ACTIVITY 1:

To solve problems in context [LO 1.6.2]

1. Split up into groups of three. Find the solutions to these problems without using your pocket calculator.

What is the total length of all the planks that he needs?

1.2 In a certain residential area trees have to be cut down because they are touching the telephone wires. If they cut 0,259 m from the one tree, 1,5 m from the next and 2,93 m from the third tree, how many metres have been removed from the trees altogether?

1.3 Three buildings have to be painted. If one of the buildings is 16,8 m tall, the second one is 23,495 m tall and the third one is 46,77 m tall, how many metres have to be painted in all?

Activity 2:

To determine the equivalence and validity of different representations of the same problem through comparison and discussion [LO 2.6.3]

ADDITION OF DECIMAL FRACTIONS

1. In Activity 2.15 you had the opportunity of solving problems by using your own methods and techniques. Now you must work with a friend. Read the problem and then work through the different solutions of the various learners.

Three buildings are 58,2 m; 63,54 and 39,249 m high respectively. How high are they altogether?

1.1 I must calculate 58,2 + 63,54 + 39,249:

It is precisely the same as 58 + 210210 size 12{ { {2} over {"10"} } } {} + 63 + 510510 size 12{ { {5} over {"10"} } } {} + 41004100 size 12{ { {4} over {"100"} } } {} + 39 + 210210 size 12{ { {2} over {"10"} } } {} + 41004100 size 12{ { {4} over {"100"} } } {} + 9100091000 size 12{ { {9} over {"1000"} } } {}

I add the whole numbers first: 58 + 63 + 39 = 160

Then I add all the tenths: 210210 size 12{ { {2} over {"10"} } } {} + 510510 size 12{ { {5} over {"10"} } } {} + 210210 size 12{ { {2} over {"10"} } } {} = 910910 size 12{ { {9} over {"10"} } } {}

Then I add the hundredths: 41004100 size 12{ { {4} over {"100"} } } {} + 41004100 size 12{ { {4} over {"100"} } } {} = 81008100 size 12{ { {8} over {"100"} } } {}

Lastly, I add everything together: 160 + 910910 size 12{ { {9} over {"10"} } } {} + 81008100 size 12{ { {8} over {"100"} } } {} + 9100091000 size 12{ { {9} over {"1000"} } } {}

= 160 + 90010009001000 size 12{ { {"900"} over {"1000"} } } {} + 801000801000 size 12{ { {"80"} over {"1000"} } } {} + 9100091000 size 12{ { {9} over {"1000"} } } {}

= 160 98910009891000 size 12{ { {"989"} over {"1000"} } } {}

= 160,989

1.2 I use notation columns to calculate the sum of 58,2; 63,54 and 39,249:

The three buildings are 160,989 m high altogether.

1.3 I must calculate 58,2 + 63,54 + 39,249.

I do it exactly like a normal addition sum but I remember to keep the commas precisely underneath each other!

58,200

63,540

+ 39,249

160,989

2. Which method do you choose?

Why?

3. How do the first two methods compare with each other?

Activity 3:

To calculate by means of selection and through the use of suitable computations (additional) [LO 1.8]

1. Let us see how well you do on your own. Calculate the following without using a pocket calculator:

1.1: 3,247 + 117,9 + 36,58

1.2: 2,36 + 18,459 + 23,7

1.3: 5,742 + 87,62 + 49,136

1.4: 48,5 + 231,8 + 9,826

2. Try to do the following without any calculations: A farmer wants to fence his camp with wire but he only has loose pieces of wire. He has a piece of 2,5 m, another piece of 0,5 m and a third piece of 1,5m. How much wire does the farmer have altogether?

3. Explain to a friend how you calculated your answer!

4. Check all your answers of 1 and 2 with a calculator.

Brain-teaser!

Can you solve the following magic squares? You may use your calculator!

Activity 4:

To solve problems in context [LO 1.6.2]

1. Split up into groups of three. Your teacher will tell you which one of the problems below must be solved by your group. You will also be given the necessary paper to work on. Remember: no pocket calculators!

2. Now compare your answer with that of a group that had to solve the same problem.

3. Explain your solution to the rest of the class.

4. Have a class discussion on the differences / similarities in your methods.

Activity 5:

To use a series of strategies to check solutions and to assess the reasonableness of the solutions [LO 1.11]

1. We have just solved a few problems and discussed the different ways to determine the answers. Work with a friend, read the following problem and take a good look at the given solutions. Make sure that you understand how the answer has been calculated.

ADDITION

A restaurant uses 9,786 ℓ milk during breakfast and 5,463 ℓ for supper. How much less milk is used for supper?

1.1 I must calculate 9,786 – 5,463

I first subtract the whole numbers: 9 – 5 = 4

Then I subtract the thousandths: 6100061000 size 12{ { {6} over {"1000"} } } {} − 3100031000 size 12{ { {3} over {"1000"} } } {} = 3100031000 size 12{ { {3} over {"1000"} } } {}

Now I subtract the hundredths: 81008100 size 12{ { {8} over {"100"} } } {} − 61006100 size 12{ { {6} over {"100"} } } {} = 21002100 size 12{ { {2} over {"100"} } } {}

Lastly I subtract the tenths: 610610 size 12{ { {6} over {"10"} } } {} − 310310 size 12{ { {3} over {"10"} } } {} = 310310 size 12{ { {3} over {"10"} } } {}

Now I add the answers: 4 + 310310 size 12{ { {3} over {"10"} } } {} + 21002100 size 12{ { {2} over {"100"} } } {} + 3100031000 size 12{ { {3} over {"1000"} } } {} = 4.323

The difference is thus 4,323 ℓ.

1.2 I do it in precisely the same way as normal subtraction but I write the commas precisely underneath each other:

9,786

− 5,463

4,323

The restaurant uses 4,323 ℓ less milk at supper time.

2. Whose method do you choose?

Why?

Activity 6:

To calculate through selection and the use of suitable computations (additional) [LO 1.8.8]

1. Now use any method and calculate the following without a calculator:

1.1: 6,42 - 2 98

1.2: 7,23 - 4,57

1.3: 8,123 - 3,545

1.4: 9,236 - 3,457

2. Check your answers with a calculator.

Brain-teaser!

Calculate 5 – 1,426

Activity 7:

To solve problems in context [LO 1.6.2]

Here is a challenge!

This assignment can be placed in your portfolio. Make sure that you read the criteria for assessment very carefully before you start. Ask your teacher for the necessary paper.

1. Look for examples of decimal fractions in your local newspaper or your favourite magazine. Cut them out neatly and paste them in below.

2. Write the decimal fractions as ordinary fractions next to or below the ones you have pasted in.

3. Now calculate the difference between the greatest and the smallest decimal fraction.

4. Calculate the sum of the two greatest decimal fractions.

5. Make a list of objects for which you would not use decimal fractions. Make a neat sketch of these objects.