Card
Sorts
in
Secondary
Mathematics
Roger Ray
Teaching and Learning Consultant
East Riding of Yorkshire School Improvement Service.
-1-
What is a card sort?
For a card sort activity, basically, information is written or typed onto
small pieces of card. At the direction of the teacher, students work
collaboratively with others to match, sort or arrange the cards.
Let’s look at very simple example.
Look at the three cards below
Y
2
3y
Y
2
Which is the odd one out and why? In other words, which two cards go
together and why?
If this activity is done with students, hopefully each of the three cards
will be selected by some of the students as the odd one out. If not you
may have to ask for suggestions as to why each card could be the odd one
out. Modifying student responses to promoting key mathematical language,
is a possibility here e.g. a response such as:
‘y over 2 is odd because it’s a fraction’
could be modified to
‘y over 2, because the other expressions have integer coefficients’ .
This ‘odd one out’ sorting activity can work well as–
 a starter activity in terms of assessment for learning (discovering
what students know and their level of experience and understanding)
 a plenary activity where hopefully students will be able to use the
new learning from the lesson to influence their decisions and
arguments.
A further extension to this activity might be to ask students to invent a
fourth card to strengthen the argument for the choice of their odd one
out.
I’ve used this simple idea to get you ‘hooked’ in reading further. If you’ve
not tried the ‘odd one out’ card sort then try it in whatever context you
are working (it is a powerful tool) and then hopefully come back for more.
Later in the document, I’ll come back with more examples of ‘odd one out’
activities.
-2-
Why use card sorts?
Card sorting has been an activity used widely in the past by many
different subject areas. However, in my experience, I have seen little use
of card sorts in secondary mathematics’ classrooms .
Here are some reasons why I like to use them.
 The activities involve visual stimuli (looking at the cards and
arrangements) auditory stimuli (discussing- putting forward
individual views and listening to views or ideas of others) and
kinaesthetic stimuli (the cards can be touched and moved around). It
therefore gives most students an opportunity to engage in their
preferred learning style.
 Card sorts stimulate discussion and the use of paired and group
work.
 Teachers can observe easily, from a distance, progress students are
making in set tasks.
 Thinking skills are required in card sorting which, when probed,
often give good insights into students’ levels of understanding of a
topic.
 Card sorts often have a variety of outcomes – this helps students to
move away from the idea that in mathematics, there is only ever one
right answer.
 Different arrangements often require verbal or written
justifications – the skills of explaining and justifying ideas are often
areas in need of development and strengthening in many students.
 Card sorts can be used as precursor activities to stimulate and
revisit previous learning and to help scaffold or prepare for the next
new learning episode.
 Skilfully used, with good questioning, card sorts can introduce
differentiated activities using the same resource
to secondary classrooms.
On the next page I have included the five National
Curriculum Thinking Skill’s categories. You may like to
scan them quickly or refer to them later after reading
about card sorts. I hope you will come to agree that card
sorting activities can make a major contribution to
meeting the National Curriculum requirement in the area of thinking skills.
-3-
Information processing
National Curriculum Thinking Skills
locate and collect relevant information
sort and classify
sequence
compare and contrast
analyse part / whole relationships
Reasoning
give reasons for opinions and actions
draw inferences and make deductions
explain what they think
make informed judgments and decisions
Enquiry
ask relevant questions
pose and define problems
plan what to do and how to research
predict outcomes and anticipate consequences
Evaluation
Creative thinking
test conclusions and improve ideas
generate and extend ideas
suggest hypotheses
apply imagination
look for alternative innovative outcomes
evaluate information
judge the value of what they read, hear and do
develop criteria for judging the value of work or ideas
-4-
What type of card sorts are useful?
I have used card sorts in the following ways but continue to develop and
pick up new ideas as a ‘ life long learner’.
Odd one out
You’ve already experienced this in the previous
example. Usually three cards are used although
actually cards are not always necessary, as the card
content can often be quite quickly written on the
teacher’s board. A good idea is for groups of three
students to work together each copying one of the
cards onto a mini-whiteboard. In feedback groups can then hold up the
card they feel is the odd one out.
Pairing
This involves students pairing cards together looking for some attribute or
relationship the most common (and closed) of these being pairing a
problem and a solution but it could be a shape and name/property etc.
