Algebraic Generalisation

Achievement Objectives Level 3 Record and interpret additive and simple multiplicative strategies, using words, diagrams and symbols with an understanding of equality Generalise the properties of addition and subtraction with whole numbers Connect members of sequential patterns with their ordinal position and use tables, graphs, and diagrams to find relationships between successive elements of number and spatial patterns

Achievement Objectives Level 4 Form and solve simple equations Generalise the properties of multiplication and division with whole numbers Use graphs, tables and rules to describe linear relationships found in number and spatial patterns

Achievement Objectives Level 5 Form and solve simple linear and quadratic equations Generalise the properties of operations with fractional numbers and integers Relate graphs, tables and rules to linear and simple quadratic relationships found in number and spatial patterns

Progressions 1: move from symbols to linear equations and on to quadratic equations 2: generalise add/sub for integers, mult/div for integers and then both for fractions 3: use and understand patterns, through linear relationships to quadratic relationships. Its all about rules, tables and graphs.

A pet hate, and an important one Algebra; Letters represent numbers not objects….they represent the number of objects. Sometimes we confuse students by placing an emphasis on objects not number…..dont! Introduce letters for unknown numbers please.

Numeracy Work through these three progressions using: Strategies and knowledge at and just in front of the appropriate stage The numeracy teaching model: materials, imaging, abstract Activities – NZ Maths, Figure it out, etc

Algebra in the strands…. Statistics –Modelling formulas Geometry –Coaster patterns –Match patterns Measurement –Area formulas Number

Algebraic Generalisation E xplain the strategy G ive another example G eneralise

Example 1

Task 1

Task = = 2  = – 1 = 2  20 – = 9 + (9+1) + (9+2) = 3  = (10–1) (10+1) = 3  = (11–2) + (11–1) + 11 = 3  11 – 3

Task 3

Task Four

Task Five 32  42 = 30     2 32  48 = 30      42 = 40     2 39  49 = 40     -1

Task Six 9  9  9  9  9  9  9 =  9 5 = (9  9)  (9  9  9  9  9) = = 9  9  9  9  9  9   9  9  9  9 = 9 2 (9 4 ) 3 = 9 4  9 4  9 4 = 9 12

Using this resource… Diagnostic Task Starter / Plenary Challenge…

Next…..patterning Handouts. Work through these and place them at the appropriate numeracy stage/curriculum level.