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Mathematics
Study guide 2/2
Grade 5
SAMPLE
LESSON ELEMENTS
The guide contains various lesson elements. Each element is important for the learning process and indicates the skill you must master.
ICON
LESSON ELEMENT
ICON LESSON ELEMENT
Think for yourself Take note! Important
Self-assessment
Research Activity Study Did you know? New concept or definition Tip
Remember/Revise
This unit covers 19 to 29.
UNIT 3
UNIT 3
TOPIC
Mental maths: Use Train Your Brain Maths Grade 5
LESSON 19 Common fractions
LESSON 20 Mass
LESSON 21
Whole numbers: Counting, ordering, comparing and representing, and place value of digits (6-digit whole numbers)
LESSON 22
Whole numbers: Addition and subtraction
LESSON 23 Views of objects
LESSON 24 Properties of 2D shapes
LESSON 25 Transformations
LESSON 26 Temperature
LESSON 27 Data handling
LESSON 28 Number patterns
LESSON 29
SAMPLE
Whole numbers: Multiplication (3-digit whole numbers by 2-digit whole numbers)
Revision: Use the CAMI programme
LESSON 19: COMMON FRACTIONS
In lesson 12, you learnt about common fractions and calculating with common fractions. Revise all the methods of working with fractions.
Before you compare or add any fractions, you must always make the denominators the same. When you multiply the denominator by a number, you must also multiply the numerator by the same number.
ACTIVITY 42
1. Complete the equivalent fractions.
DATE:
2. Use symbols (<; >; =) to show the relationship between the fractions.
2.1 4 10 2 5
2.2 10 8 5 2
2.3 2 2 3 7 3
2.4 1 1 4 5 4
2.5 3 4 1 2
3. Calculate the fractions and write the answer in the simplest form.
4. Indicate the type of fraction (proper fraction, improper fraction or mixed number).
4.1 1 2 3
4.2 5 2
4.3 3 1 5
4.4 5 6
5. Write the fractions as a mixed number in the simplest form.
5.1 5 3 = _________________
5.2 6 4 = _________________
5.3 7 5 = _________________
5.4 5 2 = _________________
5.5 13 8 = _________________
6. Read the scenarios and answer the questions in your exercise book.
6.1 Thabang wants to go on holiday. He can take leave for 2 3 of the month. If the month has 30 days, how many days’ leave can he take?
SAMPLE
6.2 Thabang has decided on his holiday destination. He will get there by train, which will take him 5 1 5 hours. If he goes by aeroplane, it will take him only 2 2 3 hours. How many hours will Thabang save if he takes the plane?
6.3 Thabang decides to take the plane to save time. Unfortunately, the flight is delayed by 1 5 6 hours. How long did the flight actually take him?
6.4 Thabang bought 6 gifts for his family and friends. Each gift takes up 1 15 of his suitcase. If he has 2 suitcases, how much space is left for his own luggage?
6.5 Lerato and her mom are making pancakes. They want to increase the recipe to make more pancakes. Her mom’s recipe uses 3 4 of a cup of water for every 1 4 of a cup of flour. How much water do they need if they want to use 1 cup of flour?
7. Which fraction is greater:
7.1 6 8 of a kilogram or 2 3 of a kilogram?
7.2 9 12 of a litre or 3 4 of a litre?
7.3 4 6 of an hour or 1 3 of an hour?
Self-assessment
Do you understand the work? Colour the faces that show what you can do.
COMMON FRACTIONS
Requirements
I can indicate common fractions on a diagram.
I can compare and indicate the relationships of common fractions.
I can calculate equivalent fractions.
I can do calculations with fractions (addition of fractions).
I can solve fraction sums with calculations.
I can convert between improper fractions and mixed numbers.
LESSON 20: MASS
Mass measures the quantity of matter (particles) in an object. For example, a gold bar is the same size as a box of Smarties (53 mm × 118 mm × 8 mm) but has a mass of 1 kg. This means the gold bar has a higher particle density, or more particles, than the box of Smarties.
It is important to remember that mass and weight are not the same, even though mass is used to describe weight. The weight of an object is determined by gravity, while mass is a constant determined by its number of particles. Out in space, where there is no gravity, a brick will have no weight, but its mass will be the same in space and on earth.
