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MATHEMATICS STUDY GUIDE 1/2 Grade 4
A member of the FUTURELEARN group
Mathematics Study guide 1/2
1804-E-MAM-SG01
Í2$È-E-MAM-SG01GÎ
Grade 4
CAPS aligned
L Young
Study Guide 1/2 G04 ~ Mathematics
CONTENTS LESSON ELEMENTS.......................................................................................................... 5 STUDY HINTS ..................................................................................................................... 6 YEAR PLAN ........................................................................................................................ 7 UNIT 1 ............................................................................................................................... 11 LESSON 1: WHOLE NUMBERS ...................................................................................... 12 Counting with whole numbers......................................................................................... 13 ACTIVITY 1 ................................................................................................................. 14 Ordering whole numbers ................................................................................................ 19 ACTIVITY 2 ................................................................................................................. 21 Place value ..................................................................................................................... 24 ACTIVITY 3 ................................................................................................................. 28 Comparing whole numbers ............................................................................................. 34 ACTIVITY 4 ................................................................................................................. 36 Representing whole numbers ......................................................................................... 39 ACTIVITY 5 ................................................................................................................. 40 LESSON 2: NUMBER SENTENCES ................................................................................ 41 ACTIVITY 6 ................................................................................................................. 42 ACTIVITY 7 ................................................................................................................. 43 ACTIVITY 8 ................................................................................................................. 45 Pairs of equivalent number sentences............................................................................ 49 ACTIVITY 9 ................................................................................................................. 50 Addition and subtraction techniques ............................................................................... 52 Commutative property of addition ................................................................................... 52 Associative property of addition ...................................................................................... 53 ACTIVITY 10 ............................................................................................................... 54 Order of subtraction ........................................................................................................ 56 ACTIVITY 11 ............................................................................................................... 56 LESSON 3: WHOLE NUMBERS ...................................................................................... 58 Addition with whole numbers .......................................................................................... 58 ACTIVITY 12 ............................................................................................................... 58 ACTIVITY 13 ............................................................................................................... 62 Subtraction of whole numbers ........................................................................................ 64 ACTIVITY 14 ............................................................................................................... 66 Estimation ....................................................................................................................... 73 ACTIVITY 15 ............................................................................................................... 76 Rounding ........................................................................................................................ 79 ACTIVITY 16 ............................................................................................................... 82 ACTIVITY 17 ............................................................................................................... 85 Compensation ................................................................................................................ 86 1
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Study Guide 1/2 G04 ~ Mathematics
Doubling and halving ...................................................................................................... 87 ACTIVITY 18 ............................................................................................................... 88 ACTIVITY 19 ............................................................................................................... 91 Testing calculations with inverse operations .................................................................. 94 ACTIVITY 20 ............................................................................................................... 96 LESSON 4: NUMBER PATTERNS (Numeric patterns) ................................................. 98 ACTIVITY 21 ............................................................................................................. 100 Input and output values ................................................................................................ 101 ACTIVITY 22 ............................................................................................................. 102 ACTIVITY 23 ............................................................................................................. 