×
3
MAKING REAL-WORLD CONNECTIONS
maths a ×
MAKING REAL-WORLD CONNECTIONS M
STEPH KING
9781380050687__text.indb 1
03/05/2022 10:17
Contents
Data handling Collecting data Representing data Interpreting data
78 80 83 85 88 90 94 96 98
How to Use This Book
iv
6
Numbers and patterns Representing and describing 3-digit numbers
2
1
4 7 9
Whole numbers and fractions Numbers and place value Comparing and ordering numbers Counting patterns Rounding numbers Representing proper fractions Comparing unit fractions and proper fractions
Place value
7
Comparing numbers Counting patterns
12 Fractions – parts and wholes14
Money and measures Telling the time Durations of time Length and height
18 20 23 25 29
2
100
Money
102
Addition and subtraction 32 Addition and subtraction facts 34 Doubles and halves 37 Adding pairs of 2-digit and 3-digit numbers 39 Subtraction with pairs of 2-digit and 3-digit numbers 43
3
Length, mass and capacity Length, height and distance
8
104
106 Sequence title: perimeter 108 Mass 111 Capacity 114 Addition and subtraction116 Totals to 100 118 Using addition and subtraction facts 121 Adding 2-digit and 3-digit numbers 123 Subtraction with 2-digit and 3-digit numbers 126 130 Counting coins and notes 132 Totals and change 134 Units of time 136 Dates and calendars 137
9
Lines and shapes
46 48 51 54
4
Straight lines and curves
Plane shapes (two-
dimensional shapes)
Right angles
Solid shapes (three-
dimensional shapes)
56
Multiplication and division60 Representing multiplication 62 Multiplying by 2 and 4 65 Multiplication tables 67 Multiplication and division facts 69 Division as equal sharing 73 Division as equal grouping 76
5
10 Money and time
ii
9781380050687__text.indb 2
03/05/2022 10:17
Contents
Subtraction with 3-digit numbers
11 Multiplication and division
190
140 142
Multiplying 2-digit numbers
194 Dividing 2-digit numbers 197
Multiplying by 3 and 6 Multiplication and division facts for 3 and 6 Multiplying teens numbers by 2, 3, 4, 5 and 6 Multiplying numbers by 10 and 100
145
16 More on measures
200
Solving problems about length, height and distance Solving problems about capacity Solving problems about mass
147
202
150 Dividing 2-digit numbers 151
205
12 Shapes and direction
154 156 158
208
Angles
Reflective symmetry
17 Shapes and angles
212 214
Position 160 13 Working with fractions 164 Equivalent fractions 166 Adding fractions 169 Fractions of quantities 171 14 Data handling 174 Collecting data 176 Representing data 179 Interpreting data 181 15 The four operations 184 Adding and subtracting multiples of 100 186 Adding pairs of 3-digit numbers 188
Lines and line segments
Describing and comparing 2D shapes (plane shapes)216 Describing and comparing 3D shapes (solid shapes) 220
18 Patterns, puzzles and problems Patterns and sequences
224 226 229
Puzzles
Creating and solving problems about addition and subtraction
231
Creating and solving problems about multiplication and division
233
iii
9781380050687__text.indb 3
03/05/2022 10:17
How to Use This Book Welcome to Max Maths !
Positivity towards mathematics – the activities provide opportunities to explore mathematics through pattern, reasoning and in meaningful contexts. While developing proficiency, students experience an enjoyment in mathematics, and an appreciation of the beauty and power woven into its fabric. Max Maths is designed specifically to support the new OECS Learning Standards for Mathematics, and to provide regular engagement in all important mathematical processes. Look out for the icons that show: problem solving
The philosophy behind the design of Max Maths is to develop confident , curious , resourceful and proficient mathematicians. The Max Maths approach comprises a comprehensive set of resources that provide: Rich mathematical experiences – each activity uses a Concrete-Pictorial- Abstract (CPA) approach to enrich learning, and develop a visual and physical intuition for mathematical concepts. This means that abstract concepts and calculations are supported with visual representations and concrete materials such as cubes or counters to bring the mathematics to life through practical activities and visual prompts for discussion and understanding. Depth of understanding – the activities use a range of questioning techniques to enable students to develop skill and accuracy alongside a deep mathematical understanding of the concepts. Each year is organised to provide progression over time, with each revisit digging deeper into the skills and mathematical thinking.
reasoning
communicating
connecting
representing Opportunities to develop each
mathematical process are built into the main activities in the Student’s Books and are clearly signposted within the challenges provided in the Teacher’s Guides.
