Í2(È-E-MAM-SG01OÎ

1

8

0

5

-

E

-

M

A

M

-

S

G

0

1

MATHEMATICS STUDY GUIDE 1/2 Grade 5

A member of the FUTURELEARN group

Mathematics Study guide 1/2

1805-E-MAM-SG01

Í2%È-E-MAM-SG01IÎ

CAPS aligned

Study Guide 1/2 G05 ~ Mathematics

CONTENTS YEAR PLAN ....................................................................................................5 LESSON ELEMENTS ......................................................................................7 UNIT 1 ..............................................................................................................9 Lesson 1: Where do numbers and digits come from? ...............................9 Lesson 2: Place values ................................................................................11 Mental maths ...................................................................................12 Activity 2.1 ................................................................................................13 Activity 2.2 ................................................................................................16 Lesson 3: Introduction to ten thousands ..................................................18 Mental maths ...................................................................................19 Activity 3.1 ................................................................................................20 Activity 3.2 ................................................................................................22 Lesson 4: Numbers greater than ten thousands ......................................23 Mental maths ...................................................................................24 Activity 4.1 ................................................................................................25 Activity 4.2 ................................................................................................27 Activity 4.3 ................................................................................................30 Lesson 5: Expanded notation .....................................................................36 Mental maths .................................................................................................37 Activity 5.1 ................................................................................................38 Lesson 6: Comparing, arranging and rounding numbers ........................40 Mental maths ...................................................................................41 Activity 6.1 ................................................................................................42 Activity 6.2 ................................................................................................45 Lesson 7: Multiples ......................................................................................46 Activity 7.1 ................................................................................................46 Activity 7.2 ................................................................................................48 Lesson 8: Adding and subtracting .............................................................51 Mental maths ...................................................................................51 Activity 8.1 ................................................................................................52 Activity 8.2 ................................................................................................53 Mental maths ...................................................................................55 Activity 8.3 ................................................................................................56 Activity 8.4 ................................................................................................57 Lesson 9: Money ..........................................................................................58 Mental maths ...................................................................................58 1

ÂŠ Impaq

Study Guide 1/2 G05 ~ Mathematics

Activity 9.1 ................................................................................................59 Activity 9.2 ................................................................................................60 Revision test ....................................................................................62 Lesson 10: Multiplication ............................................................................66 Mental maths ...................................................................................67 Activity 10.1 ..............................................................................................68 Activity 10.2 ..............................................................................................72 Activity 10.3 ..............................................................................................74 Activity 10.4 ..............................................................................................76 Activity 10.5 ..............................................................................................78 Lesson 11: Division .....................................................................................81 Activity 11.1 ..............................................................................................82 Lesson 12: Division .....................................................................................86 Mental maths ...................................................................................86 Activity 12.1 ..............................................................................................87 Activity 12.2 ..............................................................................................94 Lesson 13: Fun patterns .............................................................................95 Activity 13.1 ..............................................................................................95 Activity 13.2 ..............................................................................................96 Activity 13.3 ..............................................................................................97 Lesson 14: Special patterns .......................................................................99 Activity 14.1 ............................................................................................ 101 Activity 14.2 ............................................................................................ 103 Lesson 15: Ratio and rate ......................................................................... 104 Activity 15.1 ............................................................................................ 104 Activity 15.2 ............................................................................................ 107 Lesson 16: Data ......................................................................................... 107 Lesson 17: Time ......................................................................................... 110 Activity 17.1 ............................................................................................ 110 Activity 17.2 ............................................................................................ 111 Lesson 18: Summary ................................................................................. 112 UNIT 2 .......................................................................................................... 119 Lesson 19: Number concepts ................................................................... 119 Mental maths ................................................................................. 119 Activity 19.1 ............................................................................................ 119 Activity 19.2 ............................................................................................ 127 Activity 19.3 ............................................................................................ 130 ÂŠ Impaq

