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GM 2018
Grade 6 Maths Term 3
Contents Unit 1: Mass ......................................................................................................................... 3
Activity 1.1 - Working with units of mass .......................................................................... 3
Activity 1.2 - Reading scales ............................................................................................ 4
Activity 1.3 - Kilograms (kg) and grams (g) ...................................................................... 5
Activity 1.4 – Reading recipes .......................................................................................... 7
Activity 1.5 - Problem solving ........................................................................................... 7
Unit 2: Whole Numbers - Addition and Subtraction of 6 digit numbers ................................ 8
Activity 2.1 - Whole numbers ............................................................................................ 8
Activity 2.2 - Working with big numbers ............................................................................ 9
Activity 2.3 - Add and subtract ........................................................................................ 10
Activity 2.4 - Round off, estimate and calculate (5 digit numbers) .................................. 11
Addition ....................................................................................................................... 11
Subtraction ................................................................................................................. 11
Unit 3: Addition and Subtraction ........................................................................................ 12
Activity 3.1 - Fun with big numbers................................................................................. 12
Activity 3.2 - Addition of 6 digit numbers ........................................................................ 12
Activity 3.3 - Adding 6 digit numbers .............................................................................. 13
Activity 3.4 - Subtracting 6 digit numbers ....................................................................... 14
Activity 3.5 - Addition and subtraction word problems .................................................... 14
Unit 4: Viewing Objects ...................................................................................................... 15
Activity 4.1 - Views of geometric objects ........................................................................ 15
Activity 4.2 - Stacks of cubes ......................................................................................... 16
Activity 4.3 - Collections of objects ................................................................................. 16
Informal Assessment ......................................................................................................... 17
Unit 5: Properties of 2-D shapes ........................................................................................ 19
Activity 5.1 - Circles ........................................................................................................ 19
Activity 5.2 - Revision of 2-D shapes .............................................................................. 19
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Activity 5.3 - Angles ........................................................................................................ 20
Unit 6: Transformations and Temperature ......................................................................... 21
Activity 6.1 - Translate (slide) ......................................................................................... 21
Activity 6.2 - Reflect (flip) ................................................................................................ 22
Activity 6.3 - Rotate (turn) ............................................................................................... 22
Activity 6.4 - Measuring temperature .............................................................................. 23
Activity 6.5 - Estimating temperature .............................................................................. 24
Unit 7: Percentages ........................................................................................................... 25
Activity 7.1 - Fractions, percentages and decimals ........................................................ 25
Activity 7.2 - Calculating percentages ............................................................................ 29
Informal Assessment ......................................................................................................... 31
Unit 8: Data handling ......................................................................................................... 33
Activity 8.1 - Recording information ................................................................................ 33
Activity 8.2 - Finding the mode and median ................................................................... 34
Activity 8.3 - Data cycle .................................................................................................. 34
Unit 9: Data handling ......................................................................................................... 37
Activity 9.1 - Analysing data ........................................................................................... 37
Informal Assessment ......................................................................................................... 40
Unit 10: Numeric patterns .................................................................................................. 42
Activity 10.1 - Flow diagrams ......................................................................................... 42
Activity 10.2 - Input and output tables ............................................................................ 43
Activity 10.3 - Number sequences .................................................................................. 44
Unit 11: Length .................................................................................................................. 45
Activity 11.1 - Measurement: Units and instruments ...................................................... 45
Activity 11.2 - Estimating and measuring length ............................................................. 46
Activity 11.3 - Length conversions .................................................................................. 46
Activity 11.4 - Kilometres ................................................................................................ 48
Activity 11.4 - Calculating with measurement ................................................................. 49
Informal Assessment ......................................................................................................... 51
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Unit 1: Mass
Activity 1.1 - Working with units of mass 1. Converting and adding.
Copy and complete. a. 1
4kg = ____g b. 500g = ____kg c. 3
4kg = ____g
d. 1kg = ____g e. 11
2kg = ____g f. 2 000g = ____kg
Super Snails Recipe: 750g snails. 100g garlic. 200g cheese. 320g chopped onion. 225g butter 50g chopped parsley. g. What is the total mass of all the ingredients? Write your answer in kilograms. h. What is double the mass of all the ingredients?
Remember: The standard (SI) units used to measure mass are kilograms and grams. I can write kilograms as kg and grams as g.
1 kg = 1 000g
I hope Mr Brown will like my snails. I don’t think the snails will like him.
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2. Increasing kilograms and grams.
a. Convert this pancake recipe for 4 people to a recipe for 6 people. b. Convert this pancake recipe to a recipe for 12 people. c. Convert this recipe to a recipe for 24 people.
Activity 1.2 - Reading scales Each interval line represents 250g or 0,25kg. Each interval line represents 100 g or 0,1kg. Look at the scales on the following page and write the mass indicated by the letters A – Z. Use decimal form. Write just the letter and the mass in your book. Remember to write kg or g after your answers.
250g flour 300mℓ milk 2 eggs 1 pinch salt
5kg 5,25 5,5 5,75 6kg 6,25
5kg 5,1 5,2 5,3 5,4 5,5 5,6 5,7 5,8 5,9 6kg 6,1
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Activity 1.3 - Kilograms (kg) and grams (g) 1. Appropriate units of measurement.
• Choose the correct unit of measurement for each food item. • Write the letter and the best estimate.
A teaspoon holds approximately 5 mℓ.
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2. Calculate the total mass of the groceries. Copy and complete the table. 3. Conversions. Copy and complete the table.
g kg and g kg ≈ kg Example: 1 265g 1kg 265g 1,265kg 1kg a. 7,321kg b. 39kg 18g c 426 d. 14 725 e. 12,514kg f. 8kg 706g g. 13kg 3g h. 20 634 i. 9,016kg 4. Copy and complete the table. Colour the blocks so that their sum equals the amount
in green.
