Download Y8 Spring Term Units Document

YEAR 8: SPRING TERM
Teaching objectives for the oral and mental activities
a. Order, add, subtract, multiply and divide integers.
b. Round numbers, including to one or two decimal places.
c. Know and use squares, positive and negative square
roots, cubes of numbers 1 to 5 and corresponding roots.
d. Know or derive quickly prime numbers less than 30.
e. Convert between improper fractions and mixed numbers.
f. Find the outcome of a given percentage increase or
decrease.
o. Use approximations to estimate the answers to
calculations, e.g. 39  2.8.
g. Know complements of 0.1, 1, 10, 50, 100, 1000.
h. Add and subtract several small numbers or several
multiples of 10, e.g. 250 + 120 – 190.
i. Calculate using knowledge of multiplication and division
facts and place value,
e.g. 432  0.01, 37  0.01, 0.04  8, 0.03  5.
j. Recall multiplication and division facts to 10  10.
k. Use factors to multiply and divide mentally, e.g. 22  0.02,
420  15.
l. Multiply and divide a two-digit number by a one-digit
number.
m. Multiply by near 10s, e.g. 75  29, 8  –19.
n. Use partitioning to multiply, e.g. 13  1.4.
s. Use metric units (length, area and volume) and units of
time for calculations.
t. Use metric units for estimation (length, area and volume).
u. Recall and use the formula for perimeter of rectangles
and calculate areas of rectangles and triangles.
v. Calculate volumes of cuboids.
p. Solve equations, e.g. n(n – 1) = 56.
q. Visualise, describe and sketch 2-D shapes, 3-D shapes
and simple loci.
r. Estimate and order acute, obtuse and reflex angles.
w. Discuss and interpret graphs.
x. Apply mental skills to solve simple problems.
Handling data 1 (6 hours)
Probability (276--283)
A. Use the vocabulary of probability when interpreting the results of an experiment; appreciate that random
processes are unpredictable.
B. Know that if the probability of an event occurring is p, then the probability of it not occurring is 1 – p; find
and record all possible mutually exclusive outcomes for single events and two successive events
in a systematic way, using diagrams and tables.
C. Estimate probabilities from experimental data; understand that:
if an experiment is repeated there may be, and usually will be, different outcomes;
increasing the number of times an experiment is repeated generally leads to better
estimates of probability.
Unit : Handling Data 1
Year Group Y8
Number of 1 Hour Lessons 6
Oral and mental
Obj. f\(Summer
term)
Counting up and
down in fract. dec.
& %ages. Divide
class into 3 groups
each group shouts
out their allotted
category.
1) 0.1, 0.2, 0.3
2) 1/10, 2/10, 3/10
3) 10%, 20%, 30%
Class/Set Core
Main Teaching
Obj. A ( 1 lesson)
Students show and tell using mini-white boards events that
they think are certain, evens prob., higher than evens
probability etc.
Select examples and place them on large probability line at
front of class. Discuss positioning.
Suggest events e.g. next person to speak will be left handed,
and ask where to place the event on the prob. line.
Discuss situations where prob. can be given as a fraction
(framework 277).
Relate to number line placing probability as a fraction.
Answer questions relating to rolling dice, picking playing
cards etc. If time check if the theory works e.g. how many
red cards should I get if I pick 10 from 52 at random?
Notes
Key Vocab.
Event
Theory
Random
Predictable
Unpredictable
Revisit Y7 vocab.
Much of this revisits
Y7 work.
Plenary
Test on key words.
Why doesn’t probability
guarantee success/failure?
Who uses probability?
If I toss a coin twice will I
get at least one head?
What is the probability if it
isn’t certain?
What events are easy to give
a fraction probability to?
Why?
How do we work it out?
How can we cheat at
cards/dice?
What happens to the
probability if we cheat?
If I tossed a drawing pin
what are the outcomes of the
event?
Are the outcomes equally
likely?
Oral and mental
Obj. f (summer
term)
Counting up in
fractions until we
get a whole one.
Counting up in
fractions and saying
what is needed to
make a whole one,
e.g,
1/10, 9/10
2/10, 8/10
3/10, 7/10 etc.
Obj. a
Beat the teacher!
One student asks
mult. table
questions and the
class try to beat the
teacher to the
answer. Hopefully
the teacher will
win. Discuss the
probabilities of the
teacher winning
and relate back to
previous work.