2

Study Guide 1/2 G05 ~ Mathematics

Activity 19.4 ............................................................................................ 132 Activity 19.5 ............................................................................................ 141 Lesson 20: Fractions ................................................................................. 146 Activity 20.1 ............................................................................................ 147 Activity 20.2 ............................................................................................ 154 Activity 20.3 ............................................................................................ 159 Activity 20.4 ............................................................................................ 168 Activity 20.5 ............................................................................................ 174 Activity 20.6 ............................................................................................ 177 Lesson 21: Geometry ................................................................................ 180 Mental maths ................................................................................... 180 Activity 21.1 ............................................................................................ 181 Activity 21.2 ............................................................................................ 186 Activity 21.3 ............................................................................................ 189 Activity 21.4 ............................................................................................ 191 Mental maths ................................................................................. 191 Activity 21.5 ............................................................................................ 194 Activity 21.6 ............................................................................................ 197 Activity 21.7 ............................................................................................ 201 Activity 21.8 ............................................................................................ 208 Lesson 22: Volume .................................................................................... 211 Mental maths ................................................................................. 211 Activity 22.1 ............................................................................................ 212 Activity 22.2 ............................................................................................ 213 Activity 22.3 ............................................................................................ 215 Lesson 23: Mass and weight..................................................................... 219 Activity 23.1 ............................................................................................ 219 Mental maths ................................................................................. 219 Activity 23.2 ............................................................................................ 223 Activity 23.3 ............................................................................................ 225 Lesson 24: Calculator games ................................................................... 227 Mental maths ................................................................................. 227 Activity 24.1 ............................................................................................ 228 Lesson 25: Measuring time throughout the centuries ........................... 230 Mental maths ................................................................................. 230 Activity 25.1 ............................................................................................ 232 Activity 25.2 ............................................................................................ 234 Activity 25.3 ............................................................................................ 237 3

ÂŠ Impaq

Study Guide 1/2 G05 ~ Mathematics

Activity 25.4 ............................................................................................ 238 Lesson 26: Grids ........................................................................................ 244 Mental maths ................................................................................. 244 Activity 26.1 ............................................................................................ 245 Activity 26.2 ............................................................................................ 247 Activity 26.3 ............................................................................................ 251 Lesson 27: Money ...................................................................................... 254 Mental maths ................................................................................. 254 Activity 27.1 ............................................................................................ 254 Lesson 28: 2D shapes and 3D objects ..................................................... 258 Mental maths ................................................................................. 258 Activity 28.1 ............................................................................................ 259 Activity 28.2 ............................................................................................ 265 Lesson 29: Views ....................................................................................... 266 Mental maths ................................................................................. 266 Activity 29.1 ............................................................................................ 267 Lesson 30: Symmetry ................................................................................ 268 Activity 30.1 ............................................................................................ 268 Activity 30.2 ............................................................................................ 270 Activity 30.3 ............................................................................................ 271 Lesson 31: Revision .................................................................................. 275 Activity 31.1 ............................................................................................ 275 Activity 31.2 ............................................................................................ 279 Activity 31.3 ............................................................................................ 283 Lesson 32: Revision tests ......................................................................... 290 Activity 32.1 ............................................................................................ 290 Revision test 1 ............................................................................... 290 Activity 32.2 ............................................................................................ 292 Revision test 2 ............................................................................... 292 Activity 32.3 ............................................................................................ 294 Revision test 3 ............................................................................... 294 Revision test 4 ............................................................................... 297 Revision test 5 ............................................................................... 299

ÂŠ Impaq

4

Study Guide 1/2 G05 ~ Mathematics

YEAR PLAN UNIT 1 2 3 4 5 6

1

2

3

DATE STARTED

LESSON

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

DATE COMPLETED

Where do numbers and digits come from? Place values Introduction to ten thousands Numbers greater than ten thousands Expanded notation Comparing, arranging and rounding numbers Multiples Addition and subtraction Money Multiplication Division Division Fun patterns Special patterns Rate and ration Data Time Summary Number concepts Fractions Geometry Volume Mass and weight Calculator games Measuring time throughout the centuries Grids Money 2D shapes and 3D objects Views Symmetry Revision Revision tests Shapes in my surroundings 2D shapes Make your own 2D shapes Transformation Symmetry 5