104 ACTIVITY 24 ............................................................................................................. 105 The associative property of multiplication ..................................................................... 106 LESSON 5: WHOLE NUMBERS (Multiplication and division) ................................... 109 Multiplication ................................................................................................................. 109 ACTIVITY 25 ............................................................................................................. 118 Division ......................................................................................................................... 120 ACTIVITY 26 ............................................................................................................. 121 ACTIVITY 27 ............................................................................................................. 126 LESSON 6: TIME ............................................................................................................ 128 ACTIVITY 28 ............................................................................................................. 131 ACTIVITY 29 ............................................................................................................. 135 LESSON 7: DATA HANDLING ....................................................................................... 138 Collecting, organising, analysing and interpreting data ................................................ 138 Pictograph .................................................................................................................... 138 Pie chart ....................................................................................................................... 140 Bar chart ....................................................................................................................... 141 ACTIVITY 30 ............................................................................................................. 142 LESSON 8: PROPERTIES OF 2-D SHAPES ................................................................. 146 ACTIVITY 31 ............................................................................................................. 150 LESSON 9: WHOLE NUMBERS (Multiplication of 2-digit numbers and division of 2digit numbers by 1-digit numbers) ............................................................................... 152 ACTIVITY 32 ............................................................................................................. 153 ACTIVITY 33 ............................................................................................................. 155 ACTIVITY 34 ............................................................................................................. 159 UNIT 2 ............................................................................................................................. 162 LESSON 10: WHOLE NUMBERS .................................................................................. 163 Counting with whole numbers....................................................................................... 164 ACTIVITY 35 ............................................................................................................. 166 © Impaq
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Study Guide 1/2 G04 ~ Mathematics
Ordering whole numbers .............................................................................................. 169 ACTIVITY 36 ............................................................................................................. 171 Place values ................................................................................................................. 173 ACTIVITY 37 ............................................................................................................. 175 Comparing whole numbers ........................................................................................... 179 ACTIVITY 38 ............................................................................................................. 180 Representing whole numbers ....................................................................................... 183 ACTIVITY 39 ............................................................................................................. 184 Rounding ...................................................................................................................... 185 ACTIVITY 40 ............................................................................................................. 188 LESSON 11: WHOLE NUMBERS (Addition and subtraction) ..................................... 190 Commutative property of addition ................................................................................. 190 Associative property of addition .................................................................................... 191 Order of subtraction ...................................................................................................... 193 ACTIVITY 41 ............................................................................................................. 196 LESSON 12: COMMON FRACTIONS ............................................................................ 199 ACTIVITY 42 ............................................................................................................. 200 ACTIVITY 43 ............................................................................................................. 203 LESSON 13: LENGTH .................................................................................................... 209 ACTIVITY 44 ............................................................................................................. 211 LESSON 14: WHOLE NUMBERS (Multiply 2-digit numbers with 2-digit numbers) ........................................................................................................................ 215 Distributive property of multiplication ............................................................................ 217 Dividing numbers into factors to multiply them ............................................................. 