Example: 1kg 300g 0,2kg 0,1kg 250g 350g 450g 500g 550g a. 1kg 250g 0,4kg 150g 50g 0,3kg 550g 0,2kg 100g b. 2kg 0,3kg 500g 50g 700g 0,25kg 150g 0,6kg 100g c. 3kg 1,5kg 400g 350g 500g 0,6kg 0,2kg 300g 0,1 d. 5kg 0,3kg 1kg 0,25kg 2,5kg 300g 600g 0,4kg 200g e. 8kg 3,25kg 500g 2kg 800g 0,75kg 700g 1,5kg 50g
Food g kg peas 410g 0,410 kg jam
margarine cheese
flour sugar
Total mass g kg
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Activity 1.4 – Reading recipes Read the recipes. Each recipe is for 4 people. 1. Which recipe uses the most: a. flour? b. butter? c. sugar? 2. Which recipe uses the least: a. chocolate? b. sugar? c. flour? 3. Rewrite the measurements to make each recipe for twelve people.
Activity 1.5 - Problem solving 1. A shopkeeper sold 15,216kg of flour on Monday, 17, 742kg on
Tuesday and 2,907kg on Wednesday. He took the flour from a 50kg bag. How much flour was left in the bag?
2. A tin of fruit jam has a mass of 440g. There are 48 tins in a box. What will the mass of
the box be? Write your answer as a decimal. 3. Lindi bought a packet of sweets with a mass of 3kg and paid
R30,75. How much would a 2kg bag of sweets cost? 4. A crate of apples has a mass of 56kg. If 3
8 of the apples are bruised, how many kg can
still be sold?
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Unit 2: Whole Numbers - Addition and Subtraction of 6 digit numbers
Activity 2.1 - Whole numbers
1. Copy and complete each number pattern. a. 21 200 19 200 11 200 b. 4 625 5 000 5 500 c. 51 kg 51,2kg 51,8kg d. 7 72
3 75
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e. 4 9 16 2. Write these words as numbers. a. Five hundred and twenty one thousand one hundred and eight. b. One hundred and nineteen thousand six hundred and thirty two. c. Six hundred and forty two thousand one hundred and seventy. d. Eight hundred and seventy three thousand and thirteen. 3. Copy and complete the table. Number. Expanded Notation. The no. in words. Example: 31 504 30 000+ 1 000+ 500+ 4 Thirty one thousand five
hundred and four. a. 210 438 b. 654 773 c. 408 991 d. 61 528 e. 70 006 f. 122 357 g. 842 615 h. 910 227 i. 370 058 j. 127 809 4. What is the place value of the 9 in each of these numbers? a. 946 514 b. 280 379 c. 893 517 d. 149832 e. 106 493 f. 539 782 g. 363 798 h. 698 586
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5. Arrange these numbers from biggest to smallest. a. 19 919 11 999 11 119 19 991 19 199 b. 236 123 263 123 263 321 236 321 263 312 c. 3 450 265 3 540 600 3 500 968 d. 46 238 591 64 328 951 46 500 000 e. 123 567 480 123 657 480 123 756 480 6. Round off to the nearest 5, 10, 100 and 1 000. Copy and complete the table. 5 10 100 1 000 Example: 462 517 462 515 462 520 462 500 463 000 a. 647 128 b. 306 942 c. 227 419 d. 510 834 e. 728 863 7. Use the numbers in the block. Use each digit only once. a. Make the smallest 9 digit number. b. Make the biggest 9 digit number. You can use 1 digit twice. 8. Prime numbers. a. Write down the prime numbers between 10 and 30. b. Write the prime numbers between 50 and 70.
Activity 2.2 - Working with big numbers
8; 7; 0; 3; 5; 6; 1; 2; 4
Millions Hundred Ten Thousands Hundreds Tens Units Thousands Thousands
M HTH TTH TH H T U 3 4 2 5 6 7 9
3 000 000 400 000 20 000 5 000 600 70 9
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Copy and complete the number sentences. 1. a. 905+?=1 000 b. 775+?=1 000 c. 145+?=1 000 d. 575+?=1 000 e. 622+?=1 000 f. 354+?=1 000 2. a. 1 000-?=850 b. 1 000-?=444 c. 1 000-?=175 d. 1 000-?=903 e. 1 000-?=629 f. 1 000-?=347 3. a. 4 550+?=10 000 b. 1 250+?=10 000 c. 5 050+?=10 000 d. 4 005+?=10 000 e. 6 220+?=10 000 f. 7 415+?=10 000 4. a. 10 000-?=1 690 b. 10 000-?=900 c. 10 000-?=4 345 d. 10 000-?=6 825 e. 10 000-?=2 815 f. 10 000-?=5 001 5. A soccer stadium holds 70 000 people. There are 63 875 spectators at the match. How many empty seats are there?
Activity 2.3 - Add and subtract Copy and complete the tables. 1. Number Add 10 Add 100 Add 1 000 Add 10 000 Add 100 000 a. 342 389 b. 476 381 c. 124 123 d. 645 002 e. 137 984 2. Number Subtract 10 Subtract
100 Subtract 1 000
Subtract 10 000
Subtract 100 000
a. 438 982 b. 367 463 c. 428 394 d. 534 005 e. 238 291 3. Word Problems. There were 26 850 pine trees in a forest. A fire destroyed 11 300 trees. How many trees were left? Three new plantations were planted with 12 940, 10 635 and 15 384 trees. How many new pine trees were planted altogether?
