NSW Syllabus Outcomes
MA3-RN-01
Applies an understanding of place value and the role of zero to represent the properties of numbers
MA3-RN-02
Compares and orders decimals up to 3 decimal places
MA3-RN-03
Determines percentages of quantities, and finds equivalent fractions and decimals for benchmark percentage values
MA3-AR-01
Selects and applies appropriate strategies to solve addition and subtraction problems
MA3-MR-01
Selects and applies appropriate strategies to solve multiplication and division problems
MA3-MR-02
Constructs and completes number sentences involving multiplicative relations, applying the order of operations to calculations
MA3-RQF-01
Compares and orders fractions with denominators of 2, 3, 4, 5, 6, 8 and 10
MA3-RQF-02
Determines
MA3-GM-01
Locates and describes points on a coordinate plane
MA3-GM-02
MA3-GM-03
of measures and quantities
Selects and uses the appropriate unit and device to measure lengths and distances including perimeters
Measures and constructs angles, and identifies the relationships between angles on a straight line and angles at a point
MA3-2DS-01
Investigates and classifies two-dimensional shapes, including triangles and quadrilaterals based on their properties
MA3-2DS-02
Selects and uses the appropriate unit to calculate areas, including areas of rectangles
MA3-2DS-03
Combines, splits and rearranges shapes to determine the area of parallelograms and triangles
MA3-3DS-01
Visualises, sketches and constructs three-dimensional objects, including prisms and pyramids, making connections to two-dimensional representations
MA3-3DS-02
Selects and uses the appropriate unit to estimate, measure and calculate volumes and capacities
MA3-NSM-01
Selects and uses the appropriate unit and device to measure the masses of objects
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MEASUREMENT AND SPACE
MA3-NSM-02
Measures and compares duration, using 12- and 24-hour time and am and pm notation
MA3-DATA-01
Constructs graphs using many-to-one scales
MA3-DATA-02
Interprets data displays, including timelines and line graphs
MA3-CHAN-01
Conducts chance experiments and quantifies the probability
MAO-WM-01 Working mathematically
STATISTICS AND PROBABILITY
Develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly
iv
Units 1 2 3 4 NUMBER
AND ALGEBRA
2
1 4 , 1 5
1 10
1
,
and
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STATISTICS AND PROBABILITY
MA3-DATA-01
MA3-DATA-02
MA3-CHAN-01
MAO-WM-01 Working mathematically
v 5 6 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 NUMBER AND ALGEBRA MA3-RN-01 MA3-RN-02 MA3-RN-03 MA3-AR-01 MA3-MR-01 MA3-MR-02 MA3-RQF-01 MA3-RQF-02
AND SPACE MA3-GM-01 MA3-GM-02 MA3-GM-03 MA3-2DS-01 MA3-2DS-02 MA3-2DS-03 MA3-3DS-01
MEASUREMENT
MA3-3DS-02 MA3-NSM-01 MA3-NSM-02
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Number and Algebra
7 Michael saved $1206 in February, $986 in March and $1807 in April. What was his total for the 3 months?
8 How much is Stella’s set of 4 paintings worth if they were valued at $4125, $3250, $1899 and $5455?
UNIT 2
SET 1 Basic 1 24 + 8 2 8 × 6 3 34 – 17 4 8 4 = 32 5 27 9 = 3 6 92 7 Divide 72 by 8. 8 12 4 = 48 9 Product of 11 and 5 10 Sum of 9, 5 and 10 11 Quotient of 54 and 6 12 Cents in $8.69 13 (6 + 2) × (3 + 6) 14 Factors of 45 15 I had $20 but I spent $13.50. How much have I left? $
Measuring angles 1 3 7 0 4 2 3 6 2 8 + 2 2 0 4 + 4 7 1 9 3 3 8 7 6 4 4 7 2 0 + 6 6 6 + 7 0 8 9 5 3 6 2 5 6 3 0 7 8 7 0 3 6 0 9 8 0 8 6 0 + 9 2 4 + 7 4 3 6
Space
✍ ✍ Measure each angle using a protractor. 1 8 2 3 8 4 8 8 1
2
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SET
Addition
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Number and Algebra
1 5.8 + 3.6
2 20 × 5 × 8
3 Value of 8 in 78 321
4 4 10 of 50
5 Round 8.3 to the nearest whole number.
6 Add 1.7 to 4.4.
7 5 tickets at $1.65 each
8 Subtract the sum of 50 and 40 from 200.
To multiply by 5, multiply by 10 then halve your answer.
4 42 × 5 = 7 84 × 5 =
5 64 × 5 = 8 80 × 5 =
6 48 × 5 = 9 18 × 5 =
To multiply by 4, use the double and double again strategy.
