8, 27
on board and lead into square
numbers, triangular numbers, cubes,
square roots, etc.
Worksheet/text for exercises
Revisit negative numbers – Squaring and cubing Negative
mini-white board
numbers e.g.:
responses to teacher’s
questions.
What is the value of – 3 2?
(-3)2?
Can we predict the value of (-1) 99
‘I like’ from ‘10 minute
Inverse:
starters’.
What are square roots of 64, 9?
Conclude: every number has 2 roots
Estimate square roots and cube roots
Check answers with calculators
Worksheet/text for exercises.
Notes
Key vocab.
roots,
inverse,
square,
triangular,
cube
Plenary
Using mini-white boards,
find squares and square
roots.
Differentiate to
groups.
Support
Concentrate on
triangular
numbers,
powers of 10n,
2n etc.
What do you think
43 x 42 =
?
(law of indices)
Oral and mental
Objectives c, x
Counting stick to generate
sequences.
Hands up sequences
(Additional 10 minute
starters).
Main Teaching
2/3 lessons
Objectives D, E & F
Use flowcharts (e.g. page 145) to
generate finite, infinite sequences,
using multiples, triangular numbers,
square numbers or fractions.
Worksheet/text for exercises.
Introduce
1st term and term to term rule (p149)
with 1 or 2 examples.
Worksheet/text for exercises
Resource sheets or group work
devising sequences and rules.
Extend to nth term rules.
Year 7 growing matchstick problem
(p154) can be extended to similar
problems. Groups generating their
own picture sequences.
Resource sheets
IT/graph plotting
sequences/spreadsheet. Make links to
gradient and y intercept.
Worksheet/text for exercises.
Investigate: Paving stones p157.
Notes
Key Words
Flowchart,
sequence,
finite,
infinite
Plenary
Find rules from a given
sequence.
e.g. 5, 10, 15 …………..
6, 11, 16 …………..
Sequences at bottom of
p157.
People sitting at a table.
What is the link between
tables and people if we add
more tables. Can we
predict how many people
can sit at 100 tables etc.
Try other arrangementsplot graph- make linksnumber machinesequations etc.
YEAR 8
AUTUMN TERM
Number 2
Number of lessons: 6 one-hour lessons
Fractions, decimals, percentages (60–77)
Calculations (82–85, 88–101)
Teaching objectives:A. Know that a recurring decimal is a fraction; use division to convert a fraction to a
decimal; order fractions by writing them with a common denominator or by
converting them to decimals.
B. Add and subtract fractions by writing them with a common denominator; calculate
fractions of quantities (fraction answers); multiply and divide an integer by a
fraction.
C. Interpret percentage as the operator ‘so many hundredths of’ and express one
given number as a percentage of another; use the equivalence of fractions,
decimals and percentages to compare proportions; calculate percentages
and find the outcome of a given percentage increase or decrease.
D. Understand addition and subtraction of fractions; use the laws of arithmetic and
inverse operations.
E. Recall known facts, including fraction to decimal conversions; use known facts to
derive unknown facts, including products such as 0.7 and 6, and 0.03 and 8.
F. Consolidate and extend mental methods of calculation, working with decimals,
fractions and percentages; solve word problems mentally.
Oral and mental
Main Teaching
Notes
Plenary
Objectives b, c, m, k.
Using counting stick or
number line count
forwards/backwards in
decimals/fractions (if counting
in eighths pause for
simplification when possible).
Objectives A,E 1 -2 lessons.
Calculators
needed.
How do you know not all
fractions can be expressed as
exact decimals?
Select 10 students ask 1/10 to stand
up. Now ½. Now 3/10.
Ask for decimal equivalents.
What about ¼?
If I had 100 students could ¼ stand
up? Discuss.
Given 80 x 3 = 240 What else What about 1/3?
do I know? Use a web diagram In pairs explore relationship between
to record suggestions – these
fractions and decimals – produce
should include other decimal
table ½ = 0.5 1/3 =0.3333 etc.
mult. and divisions as well as
Discuss recurring/terminating
doubling halving etc.
decimals.
Discuss equivalents we should learn.
Mult. and dividing by 10, 100, Which are easiest to compare
1000 etc. moving digits.
fractions or decimals – generalize a
method for comparing fractions?
Tackle some questions – link to
percentages.
Is 3 ÷ 10 x 4 ÷ 10 the same as
3 x 4 ÷ 10 ÷ 10
Is this not 0.3 x 0.4?
Explore and use this method to
multiply decimals.
