An Algebra story
Background
• New PLD environment
• Development of a
diagnostic snapshot
• What we found:
–
–
–
–
Number not a big problem
No generalisations
Language of algebra an issue
No strategies
• Intervention negotiated
– length
–
what was important and
therefore worth spending
time on
– Concentrate on the language
and pedagogy using the SNP
teaching model
– Lesson structure
What we did !
The greatest enemy of understanding is coverage.
As long as you are determined to cover everything,
you actually ensure that most kids are not going to
understand. You’ve got to take enough time to get
kids deeply involved in something so they can
think about it in lots of different ways and apply it
– not just at school but at home and on the street
and so on.
(Brandt, 1993)
So what did we cover?
• The language
• Out of language came substitution and like
terms
• Patterning
• Expansions
• Equations
• Lots of revision
The language of Maths
Continually revisit using activities such as:
• Bingo
• Loopies
• Addonagons
• 4 in a row (number to algebra)
• Simple questions in context
• Reading out loud
• Unscrambling maths words
• Crosswords
Algebra language Bingo
Draw up a 3 X 3 grid and pick 9 of these and fill in your grid
X +3
3a - 2
b-3
4x + 6
3b
y-9
2x - 5
g-5
m+n
3(x – 2)
X-4
2(a + b)
2k
3x + 6
3+5+7
4A
2p + 2
Y+3
mf
6y
Loopies
• Collecting up like terms
• Using Maths language
4 in a row – number to algebra
• Mult/div or add/sub.
• Algebra
Questions in context
• Use simple knowledge questions.
• T/students read qs out loud to the class
• Students write the “maths” problem using
correct notation.
• Eg Tickets to the concert cost $58. If 4 friends
want to go what is it going to cost altogether?
• Eg Joel has $69 less than Marty who has
$350. How much money does Joel have?
Unscrambling Maths words/crosswords
etc
• http://puzzlemaker.discoveryeducation.com/WordSearc
hSetupForm.asp
• www.puzzle-maker.com/CW/
Patterning
•
•
•
•
•
•
•
•
•
•
•
•
Spatial patterns – drawing the next 2 shapes
Matching a spatial pattern to a number
Finding the next 3 terms in a number pattern
Finding the missing numbers in a number pattern
Making up a spatial pattern for a number pattern
How many objects are added to get the next term
Design a spatial pattern that adds: 4 matchsticks to get the
next term or 1 black dot and 3 yellow dots to get next term
For the pattern 24, 20, 16, describe what is happening in
words.
Find the next 2 terms - describe the rule in words
Use the number 5 and the rule to find the first 5 terms
Using tables:
“n”
match stick design………..no of match sticks needed
Patterning continued
• Complete the table (no design given)
• Now introduce some more context. Eg to hire
“the coffee man” it costs $50/hr and an $80
set up fee. Construct a table to show the cost
for 1 to 6 hours.
• Move to using rules and formulas eg
–
–
–
–
Find first 4 terms for this rule
Find the 6th term (n=6) of the number pattern 3n + 5
Complete the table using the rule m = 2n + 6
Lots of these using lots of different variables.
Move to across and down rules
and context examples
Moving towards expansions and factorising
Revisit Using PV and partitioning to multiply (L4 Stage 5)
Context question:
37 loaves of bread have been ordered for the tangi.
There are 24 slices in each loaf . How many slices have to be
buttered?
Read the question
What is the maths question?
Record it.
Provide students with a large dotty array.
What is an array/
Ask them to draw a border around the array that shows this
problem.
Now tell them to partition(what is this?) it to help them find the
total dots .Students are likely to use a variety of divisions –
discuss all.
Start by:
• Using materials, diagrams to illustrate
and solve the problem
Progress to:
• Developing mental images to help solve
the problem
Extend to:
• Working abstractly with the number
property
Using Materials
4637+
10
4
46
10
= 83
10
3
83
Encouraging Imaging
3924+
1
30
40
39
10
10
50
= 63
3
60
70
63
Using Number Properties
18
44+
From 18:
add 2 to get to 20
add 40 to get to 60
add 2 to get to 62
Total:
add 44
= 62
Solving Equations
47 +
47
= 83
83
47
83
Solving Equations
2X + 1 = X + 7
X
X
X
1
7
Solving Equations
2X + 1 = 7
X
X
7
1
Solving Equations
2(X + 1) = 18
X
1
X
18
1
Solving Equations
2(X + 1) = 18
X
1
9
X
1
9
Solving Equations
2(X + 1) = 18
X
X
18
1
1
Solving Equations
53 27
53
27
= 27
53
Solving Equations
2X - 1 = X + 7
X
X
X
7
1
Solving Equations
2X - 1 = 8 - X
X
X
8
X
1
Solving Equations
X - 1 = 2X - 7
7
X
X
X
1
Solving Equations
X+3=2
X
3
2
Key points
•
•
•
•
•
•
Present new ideas in context
Read all questions out loud
Articulate all calculations
Put calculations in words and pictures
Keep the glossary going
Ensure that students can explain their
answers.
• Use lots of reinforcement activities