Winston
Jade
Letisha
Leon
Carl
Riana
iv
9781380050687__text.indb 4
03/05/2022 10:17
How To Use This Book
This student’s book provides a teaching resource to support whole-class teaching and is designed to be accompanied by a workbook for students to write and draw in, to create a record of their achievements. Each unit provides a double-page spread designed to be talked about, prompting students’ curiosity, communication, conjecture and challenge.
Unit 1 – Numbers to 10
1 Numbers to 10
KEY questions
KEY words
Which of these words can you use to describe what you see in the picture? Equal Same as Count Number
How many leaves? How many shells? How many cubes? How many counters? How do you know you have counted them all?
2
3
There are many different activity types, carefully ordered, to help students through their learning journey.
Unit 2 – Money and measures
Analogue clocks Let’s Recap
Let’s Practise
1 Estimate and measure. Which units of measurement will you use?
The clock shows that the time is half past three.
The mass of:
Estimate: Heavier than, lighter than or the same as one kilogram?
Measure
(a) 8 exercise books (b) Your shoe
The clock shows that the time is quarter past six.
(c)
A full pencil pot
Who do you agree with? Why? What do we need to know about when reading the time on an analogue clock? Let’s Learn Together 1 It takes the minute hand 5 minutes to move from one number to the next. It takes the minute hand 60 minutes to move all the way around the clock. There are 60 minutes in 1 hour.
(d) Your games bag
2 Work together in a small group to carry out this investigation
Does the tallest person have the longest stride?
Make estimates and think about the unit of measurement you will use. Record your measurements to the nearest whole unit. Make a table of your results. What does the information tell you? Can you answer the original question?
We can use what we know about counting in multiples of five to help us work with time.
60 minutes 0 minutes
55 minutes
5 minutes
50 minutes
10 minutes
E
Leon has only part of an old tape measure. Some of the numbers have rubbed off. He uses it to measure these objects in centimetres. What is the actual measurement of each object? Explain why. 28 40 42
15 minutes
45 minutes
44
40 minutes
20 minutes
35 minutes
25 minutes
30 minutes
24
29
1
9781380050687__text.indb 1
03/05/2022 10:17
1 Numbers and patterns
KEY questions
How many more ones to make another 10? How many more tens to make another 100? What stones do you need to make the number 65? How about 165?
2
9781380050687__text.indb 2
03/05/2022 10:17
KEY words
Which of these words can you use to describe what you see in the picture?
Ones
Tens
Hundreds
Greater
Smaller
First
Second
3
9781380050687__text.indb 3
03/05/2022 10:17
Representing and describing 3-digit numbers
Can you show how 10 ones make 1 ten using beads? Can you show how 10 tens make 1 hundred using blocks? What other ways can you show?
Here is part of a number line.
80
90
100
110
Which numbers are positioned in the shaded part? Will there be more 2-digit numbers or 3-digit numbers? How many different numbers can you find?
4
9781380050687__text.indb 4
03/05/2022 10:17
Unit 1 – Numbers and patterns
Unit 2 – Money and measures
1 We can represent and describe the number 100 in different ways.
100 is the first 3-digit number
1
0
0
+ 1
100 is one more than 99 on a number line
99
100
101
100 is made of 10 tens or 100 ones
90
10
100 is 90 plus 10
100
10
10
10
10
10
10
10
10
10
10
100 is 50 + 50
10
10
10
10
10
10
10
10
10
10
We say and write the number as one hundred.
Look at the numbers represented here.
2
5
9781380050687__text.indb 5
03/05/2022 10:17
Which numbers are represented here? (a) There are
1
hundreds and
tens.
The number is We say the number as
(b)
There are
hundreds,
tens and
ones.
The number is
We say the number as
2 Use blocks or similar to represent these numbers. (a) 246 (b) 256 (c) 257 (d) 357 (e) 457
(f ) 467
Talk about any patterns you notice.
3 Describe these numbers in different ways. What representations will you use? (a) 199 (b) 101 (c) 200
E
Carl has 9 blocks. What different numbers can he make? Remember that blocks can be hundreds, tens or ones. Can you also find the largest and the smallest number?
6
9781380050687__text.indb 6
03/05/2022 10:17
Unit 1 – Numbers and patterns
Place value
Look at the numbers on the counters. What number do they represent?
1
100
1
1
100
100
1
10
10
100
1
1
1
4 hundreds 2 tens 6 ones
There are:
2 We can show the number on a place value chart.
10
1
100
4
2
6
10
1
100
1
100
1
100
1
400 20 6 426
1
426 Four hundred and twenty-six
The value of the digit 4 is 400 because it is in the hundreds place. The value of the digit 2 is 20 because it is in the tens place. The value of the digit 6 is 6 because it is in the ones place. 3 We can expand the number 426 to show the place value parts. 426 = 400 + 20 + 6 The total value is 426 .