Key Vocab.
Decimal
Fraction
Recurring
Terminating decimal
Which are the important
fractions to remember as
decimals?
What can you tell me about
a ÷ 10 x b ÷ 10?
Extend to 100, 1000 etc.
Ask some mental decimal
mult.
Why is 0.3 x 0.2 not 0.6?
How would you compare
¾ , 2/3, 0.8 and 23%?
Oral and mental
Objectives b and B
Count up in quarters without a
counting stick (do not
simplify).
Draw this on the board (pupils
can copy on mini white boards
if available).
Explain that the first diagram
shows ¼ of 1 row which is ¼ ,
the second shows ¼ of 2 rows
which is 2/4 etc.
Now count up saying a quarter
of 1 is…..a quarter of 2 is……
The penny may begin to drop
if not explain. Extent to thirds
etc.
What
fraction/percentages/decimals
of 60 could we find?
Web diagram. How do we do
it?
Main Teaching
Objectives B, C (2 lessons)
Generalize from the starter about
finding fractions of integers.
Explore a quarter of 6 is six quarters
which is one and two quarters which
is one and a half etc.
In pairs tackle some questionsextent to 2/3 etc.
Notes
Calculators may
be needed.
Explore
percentage and or Draw me a diagram to show
fraction key.
2/3 of 12 etc.
Vocab.
Unit fraction
How does ¼ of and 0.25 of and 25% Value added tax
of link? Explore with our
remembered special fractions (2/5 =
0.4 = 40% etc.
Consolidate with mixed questions –
try to use real contexts not just
numbers.
Extend to 1 ¼ of or times and
amount. Link to ¼ more then link to
125%.
Extent to percentage increase and
decrease.
Questions in context.
Explore which is cheaper 10%
discount then add on V.A.T or add
on V.A.T then give a 10% discount.
(see page 77 for more ideas).
Plenary
What is another way of
thinking of 2/3 of 12?
(12 lots of 2/3).
How do you know a fraction is
bigger than one?
How do we simplify it?
Who can explain a link
between fractions and
decimals? Decimals and
percentages? Etc.
Which are the easiest fractions
to find?
What do you think 1/3 is as a
percentage.
How does V.A.T. work?
Which is more 1/3 of £45 or
25% of £64? Why?
Oral and mental
Main Teaching (1 or 2 lessons)
Notes
Plenary
Objectives v and F
Ask questions like – what
fraction is a mm of a cm?
What percentages. What
fraction is an inch of a foot
etc?
Make a grid with some
fractions on. Ask pupils to
find equivalents. Ask which
are bigger than others and
why?
Which give recurring
decimals? Which one is twice
another etc?
Use a paper folded grid with
various squares coloured or
shaded.
Fold and ask what fraction or
percentages or decimals are
shown of rows, columns or the
whole grid.
Objective D, F, B
Explore patterns on page 69 to
interpret division by a fraction. Try
and generalize but ensure students
can make links to multiplication.
Use diagrams to help e.g. how many
2/3 in 6? Use the grids from
previous lessons.
Establish which fractions are easy to
add. Why do we not add the
denominators? Ask why ½ + ½
can’t be 2/4.
Vocab
Numerator
Denominator
Top heavy
Improper
Proper
Mixed number
Cancel
Simplify
Multiples
Verify
Why is 6 ÷ ½ not 3?
What is an equivalent
calculation?
Recap on cancelling and opposite
process. Recap on common
multiples.
Establish generalization for addition
and subtraction of proper fractions
extent to answers with mixed
numbers.
Questions involving fractions in
context.
If I use 2/3 of a pint of milk to
make a milk shake cocktail
how many cocktails could I
make with 6 pints – what’s the
‘sum’?
How would we find 6 ÷ 2/3?
Would a picture help.
Can we generalize for division
by fractions?
T ÷ a/b could be written as
what? ( b/a x T).
What fractions are easy to
add?
What questions do you ask
yourself before trying to add
fractions?
A pupil when asked to add ¾
and 3/8 did 24/32 add 12/32 is
s/he right is there a better way?
Who would add fraction?
YEAR 8
AUTUMN TERM
Shape, space and measures 1
Number of lessons:
6 one-hour lessons
Geometrical Reasoning: lines, angles and shapes (178-189)
Construction (220-223)
Solving Problems (14-17)
Teaching objectives:A.
Identify alternate angles and corresponding angles;
B.
Understand a proof that:
The sum of the angles of a triangle is 180º and of a quadrilateral is 360º;
The exterior angle of a triangle is equal to the sum of the two interior opposite angles.
