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 MathsContinually 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/WordSearch

SetupForm.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 factorisingRevisit 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 questionWhat 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 problemProgress to:• Developing mental images to help solve

the problemExtend to:• Working abstractly with the number

property

Using Materials

46 + = 83

46 83

410 10 10

3

37

Encouraging Imaging

39 + = 63

39 63

1 10 3

24

30 40 50 60 70

10

Using Number Properties

18 + = 62 44From 18: add 2 to get to 20

add 40 to get to 60add 2 to get to 62

Total: add 44

Solving Equations

47 + = 83

47 83

47 83

Solving Equations

2X + 1 = X + 7

7 XX X 1

Solving Equations

2X + 1 = 7

7 X X 1

Solving Equations

2(X + 1) = 18 X

18 X 1 1

Solving Equations

2(X + 1) = 18 X X 1 1

9 9

Solving Equations

2(X + 1) = 18 X

18 X 1 1

Solving Equations

53 - = 27

27 53

27 53

Solving Equations

2X - 1 = X + 7

7 X

1 X

X

Solving Equations

2X - 1 = 8 - X X

1 8 X X

Solving Equations

X - 1 = 2X - 7 7

1 X

X X

Solving Equations

X + 3 = 2 X

2 3

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