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MATHEMATICS STUDY GUIDE 2/2 Grade 5
A member of the FUTURELEARN group
Mathematics Study guide 2/2
1805-E-MAM-SG02
Í2%È-E-MAM-SG02WÎ
Grade 5
CAPS aligned
Study Guide 2/2 G05 ~ Mathematics
CONTENTS LESSON ELEMENTS ..................................................................................... 7 YEAR PLAN ................................................................................................... 8 UNIT 3 ........................................................................................................... 10 Lesson 33: Shapes in my environment..................................................... 10 Mental maths .................................................................................. 10 Lesson 34: 2D shapes ................................................................................ 16 Mental maths .................................................................................. 16 Lesson 35: Create your own 2D shapes ................................................... 20 Mental maths .................................................................................. 20 Lesson 36: Transformation ........................................................................ 24 Mental maths .................................................................................. 24 Activity 36.1.......................................................................................... 25 Lesson 37: Symmetry ................................................................................. 27 Mental maths .................................................................................. 27 Activity 37.1.......................................................................................... 29 Lesson 38: 3D Objects ............................................................................... 36 Mental maths .................................................................................. 36 Activity 38.1.......................................................................................... 39 Activity 38.2.......................................................................................... 40 Lesson 39: Different views of 3D objects ................................................. 42 Mental maths .................................................................................. 42 Activity 39.1.......................................................................................... 44 Lesson 40: Perimeter and area .................................................................. 47 Mental maths .................................................................................. 47 Activity 40.1.......................................................................................... 48 Activity 40.2.......................................................................................... 49 Activity 40.3.......................................................................................... 51 Activity 40.4.......................................................................................... 53 Activity 40.5.......................................................................................... 56 Activity 40.6.......................................................................................... 59 Lesson 41: Shapes and patterns in nature ............................................... 60 Lesson 42: I am an entrepreneur ............................................................... 62 Mental maths .................................................................................. 62 Activity 42.1.......................................................................................... 63 Activity 42.2.......................................................................................... 64
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Study Guide 2/2 G05 ~ Mathematics
Lesson 43: My tuck shop ........................................................................... 68 Mental maths .................................................................................. 68 Activity 43.1.......................................................................................... 69 Activity 43.2.......................................................................................... 71 Lesson 44: Entrepreneur’s day.................................................................. 74 Mental maths .................................................................................. 74 Activity 44.1.......................................................................................... 76 Activity 44.2.......................................................................................... 78 Albert’s stall.......................................................................................... 80 Lesson 45: Temperature ............................................................................ 82 Mental maths .................................................................................. 82 Activity 45.1.......................................................................................... 84 Activity 45.2.......................................................................................... 85 Activity 45.3.......................................................................................... 86 Activity 45.4.......................................................................................... 89 Lesson 46: Revision ................................................................................... 91 Mental maths .................................................................................. 91 Lesson 47: Decimal numbers .................................................................... 96 Mental maths .................................................................................. 96 Activity 47.1.......................................................................................... 99 Activity 47.2.........................................................................................100 Lesson 48: Conversion .............................................................................102 Mental maths .................................................................................102 Activity 48.1.........................................................................................104 Activity 48.2.........................................................................................104 Activity 48.3.........................................................................................105 Lesson 49: Decimal numbers ...................................................................106 Mental maths .................................................................................106 Activity 49.1.........................................................................................107 Activity 49.2.........................................................................................110 Activity 49.3.........................................................................................113 Lesson 50: Money as decimal numbers ..................................................117 Mental maths .................................................................................117 Activity 50.1.........................................................................................118 Activity 50.2.........................................................................................120 Activity 50.3.........................................................................................122 Lesson 51: Approximation of money .......................................................123 Mental maths .................................................................................123 © Impaq