C
Solve geometrical problems using side and angle properties of equilateral, isosceles and right-angled triangles and
special quadrilaterals, explaining reasoning with diagrams and text; classify quadrilaterals by their geometric
properties.
D.
Use straight edge and compasses to construct:
a. the mid-point and perpendicular bisector of a line segment;
b. the bisector of an angle;
c. the perpendicular from a point to a line;
d. the perpendicular from a point on a line.
E.
Investigate a range of contexts; space and shape.
Oral and mental
Objectives s,t
Main Teaching (3/4 lessons)
Notes
Plenary
Objectives A, B, C & E

Write “ANGLE” in capitals
on the board, identify from
the letters types of angles and
lines e.g. identify a reflex
angle. (Pupils use of correct
vocabulary essential).
Recap on
These lessons could be enhanced
using a dynamic geometry
software packages.
Additional 10-min Starters
Booklet
“Shape recognition”
“Imagining shapes.”
Write a capital ‘A’ on the
board
a
b
d
c
e
Give the size of angle a, ask
pupils to calculate and
explain how they got the
other angles.
Lucky dip bag of vocabulary.
Pupil picks out a word and
explains what it is using the
correct vocabulary.
Key Vocab.
- angles on a line
Parallel
- opposite angles
Perpendicular
- angles at a point
Horizontal
- angles in a triangle
Diagonal
- use a shape such as
Adjacent
Opposite
to bring out
Point
the above
Intersect
points
Intersection
Vertex
Draw a pair of parallel lines and a transversal on the Vertices
board. Ask pupils to indicate those angles that
Side
appear to be the same. Bring out alternate and
Angle
corresponding angles from that discussion.
Degree
Acute
Worksheet/text for examples.
Obtuse
Reflect
Additional questions:
Base angles
Vertically
1. Write a short poem about
Opposite angles
a) alternate angles
Corresponding angles
b) corresponding angles
Alternate angles
2. Write a rap about what you’ve learnt in the
Supplementary
lesson.
Complementary
Interior angle
Equidistant
Proof
Prove





Bring the class together, and
ask for pupils to read their
poem or rap.
Imagine an F shape, what
angles can you see?
Imagine z shape, what angles
can you see. What other
letters help us with angles
(X, L, etc.) and why?
How do we label angles
(conventions)? What other
conventions do we use in
geometry?
Where do people use the
skills we have developed
today?
Where might you use your
geometry skills in,
technology, sport/games,
science etc.?
Using alternate and corresponding angles, prove
that the angle sum of a triangle.
a
‘a’ alternate
‘b’ alternate
a + b + c = 180º straight line
QED!
b
c
a
b
Extend proof to angle sum of a quadrilateral,
framework p183. Also proof that the exterior angle
of a triangle is equal to the sum of the 2 interior
angles p184.
Worksheet/text for examples.
Discuss-
1. Use 2 way tables with types of properties to
place quadrilaterals in the appropriate section.
P183 NNS example at bottom of 1st
column
Pairs of equal
angles
Classify quadrilaterals by their geometric properties
Pairs of equal
sides
0
1
P17 NNS bottom of first column put
example onto OHT
2
0
1
2
Hypothesise on which spaces would have the
most/least shapes.
2. Identify and classify the 16 quadrilaterals using
a 3 x 3 pinboard or 3 x 3 dot paper.
Worksheet/text for solving problems involving
quadrilaterals and triangles.
Sheet of quads and triangles
included
Provide a convincing argument to explain
for example, that a square is a rectangle,
but a rectangle is not necessarily a square
(rhombus/Parallelogram) etc.
Objective n
Doubling/halving activity e.g.
‘Double, Halve Stick’ in
‘Additional Starters’ or loops.
Objective r and E
Imagine a quadrilateral , mark
the midpoints with a dot.
Go around the shape
clockwise and join together
the midpoint dots.
What shape do you get?
Now draw it and share it with
a partner.
I think it is always a
parallelogram – why?
Draw a rectangle.
Draw in one diagonal.
If I cut along the diagonal, I
get two congruent right
angled triangles.
By fitting together matching
sides of the 2 triangles, make
a new shape.
What is the name of the new
shape?
Explain to a partner why you
have given the shape its
name.
How many possible shapes
are there? (6)
2/3 lessons
Objectives D & E
Introduce via review of horizontal, vertical and
perpendicular.
Consider words starting with the prefix bi- to lead
onto bisect and bisector.