7
9781380050687__text.indb 7
03/05/2022 10:17
What number is represented here? (a)
1
100
100
1
100
10
100
1
100
10
100 100 100
1
10
(b) The digit 8 is in the hundreds place. Its value is
.
The digit 3 is in the tens place. Its value is
.
The digit 3 is in the ones place. Its value is
.
What number is represented here?
1
8
9781380050687__text.indb 8
03/05/2022 10:17
Unit 1 – Numbers and patterns
Answer these in your exercise book: (a) 729 The digit 7 is in the hundreds place and it represents
2
. . . . . .
The digit 2 is in the tens place and it represents The digit 9 is in the ones place and it represents
(b) 105 The digit 1 is in the hundreds place and it represents
The digit 0 is in the tens place and it represents The digit 5 is in the ones place and it represents
3 Expand these numbers to show their place value parts. (a) 292 (b) 340 (c) 538 (d) 444 (e) 835 Comparing numbers
1 We can use place value to help compare numbers. Which number is larger?
1 2
5 0
9 4
We compare the largest values first. 204 has 2 hundreds but 159 only has 1 hundred. 204 is larger (or greater) than 159.
9
9781380050687__text.indb 9
03/05/2022 10:17
Let’s compare two more numbers.
2
6 6
7 5
2 9
672 and 659 have the same number of hundreds. 672 has 2 more tens so it is greater than 659.
Find the greater value. (a)
1
2 1
3 3
1 2
hundreds is greater than
hundred.
is greater than
.
(b)
Group A and B both have the tens. Group A and B both have
hundreds so we must compare
tens so we must compare the ones.
Group A has
ones. Group B has
ones.
is smaller than Group
.
Group
10
9781380050687__text.indb 10
03/05/2022 10:17
Unit 1 – Numbers and patterns
Find the smaller number each time. (a) 86 and 106
1
(b) 280 and 208 (d) 773 and 779
(c)
663 and 672
Find the greater value each time. (a) $109 and $99
2
(b) $324 and $423 (d) $220 and $221
(c)
$994 and $968
Each group will need a set of counting blocks.
Your teacher will then call out an instruction. Show a possible 3-digit number as quickly as you can. Put your hand up when your group has finished making a number. Explain how you know your number is possible. Each group that shows a possible number scores a point. How many points can your group score after 10 instructions?
11
9781380050687__text.indb 11
03/05/2022 10:17
Counting patterns
Use counters to make a counting pattern of twos.
2 4 6 … What do you notice? What will the 6th number be? Now make a counting pattern of fives. What do you notice this time? What will the 11th number be?
1
All even numbers can be grouped exactly in twos or shared between 2 equal groups. Odd numbers cannot be grouped exactly in twos. Odd numbers leave a remainder when they are shared between 2 equal groups When we count by twos from an even number, the numbers we say are all even .
+2 +2 +2
0
2
4 7 +2 +2 +2 8 5 6
10
12
odd numbers even numbers
1
3
9
11
When we count by twos from an odd number, the numbers we say are all odd .
12
9781380050687__text.indb 12
03/05/2022 10:17
Unit 1 – Numbers and patterns
2 Look at the counting patterns for 5 and 10. 0 5
10 15 20 25 30 35 40 45 50
5
10
0 50 There are 2 fives in every 10 so the numbers in the count of 10 can also be found in the count of 5. 10 20 30 40
10
20
30
40
50
60
70
80
90
100
5
15
25
35
45
55
65
75
85
95
The ones digits in the count of 5 also make a pattern with the digits 5 and 0. This means that the count of 5 also has a pattern with even and odd numbers. 3 The numbers in the count of 10 are all even and have 0 in the ones place. 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 The 10th number in the count of 10 is 100. What will the 20th number be? 1 Count by twos from these starting numbers. Write the next five numbers that you say. Will the numbers in each count be odd or even? (a) 7, , , , , (b) 37 (c) 48 (d) 148 (e) 60 (f) 160
13
9781380050687__text.indb 13
03/05/2022 10:17
2 Count by tens from these starting numbers. Write the next six numbers that you say. (a) 160 (b) 270 (c) 380 (d) 490 (e) 500 (f ) 510 3 Jade counts by fives from 380 up to 500. (a) What is the 5th number that she says? (b) What is the 10th number that she says? (c) Will the number 454 be in her count? Explain your answer.
E
What can you show, write or say to share your thinking with others?
Fractions – parts and wholes
Cut three strips of paper. Make sure they are the same size.
