This document identifies
algebra tasks used in year 7
maths lessons in the first
half terms of the years
20082009 and 20092010. It
attempts to map them to the
maths curriculum and
suggests which could be used
for the different year 7
sets in coming years. Not
all aspects of the algebra
curriculum are covered. It
is intended that some
aspects will be covered
using other tasks and some
will be covered later in the
year.
The algebraic skills and
techniques to learn in year
7 can be broadly categorised
as shown below. These
grouping suggest a suitable
‘journey’ for the series of
lessons for the year 7 sets.

Systematic approach,
recording data and
numerical methods (N*.*,
A4.1)

Formal algebraic
fundamentals

Need for algebra

Formulae (A4.2,
A5.1, A7.1)

Symbols for unknowns
(A4.3)

Substitution (A5.1,
A7.1)

Collecting terms and
simplifying (A5.3)

Terminology (A6.1,
A3.2)

Functions (A4.3)

Sequences and patterns
(A3.1, A6.6, A7.9)

Algebraic manipulation

Solving equations
(A5.2, A6.4, A7.2,
A7.4)

Changing the subject
(A7.3)

Factorising/expanding
(A5.3, A6.2, A7.4)

Graphs

Plotting (A4.4,
A6.5, A7.8)

As tool to solve
algebraic problems
(A7.7)

Real life (A6.7,
A7.6)

Properties (A7.10)

Trial and Improvement
(A6.3)
The ‘Suggested scheme of
lessons’ section at the end
of this document would
probably take in the order
of 4 to 5 weeks to
complete. It is intended
that either interlaced with
these tasks or otherwise,
the remaining time should be
spent looking at the Number
aspects of the curriculum.
Emphasis should be given to
enrichment type activities.
It is suggested that the
Nrich activities identified
on the SOW index page be
used.
This is from Jonny Heeley’s
Masterclass (from Teachers’
TV
http://www.teachers.tv/videos/algebra
 at about 1min 15secs in)
Good to use as a ‘hook’ – it
may be better to do the
trick early in the lesson
sequence and later get the
students to explain how it
is done. It works as
follows:
Ask the students to do the
following:

Take the month of the
year you were born (1 to
12)

Multiply by 5

Add 7

Multiply by 4

Add 13

Multiply by 5

Add the day of the month
The students then give you
their results and you are
able to tell them their
birthday by breaking the 4
digit result into two
2digit numbers. Subtract 2
from first to get the month
and 5 from the second to get
the day of the month.
This is a teacher lead
activity based on Jonny
Heeley’s Masterclass (from
Teachers’ TV
http://www.teachers.tv/videos/algebra
 at about 3mins 20secs
in). A printable version
using animals and letters
instead of fruit and
vegetables is in resources
folder. Give a card to each
student (holding back an 8
and a 4). Give out one
rabbit, one elephant and one
‘n’. Tell students not to
tell each other what they
have but get them to follow
the process (and to just
play along if they have
something unusual). They
should all get the same
answer. You then go on to
show how it works with
animals and letters.
Resources:
Unknowns 
animals and letters.ppt
This is a simple little
investigation which can be
done without formal
algebra. Find a rule for
summing three consecutive
integers. This can be
useful to highlight the need
to layout numerical ‘trials’
in a logical fashion.
Further questions could be:
How does the total vary as
we move up to the next three
numbers (e.g. compare 1+2+3
to 2+3+4)? Is this always
true?
What if we consider numbers
that are two apart (e.g.
3+5+7)?
This is a good activity to
lead onto the usefulness of
symbols for unknowns. It is
also a good introduction to
the concept of proof (we can
show the rule is true for
any three consecutives).
NRICH Task:
Consecutive Numbers
Consecutive Sums
Excel Investigation
This is a task in forming
algebraic expressions and
can be used at all levels.
It would make a good
miniwhiteboard activity.
Get students to answer the
follow kind of questions:
I am n years old. My
brother is 3 years older
than me. How old is he?
What do you get if you add
our ages together?
This can then be revisited
as an introduction to
solving linear equations.
This is the well known
investigation of taking a
100grid and overlaying
smaller (to start with, 3×3)
grids. The investigation
starts by considering the
sum of the numbers in the
corners of the smaller grid
and looks for patterns
depending on its position.
This is a good task for
introducing a methodical
approach to spotting
patterns. When approached
algebraically it can
introduce ‘collecting like
terms’. This investigation
can be extended by
considering different size
larger and smaller grids (or
even unknown grid sizes).
For a set 3 taking just a
numeric approach, the
sequence of numbers in the
larger grid could be
replaced with just even
numbers, odd numbers etc.,
use of rectangles for the
smaller overlaying grid etc.
The whole investigation can
be extended further to cover
expansion (A6.2 and A7.4) by
summing opposite pairs of
corners then multiplying the
results (or multiplying then
summing).
Resources:
Grid investigation.doc
100 grid  printable.ppt
Smaller grids 
printable.ppt
Grids.xls
100 grid 
eBeam.emf
Using algebra to answer
problems about visual
patterns (made using
matchsticks). This shows
different ways to visualise
the constructions of the
algebraic expressions.
Complete the solution to
find the value of some
symbols placed in a square
given 6 different starts
This investigation is
described in the document ‘Tile
spacers.doc’. An
extract:
“In this investigation, we
will start by looking at
square tiles, and the three
types of spacers we will use
are T shaped, L shaped and +
shaped.
The investigation is to see
how many spacers are needed
for different arrangements
of tiles.”
This could be delivered over
a couple of lesson. The
fist would be to teach
methodical working,
recording of results and
identifying simple
patterns. The investigation
could be revisited later to
use it to derive formulae.
Resources:
Tile spacers.doc
There are three strands to
the work that can be done
with magic squares. The
first is to find ways of
constructing them (3x3 to
achieve different totals).
Folens Y7 T1 U1 p13 is
useful here. The second is
to practise substitution
given a formula. 10Ticks L5
P5 p20 has questions.
Lastly, the students could
find a, b and c (variables
in the formula) given
particular magic squares.
See 10Ticks L5 P5 p21 for
questions. The resources
below may be useful for
projecting the magic
squares.
Resources:
Magic squares.ppt
Magic Squares  eBeam
Blank  eBeam
This is a simplified version
of the old GCSE coursework
task. It recommended that
it is used for assessment
for tops sets already having
done a similar task (such as
the Grid Investigation).
The sheet for students (‘T
Shapes investigation.doc’)
is left very open with some
prompts for extension tasks
(changing the grid size,
changing the size of the T,
rotating the T). A
selection of grids in emf
format (suitable for eBeam)
are available for class
discussions in the ‘TShapes
– eBeam’ folder.
Resources:
T Shapes investigation.doc
Tshape grids 
printable.ppt
TShapes – eBeam
These are the type of
problem in which you start
with a number, perform a
number of functions and
always end with the same
result. Nrich has a nice
task as an introduction to
this idea called: “Your
number is…” (http://nrich.maths.org/2289).
You will need to use your
webbrowser’s zoom facility
if you are to project
these. Exercises for
students based on this idea
(first numeric then
algebraic) can be found in
10Ticks L6 P1 p15,16 (also
available as powerpoint
slides). See also Folens
7.2 Unit 7 p108 (p126) for
work on an algebraic
approach to these problems
(a lead in to the ‘Pots of
Gold’ task below).
Resources:
Think of a Number.ppt
This is part of a lesson
taken from Folens 7.2 Unit 7
p109 (p127) with worksheet
available from p115 (p133).
This is a visual approach to
expression building.
This is an investigation
similar to the Grid
Investigation but uses
calendars (so the grids are
7 squares wide and the
number 1 can be in any
column). This is suitable
for assessment of set 2 and
3 groups following the Grid
Investigation.
Resources:
Calendar.doc
http://www.coolmath4kids.com/math_puzzles/s1squares.html
This is an investigation
into counting squares in a
larger grid. It starts with
a 2x2 grid (which has 4+1=5
squares) then a 3x3 (which
has 9+4+1=14 squares) etc.
Note that tasks in italics
are not described in the
section above.
Task 
Comment 
A 
Magic birthday trick 
As a hook. To be
revisited later. 
6.2 
Unknowns: Numbers
and animals 

