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Calculation up to 100: teaching-learning trajectory and teaching materials.
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Presentatie titel
Rotterdam, 00 januari 2007
Calculation up to 100
Okahandja, October 2013
Teaching materials
1 All kind of counting materials
Teaching materials
2 10-frames
Teaching materials
2 10-frames
1 1 1 2 1 3
Teaching materials
3 Classroom number line 1 - 100
Teaching materials
5 100-beads/bottle caps string
Teaching materials
7 Empty number line
Teaching materials
6 Sun-game
Strategies calculation up to 100
43 + 35 =
58 + 26 =
85 – 32 =
72 – 37 =
SolveSolve the problems and write down your calculations.
Show the way you find your answer!
The calculations of the learners of Elim Primary School in Windhoek
The calculations of the learners of Elim Primary School in Windhoek
The calculations of the learners of Elim Primary School in Windhoek
The calculations of the learners of Elim Primary School in Windhoek
The strategies used by the learners of Elim Primary School in Windhoek
In grade 3:Counting one-by-one,Stepwise addition and subtraction/ Stringing,Splitting,Digit algorithm
In grade 4:Stepwise addition and subtraction/ Stringing,Splitting,Digit algorithm
In grade 5:Digit algorithm
Strategie 1: Counting one-by-one
Counting or calculating?
Strategie 1: Counting one-by-one
Teaching materials
All kind of counting materials
Strategie 2: Stepwise addition and subtraction/Stringing
45 + 28 =Joan has read 45 pages inher book.Today she reads 28 pages.
45 + 20 = 6565 + 25 = 70 70 + 23 = 73
Strategie 2: Stepwise addition and subtraction/Stringing
84 – 27 =I cut 27cm off a ribbon measuring 84 cm. How much is left?
Strategie 2: Stepwise addition and subtraction/Stringing
50 – 36 =I spent 36p in a shop. How much change did Iget from 50p?36p + ____p = 50p
Counting on using a number line is particularly useful in calculating change.
‘Shopkeepers strategy’
Strategie 2: Stepwise addition and subtraction/Stringing
47 + 2547 + 3 = 50,50 + 20 = 70,70 + 2 = 72
47 + 25 47 + 20 = 67,67 + 3 = 70,70 + 2 = 72
47 + 25 47 + 20 = 67,67 + 5 = 72
Strategie 2: Stepwise addition and subtraction/Stringing
Teaching materials
Numberline Sun-game 100-beads/bottle caps string Empty number line
Strategie 3: Splitting or Column calculation
47 + 2540 + 20 = 60,7 + 5 = 12,60 + 12 = 72
Strategie 3: Splitting or Column calculation
44 + 2540 + 20 = 60,4 + 5 = 9,60 + 9 = 69
4425 +60 9 +69
Strategie 3: Splitting or Column calculation
def(icit)
Strategie 3: Splitting or Column calculation
Teaching materials
10-frames bundles of sticks
Strategie 4: Digit algorithm
Which strategie do you choose?
A book with 84 pages.You are reading at thebottom of page 37.How many pages still toread?
The black t-shirt costs N$ 92 and the grey t-shirtcosts N$ 69.How much more expensiveis the black t-shirt?
N$ 92 N$ 69
The basic strategies: 1 Stepwise addition and subtraction/ Stringing
Starts with flexible countingThe ‘large number line’: 10 – 20 – 30 – 40 – 50 – 60 – 70 – 80 – 90 – 100The ‘small number line’: 1 – 2 – 3 – 4 - 5 – 6 - 7 – 8 – 9 – 10 – 11 – 12 - ….- 33 – 34 – 35 – 36 – 37 – 38 – 39 - 40- etcUse of the empty number line as a ‘notation scheme’ and ‘paradigm’
The basic strategies: 2 Splitting/ column calculation
Starts with place valueUse of the 10-frames as a ‘paradigm’Use of the ‘column notation scheme’ emphasises the place value
The teaching-learning-trajectory
Basic strategies for all learners:
Stepwise addition and subtraction/ StringingSplitting/Column calculation
Additional:Smart calculation
Exercises
46 + 23 =58 + 36 =76 – 24 =63 – 28 =
Stepwise stinging (shopkeepers method), Stepwise splitting,
Discussion
What materials are you using now in computation up to 100?
What strategies do you teach in computation up to 100?
Do you see a relationship between computation up to 20 and computation up to 100? Please, explain.
Studies
Teaching-learning trajectory ‘stepwise addition and subtraction,
Teaching-learning trajectory splitting
Teaching-learning trajectory smart calculation
Studies
How does it start?Which steps for the learners to make in the learning trajectory?Which teaching materials are usefull in the teaching trajectory?Which notation schemes do the learners use?What are the learning outcomes in this teaching learning trajectory?
Please, make the materials yourself
Use the materials and discover the possibilities to teach mathematics with these ‘easy to make’ teaching materials!
Jaap Griffioen – [email protected] Jaap de Waard – [email protected]
The 100-caterpillar
Choose two different numbers between 0 en 100, Put these numbers in order in the first and the
second part of the caterpillar, Make the number in the next part by adding the two
previous numbers, The number in the fifth part must be 100!
100
75-game5 10 15 20 25 30 35 40 45
Player 1
Player 2
Rules of the game:
Take a turn to a number,
Choose from the numbers 5, 10, 15, 20, 25, 30, 35,40, 45,
Each number can be chosen only once!
Do you have three numbers which together have 75? You are the winner!