ÂŠ Impaq

Study Guide 1/2 G05 ~ Mathematics

UNIT

3

4

DATE STARTED

LESSON 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

3D objects Different views of 3D objects Area and perimeter Shapes and patterns in nature I am an entrepreneur My tuck shop Entrepreneurâ&#x20AC;&#x2122;s day Temperature Revision Decimal numbers Conversion Decimal numbers Money as decimal numbers Approximation of money Shopping without a calculator Common fractions Operations with fractions Revision tests Data handling Probability Revision activities Additional exercises

Find Unit 1 and 2 in Study Guide 1/2 and Unit 3 and 4 in Study Guide 2/2

ÂŠ Impaq

6

DATE COMPLETED

Study Guide 1/2 G05 ~ Mathematics

Unit

1

UNIT 1 Lesson 1: Where do numbers and digits come from? Can you believe it? The first written numbers date back about 5 000 years. The Sumerians were the first people we know of who used written numbers.

These are Roman numerals:

Below are some examples of how numbers were written in the different antique number systems. Egyptian

Roman

I

HinduArabic 1



IV

4



IX

9

X

10

∩

XV

15

∩∩

XX

20

∩∩∩

XXX

30

∩∩∩∩∩

L C D

50 100 500

M

1 000

Babylonian

9

Mayan

Unit

Study Guide 1/2 G05 ~ Mathematics

1

1.

Write the following Egyptian numbers as we would write them today: Example: ∩  = 10 + 3 = 13 a)

2.

3.

∩ =

b)

∩∩∩∩  =

c)

 =

How would the Mayans have written the following numbers? a)

9 ___________________________

b)

14 __________________________

c)

27 __________________________

Do the following sum using all five different number systems. 17 + 3 = 20

4.

a)

Egyptian: __________________________________

b)

Roman: ____________________________________

c)

Babylonian: ________________________________

d)

Mayan: ____________________________________

e)

Hindu-Arabic (our number system): ______________

Which number system do you think is the easiest to use? Why? ________________________________________________

10

Study Guide 1/2 G05 ~ Mathematics

5.

Unit

1

Look at the Egyptian numbers below and use them to make any 5-digit number.

Units

Tens

Egyptian number

Thousands

Hundreds

Number

Expanded notation

Lesson 2: Place values

Important The value of each number. 1 694 = 1 000 + 600 + 90 + 4 Th H T U 1 6 9 4 What value will the cards give when put together?

In words it is

Eight thousand six hundred and twenty-one

11

It is 8 621 In numbers

ÂŠ Impaq

Unit

Study Guide 1/2 G05 ~ Mathematics

1

Mental maths

1.

2x2=

16.

3x6=

2.

2 x 10 =

17.

2x8=

3.

2 x 11 =

18.

2 x 10 =

4.

4x2=

19

2x6=

5.

3x9=

20.

2 x 12 =

6.

2x6=

21.

2x7=

7.

2x3=

22.

3x4=

8.

3x7=

23.

3x8=

9.

2x8=

24.

3x3=

10.

3x3=

25.

2x9=

11.

2x4=

26.

2x7=

12.

3 x 12 =

27.

2x9=

13.

5x2=

28.

3x5=

14.

3x2=

28.

3 x 11 =

15.

2 x 12 =

30.

3x9=

ÂŠ Impaq

12

Study Guide 1/2 G05 ~ Mathematics

Unit

1

Activity 2.1 1.

Write down the number illustrated by each diagram.

a.

b.

Th

H

T

U

a) __________ 2.

3.

Th

c.

H

T

U

b) __________

Th

d.