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Study Guide 2/2 G05 ~ Mathematics
Activity 51.1.........................................................................................125 Activity 51.2.........................................................................................126 Lesson 52: Shopping without a calculator ..............................................127 Mental maths .................................................................................127 Activity 52.1.........................................................................................128 Activity 52.2.........................................................................................131 Lesson 53: Common fractions..................................................................132 Mental maths .................................................................................132 Activity 53.1.........................................................................................133 Activity 53.2.........................................................................................134 Activity 53.3.........................................................................................136 Lesson 54: Operations with fractions ......................................................137 Mental maths .................................................................................137 Activity 54.1.........................................................................................138 Activity 54.2.........................................................................................139 Activity 54.3.........................................................................................141 Activity 54.4.........................................................................................143 Lesson 55: Revision tests .........................................................................146 Revision test 1...................................................................................146 Revision test 2...................................................................................153 UNIT 4 .......................................................................................................... 156 Lesson 56: Data handling ......................................................................... 156 Activity 56.1......................................................................................... 159 Activity 56.2......................................................................................... 161 Activity 56.3......................................................................................... 162 Activity 56.4......................................................................................... 164 Lesson 57: Probability ............................................................................... 165 Activity 57.1......................................................................................... 167 Activity 57.2......................................................................................... 168 Revision 1: Mental maths .................................................................. 169 Revision 2: Fill in >, < or =. ............................................................... 170 Revision 3: Even and odd numbers .................................................. 171 Revision 4: Number concepts ........................................................... 172 Revision 5: Mental maths .................................................................. 174 Revision 6: number concepts ............................................................ 177 Revision 7: Multiplication................................................................... 179 Revision 8: Multiplication and division............................................... 182 3
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Study Guide 2/2 G05 ~ Mathematics
Revision 9: Division ........................................................................... 183 Revision 10: Common fractions ........................................................ 185 Revision 11: Common fractions ........................................................ 186 Revision 12: Blitz test! ....................................................................... 187 Revision 13: Decimal numbers ......................................................... 190 Revision 14: Order of operations ...................................................... 193 Revision 15: Time ............................................................................. 194 Revision 16: Units ............................................................................. 197 Revision 17: Money........................................................................... 199 Revision 18: Blitz test! ....................................................................... 203 Revision 19: Blitz test! ....................................................................... 204 Revision 20: complete ....................................................................... 206 Revision 21: Complete ...................................................................... 208 Revision 22: Complete ...................................................................... 210 Revision 23: complete ....................................................................... 215 Additional Activities .................................................................................. 219 Mental maths 1 .............................................................................. 219 Mental maths 2 .............................................................................. 219 Mental maths 3 .............................................................................. 220 Mental maths 4 .............................................................................. 220 Mental maths 5 .............................................................................. 221 Mental maths 6 .............................................................................. 221 Mental maths 7 .............................................................................. 222 Mental maths 8 .............................................................................. 222 Mental maths 9 .............................................................................. 223 Mental maths 10 ............................................................................ 223 Mental maths 11 ............................................................................ 224 Mental maths 12 ............................................................................ 224 Mental maths 13 ............................................................................ 225 Mental maths 14 ............................................................................ 225 Mental maths 15 ............................................................................ 226 Mental maths 16 ............................................................................ 226 Mental maths 17 ............................................................................ 227 Mental maths 18 ............................................................................ 227 Mental maths 19 ............................................................................ 228 Mental maths 20 ............................................................................ 228 Mental maths 21 ............................................................................ 229 Mental maths 22 ............................................................................ 229 Š Impaq