Main Teaching
Obj. A,B, and C. (1 lesson)
Recap on questions about prob. of rolling a six on a dice etc.
Extend to prob. of not rolling a six. How does this relate to
our starter?
Generalise that probabilities sum to one and how we can use
this in problem solving.
Set group tasks on this theme (see 279).
Mini-plenary to check findings/answers/misconceptions.
Is probability reliable – does the theory work?
Groups roll a dice 60 times – how many sixes should we get?
Put the results from two groups together to make 120 rolls –
how does this compare? – continue adding results- discuss.
Notes
Dice needed
Try and use
probability notation
P(six) etc.
Plenary
Give a sentence about the
prob. of an event, happening
and not happening.
If I toss a coin 120 times tell
me what might happen.
If 2 pupils each toss a coin
what is the chance of at least
one getting a head?
(This leads into next lesson.
It also shows that only 2 tails
doesn’t count as a success,
with a prob. of 1/4. therefore
1 - 1/4 gives 3/4.)
Higher or lower activity.
Use A4 cards or mini-white
boards with the numbers 1
through to 10.
Cards are blue-tacked to
board or held by students at
front of class.
First card is revealed and
students have to state the
probability of the next card
being higher or lower.
Highlight the reducing
denominator as the game
proceeds.
Oral and mental
Obj. g, c & d.
Using large or
O.H.T. 100 grid ask
questions.
e.g.
Name a prime
number between 20
and 30.
Point to a cube
number – what is it
the cube of etc.
Extend to the
probabilities of
each number or
type of number
being selected.
Relate the numbers
to raffle tickets.
Ask about chances
of winning. If you
bought 10 tickets
are they best
together e.g. 1 to 10
or spread out?
Ask questions on
complements to 50,
100 25,80 etc.
Main Teaching
Obj. B (2 lessons)
Recap on possible outcomes from single events – rolling a
dice, picking a card etc. Recap on ‘equally likely’ and how
we express probabilities.
Set task to explore the outcomes of two successive events
recording results
(2 coins, two dice, 1 coin and 1 dice etc).
Discuss outcomes of tasks/experiments.
Highlight sample spaces and how to tabulate outcomes.
Do this for rolling two dice etc.
How can we use this to establish probabilities of events?
Notes
Key Vocab.
Sample
Sample spaces.
Event
Biased
How many possibilities? List the sample space.
Can we safely give a probability to any combination of
meal?
Why not? Could we sample our preferences to help us
decide? Why might our class sample not be representative?
Reinforce – equally likely.
Which number on a dice is
hardest to throw?
What sort of events can we
assign a probability to
easily?
What if we can’t?
Revisit the drawing pin
question from the last
plenary.
How might probability help a
chef with preparing lunch for
factory workers?
Explore probability of getting a six by adding the scores on
two dice. Is there more or less chance than getting a six by
rolling a single dice?
Explore menu choices e.g.
Starter
Main
Soup
fish and chips
Melon
pasta
Salad
steak and kidney pie
Plenary
Question key language.
See also probability
problems page 23
How do we work out the
prob. of throwing a six on a
dice and then picking a spade
from a pack of cards?
How many attempts should
guarantee success in the
above?
Oral and mental
Obj.A & B
Ask questions
about probabilities
of single events.
Offer a menu
choice to the group.
Predict choices
collect responses on
mini-whiteboards,
discuss number of
outcomes possible
etc.
Obj x
Put students in
groups of 6, 8, 10,
etc.
Ask for ½ or 50%
of each group to
stand up. Extend to
other fractions.
Discuss why some
groups can/ can’t
complete the task.
This activity can be
done with a line of
students at the front
of the class and a
fraction of the line
have to raise their
hands. This can be
easily related to a
number line and
probabilities.
Main Teaching
Obj. C
(2 lessons)
Further tasks looking at the sample spaces and theoretical
probabilities of outcomes. (tossing 2 coins etc.)
Tabulate outcomes then set up experiments for groups of
students to check how the experimental results compare.
Discussion on findings – perhaps group presentations.
Notes
Key Vocab.
Theory
Experimental
probability
Theoretical
probability
Demonstrate probability activity where students are invited
to draw out and replace multi-cubes from a bag. After 10
selections estimate proportion or numbers of each colour in
bag, (good opportunity to discuss proportion).