10 13 × 4 = 12 42 × 4 =
11 26 × 4 = 13 18 × 4 =
To multiply by 8, use the double, double and double again strategy.
14 13 × 8 = 16 32 × 8 =
15 21 × 8 = 17 15 × 8 =
Measurement
9 Add the product of 6 and 8 to 42.
10 Round 1561 to the nearest thousand.
11 7 100 is less than 0.5. True or false?
12 If the water in the jug is 87°C, how many more degrees before it boils?
13 If Hugo ran 0.8 km each day, how far did he run in a school week?
14 Round and estimate 399 × 19.
15 If I spent $2, $1 and 65c, how much change would I receive from $5?
16 How many 250 g bags of rice can be made from a 3 3 4 kg bag?
Each band on the radar is equal to 10 km. Estimate the distances of the submarines from the centre of the radar screen.
3 UNIT
SET 4 Extension Solve the facts. 1 ×5 2 ×7 3 ×9 3 2 2 5 5 5 7 7 7 8 9 9 6 8 8
1 Submarine A km 2 Submarine B km 3 Submarine C km 4 Submarine D km 5 Submarine E km 6 Submarine F km HMAS Pinafore radar A F D B E C SET
Multiplication strategies
3
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Number and Algebra
1 – 8 = 3
15
What is 25 cm less than a metre? cm
Space Two-dimensional shapes
Sketch a shape to match each description.
1 I am a shape with 5 sides the same length and 5 identical angles.
2 I am a shape that has 3 sides and 1 right angle.
SET 2
Addition and subtraction strategies
Add these numbers mentally.
1 37 + 49 = 5 121 + 56 =
2 68 + 75 = 6 379 + 85 =
3 81 + 67 = 7 741 + 126 =
4 99 + 36 = 8 899 + 257 =
Subtract these numbers mentally.
9 76 – 29 = 12 149 – 37 =
10 89 – 57 = 13 259 – 58 =
11 68 – 34 = 14 741 – 127 =
Round each number to the nearest 100 to estimate an approximate answer. The first one has been done for you.
3 I am a shape that has 4 sides the same length but 2 sets of angles.
4 I am a shape with 8 sides of equal length and 8 identical angles.
UNIT 4
SET 1 Basic
2 85 × 0
3 21 ÷ 3
4 400 – 150
5 72
6 Date after 11 February
7 49 ÷ 7
8 5c × 100
9 Difference between 19 and 90 10 Season before spring
11 28 7 = 4
12 Quotient of 24 and 6
13 How many quarters in 5?
14 Value of 7 in 17 940
Working Mathematically
Question Rounded to 100 Approximate answer
395 + 206 400 + 200 600
591 – 298
513 + 387
785 – 589
372 + 329
882 – 286
15
16
17
18
19
20
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Number and Algebra SET 4
1 6 × 15
2 23 100 = %
3 Value of 6 in 37 206
4 Average of 45, 25 and 35
5 3 4 of $96
6 How many faces has a rectangular prism?
7 Round 63 209 to the nearest 100.
8 If 3 kg cost $18.60, how much would 5 kg cost?
9 38 100 = 38%. True or false?
10 300 ÷ 2 × 10 – 750 + 53
Solve these missing number sentences. Each shape has the same value in every question. For example, the square is always equal to 9.
Measurement Square centimetres
Calculate the area of these rectangles in square centimetres (cm2 ).
5 UNIT
Extension
Length × Width = Area 1 2 3 1 2 3
Working Mathematically
×
54 12 × 2 = 13 ÷ = 14 × + = 33 15 72 ÷ × = 48 16 54 ÷ = ×
11
=
SET 3 Fractions, decimals and percentages Fraction Decimal % 1 2 3 4 5 6 7 Order from smallest to largest. 30% 0.29 35% 0.33 9% 0.9 0.54 49% 4% 0.21 90% 0.95 7% 0.03 8 9 10 11 12 13 14 7 10 3 10 10 100 25 100 27 100 53 100 99 100 9 100 70 100 3 4 1 4 1 2 1 2 20 100 2 Mathematical Reasoning MP_NSW_MH6_38299_TXT_4PP.indb 5 26-Aug-23 13:01:33
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Number and Algebra
Statistics and Probability Picture graphs
Subtracting 4-digit
UNIT 6
SET 1 Basic 1 8 + 7 2 3 × 4 3 13 – 4 4 6 3 = 18 5 18 6 = 12 6 32 7 Divide 12 by 2. 8 18 3 = 6 9 Product of 7 and 4 10 Sum of 7 and 14 11 Difference between 14 and 21 12 (3 + 7) × 7 13 Is 28 a multiple of 7? 14 1207, 1210, 1213, 15
has
800 m race.
