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ALGEBRA PART 1 READING AND WRITING ALGEBRA
Aim:
To get the students to read and write algebra.
INTRODUCTION
MAGIC
The idea here is to do some ‘trick’ activities to which you can easily supply the answer but that the students
will not know how to do. Hopefully it will be a ‘hook’ to capture student interest.
It’s important NOT to reveal how they are done though. The explanations will be given a bit later once the
students have been exposed to some algebraic expressions. Leave it ‘hanging’. It is returned to later.
Don’t let the students talk you into telling them!!
1.
Do something “magical”.
e.g.
2.
1 – 31 Puzzle – recommended. There is a resource for this, that can be shown on a projector.
Playing Card trick
“Think Of A Number” activity.
e.g.
Get the students to think of a number (not too big).
Add 1 and subtract 1 to/from it.
Multiply these 2 together
Get one student to come to the board and write down 6 consecutive numbers including their
answer.
One number will be a ‘square number’ minus 1, so their original number can easily be identified.
Pretend to use “telepathy” to figure out their original number. Repeat several times if you wish.
The algebra is (x  1)(x  1)  x 2  1
Get the students to think of a number.
Add 1 and subtract 1 to/from it.
Multiply these and the original number together.
Add the original number on.
Get one student to come to the board and write down 6 consecutive numbers including their
answer.
One number will be a ‘perfect cube’, so their original number can easily be identified.
The algebra is (x  1)(x  1)x  x  x 3
Get several students to write about 6 consecutive numbers on the board, one of which is their answer.
Use “telepathy” to figure out their original number.
3.
Show the Flash Mind Reader. www.cyberglass.biz/flshstuff/mindreader.php
Only do it once or twice and leave it hanging, otherwise someone will figure it out. It is returned to
later. The algebra 10x  y  (x  y)  9x
CONCEPTS OF VARIATION AND THE REPRESENTATION OF AN INFINITE NUMBER OF POSSIBILITIES
The aim here is to get students to understand there are an infinite number of possibilities in some
situations and they can all be represented by a letter. The students will begin to ‘read’ and ‘write’ algebra.
20 cm line activity.
On a sheet of paper get the students to draw a line 20 cm long.
Label the ends A and B.
CBHS Year 9 Algebra
1
Part 1 – Reading and Writing Algebra
Get them to mark a point, P, on the line to show “how your parents would feel about you getting your
drivers licence as soon as you turn 16”. They will find this odd!!
Get the students to hold them up for others to see or blue tack them to the wall.
Discuss with them the variation that can be seen and perhaps get one or two to explain why they
placed the point where they did.
Now get the students to measure how far their point P is from the end labelled A.
Tabulate some results on the board
eg
Distance from A
7
2.5
14
9.3
18.6
x
Ask how many different places P could be.
i.e. how many different distances there could be
Get idea of an infinite number
Ask how all these distances could be represented.
Get idea of using a letter x. Add into table.
Perhaps draw a diagram also
x
A
P
B
Now ask how far it is from P to B – add another column to the table and fill in.
eg
Distance from A
7
2.5
14
9.3
18.6
x
Distance from B
13
17.5
6
10.7
1.4
20 – x
Get an ‘expression’ here
Perhaps put on the diagram also
x
A
P
20 – x
B
Rectangle Perimeter 28 cm.
On a sheet of paper get the students to draw a rectangle with perimeter 28 cm.
Get the students to hold them up for others to see or blue tack them to the wall.
Discuss with them the variation in shape that can be seen but they all still have P = 28cm.
Now get the students to measure the length of one side.
Tabulate some results on the board
eg
Length of side
11
9
2
6.3
Ask how many different lengths are possible.
Get idea of an infinite number
Ask how all these lengths could be represented.
Get idea of using a letter x. Add into table.
x
Perhaps draw a diagram also
CBHS Year 9 Algebra
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x
Part 1 – Reading and Writing Algebra
Now ask what the length of the other side is – add another column to the table and fill in.
eg
Length of side
11
9
2
6.3
Length of other side
3
5
12
7.7
x
14 – x
Get an ‘expression’ here
Perhaps put on the diagram also
14 – x
x
Further Examples/Exercises
1.