Mark 2 points on the board (not horizontally
opposite). Explain that these are wild animals tied
up, and a safe pathway between them is needed.
Develop the idea of a safe path, leading onto the
construction of the perpendicular bisector.
What quadrilateral have we constructed? – Discuss
rhombus and its properties.
Vocabulary
Bisect
Bisector
Equidistant
Straight edge
Compasses
Locus
Loci
Look at the maximum number of right
angles in quadrilaterals, extend to other
polygons.
Revisit construction stressing the link to a
rhombus – could a kite’s construction be
used instead – would this help sometimeswhat have a kite and rhombus got in
common?
Demonstrate/devise construction to bisect on angle.
Pupils could practise with acute, obtuse and reflex
angles. Relate to the rhombus construction.
Introduce the construction of a perpendicular from a
point to a line by an example using the shortest
distance to a line e.g. lazy camper to a river for
water. Relate to the rhombus construction
Pupils could construct perpendiculars within a
rhombus/kite and arrowhead.
Introduce the construction of a perpendicular from a
point on a line by giving examples of who would
use the construction e.g. a builder building a wall.
Relate to the rhombus construction
Link to loci ideas.
Pupils could model loci paths according to
given instructions.
YEAR 8
AUTUMN TERM
Algebra 2
Number of lessons: 6 one-hour lessons
Equations and Formulae (112-199, 138-143)
Teaching objectives:
A.
Begin to distinguish the different roles played by letter symbols in equations, formulae and functions; know the
meanings of the words formulae and function.
B.
Know that algebraic operations follow the same conventions and order as arithmetic operations; use index notation
for small positive integer powers.
C.
Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket.
D.
Use formulae from mathematics and other subjects; substitute integers into simple formulae, and positive integers
into expressions involving small powers (e.g. 3x² + 4 or 2x³); derive simple formula
Oral and mental
Objective q
Put up
56+37=56+30
=86+7=93
and ask the pupils to tell
you about it. Why is it
incorrect, what is being
done? How could we
write it correctly? Use
this to bring out the
vocab of equality [as
page 113].
Main Teaching
1/2 lessons
Objectives A, B
Equation, Formula, Function make clear the
difference. (113)
Pupils make up in pairs or groups some
equations functions and formulae – class
discussion about the results.
Go through the written language of algebra.
2 x n = 2n etc.
[see page 113].
Go through BODMAS again emphasising
that algebra follows the same rules. Stress
how brackets inclusion changes priority.
Use brackets homework to reinforce. Look
at index notation.
Yellow
Red
Red
White
Notes
Vocabulary
Equation
Formula
Function
Variable
Substitute
Term
Expression
Plenary
Give me an example of an equation.
Are there any variables?
Are there any expressions?
Which equations can you solve?
What types of equations have lots of
solutions?
Are these functions or formulae?
Discuss observed misconceptions.
Write
2+5+7 on the board.
What other number
sentences can I write
using 2, 5 and 7?
7-2=5
7-5=2
5+2=7
If a + e = y what other
algebra sentences can I
write? Does it work for
all numbers? Discuss
variables/function etc.
Extend to a x b = c
If I know the width of yellow and red how do
I find white?
How do I write an algebraic sentence to
express this?
What about yellow + white?
(page 115).
Pupils in groups form their own diagrams and
formulae.
2 stage formulae need to be looked at – link
to earlier sequence work or growing patterns.
Group work producing patterns and formulae
perhaps.
Discuss patterns/formulae produced.
Can we transform a formula?
How?
Link to number machines.
What have we learned today?
What do we have to remember?
Objective q
Use whiteboards and
introduce the idea of
simplification.
Students discuss and hold
up whiteboard with
simplifications after each
question.
Equation matching cards.
(just simplification)
(Resource sheet 4)
3x4+2x4=5x4
Discuss – generalise write
using brackets i.e.
(3 + 2) x 4
2/3 lessons
Objective C
Vocabulary
Talk about simplifying and distributive law.
Note: try not to use ideas like “can’t add
apples and bananas” pupils must realise that
the letters represent numbers (often
measurements).
Show distributive law simply
3(a+2)=(a+2)+(a+2)+(a+2)
Show examples of how this can help write
and simplify expressions.
Put diagram on the board.
Find the area of the shape Use examples similar to those below.
not shaded.
10
12
2
a
5
b
b
How did you do it, are
there any other ways?
c
d
6
Variable
Substitute
Term
Expression
Simplify
Simplification
Homework Humdingers
(Resource sheet 8)
What does 3(a + 2) mean?
