Intermediate Phase Grade 5 • Study Guide 1/2
Mathematics Comprehensive explanations of concepts in simple language. Practical, everyday examples with visuals and diagrams to help master concepts. Learners work at their own pace. Activities that test learners’ knowledge application and reasoning. The facilitator’s guide contains step-by-step calculations and answers. Use in school or at home.
CAPS IEB Mathematics
• • • • • •
home classroom college workplace
9 781990
946424
Study Guide 1/2
2005-E-MAM-SG01
5
Mathematics Study guide 1/2
CAPS aligned
M Vos L Young
2005-E-MAM-SG01
Í4%È-E-MAM-SG01KÎ
Grade 5
Study Guide 1/2 G05 ~ Mathematics
Contents LESSON ELEMENTS.................................................................................................................................... 1 YEAR PLAN................................................................................................................................................... 2 FACT SHEET.................................................................................................................................................. 6 Whole numbers................................................................................................................................................... 6 Alternative words used for operations..................................................................................................... 6 Rounding................................................................................................................................................................ 7 Properties.............................................................................................................................................................. 8 Common fractions.............................................................................................................................................. 9 Time.......................................................................................................................................................................10 Length....................................................................................................................................................................10 Mass.......................................................................................................................................................................10 Conversions: Multiply or divide by 10, 100 and 1 000....................................................................11 2D shapes.............................................................................................................................................................12 3D objects............................................................................................................................................................13 Data handling.....................................................................................................................................................14 UNIT 1..........................................................................................................................................................15 LESSON 1: WHOLE NUMBERS...............................................................................................................16 Counting with whole numbers...................................................................................................................17 ACTIVITY 1..............................................................................................................................................18 Ordering whole numbers..............................................................................................................................22 ACTIVITY 2..............................................................................................................................................23 Place value...........................................................................................................................................................26 ACTIVITY 3..............................................................................................................................................30 Comparing whole numbers..........................................................................................................................33 ACTIVITY 4..............................................................................................................................................34 Representing whole numbers.....................................................................................................................36 ACTIVITY 5..............................................................................................................................................37 LESSON 2: NUMBER SENTENCES.........................................................................................................38 ACTIVITY 6..............................................................................................................................................40 ACTIVITY 7..............................................................................................................................................42 ACTIVITY 8..............................................................................................................................................43 Pairs of equivalent number sentences....................................................................................................47 ACTIVITY 9..............................................................................................................................................48 Addition and subtraction techniques......................................................................................................50 Commutative property of addition...........................................................................................................50 Associative property of addition...............................................................................................................51 ACTIVITY 10............................................................................................................................................52 Order of subtraction........................................................................................................................................53 ACTIVITY 11............................................................................................................................................53 i
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Study Guide 1/2 G05 ~ Mathematics
