3.5 Solve problems in context

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 + $\frac{2}{\text{10}}$ + 63 + $\frac{5}{\text{10}}$ + $\frac{4}{\text{100}}$ + 39 + $\frac{2}{\text{10}}$ + $\frac{4}{\text{100}}$ + $\frac{9}{\text{1000}}$

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

Then I add all the tenths : $\frac{2}{\text{10}}$ + $\frac{5}{\text{10}}$ + $\frac{2}{\text{10}}$ = $\frac{9}{\text{10}}$

Then I add the hundredths : $\frac{4}{\text{100}}$ + $\frac{4}{\text{100}}$ = $\frac{8}{\text{100}}$

Lastly, I add everything together: 160 + $\frac{9}{\text{10}}$ + $\frac{8}{\text{100}}$ + $\frac{9}{\text{1000}}$

= 160 + $\frac{\text{900}}{\text{1000}}$ + $\frac{\text{80}}{\text{1000}}$ + $\frac{9}{\text{1000}}$

= 160 $\frac{\text{989}}{\text{1000}}$

= 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!