algebraic generalisation. achievement objectives level 3 record and interpret additive and simple...
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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
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bah
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Algebraic Generalisation
•Explain the strategy
•Give another example
•Generalise
Example 1
Task 1
9 + 9 + 9 + 5 + 5 + 5 = 3 9 + 3 5
6 + 4 + 6 + 4 + 6 + 4 = 3 (6 + 4) 9 + 9 + 9 – 5 – 5 – 5 = 3 9 – 3 5 6 – 4 + 6 – 4 + 6 – 4 = 3 (6 – 4)
Task 215 + 16 = 15 + 15 +1
= 2 15 + 1
19 + 20 = 20 + 20 – 1 = 2 20 – 1
9 + 10 + 11 = 9 + (9+1) + (9+2) = 3 9 + 3
9 + 10 + 11 = (10–1) + 10 + (10+1) = 3 10
9 + 10 + 11 = (11–2) + (11–1) + 11 = 3 11 – 3
Task 3
12 13 = 12 12 + 12 1 =122 + 12
13 12 = 13 13 – 13 1 =132 – 13
Task Four
7 32 = 7 30 + 7 2 7 39 = 7 40 – 7 1
Task Five
32 42 = 30 40 + 2 40 + 30 2 + 2 2
32 48 = 30 50 + 2 50 + 30 -2 + 2 -2
39 42 = 40 40 + -1 40 + 40 2 + -1 2
39 49 = 40 50 + -1 50 + 40 -1 + -1 -1
Task Six9 9 9 9 9 9 9 = 97
92 95 = (9 9) (9 9 9 9 9) = 97
97 = 9 9 9 9 9 9 995 9 9 9 9 9 = 92
(94)3 = 94 94 94
= 912
Using this resource…
• Diagnostic Task• Starter / Plenary• Challenge…
Next…..patterning
Handouts.
Work through these and place them at the appropriate numeracy stage/curriculum level.
• https://www.ncetm.org.uk/resources/10848
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