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Study Guide 2/2 G05 ~ Mathematics
Mental maths 23 ............................................................................ 230 Mental maths 24 ............................................................................ 230 Mental maths 25 ............................................................................ 231 Mental maths 26 ............................................................................ 231 Mental maths 27 ............................................................................ 232 Mental maths 28 ............................................................................ 232 Mental maths 29 ............................................................................ 233 Mental maths 30 ............................................................................ 233 Mental maths 31 ............................................................................ 234 Additional mental maths ........................................................................... 235 Mental maths 1 .............................................................................. 235 Mental maths 2 .............................................................................. 235 Mental maths 3 .............................................................................. 235 Mental maths 4 .............................................................................. 236 Mental maths 5 .............................................................................. 236 Mental maths 6 .............................................................................. 236 Mental maths 7 .............................................................................. 237 Mental maths 8 .............................................................................. 237 Mental maths 9 .............................................................................. 237 Mental maths 10 ............................................................................ 238 Mental maths 11 ............................................................................ 238 Mental maths 12 ............................................................................ 238 Mental maths 13 ............................................................................ 239 Mental maths 14 ............................................................................ 239 Mental maths 15 ............................................................................ 239 Mental maths 16 ............................................................................ 240 Mental maths 17 ............................................................................ 240 Mental maths 18 ............................................................................ 240 Mental maths 19 ............................................................................ 241 Mental maths 20 ............................................................................ 241 Mental maths 21 ............................................................................ 241 Mental maths 22 ............................................................................ 242 Mental maths 23 ............................................................................ 242 Mental maths 24 ............................................................................ 242 Mental maths 25 ............................................................................ 243 Mental maths 26 ............................................................................ 243 Mental maths 27 ............................................................................ 243 Mental maths 28 ............................................................................ 244 5
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Study Guide 2/2 G05 ~ Mathematics
Mental maths 29 ................................................................................... 244 Mental maths 30 ................................................................................... 244 Unit 1 Additional exercise 1 ...................................................................... 245 Additional exercise 2 ..................................................................... 247 Additional exercise 3 ..................................................................... 249 Additional exercise 4 ..................................................................... 251 Additional exercise 5 ..................................................................... 253 Unit 2 ........................................................................................................... 254 Additional exercise 1 ..................................................................... 254 Additional exercise 2 ..................................................................... 256 Additional exercise 3 ..................................................................... 258 Additional exercise 4 ..................................................................... 260 Additional exercise 5 ..................................................................... 263 Additional exercise 6 ..................................................................... 264 Additional exercise 7 ..................................................................... 266 Additional exercise 8 ..................................................................... 268 Additional exercise 9 ..................................................................... 270 Additional exercise 10 ................................................................... 271 Unit 3 ........................................................................................................... 272 Additional exercise 1 ..................................................................... 272 Additional exercise 2 ..................................................................... 273 Additional exercise 3 ..................................................................... 275 Additional exercise 4 ..................................................................... 276 Additional exercise 5 ..................................................................... 277 Additional exercise 6 ..................................................................... 278 Additional exercise 7 ..................................................................... 279 Additional exercise 8 ..................................................................... 282 Additional exercise 9 ..................................................................... 283
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Study Guide 2/2 G05 ~ Mathematics
YEAR PLAN UNIT 1 2 3 4 5 6
1
2
3
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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
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 8
DATE COMPLETED
Study Guide 2/2 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
DATE COMPLETED
3D objects Different views of 3D objects Area and perimeter Shapes and patterns in nature I am an entrepreneur My tuck shop Entrepreneur’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
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Unit
Study Guide 2/2 G05 ~ Mathematics
3
UNIT 3 Lesson 33: Shapes in my environment
Mental maths 1.
2x2=
11.
2 x 10 =
2.
11 x 2 =
12.
3x4=
3.
6x2=
13.
2x3=
4.
3x3=
14.
3x8=
5.
3 x 10 =
15.
2x7=
6.
2x5=
16.
3x5=
7.
2x8=
17.
3 x 11 =
8.
3x6=
18.
2x4=
9.
3 x 12 =
19.
3x7=
10.
3x9=
20.
