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    This collection is included inLens: Siyavula: Mathematics (Gr. 4-6)
    By: Siyavula

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Solve problems in context

Module by: Siyavula Uploaders. E-mail the author

MATHEMATICS

Grade 5

ORDINARY FRACTIONS AND DECIMAL FRACTIONS

Module 50

SOLVE PROBLEMS IN CONTEXT

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.

  • A farmer wants to build a chicken coop with perches and needs the following timber for the job:
  • one plank of 4,3 m
  • one plank of 2,58 m
  • one plank of 3,26 m

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:

Table 1
T U t h th
5 8 2    
6 3 5 4  
3 9 2 5 5
16 0 9 8 9

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!

Table 2
0,6 0,1  
  0,5  
    0,4

Table 3
    2,6
  2,3  
2   2,2

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!

  • Taxi A needs 36,78 litres of petrol to fill its tank. Taxi B needs 29,9 litres. How many more litres of petrol does taxi A need?
  • Mrs Mmbolo is making curtains for her school’s new classrooms. If she needs 172,5 m of material for the ground floor and 98,75 m for the top storey, what is the difference in metres between the material needed for the two floors?
  • After the rainy season two dams on a farm held 459,23 kℓ and 263,587 kℓ of water respectively. What is the difference between the amount of water in the two dams? Give your answer in kℓ.
  • The difference in mass between two animals in the Kruger National Park is 4,963 kg. If the heavier animal has a mass of 75,23 kg, what is the mass of the other one?

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.

Assessment

Table 4
LO 1
Numbers, Operations and RelationshipsThe learner is 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 standards(ASs)
 
We know this when the learner:
1.3 recognises and represents the following numbers in order to describe and compare them:
1.3.3 decimal fractions of the form 0,5; 1,5; 2,5, and so on, in the context of measurement;
1.5 recognises and uses equivalent forms of the numbers listed above, including:
1.5.2 decimal fractions of the form 0,5, 1,5 and 2,5, and so on, in the context of measurement;
1.6 solves problems in context including contexts that may be used to build awareness of other Learning Areas, as well as human rights, social, economic and environmental issues such as:
  • measurements in Natural Sciences and Technology contexts;
1.8 estimates and calculates by selecting and using operations appropriate to solving problems that involve:
  • (additional) addition of positive decimals with 2 decimal places;
1.9 performs mental calculations involving:1.9.1 addition and subtraction;1.9.2 multiplication of whole numbers to at least 10 x 10;
1.10 uses a range of techniques to perform written and mental calculations with whole numbers including:
  • building up and breaking down numbers;
  • using a calculator;
1.11 uses a range of strategies to check solutions and judge the reasonableness of solutions;

Memorandum

ACTIVITY 2

3. Actually the same

ACTIVITY 3

1. 1.1: 157,727

1.2: 44,519

1.3: 142,498

1.4: 290,126

2. 4,5 m

BRAIN-TEASER!

0,8; 2,4; 1,9;

0,7; 0,3; 2,5; 2,1;

0,2; 0,9; 2,7;

ACTIVITY 6

1. 1.1: 3,44

1.2: 2,66

1.3: 4,578

1.4: 5,779

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