Algebra with Numicon. Margi Leech
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1 Algebra with Numicon Margi Leech
2 Why is it so hard? X y z New language Understanding equality Abstract Complex Different abiliaes What s the point? Deficiency in prior learning Fluency and confidence Learning without understanding
3 Algebra in the real world interacave acaviaes and videos hnp:// the- math/
4 Problems with panerns Can t see how geometry fits Time and money, other measurement Disconnects for students Place Value FracAons Decimals Basic Facts knowledge
5 Algebra, nothing new Significance of a number Number sequences Constant differences Inverse + and -, x and Using inverse to solve and check problems CommutaAve and associaave relaaonships Doubling and halving Equality and balancing equaaons AdjusAng and compensaang Finding missing numbers in balancing equaaons Brackets Factors and mulaples Working systemaacally
6 3 Concrete RepresentaAonal Abstract Numicon provides the connec4ons
7 The Numicon approach has been influenced by Bruner who explained how we learn. Bruner experience leads to representation and abstraction EnacAve internalised ac4on Iconic sensory imagery e.g. bacon and eggs Symbolic arbitrary symbols e.g. words
8 Numbers and the Number System
9 Cuisenaire rods same acaviaes
10 Place value Hundreds Tens Ones
11 Generalising 0.30, 30%, 30/100 2/3
12 NegaAve numbers 0
13 ConnecAons and language across the operaaons Oxford University Press 2015
14 Language and Symbols + and -, < and >
15 > = Oxford University Press 2015
16 Structures
17 Language and Symbols x and / Oxford University Press 2015
18 a a+2 a+4 a+6 a+8 a a+2 a+4 a+6 a+8 a a+2 a+4 a 2a 3a 4a 5a a 2a 3a 4a 5a a 2a 3a
19 Algebra- panerns of structures 2a + 3 = 17 Primary school usage of a What is a? = = 14
20 2a + 3 = = 14 Which two shapes/ numbers the same size, make 14 exactly? = 17 a = 7
21 Finding x x Hide a 4 shape in an envelope Clue: 3x + 5 = x = x = Show this to the class Write the clue on the board
22 Finding x x Hide a 4 shape in an envelope Show this to the class Write the clue on the board Clue: 3x + 5 = 17 Show 17
23 Finding x x Clue: 3x + 5 = 17 3x = 17-5 Cover 5 to show subtract five 3x = 12
24 Finding x x Clue: 3x + 5 = 17 3x = Find three shapes the same to cover the remaining shape 2. The shape is a 4 3. x is 4 4. Open the envelope! The process: = 4 4. x = 4
25 2x + 4 = 10 2x =
26 2x + 4 = 10 2x = 6 x = = 3 0
27 Finding x x Clue: 2x - 2 = 10 Hide a 6 shape in an envelope. Show this to the class. Write the clue on the board 2x 2x =
28 Finding x x 2x Clue: 2x - 2 = 10 2x = = 6 x = 6
29 2x - 2 = 8 2x =
30 2x - 2 = 8 2x = 10 x = =
31 ᵡ ᵡ 2 x + 2 = 14 2 x - 2 = 14-2
32 2 x - 2 = x = = 6 x = 6 ᵡ =
33 If x = 2 X2 + 5x + 6 = (x + 3) x (x + 2) (2) + 6 = (2 + 3) x (2 + 2) = 5 x 4 20 = 20 = Oxford University Press 2015
34 InvesAgaAon 1 Low threshold, high ceiling from InvesAgaAons with Numicon Cross Totals Use Numicon Shapes 1, 2, 3, 4 & 5 Place one shape in each square so the horizontal and veracal totals are the same Talk about any interesang panerns you noace? Odds and evens? Algebraic expressions?
35 InvesAgaAon 2 Low threshold, high ceiling from InvesAgaAons with Numicon Six squared Mark off six by six on the baseboard template Explore by filling it with your choice of shapes. Record what you have done on paper Consider mulaples, brackets, algebraic expression
36 InvesAgaAon 2 Low threshold, high ceiling from InvesAgaAons with Numicon Six squared AcAviAes to explore Use only shapes 5, 6, 7, 8, 9, 10 Use only one number shape Use only two number shapes What is the smallest number of shapes you can use?
37 Numicon Approach
38 Emphasize in your teaching RelaAonships of numbers What do I already know? Generalizing The BIG picture- contexts every Ame Small steps, repeated FuncAon of symbols + - x / = and the associated language and how they work together Describing panerns of numbers Visual supports
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