Bag with 8 red and 2
white multi-cubes
inside.
Pupils set up their own experiments using counters, playing
cards etc. to make predictions.
Discussion.
How does the increase in the number of trials affect the
reliability of your estimates?
Group work deciding how best to answer probability
problems (see 285).
Plenary
A lake contains 8 species of
fish. Anglers catch and
release fish in the lake every
day.
Could a record of their
catches lead to an estimation
of the proportion of the fish
in the lake?
What about the number of
fish in the lake?
Discuss. (Note: how are the
fish caught; does a particular
method /bait only catch
certain fish; are some fish
only caught in certain area of
the lake or a certain times of
the year; are some types of
fish cleverer and therefore
get caught less {carp}?)
Groups design and trial their own experiment to solve a
problem.
Groups write a short report on their findings and share with
the class in the plenary
Extended plenary sharing
results/findings and
discussing key
issues/misconceptions.
Algebra 3 (6 hours)
Sequences, functions, graphs(160–177)
CORE
From the Y8 teaching programme
A. Express simple functions in symbols; represent mappings expressed algebraically.
B. Generate points in all four quadrants and plot the graphs of linear functions, where y is given explicitly in terms of x,
on paper and using ICT;
recognise that equations of the form y = mx + c correspond to straight-line graphs.
C. Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs
arising from real situations.
Unit : Algebra 3
Year Group Y8
Number of 1 Hour Lessons 6
Class/Set Core
Oral and mental
Obj. a
Count up in 2’s, 3’s,
squares etc.
To illustrate idea of
mapping, teacher says
each counting number
and pupils respond with a
function.
e.g.
11
2 4
3 9 for squares etc.
Obj.B
Using mini whiteboards
or (resource sheet with x
and y axes in plastic
sleeves to create miniwhiteboard effect), plot
coordinates shouted out
by teacher. Find midpoint of two points – can
we generalise a rule? (see
worksheets).
Main Teaching
Objective A
(2lessons)
Revisit Y7 work on number machines.
Activities investigating what a machine’s functions are,
given input and output tables.
Model different ways of describing the function.
x  2x + 3
xy
y = 2x + 3
Include negative numbers and some non-integer values.
Include input and output tables not in numerical order
(see 163).
Relate to mapping diagrams. Draw mapping diagrams –
note features -parallel etc. particularly projecting mapping
lines backwards. Relate to enlargement (161).
Group work with students drawing mappings and making
generalisations about the patterns.
Group work investigating properties of functions by
combining functions. E.g.
Two mult. is same as one single mult.
Two mult. followed by a division is the same as one mult
or division. (163)
Notes
Revisit Y7 vocab.
Term
Expression
Variable
Integer
Evaluate
Substitute
Introduce
Linear function
Difference pattern
Linear sequence
Arithmetic
sequence
Notation T(n)
Some spreadsheet
work could be done
here using ‘formula
function’ to
generate output
tables from input
table.
Graphical
calculators could be
used to generate
input output tables
and later graphs of
linear functions.
Plenary
Can we generalise on how
to discover a function’s
rule?
What do we mean by the
difference method?
What is the difference
between a term and
expression?
What is the difference
between an equation and
expression?
What do we mean by a
mapping?
How is a mapping different
from an equation?
What types of shapes do
mapping lines give – what
does each shape tell us?
Generalise on what
happens when projected
mapping lines meet.
Explore x  x2
Oral and mental
Obj. a
Number
machines/mappings.
Split class into two
groups. Each group gets
one part of a function e.g.
x 2 and -3 . Teacher
calls out input and groups
operate their part of the
function. Input output
table recorded and
discussed.
Mapping diagrams
predict and confirm.
Main Teaching
Obj. A & B (2lessons)
Using axes grid plot coordinates of mappings e.g x  2x
Plot (1, 2), (-2, -4) etc.
Discuss implications of joining sets of points together
with a straight line.
Discuss which points lie above and below the line –
possibly link this to inequalities.
Discuss labelling the line and the steepness of the line.
How do we describe steepness in maths?
Explore in groups lines with equations y = mx (initially
where m is a positive integer).
Notes
Key vocab.
Linear function
Linear relationship
Slope
Gradient
Steepness
Discuss – generalise - what about other values of m?
Could use graph
package or
graphical
calculators.