Fold the first strip into 2 equal parts. Fold the second strip into three equal parts. Then fold the third strip into four equal parts. Can you name each part? Which is larger? Can you explain why?
14
9781380050687__text.indb 14
03/05/2022 10:17
Unit 1 – Numbers and patterns
Fractions are parts of a whole. When a whole is divided into 10 equal parts, each part is one tenth ( 1 __ 10 )
1
1 10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
1 __ 10 is 1 out of 10 equal parts.
2 This number line is divided into 4 equal parts.
1 4
1 2
3 4
0
1
Three-quarters ( 3 _
4 ) of the whole is coloured.
3 _ 4 is 3 out of 4 equal parts. One-quarter plus one-quarter plus one-quarter is three-quarters.
15
9781380050687__text.indb 15
03/05/2022 10:17
3 The triangle is divided into three equal parts. Two thirds ( 2 _
3 ) of the whole is coloured.
2 _ 3 is 2 out of 3 equal parts. One-third plus one-third is two-thirds.
1 3
1 3
Write the fraction of each shape that is coloured in words and numbers. (a) (b)
=
=
What fraction of each shape is shaded? Write your answer in words and in numbers. (a) (b)
1
(c)
(d)
16
9781380050687__text.indb 16
03/05/2022 10:17
Unit 1 – Numbers and patterns
2
0
1
(a) Which fractions are missing from the number line? (b) What fraction is coloured pink?
There are 10 oranges in a bag. The children eat 4 out of the 10 oranges. What fraction of the whole bag did they eat? How can you represent the problem?
3
Use your fraction strips from the Start Thinking activity. Label the fractions. Play this game with a partner. You will each need some counters. Take it in turns to spin two numbers. Make a fraction, e.g. spin a 1 and a 3 to make 1 _ 3 . Cover this fraction of a strip. Explain what fraction of the whole strip is covered in total. Miss a turn if you cannot go. The aim of the game is to be the first to cover all three of your strips. 4 3 1 2
17
9781380050687__text.indb 17
03/05/2022 10:17
2 Money and measures
18
9781380050687__text.indb 18
03/05/2022 10:18
KEY words
Which of these words can you use to describe what you see in the picture?
Longer
Shorter
Higher
Lower
Metre
Centimetre
Hour
Minute
Dollar
KEY questions
What units of measure are being used? Which race had a winning time that was equal to half an hour?
19
9781380050687__text.indb 19
03/05/2022 10:18
Telling the time
Who do you agree with? Why? What do we need to know about when reading the time on an analogue clock?
What could the time be? What could you be doing when it is an a.m. time? What could you be doing when it is a p.m. time?
Look at these clocks. What is the time?
1
20
9781380050687__text.indb 20
03/05/2022 10:18
Unit 2 – Money and measures
The minute hand has moved a quarter of the way around the clock.
The minute hand has moved half of the way around the clock.
The minute hand has moved three- quarters of the way around the clock. There is still one quarter of an hour to go until 8 o’clock.
What time is it?
1
(a)
The minute has moved the way around the clock. The hour hand is between
of
and
.
past
.
The time is
(b)
The minute has moved of the way around the clock. It needs to make a turn to complete a whole turn. The hour hand is between and . The time is to .
21
9781380050687__text.indb 21
03/05/2022 10:18
What times do the clocks show? (a) (b)
1
(c)
2 Draw hands on clock faces to show these times. (a) (b) (c)
1 _ 2 past 2
1 _ 2 past 8
Quarter to twelve
3 Mr Richards gets up at 6 o’clock. He leaves the house when the minute hand has moved 3 _ 4 of the way around the clock. What time does he leave the house?
E
The hour hands have fallen off these clocks. What could the times be? Describe where the hour hand will be positioned each time. Make up a similar problem for a friend to solve.
22
9781380050687__text.indb 22
03/05/2022 10:18
Unit 2 – Money and measures
Durations of time
Here is part of Letisha’s morning timetable for the day. The scale goes up in 1 _ 4 hour steps.
Start of day
Break time
Reading and writing lesson
9 o’clock a.m.
10 o’clock a.m.
11 o’clock a.m.
1 What is the duration of Letisha’s reading and writing lesson? We can use a number line to help find the difference between the start and end times of the lesson. Count on 1 hour from 1 _ 4 past 9 to 1 _ 4 past 10. Then count on another 1 _ 4 hour until the lesson ends at 1 _ 2 past 10. The duration of the lesson is: 1 hour + 1 _ 4 hour = 1 and 1 _ 4 hours. past 9 Reading and writing lesson 10 o’clock a.m. past 10 + hour +1 hour 1 4 1 4 1 2
Letisha’s lunch break starts at 1 _
2 past 12 and lasts for three-quarters of an hour. When does it end? Count on half an hour (two- quarters) to 1 o’clock.