2 x 12 =
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Study Guide 2/2 G05 ~ Mathematics
Unit
3
Walk around the house and garden, and see how many shapes you can spot. Look for the following shapes and give as many examples as you can of where these shapes can be found in your environment, e.g.: This is a rectangular prism. Examples are: • A block of margarine • Cereal box • Toothpaste box • Filing cabinet in the study Square
Rectangle
Rhombus
_________________
_________________
________________
_________________
_________________
________________
Circle
Sphere (ball)
Triangle
_______________
_________________
________________
________________
_________________
__________________
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Unit
Study Guide 2/2 G05 ~ Mathematics
3
Triangular prism
Cylinder
_________________
_________________
________________
_________________
_________________
________________
Cone
Hexagon
Cube
Star
________________
_________________
________________
________________
_________________
________________
Do you know 2D shapes and 3D objects? The shapes above that aren’t coloured, are two-dimensional shapes. We can easily place and copy 2D shapes onto paper. The pictures that are coloured, are three-dimensional objects. 3D objects cannot be placed onto paper and copied. Chairs, tables, computers, glasses, etc. are all examples of 3D objects.
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Study Guide 2/2 G05 ~ Mathematics
Unit
3
The following shapes may appear strange to you. Learn their names and see if you can spot them in your environment. Parallelogram
Trapezium
Properties of shapes A
B Rectangle
C Measure the sides: AB = __________
D CD = __________
AC = __________
BD = __________
AD = __________
BC = __________
AB and CD are opposite sides of the rectangle. AC and BD are opposite sides. What can you say about opposite sides of a rectangle? AD and BC are diagonals of a rectangle. What can you say about the diagonals of a rectangle?
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Unit
Study Guide 2/2 G05 ~ Mathematics
3 E
F
Parallelogram
G
H
Measure the sides: EF = __________
GH = __________
EG = __________
FH = __________
EH = __________
FG = __________
What can you say about opposite sides of a parallelogram? What can you say about the diagonals of a parallelogram? A
B
C
D
Measure the sides: AB = __________
CD = __________
AC = __________
BD = __________
AD = __________
BC = __________
All four sides of a square are the same length, and the diagonals are also the same length. You’ve measured the sides. Is ABCD a square?
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Study Guide 2/2 G05 ~ Mathematics
Unit
A
3
B
H
C Octagon
G
D F
E
Measure the sides: AB = ____________
BC = ____________
CD = ____________
DE = ____________
EF = ____________
FG = ____________
GH = ____________
HA = ____________
An octagon has eight sides. The sides of a regular octagon are all the same length. Is this figure a regular octagon? A
F
B
Hexagon
E
C
D
Measure the sides: AB = ____________
BC = ____________
CD = ____________
DE = ____________
EF = ____________
FA = ____________
A regular hexagon’s sides are all the same length. Is this a regular hexagon? 15
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Unit
Study Guide 2/2 G05 ~ Mathematics
3
Lesson 34: 2D shapes
Mental maths 1.
1x6=
11.
6x6
2.
12 x 6 =
12.
7x9=
3.
7x7=
13.
2x6=
4.
3x6=
14.
5x7=
5.
4x7=
15.
4x6=
6.
7 x 10 =
16.
6x9=
7.
5x6=
17.
7 x 11 =
8.
3x7=
18.
7x8=
9.
6x7=
19.
6x8=
10.
7 x 12 =
20.
2x7=
You’ve already been introduced to the special group of shapes called quadrilaterals (tetragons).
Can you remember what a quadrilateral is?
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Study Guide 2/2 G05 ~ Mathematics
Unit
3
A quadrilateral is an enclosed figure with four sides.
All the shapes above are called quadrilaterals. Why? Because each one has four sides.
SQUARES
Complete the following to see what you remember about squares. •
All squares have ______ sides.
•
The sides are all the same _________.
•
The angles are all __________ angles. 17
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Unit
Study Guide 2/2 G05 ~ Mathematics
3 RECTANGLES
Look at the rectangles. There are aspects that are the same for all rectangles. What are they? •
All rectangles have _______ sides.
•
The opposing sides of rectangles are the same __________.
•
All rectangles have ______ angles.
Here are some more quadrilaterals.
Parallelogram
Rhombus Trapezium
You must know these shapes!
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Kite
Study Guide 2/2 G05 ~ Mathematics
Unit
3
Do the following: 1.
2.
