Presentatie titel Calculation up to 100 Okahandja, October 2013 Rotterdam, 00 januari 2007

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 4 Classroom number snake 1 - 100

Teaching materials 5 100-beads/bottle caps string Foto van voorbeeld met doppen

Teaching materials 6 Sun-game

Teaching materials 7 Empty number line

Strategies calculation up to 100 Solve the problems and write down your calculations. Show the way you find your answer! 43 + 35 = 58 + 26 =  85 – 32 =  72 – 37 = Solve

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: In grade 5:

Strategie 1: Counting one-by-one Counting or calculating?

Strategie 1: Counting one-by-one Teaching materials All kinds of counting materials

Strategie 2: Stepwise addition and subtraction/Stringing 45 + 28 = Joan has read 45 pages in her book. Today she reads 28 pages. 45 + 20 = 65 65 + 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 I get 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 + 25 47 + 3 = 50, 50 + 20 = 70, 70 + 2 = 72 47 + 20 = 67, 67 + 3 = 70, 67 + 5 = 72

Strategie 2: Stepwise addition and subtraction/Stringing Teaching materials Numberline Number snake Sun-game 100-beads/bottle caps string Empty number line

Strategie 3: Splitting or Column calculation 47 + 25 40 + 20 = 60, 7 + 5 = 12, 60 + 12 = 72

Strategie 3: Splitting or Column calculation 47 25 + 60 12 + 72 47 + 25 40 + 20 = 60, 7 + 5 = 12, 60 + 12 = 72

Strategie 3: Splitting or Column calculation

Strategie 3: Splitting or Column calculation Teaching materials 10-frames

Strategie 4: Digit algorithm

Strategie 5: Smart strategies 5.1: The Grandstand problem 56 + 27 56 + 27 = 53 + 30 = 83 3

Strategie 5: Smart strategies 5.2: The Scale problem 68 – 29 68 – 29 = 69 – 30 = 39 +1 +1

Strategie 5: Smart strategies 5.3: Jumping too far and back 45 + 28 = 45 + 30 – 2 = 82 – 37 = 82 – 40 + 3 =

Which strategie do you choose? A book with 84 pages. You are reading at the bottom of page 37. How many pages still to read?   The black t-shirt costs N$ 92 and the grey t-shirt costs N$ 69. How much more expensive is the black t-shirt? N$ 92 N$ 69

The basic strategies: 1 Stepwise addition and subtraction/ Stringing Starts with flexible counting The ‘large number line’: 10 – 20 – 30 – 40 – 50 – 60 – 70 – 80 – 90 – 100 The ‘small number line’: 1 – 2 – 3 – 4 - 5 – 6 - 7 – 8 – 9 – 10 – 11 – 12 - ….- 33 – 34 – 35 – 36 – 37 – 38 – 39 - 40- etc Use of the empty number line as a ‘notation scheme’ and ‘paradigm’

The basic strategies: 2 Splitting/ column calculation Starts with place value Use 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/ Stringing Splitting/Column calculation Additional: Smart calculation

Discussion & Exercises 46 + 23 = 58 + 36 = 76 – 24 = 63 – 28 = Stepwise (shopkeepers method), Splitting, Smart calculation

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?

Make the materials yourself Use the materials and discover the possibilities to teach mathematics with these ‘easy to make’ teaching materials.

The 100-caterpillar 100 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!

75-game Rules of the game: Take a turn to a number, 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!