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3.5 Solve problems in context

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  • 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 : 6 1000 size 12{ { {6} over {"1000"} } } {} − 3 1000 size 12{ { {3} over {"1000"} } } {} = 3 1000 size 12{ { {3} over {"1000"} } } {}

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

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

Now I add the answers: 4 + 3 10 size 12{ { {3} over {"10"} } } {} + 2 100 size 12{ { {2} over {"100"} } } {} + 3 1000 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

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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Source:  OpenStax, Mathematics grade 5. OpenStax CNX. Sep 23, 2009 Download for free at http://cnx.org/content/col10994/1.3
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