LESSON 3: WHOLE NUMBERS...............................................................................................................54 Addition with whole numbers....................................................................................................................54 ACTIVITY 12............................................................................................................................................55 ACTIVITY 13............................................................................................................................................58 Subtraction of whole numbers...................................................................................................................59 ACTIVITY 14............................................................................................................................................61 Estimation...........................................................................................................................................................65 ACTIVITY 15............................................................................................................................................67 Rounding..............................................................................................................................................................70 ACTIVITY 16............................................................................................................................................72 ACTIVITY 17............................................................................................................................................73 Compensation....................................................................................................................................................74 Doubling and halving......................................................................................................................................74 ACTIVITY 18............................................................................................................................................75 ACTIVITY 19............................................................................................................................................77 Testing calculations with inverse operations.......................................................................................77 ACTIVITY 20............................................................................................................................................79 LESSON 4: NUMBER PATTERNS (Numeric patterns)....................................................................80 ACTIVITY 21............................................................................................................................................81 Input and output values................................................................................................................................82 ACTIVITY 22............................................................................................................................................83 ACTIVITY 23............................................................................................................................................85 ACTIVITY 24............................................................................................................................................86 The associative property of multiplication...........................................................................................87
LESSON 5: WHOLE NUMBERS (Multiplication and division).....................................................90 Multiplication.....................................................................................................................................................90 ACTIVITY 25............................................................................................................................................97 Division.................................................................................................................................................................99 ACTIVITY 26......................................................................................................................................... 101 LESSON 6: TIME.....................................................................................................................................103 ACTIVITY 27......................................................................................................................................... 108 ACTIVITY 28......................................................................................................................................... 111 LESSON 7: DATA HANDLING...............................................................................................................115 ACTIVITY 29......................................................................................................................................... 118 LESSON 8: PROPERTIES OF 2D SHAPES.........................................................................................123 ACTIVITY 30......................................................................................................................................... 128 LESSON 9: CAPACITY AND VOLUME ................................................................................................131 ACTIVITY 31......................................................................................................................................... 134 © Impaq
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Study Guide 1/2 G05 ~ Mathematics
UNIT 2.......................................................................................................................................................138 LESSON 10: WHOLE NUMBERS Counting, ordering, comparing and representing (6-digit whole numbers)....................................................................................................................................139 ACTIVITY 32......................................................................................................................................... 140 LESSON 11: WHOLE NUMBERS Addition and subtraction (5-digit whole numbers)..... 147 ACTIVITY 33......................................................................................................................................... 147 LESSON 12: COMMON FRACTIONS...................................................................................................153 ACTIVITY 34......................................................................................................................................... 156 ACTIVITY 35......................................................................................................................................... 