m20054 To determine the equivalence and validity of different representations 1.1 2009/03/10 05:34:20.127 GMT-5 2009/03/10 05:51:38.087 GMT-5 Helen Saayman Helen Saayman mark.horner@shuttleworthfoundation.org Helen Saayman Helen Saayman mark.horner@shuttleworthfoundation.org Helen Saayman Helen Saayman mark.horner@shuttleworthfoundation.org Mathematics and Statistics en

2. Learner’s own method 3.1 9 080 717 3.2 8 301 883 6 485 185

1. 4 2. 1 3 2 1 3 2 3 1 44 8 1

1. In the previous activity you had the opportunity to use your own strategies to solve problems. From the feedback in the class you would have realised that there are many ways of adding numbers. Work in pairs. Discuss the following methods of adding and explain to each other how the answers are calculated:

1.1 845 908 + 25 876 + 343 621 800 000 + 40 000 + 5 000 + 900 + 0 + 8 20 000 + 5 000 + 800 + 70 + 6 + 300 000 + 40 000 + 3 000 + 600 + 20 + 1 1 100 000 + 100 000 + 13 000 + 2 300 + 90 + 15 = 1 000 000 + (100 000 + 100 000) + 10 000 + (3 000 + 5 000) + 300 + (90 + 10) + 5 = 1 215 405 1.2

= 1 215 405 1.3 1 1 1 2 1 8 4 5 9 0 8 2 5 8 7 6 + 3 4 3 6 2 1 1 2 1 5 4 0 5 2. Can you show your friend any other method of calculation? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 3. Use any method of your choice (without a calculator) and calculate the sum of: 3.1 4 623 577 + 1 239 246 + 3 217 894 _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 3.2 2 851 416 + 4 981 235 + 469 232 _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 3.3 2 153 892 + 264 058 + 4 067 235 _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Complete the missing numbers: 1. 1. 2 1 3 4 1 ___ 2. ___ 7 9 1 2 3 8 9 2 ___ 7 4 ___ 2 8 1 6 1 7 5 ___ 9 2 1 1 ___ 2 3 3 ___ 1 4 1 1 9 1 0 0 ___ 7 1 + 1 ___ 9 1 2 3 + 1 4 3 0 ___ ___ ___ 1 ___ 0 8 5 9 5 8 5 8 7

Tick the appropriate rectangle: Yes Mostly Some-times No I can investigate adding methods and evaluate them (determine whether they are correct). (LO 1.11 en LO 2.6) * I can add correctly without a calculator. (LU 1.8) * I need more exercise in addition. * * Ask your educator to explain again and give you extra exercises.

Learning Outcome 1:The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems. Assessment Standard 1.11: We know this when the learner uses a range of strategies to check solutions and judge the reasonableness of solutions. Learning Outcome 2:The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills. Assessment Standard 2.6: We know this when the learner determines, through discussion and comparison, the equivalence of different descriptions of the same relationship or rule presented: 2.6.3: e.g. number sentences.