217 ACTIVITY 45 ............................................................................................................. 218 LESSON 15: PROPERTIES OF 3-D OBJECTS ............................................................. 223 ACTIVITY 46 ............................................................................................................. 226 LESSON 16: GEOMETRIC PATTERNS ......................................................................... 231 ACTIVITY 47 ............................................................................................................. 233 LESSON 17: SYMMETRY............................................................................................... 237 ACTIVITY 48 ............................................................................................................. 238 LESSON 18: WHOLE NUMBERS (Addition and subtraction) ..................................... 241 ACTIVITY 49 ............................................................................................................. 241 LESSON 19: WHOLE NUMBERS (Dividing 3-digit numbers by 1-digit numbers) .... 247 ACTIVITY 50 ............................................................................................................. 251
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Study Guide 1/2 G04 ~ Mathematics
References: Unit 1 ......................................................................................................... 257 References: Unit 2 ......................................................................................................... 258
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Study Guide 1/2 G04 ~ Mathematics
YEAR PLAN UNIT 1 DATE STARTED
TOPIC
DATE COMPLETED
Mental maths: Use the Train Your Brain Maths Grade 4 product LESSON 1 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (3-digit whole numbers) LESSON 2 Number sentences LESSON 3 Whole numbers: Addition and subtraction (3-digit whole numbers) LESSON 4 Number patterns: Numeric patterns LESSON 5 Whole numbers: Multiplication and division (1-digit whole number by 1-digit whole number) LESSON 6 Time LESSON 7 Data handling LESSON 8 Properties of 2-D shapes LESSON 9 Whole numbers: • Multiply (2-digit whole numbers by 1-digit whole number) • Multiply (2-digit whole numbers by 2-digit whole numbers) • Divide (2-digit whole numbers by 1-digit whole number) Revision: Use the CAMI programme
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Study Guide 1/2 G04 ~ Mathematics
UNIT 2 DATE STARTED
TOPIC Mental maths: Use the Train Your Brain Maths Grade 4 product LESSON 10 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (4-digit whole numbers) LESSON 11 Whole numbers: Addition and subtraction (4-digit whole numbers) LESSON 12 Common fractions LESSON 13 Length LESSON 14 Whole numbers: Multiplication (2-digit whole numbers by 2-digit whole numbers) LESSON 15 Properties of 3-D shapes LESSON 16 Geometric patterns LESSON 17 Symmetry LESSON 18 Whole numbers: Addition and subtraction (4-digit whole numbers) LESSON 19 Whole numbers: Division (3-digit whole numbers by 1-digit whole number) Revision: Use the CAMI programme
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DATE COMPLETED
Study Guide 1/2 G04 ~ Mathematics
UNIT 3 DATE STARTED
TOPIC
DATE COMPLETED
Mental maths: Use the Train Your Brain Maths Grade 4 product LESSON 20 Capacity/Volume LESSON 21 Common fractions LESSON 22 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (4-digit whole numbers) Whole numbers: Addition and subtraction (4-digit whole numbers) LESSON 23 Views of objects LESSON 24 Properties of 2-D shapes LESSON 25 Data handling LESSON 26 Numerical patterns LESSON 27 Whole numbers: Addition and subtraction (4-digit whole numbers) LESSON 28 Whole numbers: Multiplication (2-digit whole numbers with 2-digit whole numbers) LESSON 29 Number sentences LESSON 30 Transformations Revision: Use the CAMI programme
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Study Guide 1/2 G04 ~ Mathematics
UNIT 4 DATE STARTED
TOPIC Mental maths: Use the Train Your Brain Maths Grade 4 product LESSON 31 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (4-digit whole numbers) Whole numbers: Addition and subtraction (4-digit whole numbers) LESSON 32 Mass LESSON 33 Properties of 3-D objects LESSON 34 Common fractions LESSON 35 Whole numbers: Division (3-digit whole numbers by 1-digit whole number) LESSON 36 Perimeter, surface area and volume LESSON 37 Position and movement LESSON 38 Transformations LESSON 39 Geometric patterns LESSON 40 Whole numbers: Addition and subtraction (4-digit whole numbers) LESSON 41 Probability Revision: Use the CAMI programme
Find unit 1 and 2 in study guide 1/2 and unit 3 and 4 in study guide 2/2. Š Impaq
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DATE COMPLETED
Study Guide 1/2 G04 ~ Mathematics
Unit
1
UNIT 1 This unit covers nine lessons: Lessons 1 to 9. The table indicates the lesson topics as well as the time the learners will spend on each one.
UNIT 1 TOPIC Mental maths: Use the Train Your Brain Maths Grade 4 product
TIME AND NOTES 8 hours (divided into 10 minutes every day)
LESSON 1 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (3-digit whole numbers)
2 hours
LESSON 2 Number sentences
3 hours
LESSON 3 Whole numbers: Addition and subtraction (3-digit whole numbers)
8 hours
LESSON 4 Number patterns: Numeric patterns
4 hours
LESSON 5 Whole numbers: Multiplication and division (1-digit whole number by 1-digit whole number)
4 hours
LESSON 6 Time
6 hours
LESSON 7 Data handling
10 hours
LESSON 8 Properties of 2-D shapes
5 hours
LESSON 9 Whole numbers: • Multiply (2-digit whole numbers by 1-digit whole number) • Multiply (2-digit whole numbers by 2-digit whole numbers) • Divide (2-digit whole numbers by 1-digit whole number)
5 hours
Revision: Use the CAMI programme
5 hours
TOTAL
60 hours
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Unit
Study Guide 1/2 G04 ~ Mathematics
1
LESSON 1: WHOLE NUMBERS
Do you know what a whole number is?
Whole numbers are numbers without fractions or decimals. Whole numbers are also always positive and never negative. Remember: 0 is also a whole number. Examples of whole numbers
{0; 1; 2; 3; 4; 5; 6; ...}
If numbers such as the above are placed in curly brackets { }, we call it a set of numbers. This means that {0; 1; 2; 3; 4; 5; 6; ...} is a set of whole numbers. Look at the numbers in the table and circle the whole numbers.