163 LESSON 13: LENGTH.............................................................................................................................168 ACTIVITY 36......................................................................................................................................... 172 LESSON 14: WHOLE NUMBERS Multiplication (3-digit whole numbers by 2-digit whole numbers).................................................................................................................................................177 ACTIVITY 37......................................................................................................................................... 180 LESSON 15: PROPERTIES OF 3D OBJECTS.....................................................................................183 ACTIVITY 38......................................................................................................................................... 187 LESSON 16: GEOMETRIC PATTERNS...............................................................................................190 ACTIVITY 39......................................................................................................................................... 192 LESSON 17: SYMMETRY......................................................................................................................195 ACTIVITY 40......................................................................................................................................... 196 LESSON 18: WHOLE NUMBERS Division (3-digit whole numbers by 2-digit whole numbers).................................................................................................................................................200 ACTIVITY 41......................................................................................................................................... 204 References...............................................................................................................................................206
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Study Guide 1/2 G05 ~ Mathematics
LESSON ELEMENTS The guide contains various lesson elements. Each element is important for the learning process and indicates the skill you must master. ICON
LESSON ELEMENT
ICON
LESSON ELEMENT
Think for yourself
Take note! Important
Tips
Self-assessment
Research
Activity
Study
Did you know?
New concept or definition
Tip
Remember/Revise
1
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Study Guide 1/2 G05 ~ Mathematics
YEAR PLAN UNIT 1 DATE STARTED
TOPIC Mental maths: Use Train Your Brain Maths Grade 5
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) LESSON 4 Number patterns (Numeric patterns)
LESSON 5 Whole numbers (Multiplication and division) LESSON 6 Time
LESSON 7 Data handling
LESSON 8 Properties of 2D shapes LESSON 9 Capacity and volume
Revision: Use the CAMI programme © Impaq
2
DATE COMPLETED
Study Guide 1/2 G05 ~ Mathematics
UNIT 2 DATE STARTED
TOPIC
DATE COMPLETED
Mental maths: Use Train Your Brain Maths Grade 5
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 (5-digit whole numbers) LESSON 12 Common fractions LESSON 13 Length
LESSON 14 Whole numbers: Multiplication (3-digit whole numbers by 2-digit whole numbers) LESSON 15 Properties of 3D objects LESSON 16 Geometric patterns LESSON 17 Symmetry
LESSON 18 Whole numbers: Division (3-digit whole numbers by 2-digit whole numbers) Revision: Use the CAMI programme 3
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Study Guide 1/2 G05 ~ Mathematics
UNIT 3 DATE STARTED
TOPIC Mental maths: Use Train Your Brain Maths Grade 5 LESSON 19 Common fractions LESSON 20 Mass
LESSON 21 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (6-digit whole numbers) LESSON 22 Whole numbers: Addition and subtraction LESSON 23 Views of objects
LESSON 24 Properties of 2D shapes LESSON 25 Transformations LESSON 26 Temperature
LESSON 27 Data handling
LESSON 28 Number patterns
LESSON 29 Whole numbers: Multiplication (3-digit whole numbers by 2-digit whole numbers) Revision: Use the CAMI programme © Impaq
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DATE COMPLETED
Study Guide 1/2 G05 ~ Mathematics
UNIT 4 DATE STARTED
TOPIC
DATE COMPLETED
Mental maths: Use Train Your Brain Maths Grade 5
LESSON 30 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (6-digit whole numbers) LESSON 31 Whole numbers: Addition and subtraction (5-digit whole numbers) LESSON 32 Properties of 3D objects LESSON 33 Common fractions
LESSON 34 Whole numbers: Division (4-digit whole numbers by 2-digit whole numbers) LESSON 35 Perimeter, surface area and volume LESSON 36 Position and movement LESSON 37 Transformations
LESSON 38 Geometric patterns LESSON 39 Number sentences LESSON 40 Probability
Revision: Use the CAMI programme 5
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Study Guide 1/2 G05 ~ Mathematics
FACT SHEET Whole numbers Whole numbers are numbers without fractions or decimals. Whole numbers are always positive and never negative. Remember: 0 is also a whole number. Even numbers
•
All numbers that are divisible by 2 without a remainder. Even number end with 2, 4, 6, 8 or 0.
•
• •
Alternative words used for operations
Odd numbers
All numbers that are not divisible by 2 without a remainder. Odd numbers end with 1, 3, 5, 7 or 9.
Addition Add
More than
Add to
Sum of
Plus
Increase by
In total
Subtraction
Decrease by
Left
Less than
Less
Take away
Altogether
Deduct
Left over
Fewer than
Division
Divide
Halve
Difference between/of
Total of
Minus
Percent
Divide equally
How many times
Quotient
Half of
Per
Multiplication
Split into
Double
Of
Times
Goes into
Increase by a factor of © Impaq
And
Multiply by
Out of
Product of 6
Ratio of
Twice
Study Guide 1/2 G05 ~ Mathematics
Rounding Round to the nearest 5
0
1
2
3
4
5
6
7
8
9
10
Numbers ending with 3, 4, 5, 6 and 7 are rounded to 5. Numbers ending with 1 and 2 are rounded to the previous ten (end with a 0). Numbers ending with 8 and 9 are rounded to the next ten (end with a 0). Round to the nearest 10
Numbers smaller than 5 are rounded to the previous ten (end with a 0).
Numbers ending with 5, 6, 7, 8 and 9 are rounded to the next ten (end with a 0). Round 6 858 to the nearest 10:
Th HTU 6 858
Look at the tens column
The ones column must help you decide (8 is greater than 5, therefore the number is rounded to the next ten and ends with a 0 the answer is 6 860.)
Round to the nearest 100 Numbers smaller than 5 are rounded to the previous hundred (end with a 0). Numbers ending with 5, 6, 7, 8 and 9 are rounded to the next 100 (end with a 0). Round 6 858 to the nearest 100:
Th HTU 6 858
Look at the hundreds column
The tens column must help you decide (5 and greater are rounded to the next 100 and end with a 0 the answer is 6 900.)
Apply the same method when you round to 1 000. (The hundreds column must help you decide.)