Mass is measured in gram (g), kilogram (kg) and ton (t). In Grade 5, we only work with gram and kilogram.
You worked with mass in Grades 3 and 4. Revise what you know about mass.
How do you measure mass?
SAMPLE
We use different measuring instruments to determine mass. Measuring instruments
Balancing scale
We measure mass in kilogram and gram.
Kilogram (kg) Gram (g)
You use kilogram when measuring objects heavier than 1 000 g. Smaller objects with a mass of less than 1 kg are measured in grams.
When you convert between gram and kilogram, remember that there are 1 000 g in every 1 kg. Use the diagram below to help with the conversion between gram and kilogram.
Example
kilogram (kg) gram (g)
SAMPLE
Convert 8 153 g from gram (g) to kilogram (kg).
= 8 153 g ÷ 1 000 = 8,153 kg (Remember: 8,153 kg is 8 kg 153 g – that is 8 full kilograms and 153 grams that are not enough to make up a full kilogram, therefore, the 153 comes after the comma.)
Revise the conversion of volume in lesson 9. To simplify the calculations, you can picture a comma at the end of the number.
When you divide by 1 000, move the imaginary comma three place values to the left (because there are three zeros in 1 000).
When you multiply by 1 000, move the imaginary comma three place values to the right (because there are three zeros in 1 000).
8 1 5 3 , g ÷ 1 0 0 0 = 8 , 1 5 3 kg
Convert the following mass to gram. 4 kg × 1 000 = 4 000 g 4 ,
Use the imaginary comma and three zeros after the whole number.
There are three zeros because you are multiplying by 1 000. It is important to first write a comma and then the zeros.
When we work with or compare units of measurement, they must always be the same units.
ACTIVITY 43
DATE:
1. Read the mass on each scale and give the answer in g or kg.
2. Indicate the mass of the objects on the scales.
3. Calculate the mass.
3.1 The mass of each = g
3.2
The mass of each = kg
4. Convert the mass from kilogram to gram, or from gram to kilogram.
4.1 3 kg = __________________ g
4.2 5 315 g = __________________ kg
4.3 87,23 kg = __________________ g
4.4 954 kg = __________________ g
4.5 5,20 kg = __________________ g
4.6 3 019 g = __________________ kg
4.7 3 kg 16 g = __________________ g
4.8 7,05 kg = __________________ g
4.9 2 kg 134 g = __________________ kg
4.10 1 kg 5 216 g = __________________ kg g
5. Do the sums with mass.
5.1 6 kg + 750 g + 250 g = __________________ kg
5.2 15 kg – 750 g = __________________ kg
5.3 150 g × 5 = __________________
5.4 250 g × 5 = __________________ g = __________________ kg __________________ g
5.5 3 kg + 200 g + 600 g + 1,6 kg = __________________ kg
SAMPLE
5.6 The difference between 3 kg 35 g and 1 kg 70 g. __________________
5.7 475 kg ÷ 25 = __________________ kg
5.8 2 3 of 1,5 kg = __________________ kg
5.9 3 kg 125 g × 9 = __________________ kg
6. Write the masses in descending order.
6.1 700 g 3 kg 2 600 g 0,8 kg
6.2 4 500 g 4 kg 4 kg 200 g 4,45 kg
7. Study the table and answer the questions.
Rolene and her mom buy the following ingredients to bake a cake:
7.1 Which ingredients weigh less than 1 kg? ______________________________________________
7.2 Which ingredients weigh more than 2 kg? ____________________________________________
7.3 Which two ingredients weigh 250 g altogether? ______________________________________
7.4 Arrange the masses of the ingredients in ascending order (do not include the orange).
Self-assessment
Do you understand the work? Colour the faces that show what you can do.
SAMPLE
MASS
Requirements Can I do it?
I can determine the mass of practical objects by estimating and measuring.
I know the different measuring instruments and can take readings from them.
I know the units of measurement for mass and can use them.
I can solve problems of mass in context.
I can convert between kilogram and gram.