When designing cards for matching into pairs it is not a bad idea to put in
some cards that do not have a matched pair in the set particularly if this
highlights a misconception (3/8 = 0.38 etc.)
Grouping
Obviously, this involves grouping cards together for instance;
 For which problems on the cards would you use the sine ratio?
 Which problems are to do with the ratio 2:1?
 Sort the angles into right angles, acute, obtuse and reflex
 Group together the algebraic expressions according to their number
of terms
 Sort the fractions into bigger than and less than 0.5 etc.
# Note Venn diagrams may be useful here for cards that fit into more
than one group or do not belong to any.
Ranking
Again fairly obvious, but cards are ranked in terms of priority, importance,
value etc. Ranking decimals, fractions, directed numbers, weights and
lengths (mixed metric and imperial) are good examples.
True or false (and perhaps Uncertain).
Useful for probing students understanding of facts and statements which
have to be sorted into true and false. A further extension of this could be
 always true
 sometimes true and
 never true
-5-
This is particularly useful for algebra for example
‘2x has the same value as x2’. This of course is sometimes true (when x is
worth 2 or zero) but is generally said to be untrue by students.
‘Follow me cards’
These are sets of cards with a question on each card. Each card also has
an answer from another question. The usual format is that a student or
pair of students read their card which might say…….
‘I have 3y. Who has twice as much?’
The student with ‘I have 6y’ on their card read this out followed by the
next follow me question. The loop continues. This is fun but may only
engage some classes for all the time. The cards can be effectively used
with pairs sorting them into follow on order.
‘Can you show me’ and ‘Can you make’
I suppose this is card sorting in a sense and worth mentioning
as a successful strategy used in primary schools with
applications in secondary. You need to prepare cards with
numbers, shapes or symbols. Students can then arrange the
cards to make; equation or expressions, ‘sums’ or just hold up
cards as requested by the teacher e.g.
Can you show me a shape with one line of reflection symmetry?
Can you show me a prime number?
Can you make an expression (or equation) equivalent to this…..?
-6-
Getting organised
Before we look at some specific resources a few words about organisation.
The power of card sorting lies in students discussing and externalising
their thoughts - reasoning with each other using thinking skills. Students
will therefore have to sit or be organised in
groups. A previous booklet called ‘Paired and
group work in secondary mathematics’ may prove
useful to you if this is unfamiliar territory
(available on www.eriding.net in the mathematics
section).
Producing the cards is time consuming. Once you
have designed the content recruit whoever you can to make them, including
students. In the intense arena of teaching mathematics where time and
pace is paramount, teachers may shy away from asking students to copy out
and make a set of cards for an activity. However, if this is focused and
done in groups within a set, short, time-frame, it can: build group
cooperation, accelerate the learning and make up the ‘lost’ time. (I.e. the
card sort activity engages the students and moves forward their thinking
and understanding.)
Once you have a set of cards that are effective look after them. I’ve
always shied away from elastic bands for storage and tended to use small
money bags for each set – these in turn are dropped into a labelled freezer
bag ready for use when next needed. A really good set are worth
laminating. If you ever get really hooked and use more than one card sort
in a lesson then think about different colours or sizes to save mixing up the
sets of cards.
The next section gives examples of some sets of cards and how they might
be used. Feel free to photocopy them and use them. This document should
also be on the website www.eriding.net in the mathematics section, so you
might want to download it and edit some of the cards to produce custom
ones of you own. Please let me know if you want to share them on the
website.
-7-
Odd one out
I rarely produce cards for this activity preferring to write the items for
sorting on the teacher’s board or on mini-whiteboards. However, when
students have been working with a large set of cards during a lesson I have
sometimes selected groups of 3 or 4 cards and asked students to say which
is the odd one out and why.
In this section then I have not produced resources but instead I will try
and show the potential of ’odd one out’ through a couple of examples I’ve
used with classes.
Consider the cards
28 g
1 ounce
1 tonne
Asking students which is the odd one out and why, produced the following
responses
28g because it uses an abbreviation for the units.
28g because the others only have one unit.
1 ounce because it’s not metric.
1 ounce because it’s an imperial measurement.
1 ounce because I don’t know how much that is!
1 tonne because tonne is spelt wrong!!!
1 tonne because it is much larger than the other two.
1 tonne because you wouldn’t find anything that heavy in a kitchen
cupboard.
1 tonne because the other two are about the same weight.