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Study Guide 1/2 G05 ~ Mathematics
Properties Commutative property: Numbers may be added or multiplied together in any order. a + b = b + a a×b=b×a 10 + 8 = 8 + 10 12 × 3 = 3 × 12 18 = 18 36 = 36
Associative property: When you add or multiply numbers together, it does not matter how the numbers are grouped. (a + b) + c = a + (b + c)
13 + 24 + 22 = 13 + 24 + 22 (13 + 24) + 22 = 13 + (24 + 22)
(a × b) × c = a × (b × c)
(37) + 22 = 13 + (46) 59 = 59
3×4×2=3×2×4 (3 × 4) × 2 = 3 × (2 × 4) (12) × 2 = 3 × (8) 24 = 24
Distributive property: The distributive law of multiplication means that you can break down one or all of the numbers in a multiplication sum, multiply them separately and add the products together Regular method
(5)(8) = 40 (4)(12) = 48 47 × 45 = 2 115
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Distributive method
5(6 + 2) = (5 × 6) + (5 × 2) = 30 + 10 = 40
4(7 + 2 + 3) = (4 × 7) + (4 × 2) + (4 × 3) = 28 + 8 + 12 = 48 47 × 45 = 47 × (40 + 5) → Break down the number = 47 × 40 + (47 × 5) → Distributive property = 1 880 + 235 = 2 115 8
Study Guide 1/2 G05 ~ Mathematics
Common fractions
Numerator
1 4
Denominator
The top number (numerator) counts how many of the bottom number (denominator) there are. You can remember the difference by seeing that the denominator is down below. The denominator determines what we name the fraction, for example, quarters, eighths, etc. You may use a fractions wall to compare fractions.
Important: Before you compare or add fractions, you must always make the denominators the same. It means that you determine the Least Common Denominator (LCD). When you multiply the denominator by a number, you must also multiply the numerator by the same number.
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Study Guide 1/2 G05 ~ Mathematics
Time
Analogue time
1 minute = 60 seconds 1 hour = 60 minutes 24 hours = 1 day 7 days = 1 week 4 weeks = 1 month 12 months = 1 year 10 years = 1 decade
Digital time
Length 10 mm = 1 cm
100 cm = 1 m
1 000 m = 1 km
Mass 1 000 g = 1 kg
kilogram (kg)
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× 1 000 ÷ 1 000
10
gram (g)
Study Guide 1/2 G05 ~ Mathematics
Conversions: Multiply or divide by 10, 100 and 1 000 Convert grams to kilograms. 4 000 g ÷ 1 000 = 4 kg
Picture a comma at the end of the number.
When you divide by 1 000, move the imaginary comma three place values to the left (because there are three zeros in 1 000).
4 0 0 0 , g ÷ 1 0 0 0 = 4 , 0 0 0 kg
Convert kilograms to grams. 4 kg × 1 000 = 4 000 g
When you multiply by 1 000, move the imaginary comma three place values to the right (because there are three zeros in 1 000).
4 , 0 0 0 kg × 1 0 0 0 = 4 0 0 0 g
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Study Guide 1/2 G05 ~ Mathematics
2D shapes
Triangle
Square
3 straight sides 3 angles Rectangle
4 straight sides of equal length 4 right angles (90°)
2 long straight sides of equal length 2 shorter straight sides of equal length 4 right angles (90°)
No angles No straight sides (a curved side)
5 straight sides and 5 angles
6 straight sides and 6 angles
Circle
Hexagon
Pentagon
Heptagon
7 straight sides and 7 angles
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Study Guide 1/2 G05 ~ Mathematics
3D objects Rectangular prism
Cube (square prism)
Sphere
Cylinder
Cone
Square pyramid
Triangular pyramid
The base of the pyramid is a square and the other sides are triangles.
The base of the pyramid is a triangle and the other sides are triangles.
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Study Guide 1/2 G05 ~ Mathematics
Data handling Make a mark for each data unit. Every fifth mark goes across the group of four marks to make a group of five. It is easier to count data in groups of five.
Tally table Write down all the shoe sizes from small to large
Shoe size
Tally
2 3
|||| |
6
|||
3
||||
5
8
Teddy bear
Day 1 Day 2 Day 3 represents 6 teddy bears.
Pie chart
Grade 5 learners' maths test results
25 20 15 10 5 0
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A
B
22 The mode is the value that occurs most often in a data set. The mode of the data set is: Shoe size 3
Day
30
5
Total
Pictograph
Bar graph
Frequency
|||| |||
4
Every
Frequency indicates the answer of the count. It shows how many units of data there are.