2
1 2
+ hour
+ hour 1 4
1 2
1 4
past 12
1 p.m.
past 1
p.m.
p.m.
Count on another quarter of an hour to 1 _
4 past 1 p.m.
Letisha’s lunch break ends at 1 _
4 past 1 p.m.
23
9781380050687__text.indb 23
03/05/2022 10:18
Use the number line to work out the duration of Letisha’s maths lesson.
1
Mathematics lesson
11 o’clock a.m.
12 o’clock p.m.
1 o’clock p.m.
hour from 11 o’clock to
o’clock. Then count
Count on
an hour until the lesson ends at 1 _
on another
2 past 12 p.m. The
duration of the lesson is:
+
=
and
hours.
1 Draw a number line to work out the duration of these activities.
Start time
End time
1 _ 4 past 8 1 _ 2 past 10 9 o’clock
(a) Letisha walk to school
9 o’clock
(b) Break time
11 o’clock
(c)
Start of day until lunch
Half past 12
2 Complete the table to show the time each activity finishes.
Activity
Art lesson 1 _ 4 past 2 p.m.
Cricket club 1 _ 2 past 3 p.m.
Tea time TV time
1 _ 4 to 6 p.m. 1 _
2 past 6 p.m.
Start time
Duration
Three-quarters of an hour 1 and a half hours Half an hour 2 hours
End time
Use the internet to find pictures that show different activities with durations of approximately 1 _ 4 hour, 1 _ 2 hour and 1 hour. Make a presentation of your pictures e.g. as a collage or a slideshow.
24
9781380050687__text.indb 24
03/05/2022 10:18
Unit 2 – Money and measures
Length and height
What might you measure in centimetres? What might you measure in metres? Try out your ideas. Explain your choices.
Shorter lengths are measured in centimetres. Centimetres are also used to measure longer lengths more accurately, e.g. 2 metres and 45 centimetres. Metres are used to measure longer lengths, heights or distances. 1 Letisha measures the length of objects that are in her pencil case. She lines up the ‘0 cm’ mark with one end of the object and reads the measurement at the other end. The paper clip is 3 cm long.
The pen is 12 cm long.
0 1 2 3 4 5 6 7 8 9 101112131415
25
9781380050687__text.indb 25
03/05/2022 10:18
2 Leon estimates the lengths of these lines. He then uses a ruler to measure them.
(a)
Estimate:7 cm
Actual: 8 cm
(b)
Estimate:5 cm
Actual: 5 cm
(c)
Estimate: 17 cm Actual: 16 cm
Let’s measure and compare different objects using metre rulers. How much taller is the tree than the chair?
3
1 m
The chair is 1 metre high. The tree is 3 metres tall. The tree is 2 metres taller.
1 m
1 m
1 m
26
9781380050687__text.indb 26
03/05/2022 10:18
Unit 2 – Money and measures
Write the length of each object.
1
(a)
cm
(b)
cm
(c)
cm
0 1 2 3 4 5 6 7 8 9 101112131415
The 1-metre rulers are not drawn to scale. (a) What is the length of each line? 1 m X 1 m 1 m 1 m
2
1 m 1 m 1 m
Y
(b) How much longer is line X than line Y?
Use a ruler to draw two lines, A and B. Line A is 11 cm long. Line B is 3 cm longer than line A.
1
27
9781380050687__text.indb 27
03/05/2022 10:18
2 Estimate the length of each line. Then use a ruler to find its actual length. (a) Estimate: Actual: (b) Estimate: Actual: (c) Estimate: Actual: 3 Estimate and measure. Will you use centimetres or metres? (a) Copy and complete this table. Estimate Actual Length of book Length of calculator Height of door Length of classroom Distance you can throw a bean bag
(b) Compare the lengths of the items you measured in centimetres. is cm longer than .
E
The children are taking part in some races. The running race is 200 m longer than the hurdle race. The hurdle race is 500 m shorter than the cycle race. What could be the lengths of each race? Work with a partner to find at least three different solutions.
28
9781380050687__text.indb 28
03/05/2022 10:18
Unit 2 – Money and measures
Money
Choose two coins, two notes or one of each, e.g. 25c and 10c, or $10 and 5c.
How many different amounts can you make?
Here are some more notes. $20 (twenty dollars) is equal to two $10 notes. $50 (fifty dollars) is equal to five $10 notes.