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Activity 2.4 - Round off, estimate and calculate (5 digit numbers) Addition Use the examples below to complete each addition calculation. Number 13 841 + 25 634 = ? nearest 10 13 840 + 25 630 = 39 470 nearest 100 13 800 + 25 700 = 39 500 nearest 1 000 14 000 + 26 000 = 40 000 Work out 13 841
+ 25 634 39 475
1. a. 25 163 + 16 249 b. 25 827 + 16 254 c. 15 936 + 17 485 d. 32 464 + 19 876 e. 16 735 + 12 849 f. 26 351 + 32 986 Subtraction Use the examples below to complete each subtraction calculation. Number 65 738 – 23 465 nearest 10 65 740 – 28 470 = 37 270 nearest 100 65 700 – 28 500 = 37 200 nearest 1 000 66 000 – 28 000 = 38 000 Work out 65 738
- 28 465 37 273
2. a. 93 265 – 38 516 b. 77 390 – 38 426 c. 51 876 – 37 499 d. 84 912 – 36 451 e. 63 257 – 46 189 f. 70 532 – 36 472
The easiest way to estimate an answer is to round off each number to the nearest 10, 100, 1 000, 10 000 or 100 000…
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Unit 3: Addition and Subtraction
Activity 3.1 - Fun with big numbers 1. Write each number in expanded notation and in words.
a. 756 893 b. 93 089 c. 40 312 40 000+ 300 + 10 + 2 d. 270 001 e. 598 304 Five hundred and ninety eight
thousand three hundred and four. f. 160 244 g. 350 025 h. 32 381 i. 22 990 j. 100 304 2. Write the number sentences. Example: 29 576 – 10 000 = 19 576. How quickly can you do these? 4. a. Add 45 000 and 17 000 5. a. Decrease 62 000 by 13 000 b. Subtract 15 500 from 100 000 b. Increase 28 000 by 18 000 c. 12 500 plus 7 500 c. Subtract 86 400 from 100 000 d. The sum of 75 000 and 28 000 d. The sum of 37 400 and 12 800 e. Take 12 500 from 40 000. e. Round off 749 500 to nearest 100 000
Activity 3.2 - Addition of 6 digit numbers 6 digit numbers are very large numbers and it is important to write them correctly.
25 678 3 492 50 261 3 970 26 000 4 732
3. 29 576 30 000 17 250 45 000 10 000 54 000
+ 1 500 - 3 000 - 10 000 + 7 000
M HTH TTH TH H T U 4 6 8 3 5 2 7
Always leave a gap between millions and hundred thousands.
Always leave a gap between thousands and hundreds.
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1. Write the numbers like the example given below. Remember to leave gaps in the correct places.
a. two million four hundred and eighty seven. b. five million two hundred thousand and fifty. c. one million fifty five thousand two hundred and forty. d. eight million three hundred and twenty one thousand and six. e. six million twenty one thousand and nine. 2. a. 594 000 + ? = 1 000 000 b. 470 000 + ? = 1 000 000 c. 120 000 + ? = 1 000 000 d. 35 000 + ? = 1 000 000 e. 990 000 + ? = 1 000 000 f. 99 000 + ? = 1 000 000 3.
Activity 3.3 - Adding 6 digit numbers
To which hundred thousand is each number closest?
Example: Four million three hundred and seven thousand and forty two.
4 307 042 = 4 000 000 + 300 000 + 7 000 + 40 + 2
Drawing columns with the headings M, HTH, TTH, TH, H, T and U might help you.
550 000 +100 000 +10 000 +50 000
+ 15 000 +100 000 +60 000 + 5 000
100 000 200 000 300 000 400 000 500 000 600 000 700 000 800 000 900 000
a. 321 645 b. 550 000 c. 680 492
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a. 321 645 is closer to 300 000 than 400 000. 321 645 ≈ 300 000. b. 550 000 is halfway between 500 000 and 600 000. 550 000 ≈ 600 000. c. 680 492 is closer to 700 000 than 600 000. 680 492 ≈ 700 000. 1. Round off each number to the nearest 100 000. a. 163 290 b. 745 384 c. 450 000 d. 780 621 2. Look at the example below and then complete each addition calculation. Number Nearest 100 000 Work out 348 125 + 392 408 300 000 + 400 000 = 700 000 348 125
+ 892 408 1 240 533
a. 326 184 + 139 206 b. 456 789 + 235 610 c. 292 611 + 491 302 d. 356 249 + 351 924 e. 332 819 + 256 030 f. 293 128 + 423 605 g. 130 495 + 502 319 h. 506 311 + 279 832 i. 712 389 + 113 042
Activity 3.4 - Subtracting 6 digit numbers Look at the example below and complete each subtraction calculation. Number. Round off to nearest
100 000. Work out. Check with inverse
operation. 896 423 – 348 594 900 000 – 300 000 =
600 000 896 423 - 348 594 547 829
547 829 + 348 594 896 423
a. 946 392 – 328 564 b. 354 786 – 215 558 c. 875 321 – 564 290 d. 873 475 – 345 129 e. 878 578 – 657 494 f. 678 578 – 465 594 g. 267 328 – 242 218 h. 345 945 – 132 684 i. 987 475 – 545 129
Activity 3.5 - Addition and subtraction word problems
1. The Sibisi family bought a house for R532 500. They paid a deposit of R145 200. How much do they still owe?
2. What is the difference between R400 000 and the sum of 238 590 and R106 250?
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3. A shoe factory produced 152 480 pairs of black school shoes and 107 240 pairs of brown school shoes. How many pairs of shoes did they produce altogether? Write an interesting word problem of your own for: 375 412 and 654 321. Solve the problem.
Unit 4: Viewing Objects
Activity 4.1 - Views of geometric objects 1. Draw the shape you will see from the view indicated.
Remember, objects can be viewed from the side….
or from above…
or from in front/back of the object.