C
D
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Study Guide 1/2 G05 ~ Mathematics
Unit
1
UNIT 1 This unit covers lessons 1 to 9.
UNIT 1
TOPIC Mental maths
LESSON 1 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (4-digit whole numbers) LESSON 2 Number sentences
LESSON 3 Whole numbers (Addition and subtraction) (5-digit whole numbers) LESSON 4 Number patterns (Numeric patterns)
LESSON 5 Whole numbers: Multiplication (2-digit whole number by a 2-digit whole number) and division (3-digit whole number by 1-digit whole number) LESSON 6 Time
LESSON 7 Data handling
LESSON 8 Properties of 2D shapes LESSON 9 Capacity and volume
Revision: Use the CAMI programme 15
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Unit
1
Study Guide 1/2 G05 ~ Mathematics
LESSON 1: WHOLE NUMBERS This lesson is a revision of Grade 4 work. Do you still remember what a whole number is? Whole numbers do not have fractions or decimals. Whole numbers are always positive and never negative. Remember: 0 is also a whole number. Examples of whole numbers
{0; 1; 2; 3; 4; 5; 6; ...}
1 2
0,5
If numbers 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.
Study the numbers in the table and circle the whole numbers.
1,9
153
10
100
-650
0
6 124
85
-8,98
99
-7
56 11
In this lesson, you will: • count • order • compare • represent and • indicate place value of whole numbers © Impaq
16
–
33
15
4
4
Study Guide 1/2 G05 ~ Mathematics
1
Unit
Counting with whole numbers In Grades 3 and 4, you learnt how to count with whole numbers. Do 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. +2
2
4
+2
6
+2
+2
8
10
+2
12
You may start with any number. Study the numbers. Do you see you can start at any number and count in whole numbers? +2
63
65
+2
67
+2
69
+2
71
+2
73
In the above examples, you counted on or forwards.
Using whole numbers, you can also count back or backwards. Study the numbers below and complete the missing numbers. Count back in 3s.
–3
53
–3
50
–3
–3
47
–3
41
17
–3
38
–3
32
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Unit
1
Study Guide 1/2 G05 ~ Mathematics
You will now count with bigger numbers. Study the numbers and complete the missing numbers. You must determine whether you need to count on or back, and by how many.
5 430
5 455
5 480
5 530
5 555
5 605
5 630
Complete the missing numbers.
9 999
9 949
9 899
9 849
9 699
9 649
Let’s apply what you have learnt.
ACTIVITY 1
DATE:
1.
Write the set of whole numbers between 1 915 and 1 921.
2.
Indicate whether the numbers are whole numbers. Colour the correct circle.
__________________________________________________________________________________________________
Numbers
Whole number: yes or no?
Example:
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Numbers 5 013
35
2.3
2.1
9 658
2.4
1
2.2
1 414,3
2.5
8 123
18
3
Whole number: yes or no?
Study Guide 1/2 G05 ~ Mathematics
3.
Unit
1
Logan is on a treasure hunt and discovers a message coded in numbers. If he can decipher the message, he will know where to find the largest treasure chest. The message is written in a ‘letter-number’ code. It means the letters have been replaced with numbers. Complete the missing numbers to decipher the message.
A
B
C
D
E
F
G
H
I
J
K
L
M
1 000
N
1 500
O
2 000
P
2 500
Q
3 000
R
3 500
S
4 000
T
4 500
U
5 000
V
5 500
W
6 000
X
6 500
Y
7 000
7 500
8 000
8 500
9 000
9 500
10 000
15 500
16 000
16 500
17 000
17 500
18 000
18 500
Number pattern 3.1
8 800; 8 650; ____________________ ; 8 350; ...
3.3
2 375; 4 750; ____________________ ; ...
3.2 3.4 3.5
Z
Letter
____________________ ; 1 010; 1 020; 1 030; ... ____________________ ; 6 000; 7 000; ...
8 000; 9 000; ____________________ ; 11 000; ...
Logan will find the world’s largest treasure chest in ______________________________________.