I hope you will agree – some interesting and informed responses begging to
be followed up by some probing questions. Again, this type of activity could
be before new learning is about to begin or after new learning has taken
place.
Remember, the follow on activity could be for students to write a fourth
card to strengthen the argument for their choice of odd one out. An
alterative is for the teacher to insist that one particular card be the odd
one out and further cards have to be designed (by the students) to make
this obvious.
-8-
Here I’ve used three shapes. Responses could be about number of sides,
angles, parallel sides, types of symmetry etc.
Remember the idea is for students to discuss, in pairs or groups, their
ideas and arguments and then share them with the class. It will engage all
students especially if you stress that in feedback you will be selecting
conscripts to respond instead of asking volunteers.
An alternative would be to allocate different shapes to different pairs or
groups asking them to justify why their shape is the odd one out etc.
As a teacher, if you use this idea in a plenary, all you have to do is think of
three (or more if you want) card examples for students to sort. The
examples, of course should allow students to demonstrate their new
learning. The shape example could be used after new learning about
symmetry or properties etc.
-9-
Pairing
Some students enjoy pairing cards. I suppose this is because it is a closed
activity. Matching equivalent fractions and then algebraic expressions are
the examples I’ve produced for you. I’ve added in a few that don’t pair up
just to spice things along. You could use this activity to pair equivalent
areas, equations, ratios, angles, answers to sums, ways of saying things,
clock times, measurements etc.
A short activity that many students enjoy with pairs is this;
 Shuffle the cards and lay them face down on the table.
 Students take turns, in their pairs or groups, to turn over two cards
at a time.
 If the cards are equivalent to each other, the student keeps the
cards and has another go.
 If the cards are not equivalent, the cards are turned over again (and
left in the same position) and the next player chooses two cards to
turn over and match.
 Play continues until all the cards are gone.
 The winner is the player with most cards.
As with any game or indeed card sort remember to ask students about
their strategies used in games and sorting activities.
- 10 -
Pairs – fractions and decimals
0.8
8/10
½
2/5
0.4
0.5
3/4
0.34
1/5
0.2
0.75
3/8
0.125
0.25
- 11 -
Pairs – algebraic expressions
2
bxb
b
2a +3a
5a
m÷3
m
3
3a + 3b
6ab
6a x b
3(a + b)
½a
a
2
axa
2
a
- 12 -
3
Grouping
I have found grouping the most useful card sort activity in my lessons and
will try and illustrate this through tried and tested examples. The idea is
that cards are sorted according to given criteria.
Example 1
Take a look at the trig. card sort sheets 1, 2 and 3 which when cut out
form one set of cards. These of course are little different from simple
diagrams often displayed in text book exercises.
These were used initially with a group of students who had done some work
on identifying which trig. ratios could be used to solve triangles.
The initial instruction to pairs of students was to sort the cards.
Some quickly cottoned on but after a minute or two all the groups agreed
that we should sort the cards into which trig ratio might be used to find
the side labelled with a letter (yes even though sorting the card in
alphabetical order for the labelled sides was easier).
An alternative would have been to allocate a ratio to each group giving
them the task of finding the relevant cards for that ratio. Pairs or groups
undertaking the same task could then compare selections.
This worked really well. An interesting observation was that a group of
girls who completed the task at lightning speed, did it not as expected (by
identifying adjacent, opposite and hypotenuse and applying a rule or
rhyme). They found a triangle that needed the cosine ratio and then found
other triangles that matched the pattern of sides and angle. They even
described the pattern as cosy because they were all near to each other.
Similarly they thought the tangent could be viewed as a sort of T shape.
Groups ‘envoyed’ (looked at each others sorted cards) and eventually all the
students were in agreement as to which ratio to use with which card.
Lots of possibilities were then possible e.g.
 We could further divide each set of cards into two types where the
sides to be found were either denominators or numerators in the
ratio equations.
 We could solve a particular card problem as an example.
 Other cards could be solved as directed by the teacher or as
selected by students allowing for differentiation.
Homework involved (after a demonstration) students selecting a card and
writing an exam question that would lead to solving that exact triangle on
their selected card. Next lesson would involve these being displayed to
other students who would identify which card had been used.
The cards were a feature of several lessons. They promoted group work,
discussion, interest & learning and yet the cards contained no more than
simple questions found in text books.