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Activity 4.2 - Stacks of cubes 1. Draw the top, front and side views of each stack.
Activity 4.3 - Collections of objects
We drew this stack of blocks looking at it from the side, front and top…
…and this is what we drew…
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1. Identify whether the view is from the side, top or front. Write only the letter and the correct view.
Informal Assessment Mass
1. Copy and complete the table. 2.
g kg and g kg ≈ nearest kg a. 2 581 g b. 6,273 kg c. 13kg 91g d. 6 045g e. 20,036kg 2. Solve the word problems. a. A book has a mass of 363g. What will the mass of 12 books be? b. A shop sells potatoes at a cost of R9,50 a kg. How much did Dad pay if he bought 8 kg? Whole numbers 3. Copy and complete the number patterns. a. 8 875; 9 000; ____; ____; 9 375; ____; ____; ____ b. 67,8; 67,6; ____; 67,2; ____; ____; ____; ____
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4. Ordering: Arrange the numbers from biggest to smallest: Underline the even numbers in green and the odd numbers in blue. 5. Copy and complete the table.
Number Expanded notation No. in words. a. 257 106 b. 738 994 c. 605 281 6. Round off. Copy and complete the table.
≈ 5 ≈ 10 ≈ 100 ≈ 1 000 a. 132 673 b. 915 846 c. 206 712 Addition and subtraction 7. Copy and complete the number sentences. a. 618 + ? = 1 000 b. 1 000 - ? = 555 c. 5 500 + ? = 10 000 d. 10 000 - ? = 2 750 e. 585 000 + ? = 1 000 000 f. 1 000 000 – 45 000 = ? 8. Add. Check your answer by using subtraction. a. 85 748 + 27 695 b. 77 345 + 18 426 c. 332 819 + 256 076 d. 712 369 + 213 054 Viewing objects 9. Draw the top, side and front view of the stack of cubes below.
626 226 662 226 626 662 626 262 662 626 662 622
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10. Match each picture with the correct view. Write only the letter and the correct view.
Unit 5: Properties of 2-D shapes
Activity 5.1 - Circles A circle is a 2-D closed shape. The circumference is always the same distance from the centre.
circumference is the distance around a circle.
diameter is a line segment that connects 2 points on the circumference and passes
through the centre. radius is a line segment from the centre
of the circle to any point on the circumference.
1. Draw and label circles in your book.
a. Measure a length of 3 cm on your ruler with your pair of compasses. Now draw a circle with a radius of 3 cm. Fill in the labels circumference, radius, centre and diameter.
b. Draw circles with a radius of: a. 4 cm b. 4,7 cm c. 5,2 cm d. 3,6 cm
Activity 5.2 - Revision of 2-D shapes 1. Use your knowledge of 2-D shapes to label each shape.
circumference
Radius Centre
diam
eter
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2. Draw 2 columns in your book and write True and False at the top. Write only the letters a to j and next to each letter write whether the statements are True or False. Statement True False a. The opposite sides of a square are equal in length. b. A triangle can have 2 sides of equal length. c. A circle has only 1 side. d. The distance from the centre of a circle to the
circumference of a circle is not always the same.
e. A triangle can have 2 right angles. f. A parallelogram has opposite sides equal and parallel. g. A pentagon has 7 straight sides. h. A rectangle is a quadrilateral. i. A circle is twice as big as a semi-circle. j. A circle can have more than 1 centre.
Activity 5.3 - Angles The angle between 2 lines is how much you have turned 1 of the lines. 1. Label these angles, using the correct angle names.
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Unit 6: Transformations and Temperature Transforming a shape or object means changing its appearance by moving it. We have names for the different ways we move shapes. Translation (slide) Reflection (flip) Rotation (turn)
Activity 6.1 - Translate (slide) Translation is when a shape slides from 1 place to another without rotating or flipping over. Example: The rectangle has moved 4 squares to the right. 1. Look at the patterns below and complete the sentences.
- - - - - - - -
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Activity 6.2 - Reflect (flip) Reflection is a mirror image of a shape or object. The shape or object is flipped equally over a line of symmetry. 1. Copy the shape onto square paper. Draw the line of symmetry (reflection line) of each pair of shapes.
Activity 6.3 - Rotate (turn) Rotation is when a shape is turned around a fixed point. Look at this example.
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1. Say if the following shapes have a half turn or quarter turn. a. b. 2. Describe the rotation of each picture.
Activity 6.4 - Measuring temperature
The metric unit for measuring temperature is degrees Celcius (°C). These are analogue thermometers. The temperature is marked on the thermometer and the liquid inside the tube expands when the temperature rises. A comfortable body temperature for humans is 37 °C. This is an example of a digital thermometer. The temperature is shown in numbers/digits. The temperature reading is taken by sensors that are sometimes made out of metal wires.
a. b. c. d.
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Copy and complete. 1. a. Based on temperature, _______ is very ill. b. Based on temperature, ________ is healthy. c. Based on temperature, ________ is getting better. d. Write down 3 temperatures that children may have when they are not feeling well. Write the temperatures from lowest to highest. 2. a. The classroom is 7,4 °C warmer than the playground. It is 13,5 °C inside the What is the temperature outside? b. Yesterday it was 14,3 °C outside. It has dropped 5 °C today. What is the temperature today?
Activity 6.5 - Estimating temperature 1. Choose the correct temperature.
a. normal body temperature 25 °C 32°C 37°C b. hot coffee 40 °C 80 °C 110 °C c. boiling water 60 °C 100 °C 80°C d. bath water 10 °C 40 °C 80 °C e. ice lolly 10°C 0 °C 20 °C f. sick child 39 °C 37 °C 42 °C g. inside a refrigerator 5°C 20 °C 30 °C h. hot oven for baking 180 °C 100 °C 250 °C i. cold winter day 25 °C 18 °C 12 °C j. hot summer day 10 °C 15 °C 30°C
Jack George Siya
39,8°C 37°C 38,1°C
0 °C: ice 10 °C cold 20 °C: warm 30 °C: hot
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2. Write each temperature and the season you think it represents.