Extend to y = mx + c
Groups of students design
their own function. Other
groups give inputs and
receive outputs. First
group to guess function
receives points.
Discuss – generalise - make conjectures.
How does this link to sequences, mappings and
rules/number machines?
Extent to y = x2 y = 1/x
Revisit
axes
coordinates
quadrants
Plenary
Which would give the
steepest graph line y = x
y = 2x ?
What do we mean by
steep?
Teacher offers an equation
and asks students to
respond with an equation
that will give a steeper
line/less steep line etc.
What do all straight line
graphs have in common?
How do we show a
negative gradient?
What about a gradient of
1.5. How does 3/2 help?
Revisit mixed number/imp.
fraction conversion (obj. e)
What is an intercept?
How do we remember how
to plot co-ords?
X is a cross (across)
Y’s up (wise up)
(x, y) is alphabetical.
Human graphs. Students
stand as in picture. If the
origin is where their
sternum is now, they have
to model equations shouted
out by the teacher.
(y = 0, y = 2, y = -2,
y = 2x, y = 2x + 2 etc.)
Oral and mental
Obj. B
Revisit ‘human graphs’
see what has been
remembered.
Main Teaching
Notes
Obj B. (2lessons)
Present various graphs of straight lines where gradient and
intercept can/cannot be seen. Students have to guess or
accurately state the equation of the line.
Count up in coordinates
of functions
e.g. y =2x +1
(0, 1), (1,3), (2,5)etc.
Group activity – students have to produce their own graph
(could be on OHT acetates for class to see).
Group presents their graph or graphs and other groups
have to state the equation, predict some points on/not on
the line, calc. the gradient, note the main features etc.
Display graphs and invite
comments.
Obj C
Students explore situations from real life to give straight
line graphs (conversion graphs, cost of using mobile
phone per month, car hire £50 + £40 per day etc.)
Can we form equations?
How do they relate to y = mx + c ?
What does the gradient and intercept tell us in real life?
Plenary
Ask for sentences
describing what to look for
when first looking at a
function graph (may be
produce a worded flow
chart).
Generalise on what we
know now – relate back to
objectives.
Mini-whiteboards in pairs
sketch and show graph
lines from information
given by teacher (e.g.
..with a gradient of 2,
;;;passing through (5, -5)
with a negative
gradient…with equation y
= …. parallel to
……..etc.
Questions about real life
situations that lead to linear
functions. How do graphs
help? What must we be
careful of, if we compare
graphs? How could we
cheat?
Add data and ask for
further comments –
suggestions of functions
etc.
Link sequences mappings
functions and real life
situations together.
Multiplicative Relationships
See N.N.S. minipack (6 hours)
This is a detailed mini-pack.
Note that adjustments to the sample medium term plans have been made to accommodate this important mini-pack.
 Handling Data 2 was another mini-pack and should have been taught in the autumn term.
 Handling Data 1 has been placed in the spring term.
 The objectives of Multiplicative Relationships are from the strand on number so the list of objectives addressed in Number 2, 3 & 4 is
reduced.
 The units Number 3 and Number 4 should be taught after this unit.
 The objectives for the unit Solving Problems are addressed in the units, Number 2, Multiplicative Relationships (this unit), Number 3 and
Number 4
 SSM3 moves to summer term.
Number 3 (9 hours)
Place value (36–47)
Calculations, (92–107, 110–111)
Calculator methods (108--109)
CORE
From the Y8 teaching programme
A. Read and write positive integer powers of 10; multiply and divide integers and decimals by 0.1, 0.01.
B. Order decimals.
C. Round positive numbers to any given power of 10; round decimals to the nearest whole number or to one or two decimal
places.
D. Consolidate and extend mental methods of calculation, working with decimals, squares and square roots, cubes and cube
roots; solve word problems mentally.
E. Make and justify estimates and approximations of calculations.
F. Consolidate standard column procedures for addition and subtraction of integers and decimals with up to two places.
G. Use standard column procedures for multiplication and division of integers and decimals, including by decimals
such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations.
H. Check a result by considering whether it is of the right order of magnitude and by working the problem backwards
I. Carry out more difficult calculations effectively and efficiently using the function keys of a calculator for sign change,
powers, roots and fractions; use brackets and the memory.
J. Enter numbers and interpret the display of a calculator in different contexts (negative numbers, fractions, decimals,
percentages, money, metric measures, time).