LESSON 21: WHOLE NUMBERS
Counting, ordering, comparing and representing, and place value of digits (6-digit whole numbers)
This lesson again covers whole numbers. In terms 1 and 2, you studied whole numbers quite comprehensively, but revise lesson 1 if you need to refresh your memory.
Whole numbers do not have fractions or decimals. Whole numbers are always positive and never negative. Remember: 0 is also a whole number.
A set of whole numbers: {0; 1; 2; 3; 4; ...}
You must be able to do the following with whole numbers:
• Count on and back in 2s, 3s, 5s, 10s, 25s, 50s and 100s
• Do calculations with 6-digit numbers (you have not worked with 6-digit numbers before)
• Arrange number sets
• Build and arrange different numbers
• Break down numbers into place values
• Give number names
• Indicate place values
• Use expanded notation (all three methods)
• Compare whole numbers
Do you still remember place value? You studied the place values of 4-digit numbers in lesson 1. In this lesson, we will work with 6-digit numbers.
ACTIVITY 44
DATE:
1. Give the set of whole numbers between 613 546 and 613 553.
2. Are the numbers whole numbers? Only write 'whole number' or 'not a whole number'.
3. Fill in the missing number to complete the number patterns.
3.1 12 232; 12 234; _______________; 12 238
3.2 100 103; 100 100; _______________
3.3 52; 44; 36; _______________; 20
3.4 7; 14; _______________; 28; 35
3.5 102; 204; 408; _______________
3.6 13 770; _______________; 1 530; 510
3.7 45; 225; _______________; 5 625; 28 125
4. Do the calculations to complete the diagrams.
4.1
4.2 42 221 – 20 = _________________________
4.3
5. Arrange the numbers as shown in brackets. (‘Descending’ means from great to small and ‘ascending’ means from small to great.)
6.1 Write the largest number you can make with these digits.
6.2 Write the number name of the number you made in 6.1.
6.3 Write the smallest number you can make with these digits.
6.4 Write the number name of the number you made in 6.3.
7. Study the number:
712 054
7.1 What is the numerical value of the 2? __________________________
7.2 What is the numerical value of the 5? __________________________
7.3 What is the place value of the 0? ___________________________
7.4 What is the place value of the 7? ____________________________
7.5 What is the place value of the 4? ____________________________
7.6 Write the number in expanded notation (in all three methods).
Method 1 Method 2 Method 3
7.7 10 000 less than 421 458 is _________________________________.
7.8 100 more than 421 458 is _________________________________.
7.9 100 000 less than 421 458 is _________________________________.
8. Compare the numbers with <,> or =.
8.1 383 565 ______ 383 656
8.2 945 939 ______ 954 293
8.3 727 989 ______ 721 999
8.4 465 283 ______ 456 283
8.5 103 419 ______ 103 419
9. Morison is planning his birthday party. He compares the prices of food and snacks at a few shops. His favourite chips are chutney flavoured and he finds the following price options:
SAMPLE
chips
(48 × 30 g)
R139,95
(1 × 125 g)
R14,95
9.1 How many packets of Frimax chips are needed to make up 1 packet of Simba chips?
9.2 About how much will 1 packet of Frimax chips cost? Tip: First round off the total amount to the nearest whole number.
Frimax
Simba chips
9.3 Will it be cheaper to buy a few packets of Simba chips or to buy the Frimax chips?
9.4 Which option would you choose? Give a reason for your answer.
Self-assessment
Do you understand the work? Colour the faces that show what you can do.
WHOLE NUMBERS
Requirements
I can count on and back in 2s, 3s, 5s, 10s, 25s, 50s and 100s.
I can work with 6-digit whole numbers.
I can arrange number collections in descending and ascending order.
SAMPLE
I can build and arrange different numbers.
I can break down numbers into place values.
I can give number names.
I can indicate place value.
I can do expanded notation (all three methods).
I can use symbols (<, > or =) to compare whole numbers.
LESSON 22: WHOLE NUMBERS
(Addition and subtraction)
In this lesson you will practise adding and subtracting 5-digit numbers. Revise lesson 3 if you need to refresh your memory.