much further does he need to run to finish the race? m
Peter
run 550 m of an
How
1 5 0 0 0 2 8 0 0 0 – 3 0 0 0 – 4 0 0 0 3 5 4 2 5 4 8 9 6 0 – 3 0 0 0 – 4 0 0 0 5 6 9 8 2 6 8 5 3 6 – 3 4 2 1 – 3 4 2 5 7 8 5 1 6 8 8 6 4 3 – 3 3 4 4 – 4 4 6 1 9 5 9 4 1 10 6 3 8 1 – 3 7 9 9 – 1 2 9 5 11 8 1 6 1 12 7 5 6 4 – 3 4 2 9 – 3 8 1 8 SET 2
numbers Red Brown Black Hair colours year 6 Fair Blond
the key to answer the questions. How many children had:
red hair?
brown hair?
black hair?
fair hair?
blond hair?
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Use
1
2
3
4
5
KEY
Number and Algebra
SET 3 Revising 3-digit division
1 Value of 7 in 73 256
2 Write 8 100 as a percentage.
3 1.8 m = cm
7 Share $64 among 8.
8 How many fives in 90?
9 450 ÷ 10
10 What is the quotient when 357 is divided by 7?
11 Share 424 blocks among 4 groups.
12 Lisa’s mum won $924 in the lottery. If she shared it with another 6 people, how much did each person receive?
13 540 spectators were seated in 10 rows. How many in each row?
14 A group of 217 boys was divided into 7 teams. How many in each team?
Space Constructing angles
Use a protractor to create these angles.
4 Round 3.9 to the nearest whole number.
5 Average of 43, 36 and 50
6 3113, 3128, 3143,
7 92 – 5
8 Would a hot summer’s day be 20ºC, 35ºC or 100ºC?
9 How many grams in 7.3 kg?
10 Round 29 306 to the nearest 1000.
11 3 10 of 200
12 Perimeter of a pentagon with sides of 1.5 cm
13 How many axes of symmetry has a square?
14
15 Tom ate 25% of the cake. Jill ate 0.27 of it and Max ate 33 hundredths of it. How much was left?
16 How much does 9 kg of meat cost at $3.50 kg?
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7 UNIT
SET 4 Extension 1 2 3 3 969 4 568 5 175 4 5 6 6 156 7 763 8 744
3 5 = 40
✍ ✍ ✍ ✍ ✍
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Number and Algebra
SET 2 Addition of 4-digit numbers
Number and Algebra Negative numbers
Bill’s Bus Service charges customers $2 for every kilometre they travel. Calculate the distance and the cost for each journey.
Journey Metres Cost
1 A to C via B
2 B to E via C and D
3 F to B via G and A
4 E to A via F and G
5 G to D via A, B and C
6 B to F via C, D and E
7 F to C via G, A and B
Calculate the answers. The number lines may help you.
UNIT 8
SET 1 Basic 1 9 × 5 2 16 – 9 3 14 + 8 4 42 5 16 4 = 12 6 18 3 = 6 7 Divide 35 by 7 8 20 20 = 40 9 × $28 10 Quotient of 25 and 5 11 Factors of 9
Are 18 and 24 multiples of 6?
Is 21 a prime number?
How many cm in 7 m?
Phillip spent $6.50 and $4.50. What was the total amount he
$ 1 4
12
13
14
15
spent?
1 –2 + 4 + 3 – 6 = 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 0 2 –8 + 3 + 5 – 7 = 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 0 3 –6 + 7 – 9 + 2 = 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 0
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2200m
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Number and Algebra SET 4 Extension
Draw beads on the abacuses to represent the numbers.
1 257 379 2 703 825
1 160 – 85
2 =
3 Value of 7 in 86 791
3 Write the number sixty-four thousand, nine hundred and twenty-eight.
4 What are the next 2 numbers after 52 817?
5 How many whole dollars in 19 361 cents?
6 Round 46 985 to the nearest thousand.
7 Subtract 1000 from 158 695.
8 What number is ten thousand less than 262 340?
9 How many hundreds are in 34 972?
10 What number is one thousand more than 442 186?
11 What are the 2 numbers before 214 901?
12 What is the next odd number after 25 131?
13 What number is ten thousand less than 985 970?
4 Complete this sequence: 5404, 5504, 5604, ,
5 How many months in half a year?
6 × 48 + 207
7 Round $18.61 to the nearest dollar.
8 Average of 45, 26, 39 and 450
9 180 seconds = minutes
10 How much is 4 kg at $1.70 a kg?
11 1 km ÷ 4 = m
12 Place in a sequence: , , ,
13 9:25 + 58 minutes
14 $0.72 × 9
15 How much change would I receive from $20 if I bought three $1.85 ice creams?
16 If 3 kg cost $1.95, how much would 10 kg cost?
17 Round to estimate an answer to 51 × 494.
Measurement and Space Classifying three-dimensional objects