1
2 Is the amount of money in each purse the same?
$20 and $20 and $10 is $50 in total. $10 and $10 and $10 and $20 is $50 in total.
29
9781380050687__text.indb 29
03/05/2022 10:18
(a) What different combinations of coins can we use to pay for the banana?
3
0
25
50
75
0
25
50 60 7075
(b) What other combinations of coins can you use?
Write the amounts shown here. (a)
1
There are
dollars.
There are
cents.
There are
dollars and
cents in total.
(b)
dollars.
There are
There are
cents.
There are
dollars and
cents in total.
(c)
dollars.
There are
There are
more dollars.
There are
dollars in total.
30
9781380050687__text.indb 30
03/05/2022 10:18
Unit 2 – Money and measures
Use counting to help find the totals. (a)
1
(b)
(c)
Write the total amounts in each purse.
2
3 What different coins can you use to buy each item? Find at least three different ways. (a) (b)
99c
$2
$46
With a partner find different routes through the maze to collect enough money to pay for this item exactly. Record the amounts along the way each time. Make a similar puzzle for others to solve, e.g. for an item costing $38.
$1
$10
$1
$20
$5
$5
$5
$10
$5
$5
$10
$20
$1
$5
$10
$20
$5
$2
$10
$5
31
9781380050687__text.indb 31
03/05/2022 10:18
3 Addition and subtraction
KEY words
Which of these words can you use to describe what you see in the picture?
Add
Subtract
Double
Difference
Total
Pair
Dozen
KE
32
9781380050687__text.indb 32
03/05/2022 10:18
KEY questions
How far is the flight from Belize to Jamaica? What different number sentences can you make up about the picture?
33
9781380050687__text.indb 33
03/05/2022 10:18
Addition and subtraction facts
What are the missing values in the part-whole diagrams? (a) (b) (c)
10
What could the missing numbers be on these part-whole models?
10
Write all the addition and subtractions facts for 10.
1 What addition and subtraction facts are represented here? 60 + 40 is an addition fact for 100 60 ones + 40 ones = 100 ones 6 tens + 4 tens = 10 tens
100 ones – 40 ones = 60 ones 10 tens – 4 tens = 6 tens
34
9781380050687__text.indb 34
03/05/2022 10:18
Unit 3 – Addition and subtraction
2 We can find other addition and subtraction facts for 100.
6 tens + 3 tens = 9 tens 5 ones + 5 ones = 1 ten
65 + 35 = 100 100 − 35 = 65
1 Write the matching addition and subtraction facts. (a) tens + tens =
tens
+
=
tens −
tens =
tens
−
=
(b)
tens +
tens =
tens
+
=
tens −
tens =
tens
−
=
(c)
tens +
tens =
tens
+
=
tens −
tens =
tens
−
=
35
9781380050687__text.indb 35
03/05/2022 10:18
What are the missing values? (a) 100 (b) 100 100 100
1
(c)
10 (d)
20 80
20 80
10
100
100
20 80
10
20 80
10
40
60
50
40
60
50
100
100
40
60
50
40
60
50
Solve these problems. (a) Riana has 100 cents. She spends 45 cents. How many cents does she have left? (b) There are 65 marbles in a jar and 35 marbles in a box. How many marbles in total?
2
E
Work with a partner or in a small group. Use 10 sticks of 10 cubes. Divide them into two groups of sticks, e.g. 70 and 30 Half one of the sticks of 10 cubes. Put one half with each of the two groups.
Write an addition and then a subtraction sentence, e.g. 65 + 35 = 100 and 100 − 65 = 35. How many different ways can you do this?
36
9781380050687__text.indb 36
03/05/2022 10:18
Unit 3 – Addition and subtraction
Doubles and halves
Let’s double and halve some numbers.
1
What is half of 68?
What is double 23?
23 + 23 = 20 + 20 + 3 + 3 = 40 + 6 = 46 So, double 23 is 46.
68 = 60 + 8
= 30 + 30 + 4 + 4 = 34 + 34
So, half of 68 is 34.
1 Use counting blocks to help double these numbers. (a) (b) (c)
2 Use counting blocks to help halve these numbers. (a) (b) (c)
37
9781380050687__text.indb 37
03/05/2022 10:18
Form 2 lines at the front of the classroom. Your teacher will say a number between 1 and 50 to the pair of learners at the front of the line. The first learner to double the number moves to the back of the line. The other learner must sit down. Continue until there is only 1 learner left standing. This learner is the Doubling Champion! You can also play this game by halving the numbers.