Unit 7: Percentages Percentage means “per hundred”. Percentage is a fraction and the denominator is always 100.
Activity 7.1 - Fractions, percentages and decimals 1. Write the fraction and percentage of each blue area. Write the fraction and percentage of each red area. Example:
1 whole = 100% 35100
= 35% 10100
= 10% 25100
= 25% 7100
= 7%
blue: 96100
= 96% red: 4
100 = 4%
summer autumn
winter
spring
Challenge
3. a. The temperature rises by 4 °C from -2 °C. What is the new temperature? b. The temperature has fallen from 10 °c to -5°C. How far has it fallen?
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2. Copy and complete the table. Percentage Fraction Decimal Example: 20% 20
100 0,20
a. 35% b. 82% c. 18% d. 44% e. 67% f. 73% g. 99% 3.
b. c.
d.
1 whole = 100%
14
12 3
4
25% 50% 75% 100%
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Copy and complete. Example: 100% means all of the whole. a. ____ means 1
2 of the whole.
b. 25% means ____ of the whole. c. ____ means 3
4 of the whole.
4. Copy and complete. a. 10% means ____ of the whole. b. 30% means ____ of the whole. c. ____ means 7
10 of the whole.
d. ____ means all of the whole. 5. Write the fraction and percentage of each blue shaded area. Write the fraction and percentage of each red shaded area. Example:
110
210
310
410
510
610
710
810
910
1010
10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
610
= 60100
= 60% 410
= 40100
= 40%
a.
b.
c.
d.
e.
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7. Copy and complete the table.
fraction tenths hundredths percent decimal Example: 3
5
610
60
100 60% 0,60
a. 12
b. 15
c. 35
d. 45
8. Copy and complete the table.
fraction hundredths percent decimal Example: 2
20
10100
10% 0,10
a. 14
b. 150
c. 125
d. 34
9. Write the fraction, percentage and decimal for the shaded areas. 10. Match the fractions, percentages and decimals. Write them in your book.
Fractions Percentages Decimals 12 1
4 1
5 2
5 1
20 45 3
4 3
5 125
20% 60% 75% 5% 50% 4% 25% 80% 40%
0,8 0,25 0,04 0,75 0,6 0,4 0,05 0,2 0,5
a.
Fraction: Percentage: Decimal:
b. Fraction; Percentage: Decimal:
c. Fraction: Percentage: Decimal:
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Activity 7.2 - Calculating percentages
1. Copy and complete.
a. 50% of R1= b. 25% of R1= c. 75% of R1= d. 100% of R1= e. 20% of R1= f. 40% of R1= g. 60% of R1= h. 80% of R1= 2. Copy and complete the table. Item Cost Discount sale price Example: radio R300 20% / 1
5 of R300
= R60
R300- R60= R240
a. soccer ball b. tennis racket c. paint d. T-shirt e. chocolates f. watch
How do I calculate 50% of R1?
You know that 50% = 12 so half of 100c is 50c.
How do I calculate 25% of R1?
25%= 25
100 = 1
4.
14 of 100c = 100c ÷ 4 = 25c.
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3. Copy and complete.
percentage fraction fraction in simplest form
Example: 10% 10100
1
10
a. 20% b. 25% c. 30% d. 40% e. 50% f. 60% g. 70% h. 75% i. 80% j. 90% 4. Copy and complete. a. 25% of R260= b. 75% of R100 c. 50% of R600= d. 75% of R40= e. 10% of R65= f. 50% of R400= g. 20% of R50= h. 10% of R220= i. 10% of R250= j. 25% of R16= 5. Solve these word problems.
There are 120 learners in Grade 6. a. 25% of the learners are boys. How many learners are boys? How many learners are girls? b. 20% of the learners are absent from school because of a bus strike. How many learners were present? How many learners were absent? c. 60% of the learners are in the school choir. How many learners are in the choir? d. 10% of the learners play in soccer matches on a Wednesday. How many learners play in soccer matches?
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Informal Assessment 1. Transformations Look at the patterns below. Describe the pattern.
2. Describe the rotation of each picture. a. b. c. 3. 2-D shapes. Write the name of each 2-D shape. a. b. c. d. e. f. g. h. i.
a. b.
c.
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4. Name the angles.
5. Temperature Choose the correct temperature. a. Normal body temperature 35°C 37°C 39°C b. Bath water 10°C 40°C 80°C c. Cold winter day 12°C 20°C 30°C d. Hot oven for baking 90°C 180°C 280°C 6. The classroom temperature is 4,6°C warmer than outside. It is 16,8°C inside the classroom. What is the temperature outside? 7. Percentages Write the fraction and percentage of the shaded area of each block.
8. Copy and complete the table. fraction hundredths percent decimal a. 1
4
b. 25
c. 420
a. b.
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9. Work out: a. 25% of R200 b. 10% of R45 c. 50% of R118 d. 75% of 500 10. There are 120 Grade 6 learners. 15% of the learners are absent from school because of the flu. How many learners were absent?
Unit 8: Data handling
Activity 8.1 - Recording information Can you remember the 3 important headings to be used when creating a tally? 1. Tally marks. Copy and complete the tally chart to record the information shown in the table. Key: Yes No x Do you have
a sister? Are you a boy?
Do you like apples?
Do you like to read?
Do you enjoy sport?