- 13 -
It is worth noting that a further card sort was used to develop
understanding.
2
3
6
=
x
÷
Student were asked using the above cards to form as many relationships as
they could.
Then, being told that b/c = a they were asked to write as many
relationships as they could.
This proved immensely useful later when rearrangement was required to
change the subject of a trig. ratio – particularly when the unknown was a
denominator.
This was not my lesson but one that I planned with a teacher as part of a
coaching cycle. The target was to engage students through different
teaching strategies.
It was met!
Example 2
Have a look at the nine cards for dividing by decimals (they are after the
trig sheets).
I was asked to do a demonstration lesson working with a group of bright Y8
students. The learning outcome was to be that they should be able to
divide by decimals.
After some precursory work in the starter activity exploring how they did
division and how they could divide and multiply by 10, 100, 1 000 etc.. I
gave them the card sort and asked them to sort the cards.
It was interesting to listen to the discussion and watch them struggle for
direction. However, they quickly picked up that no help was on offer. We
had a mini-plenary and discussed ideas and the consensus was that some of
the division sums had the same answer and that that was how they should
be sorted (some even referred to the lesson objective on the board and
made the link using the word equivalent!).
In pairs they then did the sorting into equivalent calculations. Those who
finished quickly had to devise an extension task. Two groups came up with
 What is the pattern?
 Make up some more equivalent divisions.
- and they did.
We then organised the cards as they appear on your sheet and they
described ‘the pattern’.
I asked them which calculations were easier to do and they quickly got the
idea of how to create an equivalent calculation to make life easier.
- 14 -
This was followed by groups working on written problems (not all working on
the same problems). The most interesting of these was;
There are 8 quarter hours in 2 hours. What has this to do with 2 ÷ 0.25 =
8?
In the plenary students gave good responses on mini-whiteboards to my
question‘What would they do if faced with a division by a decimal?’
We also looked at why our method worked through revisiting cancellation
of fractions.
A lot of learning took place in that classroom that day and not just for the
students. I learnt (and so did the observers) how a simple use of a card
sort and group work could engage students in learning in a topic I would
previously have described as dull.
A further set of sort card called ‘shape’ appears after division by decimals.
If you had several sets of these think of ways you could use these with
students with different age ranges and different attainment levels to
promote learning.
- 15 -
Trig. Card Sort Sheet 1
10
a
12
500
700
b
10.5
c
18
480
d
460
e
450
f
42
390
100
g
55
720
600
81
h
- 16 -
Trig. Card Sort Sheet 2
j
10
12
0
32
650
i
10.5
25
480
430
k
l
2.5
n
0
44
m
380
1000
o
p
330
81
11
- 17 -
810
Trig. Card Sort Sheet 3
12
19
r
150
730
q
1.05
17
s
640
510
t
u
1000
520
2.5
370
v
w
111
360
801
x
- 18 -
790
Division by decimals card sort
36 ÷ 9
3.6 ÷ 0.9
0.36 ÷ 0.09
360 ÷ 9
36 ÷ 0.9
3.6 ÷ 0.09
3600 ÷ 9
360 ÷ 0.9
36 ÷ 0.09
- 19 -
Shapes
- 20 -
Ranking
Here cards are ranked in terms of importance or value. Values can be
placed on a number line. The examples of ranking that follow on the next
two pages are of mass and length. Some conversion work may have to
preceded the card sort but don’t underestimate students’ ability to seek
out information for themselves to enable them to rank and compare.
Remember that discussion between students (and between students and
teachers) about why cards have been ranked in a particular order is a rich
experience.
Another area you may want to explore is the development of bodmas (or
bidmas). Presenting students with a series of calculations involving several
operations, brackets, indices, division, multiplication, addition and
subtraction and asking them to prioritise them, is a common starting point.
Writing the operations on card and sorting them can prove engaging for
students.
Problem solving sequences or course work support checklists can also be
transferred to card for sorting into appropriate order.
Other subject areas use an idea called diamond ranking where cards are
arranged in a diamond pattern like this:
Most important
Least important
This can be useful in mathematics. E.g. imagine after groups of students
have brainstormed ideas about how to write a good questionnaire – these
could be placed on card and sorted as above in terms of importance.
- 21 -
Mass – card sort.