Adding pairs of 2-digit and 3-digit numbers
Look at these additions. Use estimates to sort them into the boxes below. Do not work out the answers. Explain your thinking to your partner. 20 + 80 45 + 45 52 + 50 29 + 84 43 + 36 32 + 33 75 + 25 79 + 18 68 + 45
38
9781380050687__text.indb 38
03/05/2022 10:18
Unit 3 – Addition and subtraction
Let’s add 32 to 55
Let’s add 30 to 55
2
1
+10
+1
+1
+10 +10
+10
+10 +10
55
55
65
75 85
86
87
65
75 85
+
=
+
+
+
=
=
Let’s add 32 to 155
3
+10
+10
+10 +2
155
165
175
185187
+
=
+
+
=
4 We can think about the place value of both numbers to help us add. Now let’s add 43 to 55.
55
+ 43
50 5
40 3
55 + 43 = 50 + 5 + 40 + 3 = 90 + 8 = 98
39
9781380050687__text.indb 39
03/05/2022 10:18
Now let’s add 43 to 155.
5
1
5
5
1
9
8
155 + 43 = 100 + 50 + 5 + 40 + 3 = 100 + 90 + 8 = 198
1 Use blocks or sketch number lines to help complete these additions. (a) 63 + 20 = (b) 63 + 24 = 63 + + =
(c)
163 + 24 = 163 +
+
=
Add 53 to each of these numbers. 34 + 53
2
34 + 53 =
+
+
+
=
+ =
40
9781380050687__text.indb 40
03/05/2022 10:18
Unit 3 – Addition and subtraction
234 + 53
+
+
+
+
=
=
+
+ =
2
3
4
2
3
4
3 The farmers use 324 metres of fencing for a larger field. They use another 65 metres of fencing for a smaller field. How much fencing is used in total? metres
+
=
+
+
+
+
=
+
+
=
4
Add 30 cents to the money here. c+30c= + +
+
+
=
+
+
=
cents
41
9781380050687__text.indb 41
03/05/2022 10:18
Copy and complete. (a)
1
(b)
(c)
46 + 20 = 46 + 23 = 146 + 23 = 146 + 33 =
25 + 60 = 25 + 64 = 325 + 64 = 325 + 74 =
31 + 40 = 31 + 46 = 431 + 46 = 531 + 56 =
2 Use estimates and reasoning to help find the correct solution each time. (a) 237 + 40 = 278 237 + 40 = 277 (b) 325 + 64 = 389 325 + 64 = 489 (c) 406 + 83 = 489 406 + 83 = 499 (d) 544 + 53 = 697 544 + 53 = 597
3 Winston has 465 cents to spend at the fair. Riana has 30 cents more. How much does Riana have? cents
E
represents a 2-digit multiple of 10
Find all the possible values of
and
362
42
9781380050687__text.indb 42
03/05/2022 10:18
Unit 3 – Addition and subtraction
Subtraction with pairs of 2-digit and 3-digit numbers
Let’s subtract 43 from 74.
Let’s subtract 40 from 74.
2
1
–10 –10 –10
–1 –1 –1 –10
–10
–10 –10 –10
74
74
31 32 33 34
44 54 64
34
44 54 64
−
=
−
−
−
=
=
Let’s find 286 − 32.
Let’s subtract 43 from 174
4
3
–3 –10 –10 –10 –10
131 134
144 154 164 174
−
=
−
−
=
−
2
8
6
=
286 − 32 = 200 − 0 = 200 80 − 30 = 50 6 − 2 = 4 200 + 50 + 4 = 254
43
9781380050687__text.indb 43
03/05/2022 10:18
(a) Subtract 40 from 62.
(b) Subtract 40 from 262.
1
10
10 10 10 10 10
1
1
62 − 40 =
2
6
2
262 − 40 =
Use blocks or sketch number lines to help complete these subtractions.
2
86 − 25 = 86 −
−
=
−
=
186 − 25 = 186 −
−
=
−
=
3 Jade runs 475 metres. Leon runs 42 metres less than Jade. How far does Leon run? metres
−
475 − 42 = 475 −
Jade
=
−
Leon
=
42 m
4 Which is the most likely answer to 675 − 43?
The most likely answer is
because ______________________
________________________________________________________
44
9781380050687__text.indb 44
03/05/2022 10:18
Unit 3 – Addition and subtraction
Copy and complete. (a)
1
(b)
(c)
85 − 40 = 85 − 43 = 185 − 43 = 185 − 44 =
72 − 30 = 72 − 31 = 272 − 31 = 372 − 31 =
96 − 60 = 96 − 64 = 396 − 64 = 596 − 66 =
2 Use estimates and reasoning to help find the correct solution each time. (a) 274 − 50 = 214 274 − 50 = 224 (b) 365 − 64 = 301 365 − 64 = 291 (c) 458 − 44 = 424 458 − 44 = 414 3 Carl cycles 485 metres. Winston cycles 52 metres less than Carl. How far does Winston cycle? metres
E
Letisha has 285 cents in her money box. She spends some 10 cent coins at the shop and gets no change. Letisha still has more than $1 in her money box.