Use a peg board or dotted paper and create as many different quadrilaterals as you can. Create the following quadrilaterals on your board (if you have one). Then draw each shape on dotted paper and write down its name. Shape
Name
Describe the quadrilateral All four ______ are not the same ________, but __________ sides are the same length. All four ______ are __________angles. All four ______ are not the same ________, but __________ sides are the same length. No _________ angles. All _________ sides are the same _______. All four ________ are ______ angles. All _________ sides are the same _______. No ________ angles.
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Unit
Study Guide 2/2 G05 ~ Mathematics
3
Lesson 35: Create your own 2D shapes
Mental maths 1.
8x4=
11.
3x0=
2.
3x2=
12.
4x2=
3.
5x4=
13.
3x7=
4.
3x8=
14.
9x4=
5.
0x4=
15.
3x3=
6.
3x4=
16.
4x4=
7.
10 x 4 =
17.
12 x 4 =
8.
3x5=
18.
3x6=
9.
7x4=
19.
6x4=
10.
3 x 12 =
20.
3x9=
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Study Guide 2/2 G05 ~ Mathematics
Unit
3
Measure the lengths of the lines below. A
B
C
E
D F
Draw the following shapes on a sheet of paper. You are going to cut them out. 1. Use AB to draw a square. 2. Use AB and CD to draw a rectangle. 3. Use EF to draw a triangle. 4. Use AB and EF to draw a kite. 5. Draw any shape of your choice. Now cut out the shapes and complete the table. Shape Number Number of Are all the of sides angles angles the same size? Square
Are all the sides the same length?
Rectangle
Triangle
Kite
Your own shape
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Unit
Study Guide 2/2 G05 ~ Mathematics
3
How many triangles can you see below?
Let’s build with matches We are going to build shapes using matches. Use as few matches as possible to build the shape in question. 1. 2. 3. 4. 5.
How many matches do you need to build 5 triangles? How many matches do you need to build 3 squares? How many matches do you need to build 4 rectangles? Use 10 matches to build a house. Use 20 matches to build any shape of your choice.
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Study Guide 2/2 G05 ~ Mathematics
Unit
3
A game with dots and squares • •
Two players are needed. Players take turns to connect two dots alongside each other. You may only draw horizontal or vertical lines – no diagonals are allowed. If you draw the last line of a square, write your initials inside the square. When there are no dots left, count the squares. The person whose initials appear the most, is the winner.
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Unit
Study Guide 2/2 G05 ~ Mathematics
3
Lesson 36: Transformation
Mental maths 1x6=
1.
6x6=
11.
2.
7x9=
12.
12 x 6 =
3.
2x6=
13.
7x7=
4.
5x7=
14.
3x6=
5.
4x6=
15.
4x7=
6.
6x9=
16.
7 x 10 =
7.
7 x 11 =
17.
5x6=
8.
7x8=
18.
3x7=
9.
6x8=
19.
6x7=
10.
2x7=
20.
7 x 12 =
We can arrange shapes in different ways to create patterns.
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Study Guide 2/2 G05 ~ Mathematics
Unit
3
Let’s see what happens to the triangle when we shift the shape. Translation: The triangle shifts or glides to the right without changing direction.
Reflection: The triangle is reflected in a line of symmetry. We can see the triangle’s mirror image.
Rotation: We turn or rotate the triangle around a set point.
Activity 36.1 1.
Complete the following patterns and give the mathematical term for each. a)
___________________________________ b)
___________________________________ c)
___________________________________ 25
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Unit
Study Guide 2/2 G05 ~ Mathematics
3
2.
The man laying the tiles hasn’t finished the job. Please help him. Mom has three pictures that she would like to hang on the wall. Please help her to hang the last one.
3.
Complete the sentences. b.
a.
a. The triangle moves ___ block down and ___ block to the right. b. The square moves ___ blocks down and ___ blocks to the left. c.
d.
c. The hexagon moves ___ blocks ___ and ___ blocks ___. d. The triangle moves ____ blocks ___ and ___ blocks ___.
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