A line AB is 45cm long with a with a point P somewhere along it.
What is an expression for the distance AP?
(Answer x)
What is an expression for the distance PB?
(Answer 45 – x)
2.
What are expressions for the sides of any rectangle with a perimeter of 50cm
(Answer x and 25 – x)
3.
A triangle has a perimeter of 30cm and one side is 8cm. What are expressions for the lengths of the
other two sides?
(Answer x and 22 – x)
4.
An isosceles triangle has a perimeter of 40cm and a base length of x. What is an expression for the
lengths of the two equal sides?
(Answer (50 – x)  2)
5.
An isosceles triangle has a perimeter of 40cm with equal sides of length x. What is an expression for
the length of the base?
(Answer 40 – 2x)
SUMMARISING NUMBER PATTERNS
1.
Consider the table below
4 x 2
=
8
4 x 5
=
20
4 x –1
=
–4
4 x 7
=
28
4 x –3
=
–12
Any number could have been chosen here. How could all the infinite possibilities be represented?
4 x x
or just 4x.
We could also write 4x = y as the last number is changing also.
2.
Write an expression to represent the table below.
3 x 4
+ 2
=
14
3 x –2
+ 2
=
–4
The expression representing all possibilities is 3x + 2
3 x 8
+ 2
=
26
or 3x + 2 = y
3 x –5
+ 2
=
–13
CBHS Year 9 Algebra
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Part 1 – Reading and Writing Algebra
4x and 3x + 2 are called “Algebraic Expressions”
x and y are called “variables” because the numbers they represent vary.
Exercises
Write expressions for the number patterns in each of the following tables.
1.
3.
2 x 6 –
5
=
7
2 x –1 –
5
=
2 x 3 –
5
2 x –7 –
5
2.
–5 x 6
+ 3
=
–27
–7
–5 x –1
+ 3
=
8
=
1
–5 x 3
+ 3
=
–12
=
–19
–5 x –7
+ 3
=
38
2 x 6 + 6
=
18
7 x 3
– 3
=
18
2 x 9 + 9
=
27
7 x 8
– 8
=
40
2 x 3 + 3
=
9
7 x 5
– 5
=
30
2 x 7 + 7
=
21
7 x 2
– 2
=
12
4.
Expressions For Consecutive Integers, Multiples and Even/Odd Numbers
Write down all the
1.
Pairs of consecutive integers.
Answer x, x + 1 or x, x – 1
2.
Multiples of 2
Answer 2x
3.
Multiples of 3
Answer 3x
4.
Multiples of 7
Answer 7x
5.
Even numbers
Answer 2x same as mults of 2
6.
Odd numbers
Answer 2x + 1 or 2x – 1
Extension
Write down expressions for
1.
All the 2 digit numbers
Answer 10x + y
2.
All the 3 digit numbers
Answer 100x + 10y + z
3.
All the 6 digit numbers
1,000,000a + 100,000b + 10,000c + 1000d + 100e + 10f + g
4.
All the numbers 1 more than the multiples of 2
2x +1
5.
All the number 4 less than the multiples of 5
5x – 4
6.
All the numbers that are the sum of the multiples of 3 and the multiples of 5
3x + 5x
7.
All the numbers that are the difference between the multiples of 7 and the multiples of 4.
7x – 4x
Explanations of the ‘Magic’
1.
31 puzzle
Every number between 1 and 31 can be formed by adding some of the numbers 1, 2, 4, 8 and 16
together.
1 is on card A only, 2 on card B only, 4 on card C only, 8 on card D only and 16 on card E only.
When you tell me which cards your number is on I just add whichever of 1, 2, 4, 8 or 16 together.
CBHS Year 9 Algebra
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Part 1 – Reading and Writing Algebra
2.
3.
Think of a Number
(a)
(x  1)(x  1)  x 2  1
(b)
(x  1)(x  1)x  x  x 3
Flash Mind Reader
10x  y  (x  y)  9x
eg
no.
add digits
subtract
26
–8
18
43
–7
36
75
–12
63
10x + y
– x+y
9x
all multiples of 9
CBHS Year 9 Algebra
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Part 1 – Reading and Writing Algebra