Unit : Number 3
Number of 1 Hour Lessons
Oral and mental
Obj. b
Hold up or
shout out
numbers –
students have to
respond with
number rounded
to nearest 10,
100, tenth etc.
In groups come
up with a
sentence to help
explain what to
do. Relate to
number line
not just rules.
9
Year Group
Y8
Class/Set
Core
Main Teaching
Obj. C (1 or 2 lessons)
Discuss rounding to nearest whole number and one/two decimal
places.
In pairs use calculators to explore how to write the answers to
calculations like:
1 ÷ 3, 1 ÷ 7, £3.23 ÷ 5 £4.27 x 1.63
Pairs then complete some calculation drawn from real life
situations involving rounding.
Highlight £1.9 and £1.90 and 190p
Generalise on the rounding of money, metres kilometres etc.
1 ÷ 3 can be written as 1/3 which is a fraction. How does it look
as a decimal? List fractions and their decimal
equivalents/approximations using rounding where needed.
Notes
Highlight the idea of
conventions in
rounding
Note calculator
conventions.
Link to other
conventions in maths.
Key Vocab.
Recurring decimal
Terminating decimal
Plenary
Discuss generalisations for
rounding drawing from
ideas/misconceptions in
lesson.
How do calculators round?
Which fractions have exact
decimal equivalents? Why?
Explore/restate conventions
for writing money.
Why does the £ sign come
first? Do other currencies do
this?
Present provocative
statements or calculations
and ask for comments.
e.g. I need a piece of wood
2.333333metres long –how
did I get this answer? What
should I do?
Revisit key vocab.
Oral and mental
Obj A
Counting up
and down in
powers of 10
Perhaps have
groups one
setting the
power another
saying the
number and
another saying
the number of
zeros. Extent to
powers of 100.
Main Teaching
Obj. I, D, H and E (1 or 2 lessons)
Link powers to roots (square and cube) explain notation.
Identify squares and cubes on a 100 grid. Estimate the square
roots and cube roots of some numbers chosen on a 100 grid –
justify answers. Use a calculator to find square roots (without
using the square root key). Explain the use of the square root
key – extend to cube and cube root if scientific calc. available.
Use squaring and square rooting in context. E.g. a square has an
area of 90 square units. What must be the length of each side –
extend to volume of a cube. Perhaps explore Pythagoras’
theorem in an informal way!
Explore square roots and squares of negative numbers – draw
conclusions.
Evaluate 4 x (6.78)2 using a calc. explore use/non-use brackets
etc. review BODMAS.
Notes
Scientific calculators
are needed.
Consider difficulties
if students have
different makes
/models of their own
calculator.
Key Vocab.
Justify
Billion
Index
Power
Square (root) √
Cube (root) 3 √
Cube number
To the power of
Plenary
How many ways are there of
doing 4 x (6.78)2 ?
How do we estimate the
answer?
How do we round a
calculator answer?
Does a calculator use
BODMAS?
How do we estimate a root?
How can we check our
square root makes sense?
Work through some
calculations on a calculator.
Oral and mental
Obj.A
Obj. b
Have operation
cards ÷10, x 10,
÷100, x100 etc.
to hold up or
write these
operations on
the board.
Offer a number
and then an
operation – ask
students to
respond with
solution. Mix
and match the
operations –
discuss joint
effect of
combined
operations.
Obj F
What is 0.2 less
than……more
than….etc.
Offer incorrect
solutions to
addition and
subtraction
‘sums’ in
column form.
Discuss –
explore
misconceptions.
Main Teaching
Obj. B (1 or 2 lessons)
Explore strategies for ordering decimals. Perhaps use target
boards with sets of four decimals. Label them a, b, c, and d,
then students have to order them (like fastest finger first in who
wants to be a millionaire). This could be an alternative starter.
Obj. A
Explore multiplication. Establish that other operations have the
same effect e.g. x 0.1 is the same as ÷10. Discuss why.
Generalise- link to fractions. Discuss making bigger and
smaller.
Extend to mult. by 0.01 etc. perhaps redo the starter activity
using new knowledge.
Move on to ÷ 0.1 and 0.01 with a calculator as above.
Extend to combinations of operations
Obj F
Build in a check on, or do a lesson on addition and subtraction of
decimals. Work from mental to jotting to column methods. (see
pg 37)
Apply skills in contexts.