0,9
101
10
24
-24
0
198
3
-4,1
4
-2
13 9
In this lesson, you will do the following with whole numbers: • count • order • compare • represent • indicate place value © Impaq
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Study Guide 1/2 G04 ~ Mathematics
Unit
1
Counting with whole numbers In Grade 3 you learnt how to count with whole numbers. Can you still remember how to count in 2s? Let’s revise counting in 2s. When you count in 2s, always add 2 to the previous number to get the next number.
You can start with any number. Look at the numbers. Do you see that you can start at any number and count in whole numbers?
In the above examples, you counted on or forwards. Using whole numbers, you can also count back or backwards. Look at the following numbers and complete the blank blocks. Count back in 3s.
Now that your memory has been refreshed, you can apply what you have learnt.
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Unit
Study Guide 1/2 G04 ~ Mathematics
1 ACTIVITY 1
1.
Write the set of whole numbers between 915 and 921. _________________________________________________________________ _________________________________________________________________
2.
Indicate whether the numbers are whole numbers or not. Colour the correct circle. Numbers
Whole number: yes or no?
Example:
35 658 14,3 53 3 1 412
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Study Guide 1/2 G04 ~ Mathematics
1
Study the number lines. You are not told what number to count with, nor whether you are counting on or back. Complete the number lines.
Example
3.
Unit
3;
13;
23;
3.1
96;
101;
106;
413;
410;
3.2
33;
43 ...
407;
...
3.3
8;
108;
308;
...
3.4
12;
9;
3;
0
3.5
10;
35;
60;
15
85;
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Unit
Study Guide 1/2 G04 ~ Mathematics
1
4.
There are three Grade 4 learners in the class that like to play with marbles. Each learner keeps their marbles in a different size bag. Andrew’s bag can hold 10 marbles. Sibongile’s bag can hold 25 marbles. Timmy’s bag can only hold 3 marbles. Look at the following example and count in 10s, 25s and 3s to determine how many marbles each learner has. Learner
Number of bags
Andrew
Sibongile
Timmy
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Number of marbles
Study Guide 1/2 G04 ~ Mathematics
5.
Unit
1
Complete the flow charts.
5.1
5.2
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Unit
Study Guide 1/2 G04 ~ Mathematics
1 Self-assessment
After you have completed this topic, you should be able to do the following. Look at the requirements (the things you must be able to do) and colour the face that best describes your skill or ability. COUNTING IN WHOLE NUMBERS Requirements I can count on and back in 2s.
I can count on and back in 3s.
I can count on and back in 5s.
I can count on and back in 10s.
I can count on and back in 25s.
I can count on and back in 50s.
I can count on and back in 100s.
I can do all of the above up to the number 1 000.
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Can I do it?
Study Guide 1/2 G04 ~ Mathematics
Unit
1
Ordering whole numbers
Ordering means to arrange or organise numbers.
ordering = arrange We can order or arrange numbers in different ways:
from LARGE to small
OR from small to LARGE
Study the set of numbers.
Arrange the numbers from large to small. Step 1:
Choose the largest number and write it down first. The largest number in this set is
Step 2:
Now cross out the largest number in the number set.
You can no longer choose the number 537.
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Unit
Study Guide 1/2 G04 ~ Mathematics
1
Step 3:
From the remaining numbers, choose the largest number and write it next to 537.
Step 4:
Now repeat steps 2 and 3 until you have crossed out all of the numbers. When you are done, the set of numbers must look as follows:
You have now arranged the number set from largest to smallest. Can you arrange the following set of numbers from small
to large?
Tip: Start by choosing the smallest number, not the largest one. Write your answer in the box below.
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Study Guide 1/2 G04 ~ Mathematics
Unit
1
ACTIVITY 2
1.
Arrange the numbers from small to large. Question
2.
1.1
321 645 256 782 127
1.2
56 72 201 114 98
1.3
724 568 147 274 355
1.4
65 34 12 47 71
1.5
527 471 298 638 138
Answer
Arrange the numbers from large to small. Question 2.1
620 541 635 514 623
2.2
36 48 21 65 57
2.3
116 98 53 76 110
2.4
58 39 44 28 13
2.5
457 325 147 471 352
Answer
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