m22821 To determine the equivalence and validity of different representations 1.1 2009/05/02 03:20:37.699 GMT-5 2009/05/02 03:30:24.392 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

1.1 Counting on 1.2 Take away 11 400 every time and add the rest 1.3 Keep 1 000s, 100s and 10s apart and add 1.4 Counting on: first 10 000s, then 1 000s, then 100s, then 10s and lastly units 1.5 Self-explanatory 1.6 Carry over method 2. Own answer 3.2 Short method of addition, without carry over numbers 3.3 a) 83 320 b) 105 935 Leaner Section

1. In Activity 2.6 you used your own techniques and strategies to solve the problems. DID YOU KNOW? There are many other ways in which we can add numbers. Form six groups. Each group must discuss one of the following methods and then explain how the answer is calculated. 1.1 I calculate 11 468 + 23 957 like this: 11 468 + 20 000 → 31 468 + 3 000 → 34 468 + 900 35 368 + 50 → 35 418 + 7 = 35 425 1.2 I prefer to calculate the answer as follows: 11 468 + 23 957 = (11 400 + 11 400) + (68 + 12 557) = (11 400 + 11 400 + 11 400) + (68 + 1 157) = 34 200 + 1 225 = 35 425 1.3 Look carefully! This is how I do it!

1.4 My method of addition looks like this: 11 468 + 23 957 = 10 000 + 20 000 → 30 000 + 1 000 + 3 000 34 000 + 400 + 900 → 35 300 + 60 + 50 35 410 + 8 + 7 = 35 425 1.5 I work like this:

1.6 I find it best to write it down like this: 11 468 + 23 957:

2. Which method do you find easiest? Motivate your answer. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 3. Work with a friend and study the following method:

3.2 Explain the method to another friend. 3.3 Now use this method to calculate the sum of the following: a) 35 691 + 47 629 _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ b) 82 179 + 23 756 _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Let us see how you have done! Mark the relevant box: I understand all the methods. most of the methods. **only one or two of the methods. ** Ask the members of your group / your educator to explain it to you again.

Work in groups of 4. Can you think of any OTHER methods to calculate the sum of 11 468 + 23 957?

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 counts forwards and backwards in whole number intervals and fractions; 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.