4.3 
Summing consecutive
numbers 
Both numerically
algebraically 
4.1, 5.3, 6.2 
Me and my brother 

4.3, 5.3, 6.1 
Algebra terminology 

6.1 
Simplifying
expressions 

5.3 
Grid investigation 
Include extensions 
4.3, 5.3, 6.2, 7.4 
Factorising


6.2, 7.4 
Magic squares 

5.1, 5.2, 7.1 
Nrich: 7 squares 

4.1, 5.1, 6.6 
Nrich: What's it
Worth 

4.3, (AB.2) 
Linear sequences
including
termtoterm and nth
term 

6.6 
Think of a number 

4.3, 5.1 
Magic birthday trick 
Revisited 
6.2 
Solving linear
equations 

5.2, 6.4 
Tshapes 
Individually for
assessment 

Topics not covered above
(levels 5 and 6) for later
in the year: A6.3, A6.5,
A6.7
Task 
Comment 
A 
Tile spacers 
First part 
4.1 
Linear sequences
including
termtoterm and nth
term 
Generating sequences
only 
4.1, 5.1 
Tile spacers 
Revisit 
4.2, 5.1 
Grid investigation 
Summing only 
4.3 
Think of a number 

4.3, 5.1 
Pots of gold 

4.3 
Nrich: What's it
Worth 

4.3, (AB.2) 
Expanding brackets 

5.3 
Grid investigation 
Next part 
5.3 
Solving linear
equations 

5.2 
Calendar
Investigation 
Individually for
assessment 

Topics not covered above
(levels 4 and 5) for later
in the year: A4.4
Task 
Comment 
A 
Supporting number
work 
Adding and
multiplying 

Number patterns
(even, odd,
multiples, squares,
etc.) 

3.1, 4.1 
Grid Investigation
(summing) 
Numeric approach
only 
3.2, 4.1 
Think of a number 

4.3, 5.1 
Pots of gold 

4.3 
Magic squares 
Constructing and
substitution only

5.1 
Substitution games 

5.1 
Formulae in words 

4.2 
MyMaths: Function
Machines 

3.2, 4.3 
Calendar
Investigation 
Individually for
assessment 

How many squares? 
For assessment 

Topics not covered above
(levels 3  5) for later in
the year: A4.4, A5.2, A5.3