2 oz
3 oz
30g
40g
4 oz
100g
1 lb
½ lb
¼ lb
¾ lb
2oz
200g
2oz
500g
1kg
2oz
3kg
2oz
½ kg
2.3 lb
2oz
6.1 lb
2oz
750g
¾ kg
½ oz
10g
20mg
500mg
½g
0.5g
1tonne
1ton
0.25g
1 200kg 1 000 lb
- 22 -
Length – card sort.
1 foot
12 inches
30cm
1 inch
2.5cm
50cm
2 feet
1 yard
1 metre
39 inches
5 cm
2oz
95cm
2oz
36 inches
50mm
2oz
91cm
2oz
1km
1 mile
1.7km
1 000
metres
6 inches 2 ½ cm
½ km
½ metre
2oz
2 inches
2oz
600
metres
750
metres
3/4km
½ mile
50yards
40 metres
- 23 -
True or false (and perhaps uncertain).
Students are constantly trying to make sense of information and ideas
presented to them by the media, life in general and teachers. The simple
alternatives of right and wrong or true or false are early decision making
strategies to help form opinions & feelings and are the scaffolding on
which to develop reasoning. Therefore making decisions on whether a
statement is true of false is familiar to students. The trick is to pose
questions which cause cognitive conflict and move students out of what has
been named their ‘zone of proximal comfort’ to challenge their thinking,
which is why I’ve added the category uncertain. Encouraging students to
reason about statements in terms of always true, sometimes true and never
true is a useful strategy particularly when algebraic expressions are
involved.
Asking student to state their degree of confidence in their choices in
terms of:
 certain,
 fairly sure &
 unsure
can be useful especially when students compare their levels of confidence
and adjust their views in light of peer discussion.
The two examples I’ve given on the next two pages are for algebra and
number.
A good activity to try is to have statements on cards posing as information
gleaned by students from a chart or graph. Your students then have to
decide whether the statements are true or false by interpreting the chart
or graph themselves.
- 24 -
Algebra true or false
(2ab)2 = 2ab2
(2ab)2 = 4ab2
m
m2
2

m
3
(-3a2)3 = -27a6
2
3
y = 2y
m 1

m
2
2
9
3
2
-2(2m – 3) = -4m - 6
y0=1
m
m
3(2a – 7) = 6a - 7
If
a
c
c
b
b

then
a
2 3
(a ) = a
5
2a2 x 3a3 =5 a5
5
a xa =a
- 25 -
Number true or false
2–6=6-2
2 x 3=3 x 2
4÷2=2÷4
4 divided by a half is 2
3+3=3
2
2+2=2
2
3
2x3+2x3=5x3
3 =9
- 2 – 3 = +5
2(3 + 4) =
2 ÷ 3 = 2/3
2x3+2x4
¼ + ¼ =1/8
0.3 = 1/3
- 10 – 8 = -2
- 26 -
Follow me cards
As mentioned earlier, these are sets of cards with a question on each card.
Each card also has an answer from another question. The usual format is
that a student or pair of students reads out aloud their card which might
say…….
‘I have 3y. Who has twice as much?’
The student with ‘I have 6y’ on their card read this out followed by the
next follow me question. The loop continues hence the term ‘loop cards’
which is sometimes used to describe them.
Have a look at the algebra set and the fraction & decimal equivalents set
I’ve used in the examples, if you have not seen them before, and then read
on.
If you or your students design their own cards a set of blanks can be
useful and I’ve included a set after the example. You must remember two
simple rules when designing a set of ‘follow me cards’.
1) The last card’s answer should refer back to the first card to
complete the loop
2) All answers should be different.
Following these rules means any card can be used as a starting point and
only one student or group of students will respond to a question from a
card.
An interesting variation on using a set of ‘follow me cards’ card is to divide
the cards amongst groups of 4 students and begin the game. Groups have
10 seconds to respond to a question. If no one responds the group who are
found to have the correct response lose a life and the game continues. The
winning team is the one with the fewest lives lost.
Only one set of ‘follow me’ cards is needed if they are used for a
traditional class activity. However, multiple sets are extremely useful to
give to pairs or groups of students. They can then engage in sorting the
cards into a connecting loop on a table top.
A good tip is to have a check sheet of the loop to hand or the master
photocopy before it is cut up into cards.
Many students I have worked with have enjoyed designing and preparing a
follow me set of cards as an extension activity or an extended piece of
homework. You may be surprised at how challenging they make the
questions!