Notes
Calculators needed.
Possible spreadsheet
activity entering
formulae and filling
down to operate the
formula on
consecutive numbers
and generalising on
the effect.
Key Vocab.
Counter example
Plenary
Revisit generalisations.
Revisit oral and mental
starter incorporating new
skills.
Check understanding and
links e.g.
Why is x 0.1 the same as ÷10
Extend activities to x 0.2 and
0.02 and division.
Make provocative statements
like multiplying always
makes bigger.
Multiplying by 0.1 always
makes numbers smaller (0.1
x -2 )? Explore counter
examples.
Explore misconceptions in
decimal addition and
subtraction.
Oral and mental
Obj. i and k
‘Larger or
smaller?’
Ask the
question for
problems like
14 x 0.1
14 ÷ 0.1
18 ÷ 0.01
Pupils respond
with mini-white
boards or left
and right hand
up for larger
and smaller
respectively.
Make a web
diagram. Given
the ‘sum’ in the
box tell me
something else
we know. Add
new boxes to
the end of the
arrows.
0.4 x 3 = 1.2
(see worksheets
for blank web
diag)
Main Teaching
Obj. G
((2 lessons +)
Explore equivalent calculations. Present ideas first and ask for
students in pairs to agree on generalisations. E.g.
Is 1.4 x 3 the same as 14 ÷ 10 x 3 and the same as 14 x 3 ÷ 10 ?
How does the last version help us to do the calculation?
Demonstrate ways of doing 1.4 x 3
Notes
Calculators needed.
Use estimating and inverse
operations to check answers.
Try grid multiplication method.
3
1
0.4
3
1.2
Plenary
Discuss generalisations.
Explore ‘difficult’ questions.
Explore worded questions
and contexts. (area, volume,
proportion etc.)
Investigate shortcuts and
equivalence.
e.g
8 x 0.25
8x¼
25% of 8
= 4.2
Establish methods for mult. of decimals. Extend to 1.4 x 1.3
using 1.4 x 1.3 and then ÷ 10 twice or grid multiplication.(see
pg 105). Incorporate estimates (objectives E and H). What
about grid mult? May have to explore 0.3 x 0.4.
160
16
=
and how this relates to
4
0 .4
the opposite of cancelling fractions.
How do we use this to make division easier? Generalise –
practise (see page 107). Extend to division by 1.2 etc. (using
chunking).
Relate to practical contexts.
Address misconceptions.
Model solutions – explore
different methods decide
which is more efficient.
Explore 16 ÷ 0.4 relate to
0.2 x 0.3 = 0.6 is this true?
Chunking or method
of division may need
revisiting.
A student had to do 16 ÷ 0.4
She did
160
16
=
4
0 .4
now 160 ÷ 4 = 40
so the answer is 40 ÷ 10 = 4
What is wrong with her
thinking?
Oral and mental
Questions on all
of previous
work.
Present a
selection of
‘sums’ and a
selection of
answers – invite
students to
match ‘sums’ to
answers and
justify their
decisions.
(see
worksheetssums and ans)
Main Teaching
(1 or 2 lessons) Obj. J
Demonstrate the use of a fraction key on a calculator.
Explore operations with fractions (four rules). Try squaring and
square rooting fractions. Try repeated addition of 1/16 etc. –
relate to imperial spanner sizes which increase in increments of
1/16 inches (gap across nut). Ask questions like 3/16” , what
size bigger comes next?
Explore how to enter 3 hours 15 min. or even 3hours 17min.
etc.
How would this help with speed calculations – do some.
Address misconceptions.
Set up group work using a calculator to solve problems
incorporating BODMAS and fractions and decimals.
Notes
Calculators with
fraction facilities.
Plenary
Discuss best ways or
alternative tackling
calculations on a calculator.
Address misconceptions.
Add 2 feet 6inches and 3 feet
5 inches using a calculator.
Explore other calculations
with imperial units.
Revisit 6 x (3.2)2 and ways
of estimating and doing on a
calculator.
Explore use of change sign key. When is it useful?
Use memory key or constant function to do metric/currency
conversions.
Explore the use of the reciprocal key perhaps and how it might
4.2
help in the calculation
6.7  2.1
Model the speed of
100miles in 3hours 20min as
100 ÷ 3.2 and discuss.
What does 3.2 hours mean
really?