Lizzy x x x Sipho x x Vuyo x x Lindi x x Joe x x Zorno x x Jill x Billy x Patricia x x Thabo x How are you going to set out your tally? Tally marks Total Have a sister Am a boy Like apples Like to read Enjoy sport Use the above information to answer the following questions: a. How many of the children are girls? b. How many of the children do not like apples? c. How many of the children like to read AND enjoy sport? d. How many of the children do not have a sister?
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Activity 8.2 - Finding the mode and median Always remember to put the numbers in order before finding the mode and median. 1. Find the mode and the median of these numbers. a. 17 28 83 70 28 61 48 28 61 13 51 ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ Mode: ____ Median: ____ b. 651 946 535 946 374 203 171 946 535 152 213 ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ Mode: ____ Median: ____ 2. Mass of 35 children in kilograms. Find the mode and the median. ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ Mode: ____ Median: ____
Activity 8.3 - Data cycle The data cycle steps: 1. Ask a question. 2. Collect and organise data. 3. Represent data. 4. Analyse and interpret data. 5. Report on data.
This list of numbers is not in order: 11 13 9 8 15 13 6 8 11 13 7 This is the same list of numbers, in order: 6 7 8 8 9 11 11 13 13 13 15
Mode: the number which appears the most = 13 Median: the number which is in the middle of the list = 11
52 54 55 48 58 55 52 55 58 53 52 54 55 50 55 52 53 50 55 55 54 54 48 53 52 53 52 58 52 58 55 52 54 55 50
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GM 2018
1. Ask a question: 2. Collect and organise data:
• Interview 25 learners. • Each learner may only choose one type of fruit shown above. • Draw up a tally chart to show which fruits are chosen. • Record the choices under boys and girls.
Example: Type of fruit Tally marks Total apples boys
girls bananas boys
girls oranges boys
girls pears boys
girls grapes boys
girls 3. Represent the data: a. Use your data to draw a pictograph. Set out your pictograph like this: Type of fruit No. of boys No. of girls Total apples bananas oranges pears grapes Key: = 2 learners. b. Use your data to draw a double bar graph.
!!! Besides the bars themselves, remember to fill in the other 5 pieces of
information !!!
I want to find out which fruit is the most popular amongst the learners in my class.
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GM 2018
Set out your double bar graph like this:
Key: Boys Girls 4. Analyse and interpret the data: Look at your double bar graph and answer the following questions:
a. Which type of fruit was most popular amongst the boys? b. Which type of fruit was least popular amongst the girls? c. How many learners altogether liked apples the most? d. How many learners altogether liked grapes the most? e. How many more learners chose apples over oranges? f. Which type of fruit was the mode amongst the learners? g. Predict which type of fruit would be most popular if you interviewed 300 learners.
Give a reason for your answer. h. If the school tuckshop sold apples for 50c each, how much money would they
collect? 5. Report on your data: Write a paragraph on your data using the answers to the questions above. Set out your paragraph like this:
The ____ was the most popular type of fruit amongst the boys. Amongst the girls, ____ was the least popular fruit. ____ learners liked apples the most and ____ learners liked grapes the most. ____ learners preferred apples to oranges. The type of fruit which was the mode was ____. I think the most popular type of fruit if I interviewed 300 learners would be ____ because _________________ ____________________________. The tuckshop would collect ____ if they sold apples to all the learners who liked them best.
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GM 2018
Unit 9: Data handling
Activity 9.1 - Analysing data 1. A double bar graph.
Look at the double bar graph showing rainfall in Durban and Cape Town and answer the questions. a. In which month does Durban
have the most rain? b. In which month does Cape
Town have the most rain? c. In which month does Durban
have the least rain? d. In which month does Cape Town have the least rain? e. Is Durban in a winter or summer rainfall region? Give a reason for your answer. f. Is Cape Town in a winter or summer rainfall region? Give a reason for your answer. g. Which city has the highest annual rainfall? h. What is the difference in the rainfall in March for these two cities? i. What is the difference in the rainfall in December for these two cities? j. Predict which city would have the most rain in May the following year. Why? k. What is the total annual rainfall for:
• Cape Town? • Durban?
2. Look at the double bar graph showing cars passing my school and then answer the questions. a. On which day is the traffic the
heaviest in the morning? b. On which day is the traffic the
heaviest at lunch time? c. On which day is the traffic the
lightest in the morning? d. On which day is the traffic the
lightest at lunch time? e. How many more cars are
there on a Monday morning than later on in the day?
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GM 2018
f. How many more cars were counted on Wednesday morning than on Tuesday morning?
g. How many cars were counted in the mornings? h. How many cars were counted at lunch time? i. What is the total number of cars counted in the week? j. Predict when you think the most number of cars would be counted in the following
week. Give a reason for your answer. k. Why do you think there are fewer cars counted at lunch time than early in the
morning? l. Give a reason for your answer.
3. A pie chart: Farming. Look at the pie chart and then answer the questions.
The pie chart shows how Sizwe has divided the land on his farm. He uses his farm to grow crops and he keeps a few goats.
a. What percentage of the land is used to:
• grow mealies? • grow wheat? • grow apples? • grow potatoes? • farm goats?
b. What fraction of the land is used to farm goats? c. What fraction of the land is used to grow crops? d. If Sizwe’s farm is 4 000m , how many m does he use for:
• the goats? • the mealies? • all the crops together?
e. Do you think Sizwe makes more money from selling his mealies or his potatoes? Give a reason for your answer. f. If Sizwe decided to stop growing apples and planted more wheat, what percentage of his land would he then use for wheat?