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Unit
4.
1
Study Guide 1/2 G05 ~ Mathematics
The Grade 5s made slime in their Life Skills class. Three learners put beads in their slime. Lucinda put 10 beads in each container, Marli put 150 beads in her containers and Sibongile put 50 beads in each of her containers. Study the representation and count in 2s, 3s, 5s, 10s, 25s or 50s to complete the table. Learner
Number of containers
Number of beads
Lucinda
*Draw the beads in each container.
Marli
150
Sibongile
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Study Guide 1/2 G05 ~ Mathematics
5.
Complete the flow charts. 5.1 – 10
– 10
– 10
+ 25
+ 25
+ 25
– 10
3 190
1
Unit
5.2
+ 25
412
Self-assessment Do you understand the work? Colour the faces that show what you can do. COUNTING WITH WHOLE NUMBERS Requirements
Can I do it?
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 the above up to the number 10 000.
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Unit
1
Study Guide 1/2 G05 ~ Mathematics
Ordering whole numbers In Grade 4 you learnt how to order and arrange numbers in a specific order. Do you still remember how it works? Briefly revise ordering whole numbers. Ordering means to arrange or organise numbers.
order = arrange
We can order or arrange numbers in different ways: from GREAT to small
OR from small to GREAT Study the number set:
{4 952; 4 592; 5 942; 2 924} Arrange the numbers from great to small. Step 1:
Step 2:
Choose the greatest number and write it down first. The greatest number in this set is 5 942.
Now cross out the greatest number in the number set.
{4 952; 4 592; 5 942; 2 924} You can no longer choose the number 5 942.
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Study Guide 1/2 G05 ~ Mathematics
Step 3:
1
Unit
From the remaining numbers, choose the greatest number and write it next to 5 942.
5 942; 4 952;
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 like this:
{5 942; 4 952; 4 592; 2 924} You have now arranged the number set from greatest to smallest.
Can you arrange the following number set from small to great?
{5 667; 5 676; 5 766; 6 756; 6 657} Tip: Start by choosing the smallest number, not the greatest one. Write your answer in the box below.
ACTIVITY 2 1.
1.
DATE:
Arrange the numbers from small to great.
Question
1.1 1.2 1.3 1.4 1.5
8 812
2 390
6 511
2 067
6 749
7 100
7 214
3 113 5 480
8 121 3 904
5 110
2 607
5 332
4 553
4 535
4 335
5 433
5 343
9 191
1 919
9 119
1 991
1 199
23
4 533
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Unit
2.
1
Study Guide 1/2 G05 ~ Mathematics
Arrange the numbers from great to small.
2.1 2.2 2.3 2.4 2.5
4 312
1 088
8 420
3 733
4 231
9 124
3 420
2 607
3 398
4 568
4 586
4 685
4 658
4 865
2 131 2 113
2 311
3 211
3 121
5 559
5 955
9 555
5 595
Question
3.1 3.2 3.3
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5 686
Build and arrange the numbers. You may build any 6 numbers for each question. Example
3.
Question
Write down the numbers you can build with 6, 3 and 2. Arrange them from small to great. 236; 263; 326; 362; 623; 632
Write down the numbers you can build with 1, 4, 3 and 5 and arrange them from great to small. Write down the numbers you can build with 7, 2, 1 and 9 and arrange them from small to great. Write down the numbers you can build with 6, 8, 1 and 6 and arrange them from great to small.
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Study Guide 1/2 G05 ~ Mathematics
3.4
3.5
1
Unit
Write down the numbers you can build with 0, 9, 1 and 2 and arrange them from small to great. (Use 0 as a significant digit only, in other words, as a placeholder. Leading 0s – 0s used as the first digit in a number – are not significant.) Write down the numbers you can build with 1, 9, 1 and 1 and arrange them from great to small.
Self-assessment Do you understand the work? Colour the faces that show what you can do. ORDERING WHOLE NUMBERS Requirements
Can I do it?
I can arrange number sets from great to small. I can arrange number sets from small to great. I can build and arrange different numbers.
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