Algebra 4 (6 hours)
Equations and formulae (112–113, 122–125, 138–143)
A. Begin to distinguish the different roles played by letter symbols in equations, formulae and functions; know the meanings of
the words formula and function.
B. Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets)
using appropriate methods (e.g. inverse operations, transforming both sides in the same way).
C. Use formulae from mathematics and other subjects; substitute integers into simple formulae, including examples that
lead to an equation to solve; derive simple formulae.
Unit : Algebra 4
Year Group Y8
Number of 1 Hour Lessons 6
Class/Set Core
Oral and mental
Main Teaching
Obj. a
(2 lessons)
Ask which is bigger Obj. B
Consolidate forming and solving linear equations with one
a
a, 2a, , or a2
unknown on one side of the equation.
2
Can we order them? Develop to equations with brackets.
What do they mean? If 2(x + 3) = 12 is x + 3 = 6 OK? (see page 125)
Explore thinking about best method of solving. Relate to
What if a = 0.5?
Discuss and develop contexts where possible.
Relate to worded questions leading to equations. E.g.
with other values.
An isosceles triangle has a perimeter of 20cm and sides
Can we think of a
3x, 3x and 3x + 2. Calculate the lengths of each side.
value to make each
term the smallest?
Try arithmagon activities number walls etc. (page 122 and
123).
What function does
this graph show?
(say y =x + 4).
Ask for values of x
given y etc.
Solve linear equations with the unknown on both sides.
Use practical examples to visualise simple situations e.g.
Opposite sides of a rectangle are 3x + 12 and 5x + 8 how
long is each of the opposite sides?
One side of my rectangular garden has 6 fencing panels and a
1metre gap for a gate. The opposite side has 4 fencing panels
and a 3metre gap for my car. How long is each panel?
Students in groups should be given opportunities to develop
and form their own equations.
Notes
Key Vocab.
Expression
Equation
Expand
Simplify
Solve
Encourage checking
by substitution.
Plenary
Explore misconceptions.
Make provocative
statements e.g.
‘to solve an equation always
multiply out the brackets
first’
‘a2 is always bigger than a’
Generalise on possible
strategies for solving
equations particularly
worded questions.
Model solutions.
Touch on equations with
unknowns on both sides or
perhaps with squared terms.
What about fractions
negatives etc.?
Generalise on techniques
and checking answers.
Discuss solutions.
Ask students to demonstrate
their solutions.
Relate to work/real life
problem solving.
Encourage use of key
vocabulary.
Extend to fractions and
powers in equations.
Oral and mental
Obj x and B
I think of a number
double it and add 6.
If my answer is 16
what is the number
etc?
Extend to
n(n-l) = 56
x ÷ 2 + 4 =16 etc. in
words
After each problem,
students model
equation and
solution.
Pupils set their
problems to class.
Obj A
Matching equivalent
algebraic
expressions.
E.g.
2(x + 2) and
2x +4
n x n x n and n3
Discus
Main Teaching
Obj. A, B and C (2 lessons).
Review ideas of collecting like terms simplification and key
vocab.
Explore ideas of functions (relate to algebra 3) equations and
formulae.
Revisit restaurant tables’ activity (from last term).
Notes
Key Vocab
Expression
Term
Equation
Formula
Function
Like terms
Solve
Simplify
Plenary
Check key vocab.
Model links between
practical restaurant tables
problem and formulae,
equations, data tables,
graphs, functions and
mappings etc.
What have we learned?
If we don’t have a T=
formula what skills do we
need to use the P= formula
to calculate T given P?
Make a table of values for people and tables.
T
P
1
6
2
8
3
10
Revisit linear functions, graphs and rules to model this
situation and make links. Establish formula.
P = 2T + 4
Experiment with substitutions of T.
What if we knew P. Could we work out T. Set problems –
investigate for other arrangements. Can we create a formula
T=?
Formulae from every day life and other areas from the
curriculum. (Speed, electricity, mobile phone costs, angles in
a pie chart, Celsius to Fahrenheit etc.)
Substitution into formulae to find subject value.
Substitution into formulae to find vale of a non- subject
variable given the value other variables in a formula.
Model some other formulae
from every day life.
Explore generalisations and
tips for substitutions.
How are formulas used in
spreadsheets?
Model
misconceptions/incorrect
substitution e.g.
2x2 and (2x)2
x
x3
and
+3
3
3