2 2
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GM 2018
4. A pie chart: population. Look at the pie chart and answer the questions. This pie chart shows how many people live in each province in South Africa.
a. What percentage of the population lives in:
• KwaZulu Natal? • Northern Cape?
b. Which province has the highest population? Why do you think so many people live there? c. Why do you think so few people live in the Northern Cape? d. Which 3 provinces have a similar population? e. What percentage of our population lives in the Northern Cape, Western Cape, Eastern Cape and KwaZulu Natal altogether? f. If the total population is 50 million, approximately how many people live in:
• Limpopo, Free State, Northern Cape and North West altogether? • Western Cape and Eastern Cape altogether? • KwaZulu Natal?
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GM 2018
Informal Assessment A project: The Weather data cycle. 1. Ask a question:
2. Collect and organise data:
• Use these symbols to record your data.
• Only record one weather condition on a day. • Copy and complete the weather calendar.
My weather calendar for 4 weeks.
Mon Tues Wed Thurs Fri Sat Sun Week 1 Week 2 Week 3 Week 4
3. Represent data: Use the data from your calendar page to complete the tally chart. Example: Weather condition No. of days Total
I want to find out how many rainy, cloudy, sunny and windy days there are in 4 weeks.
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GM 2018
Now, use your data to draw a bar graph: -------------------------------------------------------- 4. Analyse and interpret the data: Write 6 questions and their answers from the data represented on your graph. 5. Report on your data:
Use the answers to your questions to write a paragraph summarising the data you have collected.
20 18 16 14 12 10 8 6 4 2 0
------
------
------
------
------
------
---
---------------------------------------------------
Remember to fill in your heading and label the axes.
Example: • How many rainy days were there in 4 weeks? • What was the most common weather condition over
the 4 weeks? • Which week had the most sunny days?
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GM 2018
Unit 10: Numeric patterns
Activity 10.1 - Flow diagrams What does numeric mean? …Numeric means number. 1. Write the correct rule for each flow diagram. 2. These flow diagrams have a 2 stage rule. Write the correct rule for each diagram.
6 8 10 12 20 30
120 160 200 240 400 600
15 30 45 60 75 90
30 45 60 75 90 105
108 90 72 54 36 18
99 81 63 45 27 9
200 400 450 550 700 1 000
4 8 9 11 14 20
? ?
? ?
a. b.
c. d.
Rule: ____ Rule: ____
Rule: ____ Rule: ____
2 3 4 7 9 12
X 7
25 32 39 60 74 95
20 50 75 100 125 150
44 69 94 119 144 169
+ 25
100 90 80 70 60 50
20 18 16 14 12 10
10 20 30 40 50 60
20 30 40 50 60 70
÷ 10 - 10
a. b.
c. d.
?
? ?
? Rule: ____ Rule: ____
Rule: ____ Rule: ____
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GM 2018
3. These flow diagrams have a 2 stage rule and both rules have been left out. Write the correct rules for each flow diagram.
Activity 10.2 - Input and output tables We can also write numeric patterns as an input and output table. 1. Copy and complete each table and write the rule. input 1 2 3 4 5 6 7 8 9 10 output 12 24 Rule: ____ input 1 2 3 4 5 6 7 8 9 10 output 17 34 Rule: ____ input 1 2 3 4 5 6 7 8 9 10 output 2,5 3,5 4,5 Rule: ____ input 10 20 30 40 50 60 70 80 90 100 output 3 13 23 Rule: ____
Try this! 7 8 9
X 5 X 10 35 000 40 000 45 000 ?
10 20 30 40 50 60
100 200 300 400 500 600
2 4 6 8 10 12
1 3 5 7 9 11
a. b.
? ? ? ?
a.
b.
c.
d.
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GM 2018
input 1 2 3 4 5 6 7 8 9 10 output
12 1 11
2
Rule: ____ The rule for this table has 2 operations. Find the rules. input 1 2 3 4 5 6 7 8 9 10 output 21
2 41
2 61
2 81
2
Rule: ____
Activity 10.3 - Number sequences 1. Copy and complete each number sequence and write the rule. 187 200 213 343 Rule: ____ 589 564 539 264 Rule: ____ 1; 6; 3; 8; 5; 10; 7; ___; ___; ___; ___; ___ Rule: ____ 6 400; 3 200; 1 600; 800; ___; ___; ___; ___;___; ___; ___ Rule: ____ 2; 4; 8; 16; ___; ___; ___; ___; ___; ___; ___; ___ Rule: ____ 8; 24; 72; 216; ___; ___; ___; ___: ___: ___; ___ Rule: ____
e.
f.
a.
b.
c.
d.
e.
f.
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GM 2018
Unit 11: Length
Activity 11.1 - Measurement: Units and instruments 2. What unit of measurement would you use to measure the following? Say whether you would measure in kilometres, metres centimetres or millimetres.
1 centimetre = 10 millimetres (mm) 1 metre = 100 centimetres (cm) 1 metre = 1 000 millimetres (mm) 1 kilometre = 1 000 metres (m)
1. a. Convert to cm: 1
2m 1
4m 1
10m
b. Convert to m: 1
2km 1
4km 1
10km
c. Convert to mm: 1 cm 1
2cm
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GM 2018
Activity 11.2 - Estimating and measuring length
1. Choose the correct measurement.
2. Estimate and then measure the following.
Activity 11.3 - Length conversions
I must remember these!
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GM 2018
1m = 100cm 1m = 1 000mm 1cm = 10mm 12m = 50cm 1
2m = 500mm 1
2cm = 5mm
14m = 25cm 1
4m = 250mm 1
4cm = 2,5mm
15m = 20cm 1
5m = 200mm 1
5cm = 2mm
110
m = 10cm 110
m = 100mm 110
cm = 1mm 1. Copy and complete the table.
metres (m) centimetres
(cm) millimetres (mm)
metres and centimetres
Example: 1,75 175 1 750 1m 75cm a. 5 250 b. 3m 82cm c. 24,25 d. 724 e. 5m 10cm f. 2 000 g. 18,50 h. 405 2. The mothers at Pendla Primary are making a big school flag. They buy: 1
4m red
material, 118m black material, 11
8m yellow material and 3
4m green material. How many
metres and centimetres of material did they buy altogether? 3. Nomfundo uses 21
5m of rope to make a basket. How many metres of rope will she need
to make 22 baskets?