How do you know?
What about (a + 2) 3 ?
If I have an apple and I label it ‘a’.
What could ‘a’ stand for?
Mass, cost, width, height, calorific
value…
What could it not stand for?
Apple, colour, variety…
If m = 4 are the values of the
following the same?
3m²
(3m)²
Show all
Simplify to same expression
(7-a) x 5 + (5-b) x 3 + a x 3
etc.
Use other diagrams.
Number Tricks sheet.
Either read out or put on OHP.
(Resource sheet 9).
10
b
3a
b
Find shaded area for each shape.
Oral and mental
Main Teaching
1/2 lessons
Tell a story. Andrew buys 4
Objective D
bags of sweets. He doesn’t
Exercises needed on forming
know how many sweets are in
expressions/equations/formulae
each bag but he does know that Use whole class teaching on
they are all the same. He gave expressions for 1 more than a
one bag to his brother and sister variable, 1 less, 3 times a variable,
to share equally, how many
what about add one then times by 3?
does each have? He gives
etc.
another bag to his friend John
Talk about what can change and what
who already has 4 sweets, how can’t change– variables and
many does John have? Andrew constants.
eats 2 sweets, how many does
he have left?
Use page 143 for ideas of formulae to
At each pause, pupils respond
derive.
with expressions.
Perhaps give a value for the
number of sweets in the bag
originally and then substitute
into the expressions formed.
Notes
Plenary
Objective x
What happens when you have more
than 2 variables?
Address observed misconceptions.
Model different ways of expressing
division.
Relate to problem solving in science
and the real world.
YEAR 8
AUTUMN TERM
Shape, Space and Measures 2
Number of lessons: 6 one-hour lessons
Measures and mensuration (228 – 231, 234 – 241)
Solving Problems (18 – 21)
Teaching objectives:A.
Use units of measurement to estimate, calculate and solve problems in everyday contexts involving length, area,
volume, capacity, mass, time and angle; know rough metric equivalents of imperial measures in daily use (feet, miles,
pounds, pints, gallons).
B.
Deduce and use formulae for the area of a triangle, parallelogram and trapezium; calculate areas of compound
shapes made from rectangles and triangles.
C.
Know and use the formula for the volume of a cuboid; calculate volumes and surface areas of cuboids and
shapes made from cuboids.
D.
Investigate in a range of contexts: measures.
Main Teaching
2/3 lessons
Objectives B, A
Follow on from length conversion
grid to discuss the units of area.
Use information grids
Revise area of rectangle.
(enlarged) to check conversions Demonstrate area of triangle is half that
by asking:
of rectangle by cutting.
Oral and mental
Objective v
 Which are the same?
 Which are greater than…?
 Which are less than…?
Etc.
Consider other triangles by
demonstration or use spotty grids
(p 237)
Notes
Reinforce vocabulary:
area,
square,
centimetre,
square metre,
square millimetre
Plenary
Why do we use squares to measure
area rather than:
circles
rectangles
triangles
hexagons?
These lessons could be
enhanced using a
dynamic geometry
software package.
How would you work out the area of
the shaded square given the base and
height of each right angle triangle?
Worksheet/text for exercise
Consider compound areas of rectangles
and triangles.
Vertical height
Worksheet/text for exercise.
Demonstrate area of parallelogram by
cutting. Emphasise perpendicular
height rather than sloping side. Group
work – drawing sets of parallelograms
with same area. Is the rhombus just a
special case of a parallelogram?
Altitude
Perpendicular
Area
How do we get a triangle with the
same area as a given parallelogram?
What about a trapezium. (same base
twice height).
Given a square how can we produce a
parallelogram with the same area? (cut
diagonal and reform the two triangles
created). What about a rhombus?
Worksheet/text for exercise.
Pupils to investigate area of a
trapezium as introduction.
Discuss pupils’ answers bringing out
the mean of the two sides multiplied by
height.
Worksheet/text for exercise.
How can we draw sets of triangles
with the same area?
Mean
Trapezium
Why is the area of a rhombus – half
the product of the diagonals? (Use the
4 right angles triangles).
Why do we use the mean in the
trapezium formula?
Oral and mental
Objective l
Tables practice using counting
stick or verbal loop e.g. start off
with 3 x 7 and ask a pupil to
answer. That pupil then asks
the person next to them a
number fact and so on.
Lead onto multiplying 3
numbers together.
Main Teaching
2/3 lessons
Objectives C, A
Notes
Plenary
Reinforce length units and area units.