Make sure you can use these techniques when you do calculations for written work and mental maths:
1. Breaking down numbers
2. Writing numbers underneath one another
3. Writing numbers next to each other
4. Estimation
5. Rounding
6. Compensating
7. Doubling and halving (remember the new method of breaking down numbers)
Also remember that addition and subtraction are inverse operations of one another and you can use the inverse operations to test your answer.
ACTIVITY 45
Addition and subtraction of whole numbers
DATE:
1. Break down the numbers to complete the addition and subtraction sums. Do the sums in your exercise book.
1.1
2. Use any valid method to do the calculations. Test your answers with the inverse operations (and show your test). Do the sums in your exercise book. 2.1
3. Read the word sums, write down the appropriate number sentence and calculate the answer. Do the sums in your exercise book.
3.1 Tiana and Briana find a scale in the garage. The scale measures in pounds (like in America), not kilograms. Tiana’s dad weighs himself on the scale and gets a reading of 194 pounds. Briana and Tiana get on the scale together and it shows a reading of 273 pounds. How many pounds more do Tiana and Briana weigh than Tiana’s dad?
3.2 Ellis sells toffee apples. He makes 12 456 toffee apples to sell in a week. On Monday he sells 1 456. On Tuesday he sells 1 356. On Wednesday and Thursday, he sells an equal number – 2 516 per day – and on Friday he sells 3 002 toffee apples. Does he have enough toffee apples left to sell at least 3 500 on Saturday?
3.3 Kiara and her friends pick up litter on the playground. Kiara picks up 54 pieces of rubbish. Phia picks up 63 pieces, and Riana and Kabelo pick up 59 pieces. Simon also picks up litter. If they collect 297 pieces of rubbish altogether, how many pieces did Simon pick up?
3.4 Thabiso and his brother Samuel are training for cross-country season and follow a specific training programme. The programme recommends that athletes who are not fit yet must do the following: in week 1, run 7 km per day; in week 2, they must run 1 1 2 times the distance per day; in week 3 they must run double as far; and in week 4, double the distance of week 2. How many kilometres did Thabiso and Samuel run in a month if the month had 4 weeks and they trained for 6 days a week?
Estimation
4. Estimate whether you have enough fuel in your car to travel the given distances. Do the sums in your exercise book.
SAMPLE
4.1 From Piketberg to Springbok. You have enough fuel for 420 km.
4.2 From Vanrhynsdorp to Malmesbury. You have enough fuel for 240 km.
4.3 From Keetmanshoop in Namibia to Vanrhynsdorp. You have enough fuel for 650 km.
5. Use estimation to solve the word sums. Do the sums in your exercise book.
5.1 Every day PostNet receives 12 452 parcels to courier. 451 parcels are insured. Determine how many parcels are not insured.
5.2 CJ’s family enjoys camping and visits the Almega campsite in Dinokeng over the weekend. Almega is 71,2 km away. The campsite manager tells them that Mystic Monkeys is not far, so they decide to drive there on Saturday. CJ’s dad resets the car’s odometer and measures the distance from Almega to Mystic Monkeys as 23,7 km. Estimate how far CJ and his family drove from their house and back again over the weekend.
5.3 Andrea wants to buy her friend a gift, but she must buy the essentials on her shopping list:
• Shampoo: R67,00
• Perfume: R675,25
• Jacket: R230,95
• Colour pens: R199,95
She wants to buy her friend a watch:
SAMPLE
If Andrea gets R1 200 pocket money, will she have enough money to buy her friend a gift? Use estimation.
Doubling and halving
6. Double the numbers. You may use any method. Do the sums in your exercise book.
6.1 520 6.4 54 899
6.2 5 625 6.5 63 125
6.3 12 856
7. Halve the numbers. You may use any method. Do the sums in your exercise book.
7.1 15 966
7.3 12 322
Rounding
8. Round the numbers to the nearest 5, 10, 100 and 1 000.
2
• Omvattende verduidelikings van konsepte in eenvoudige taal.
• Praktiese, alledaagse voorbeelde met visuele voorstellings en diagramme wat leerders help om konsepte te bemeester.
• Leerders werk teen hul eie pas.
• Aktiwiteite wat leerders se toepassing van kennis en hul redeneervermoë uitdaag.
• Die fasiliteerdersgids bevat stapvirstapbewerkings en antwoorde.