I must remember this!
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GM 2018
Activity 11.4 - Kilometres
Kilometres are used to measure long distances.
1. Look at the table below and calculate the distances. places km m Example: East London to
Cape Town 1 042 1 042 000
a. Nelspruit to Pretoria b. Johannesburg to
Port Elizabeth
c. Windhoek to Bloemfontein
d. Durban to East London
2. The Singing Brothers tour of South Africa. a. Calculate the distance The Singing Brothers travel on their tour of South Africa. The route they travelled is: Cape Town George Port Elizabeth East London Durban Bloemfontein Johannesburg Cape Town. b. How much is this less than 10 000km?
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GM 2018
Activity 11.4 - Calculating with measurement The Grade Six group held a long jump competition. These were the longest distances jumped. 1. Write these distances from shortest to longest.
a. b. c. 2. Copy and complete. a. 5m + 30cm + 7mm = ____m b. Double 99cm = ____m ____cm c. 450cm x 4 = ____m ____cm d. 31
4km + 41
2km + 1 1
10km = ____km
e. 90mm + 80cm + 40m = ____mm f. 50m – 300cm = ____m 3. Estimate and then measure the length of the lightning flash in mm.
4. A long distance truck driver travels from Pretoria to Cape Town. Each trip is 1 463km long. He has made 124 trips. What distance has he travelled altogether?
5. The distance to work and back is 124km. If I have travelled 7 440km, how many trips have I made?
6. I rent a car and travel 2 480km. a. How many km must I pay for? b. If I pay R2,50 per km, how much do I pay?
3,67m 3,07m 3,70m
3,49m 3,06m 3,60m
3,50m 3,05m 3,69m
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GM 2018
Mental Maths with Vocabulary.
1.1. How many grams in 21
2kg ?
2. Round off 728 863 to the nearest 10. 3. Write the first 5 multiples of 7. 4. A half circle is called a ____. 5. Normal body temperature is about ____. 6.What is the total of 0,45kg and 1,8kg ? 7. One fifth of R300 = ____. 8. What is the median: 10; 11; 12; 13; 15 ? 2.1. 10 000 less than 500 000 = ____. 2. Write 408 991 in expanded notation. 3. Write all the factors of 20. 4. Write 39m 18cm as centimetres. 5. Write 20% as a common fraction. 6. Write 910 227 in words. 7. 40% of R1 = ____c. 8. Round off 728 863 to the nearest 100. 3.1. Three eighths of 56m = ___. 2. Write all the factors of 18. 3. 100 000 more than 238 691 is ____. 4. Write the place value of the 7 in 35,74. 5. Divide 6 000 by 100. 6. Write the next 3 numbers: 1; 5; 10; 16. 7. One quarter of R180 = ____. 8. Round off 728 863 to the nearest 1 000. 4.1. How many twelves in 108? 2. The boiling point of water is ____. 3. Write half as a percentage. 4. Twenty percent of R50 = ____. 5. 50 divided by 7. What is the remainder? 6. Write seven multiples of nine after eighteen. 7. Write three hundredths as a decimal. 8. The smallest angle is a(n) ____. 5.1. A tin of baked beans has a mass of: 450g; 450kg or 45g ? 2. Write the number seventy thousand and six. 3. Write the smallest six digit number using a 2; 6; 8; 0; 5; 7. 4. The distance around the outside of a circle is called the ____. 5. Write from heaviest to lightest: 1
2kg; 100g; 250g; 1
5kg.
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GM 2018
6. True or false: a circle has only one side. 7. A number multiplied by nine gives seventy two. What is the number? 8. What is the value of the underlined digits in 23 567. 9. Write the next four numbers.
Informal Assessment 1. Data handling. Study the bar graph and answer the questions.
a. How many learners were surveyed? b. Which career is most popular? c. Which career is least popular? d. What is the difference between the number of learners who want to be doctors and the number who want to be athletes? 2. Find the mode and the median of the following numbers: 12; 16; 22; 12; 8; 12; 16; 13; 15; 12; 19; 16; 12; 11; 10; 9; 12 3. Numeric patterns. Write the correct rule for each flow diagram.
12ℓ 1ℓ 11
2ℓ
1 3 5 7 9 11
9 27 45 63 81 99
30 60 90 120 150 180
18 28 38 48 58 69
a. b.
÷ 3
Rule: ____ Rule: ____
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GM 2018
3. Copy and complete.
input 1 2 3 4 5 6 7 8 9 10 output 15 30 45 150 Rule: ____ 4. Copy and complete.
2; 6; 18; 54; ____; ____; ____; ____; ____; ____ Rule: ____. 5. Length. Copy and complete the table.
m cm mm m and cm a. 25,25 b. 410 c. 3 000 d. 6m 20cm 6. Word problems. The teacher bought material to school to make costumes for the concert. She bought: 21
4m of blue material
312m of yellow material
118m of red material and
34m of green material.
How many metres and centimetres of material did she buy altogether? 7. Use Table 1 to calculate the distances
a. Bloemfontein to Durban. b. Kimberley to Cape Town. c. Johannesburg to Beaufort West. d. On holiday, John travelled from Colesburg to Beaufort West to Cape Town to Mossel
Bay to East London and back to Colesburg. e. How many km did John travel altogether?
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GM 2018
Table 1