Discuss surface area of a cuboid.
Discuss volume and the units. Say
cubic metres not metres cubed.
Useful equipment:
a litre cube filled with
1 cm³ gives the pupils
something tangible on
which to base the theory.
How do we find the volume of a
cuboid measuring 7 cm x 5 cm x
0.2m?
Review volumes of cuboids and
devise a formula.
Worksheet/text for exercises.
Extend to shapes made up of cuboids.
Worksheet/text for exercises.
Show how to calculate the surface
area of a cuboid using a net or
alternative method.
Worksheet/text for exercises.
How do we find its surface area?
If the volume of a cuboid is
increased, does its surface area
always increase?
Oral and mental
Objective u
Estimate length in classroom
(already measured)
Estimate volume (bring in
various bottles)
Cut cone shape top of a plastic
bottle to leave a cylinder of the
same base radius and height.
Compare volumes (estimate
ratio). Demonstrate with sand
or water by pouring from cone
to cylinder.
Objective r
Ask students to describe the
cone and cylinder.
Describe a common 3D or 2D
shape and ask students to
Main Teaching
1/2 lessons
Objectives A, D
Review volume units (from last
lesson).
Discuss appropriate units to measure
the volume of:
 A matchbox
 A telephone
 The school hall
Notes
Key Vocabulary:
cubic millimetre
cubic centimetre
cubic metre
hectare
ounce
pound
foot
mile
pint
gallon
tonne
Lead on from volume to mass and
capacity and discuss units of weight g,
Try and bench mark
kg, tonne and units of capacity ml, l.
measurements.
E.g. coke can holds
Consider imperial units of oz, lb, ft,
330ml.
mile and then pint and gallon.
A ruler is 15 or 30cm etc.
Rough equivalent to learn:
1 kg = 2.2 lb
1oz = 30 g
1 mile = 1.6km
1km = 0.6 miles
1 litre is just less than 2 pints.
Rhyme (‘A litre of water’s a pint and
three quarters’).
Plenary
Examples such as:
Apples are sold at 40p per kg and
24p per pound.
Which are the cheapest apples?
Explain how you worked it out.
Further example framework p21
Check/match conversions.
Check units – what would we
measure in hectares?
Check bench marks – what is about
100metres, a km? etc.
Who would use ounces? etc.
visualise it as you describe it
using key vocab.
Ask them to guess what it is
(table, stereo earphones, mobile
phone, gear stick etc.) See
‘Imagine’ worksheet in the
summer term.
Invite pairs to develop their
own descriptions for the class
to draw.
Worksheet/text or group activities for
conversion exercises.
Discuss appropriate units of area to
measure the area of:
 Thumb nail
 Desk
 Classroom floor
 London
 Playing field
Make last one appropriate so that
hectare (ha) is introduced as
1 ha = 10 000m²
Use problems to illustrate conversions
between one unit and another e.g.
 A rectangular field measures 250m
by 200m – what is its area in
hectares?
 Each side of a square tablecloth
measures 120cm. Write its area in
square metres.
Worksheet/text for exercises.
Handling Data 2 (6 Hours) Autumn Term See Y8 Mini pack – handling data (note additional calculator
work may be needed).
Handling data (248–273)
Solving problems (28–29)
A. Discuss a problem that can be addressed by statistical methods and identify related questions to
explore.
B. Decide which data to collect to answer a question, and the degree of accuracy needed; identify
possible sources.
C. Plan how to collect the data, including sample size; design and use two-way tables for discrete data.
D. Collect data using a suitable method, such as observation, controlled experiment using ICT, or
questionnaire.
E. Calculate statistics, including with a calculator; recognise when it is appropriate to use the range,
mean, median and mode; plus Y7 objectives - construct and use stem-and-leaf diagrams. Calculate
statistics for small sets of discrete data:
 Find the mode, median and range:
 Calculate the mean, including from a simple frequency table, using a calculator for a large number
of items.
F. Construct, on paper and using ICT:
- pie charts for categorical data;
- bar charts and frequency diagrams for discrete data;
- simple scatter graphs;
- identify which are most useful in the context of the problem.
G. Interpret tables, graphs and diagrams for discrete data and draw inferences that relate to the
problem being discussed; relate summarised data to the questions being explored.
H. Communicate orally and on paper the results of a statistical enquiry and the methods used, using
ICT as appropriate; justify the choice of what is presented.
I. Solve more complex problems by breaking them into smaller steps or tasks, choosing and using
resources, including ICT.