Presentatie titel Calculation up to 100 Okahandja, June 2014 Rotterdam, 00 januari 2007

As in calculation <10 and calculation <20, it´s in calculation <100 very important learners learn how to solve problems by making use of structures. We all know now three phases: Addition and subtraction by counting (not effective at last) Addition and subtraction by using models (smart teaching materials) Addition and subtraction in a formal way. This last phase is the final phase.

10 frames

10 frames

Classroom number line 1 - 100

Classroom number snake 1 - 100

Number snake 1-100, combined with the empty number line

Sun-game

Empty number line

Strategies calculation up to 100 Intermezzo: How did you do it? 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 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: what about your strategies?

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

Stepwise addition and subtraction/Stringing 84 – 27 = I cut 27cm off a ribbon measuring 84 cm. How much is left?

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

Stepwise addition and subtraction/Stringing Teaching materials supporting stepwise addition/subtraction (stringing) Numberline Number snake Sun-game 100-beads/bottle caps string Empty number line

Splitting or Column calculation. This strategy is based on number value. 47 + 25 40 + 20 = 60, 7 + 5 = 12, 60 + 12 = 72

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

Splitting or Column calculation

Splitting or Column calculation Teaching materials, supporting splitting or column calculation 10-frames

Strategie 4: Digit algorithm

Smart strategies (a higher level of calculation) The Grandstand problem (in case of addition) 56 + 27 56 + 27 = 53 + 30 = 83 3

Smart strategies The Scale problem (in case of subtraction) 68 – 29 68 – 29 = 69 – 30 = 39 +1 +1

Smart strategies Jumping too far and back (learners think of the nearest decade) 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. The most natural way of addition and subtraction Splitting/Column calculation. You need to know if the numbers get bigger ad you want to add and subtract without a calculator 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?

The 100-caterpillar 100 Just for fun 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! Just for fun

75-game Just for fun 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! Just for fun