- 27 -
Follow me - fractional and decimal equivalents
I have
one half.
Who has a decimal
equivalent?
I have
0.5
Who has half of me
as a decimal?
I have
0.25
Who has my
fraction equivalent?
I have
one quarter.
Who has three times
as much as a
fraction?
I have
three quarters
Who has my
decimal equivalent?
I have
0.75
Who has 0.25 more?
I have
one whole one.
Who has me divided
by 10 as a fraction?
I have
one tenth
Who has my
decimal equivalent?
I have
0.1
Who has 3 times me
as a decimal?
I have
0.3
Who has my
fractional
equivalent?
I have
three tenths
Who has twice as
much as a fraction?
I have
six tenths
Who has my
equivalent as a
decimal?
I have
0.6
Who has 0.2 more?
I have
0.8
Who has my
equivalent fraction?
I have
eight tenths
Who has three
tenths more?
I have
1.1
Who has
one tenth more as a
decimal?
I have
1.2
Who has 0.3 more?
I have
1.5
Who has me divided
by three as a
fraction?
- 28 -
Follow me - algebra
I have
2a
I have
4a
Who has
Twice as much?
Who has
4 more?
I have
4a + 4
Who has
One quarter as
much?
I have
a+1
I have
a–2
I have
a-3
Who has
3 less ?
Who has one less?
Who has
2a more?
I have
3a – 3
I have
9a – 9
I have
18a – 18
Who has three times
as much?
Who has double
this?
Who has 2 less?
I have
18a – 20
I have
18a
I have
16a
Who has 20 more?
Who has 2a less?
Who has 20a less?
I have
-4a
I have
-6a
I have
-12a
Who has 2a less?
Who has double
me?
Who has 3a more?
I have
-9a
I have
-9a + 6
I have
-9a - 1
Who has 6 more?
Who has 7 less?
Who has
11a + 1 more?
- 29 -
Follow me blank
I have
I have
I have
Who has
Who has
Who has
I have
I have
I have
Who has
Who has
Who has
I have
I have
I have
Who has
Who has
Who has
I have
I have
I have
Who has
Who has
Who has
I have
I have
I have
Who has
Who has
Who has
I have
I have
I have
Who has
Who has
Who has
- 30 -
‘Can you show me’ and ‘Can you make’
Again, as mentioned earlier, this is not strictly a card sort activity but can
be made into one. For instance if the numbers from one to ten are on
cards, students could sort them into odds & evens, multiples of 3 & not
multiples of 3 etc. Pupils can also be invited to show me (the teacher) a
card with a particular attribute. They could also be asked to make a sum,
equation, inequality, relationship etc..
The following could be made into sets of cards for these types of activity.
Show me
- 31 -
Show me cards.
1
5
9
÷
a
√
2
6
0
x
b
<
>
3
7
+
(
c
>
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4
8
)
:
=
The last sheet shows cards with numbers from 1 to 9 in a 3 x 3 grid (magic
square – numbers). When cut out, these have to be arranged in a 3 x 3 grid
to produce a ‘magic square’ i.e. an arrangement where each row and column
(and each of the two diagonals) sum to the same amount (15).
Also the last sheet shows a 3 x 3 grid of algebraic expression. These were
developed by the National KS3 Strategy for a course I delivered to
teachers. These algebraic expressions also have to be sorted into a magic
square.
The plenary after the two card sort activities had been completed, looked
at meta-cognition (thinking about thinking) identifying how teachers used
their thinking to find solutions.
These are good activities for students too, since they use reasoning and
thinking skills in the context of collecting like terms in an interesting
framework.
Incidentally, if you solve the algebraic magic square – you can (by
substituting values for a and b) produce any number of magic squares –
‘cool’ as one student described it.
Part of my role as a teaching and learning consultant is to develop teaching
and learning strategies in mathematics particularly towards the greater
engagement of student in lesson. Engagement and enjoyment form a
powerful combination particularly when the outcome s learning. This is at
the heart of what many teachers strive for in classrooms. I hope my
suggestions support your work with students.
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Magic square
(numbers)
1 2 3
4 5 6
7 8 9
Algebra Magic Square
a + 4b
8a + 3b
3a + 8b
6a + 9b
4a + 5b
2a + b
5a + 2b
7b
7a + 6b
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