H

T

U

c) __________

Th

H

T

U

d) _________

Write each of the following numbers in words. Example: 7 183 = Seven thousand one hundred and eighty-three a)

474

_________________________________________

b)

6 478

_________________________________________

c)

2 730

_________________________________________

d)

7 643

_________________________________________

Write each of the following numbers in digits. Example: Six thousand and sixty-three = 6 063 a)

Nine hundred and twenty-three ____________

b)

Five thousand two hundred and fifty-three ____________

c)

Six thousand five hundred and twenty-two ____________

d)

Seven thousand ______________

e)

One thousand two hundred and two ___________

13

ÂŠ Impaq

Unit

Study Guide 1/2 G05 ~ Mathematics

1

4.

5.

6.

Fill in the correct relational symbol: >, < or =. a)

575

500 + 50 + 5

b)

5 062

5 000 + 60 + 2

c)

3 516

3 000 + 200 + 50 + 8

d)

8 437

(8 x 1 000) + (3 x 100) + (4 x 10) + (8 x 1)

Complete the following. a)

2 894; 2 895; ____; ____; 2 898; 2 899; ____; ____; 2 902

b)

3 200; 3 100; ____; ____; ____; 2 700; ____; ____; ____

c)

4 582; 4 592; ____; ____; 4 622; 4 632; ____; ____; ____

d)

____; ____; ____; 6 205; ____; 6 215; 6 220; ____; ____

Write each digit in the correct column. Thousands

a.

387

b.

704

c.

4 205

d.

8 390

e.

4 100

ÂŠ Impaq

Hundreds 3

14

Tens 8

Units 7

Study Guide 1/2 G05 ~ Mathematics

Unit

7.

Write the correct number in the space provided.

8.

Write each number in expanded notation (use any method).

1

Example: 7 845 = 7 000 + 800 + 40 + 5 Or 7 845 = 7Th + 8H + 4T + 5U Or 7 845 = (7 x1 000) + (8 x 100) + (4 x 10) + (5 x 1) a)

386_______________________________________________

b)

3 345______________________________________________

c)

4 766______________________________________________

d)

9 583______________________________________________

15

ÂŠ Impaq

Unit

Study Guide 1/2 G05 ~ Mathematics

1

Activity 2.2 1.

Count the cubes.

a) _____________________

16

Study Guide 1/2 G05 ~ Mathematics

Unit

2.

Count the place values and write down the total.

3.

Complete the following.

4.

a)

8 000 + 400 + 30 + 2 = ______________________

b)

3 000 + 800 + 50 + 6 = ______________________

c)

1 000 + 300 + 70 + 4 = ______________________

d)

6 000 + 4 = _______________________________

1

Complete the following. a)

8 163 = 8 thousands + 1 hundred + 6 tens + 3 units

b)

6 524 = __________________________________

c)

7 865 = __________________________________

d)

9 534 = __________________________________

17

ÂŠ Impaq

Unit

Study Guide 1/2 G05 ~ Mathematics

1

5.

Just for fun! You dropped pebbles on the board and this is the result. What is the answer if you add all the numbers together?

_____________________

Lesson 3: Introduction to ten thousands

Important The place value table currently looks like this: Th H T U What is the next place value to the left? TTh = ten thousand = 10 000 It is added to the left: TTh Th H T U This order ALWAYS remains the same.

ÂŠ Impaq

18

Study Guide 1/2 G05 ~ Mathematics

Unit

1

Important • • • •

10 units = 10 x 1 = 10 10 tens = 10 x 10 = 100 10 hundreds = 10 x 100 = 1 000 10 thousands = 10 x 1 000 = 10 000

Mental maths

1.

2x3=

16.

3x6=

2.

4 x 10 =

17.

4x8=

3.

3 x 11 =

18.

4 x 10 =

4.

4x3=

19

3x3=

5.

3x6=

20.

3x9=

6.

4x6=

21.

2x7=

7.

8x3=

22.

4x4=

8.

3x7=

23.

3x8=

9.

5x8=

24.

3x3=

10.

5x3=

25.

2x9=

11.

4x4=

26.

4x7=

19