45
9781380050687__text.indb 45
03/05/2022 10:18
4 Lines and shapes
KEY words
Straight
Curve
Open
Closed
2D shapes
3D shapes
Vertical
Horizontal
Side
Angle
Face
Edge
Vertex (vertices)
46
9781380050687__text.indb 46
03/05/2022 10:18
KEY questions
How many different plane shapes can you see? Can you name all the solid (3D) shapes? What are the shapes of their faces?
47
9781380050687__text.indb 47
03/05/2022 10:18
Straight lines and curves
We can draw a semi-circle using a straight line and a curve.
How can you describe these lines?
Where can you see similar lines around you? Do you know what these lines are called?
48
9781380050687__text.indb 48
03/05/2022 10:18
Unit 4 – Lines and shapes
1 This picture is made up of curves and straight lines. How many of each can you see?
straight lines.
There are
curves.
There are
2 Vertical lines go straight from top to bottom.
top
bottom
Horizontal lines go straight from left to right.
left
right
49
9781380050687__text.indb 49
03/05/2022 10:18
1 Use a ruler or straight edge to help draw 3 horizontal lines and 3 vertical lines.
1 Jade and Winston have been sketching lines. Jade: I have sketched straight lines. Winston: I have sketched curves.
(a) Check the children’s sketches. Explain the mistakes they have made. (b) Now sketch some more lines that Jade and Winston can use.
Here are some shapes.
2
(a) How many horizontal lines can you see in total? (b) How many vertical lines can you see in total?
50
9781380050687__text.indb 50
03/05/2022 10:18
Unit 4 – Lines and shapes
Plane shapes (two-dimensional shapes)
What information is missing from this table? Can you sketch each shape? Name of shape Number of sides Number of angles Square Rectangle 3 3 1 0
1 Plane shapes are two-dimensional (2D). We cannot pick them up. Look at these shapes.
pentagon octagon 5 straight sides 6 straight sides 8 straight sides 5 angles 6 angles 8 angles How many pentagons, hexagons and octagons can you see here? There are: hexagon
pentagons hexagons octagons.
51
9781380050687__text.indb 51
03/05/2022 10:18
2 Each of these shapes have sides of equal length. Their angles are equal too. We call these shapes ‘regular’.
Rectangles are different. They have two pairs of equal length sides. Two opposite sides are longer and two opposite sides are shorter.
A square is a special rectangle because it is regular. Both pairs of opposite sides are equal in length.
3 These shapes are also hexagons because they have 6 straight sides and 6 angles, but they are not regular.
What shape am I? (a) I have 3 straight sides and 3 angles.
1
(b) I have 6 angles and 6 straight sides.
(c) I have 8 straight sides and 8 angles.
(d) I have 1 curved side and 1 straight side.
52
9781380050687__text.indb 52
03/05/2022 10:18
Unit 4 – Lines and shapes
(e) I have 5 angles and 5 straight sides.
(f ) I have 2 pairs of equal length sides.
What shapes can you draw? (a) Draw three different shapes, all with 3 vertices and 3 sides. (b) Draw three different shapes, all with 4 vertices and 4 sides.
2
Which is the odd shape out each time? (a) 1 2 3
1
(b)
3
1
2
2 I am thinking of a shape. It has two more angles than a square. What shape is it? Sketch some examples.
Use a computer drawing program to create a picture using 2D shapes and lines to go in your own class art exhibition. Remember to include some open and closed curves. Cross - curricular
53
9781380050687__text.indb 53
03/05/2022 10:18
Right angles
1 These shapes are called triangles . All triangles have 3 sides and 3 angles.
side
side
right angle
angle
angle
This triangle has no right angles
This triangle has 1 right angle
side
angle
This triangle has no right angles
A right angle is a quarter turn. Use a clock face and move the minute hand from 12 to 3 on a clock. It has moved through a quarter turn or a right angle.
54
9781380050687__text.indb 54
03/05/2022 10:18
Unit 4 – Lines and shapes
Which of these shapes have right angles?
2
Both the rectangle and the square have 4 right angles. This pentagon does not have any right angles.
1 How many right angles does each shape have?
right
right
right right
angles
angles angles angles
Copy and complete this sentence. A ______________ turn can be described as a right angle.
1
2 Order these shapes from the greatest number of right angles to the fewest.
C
A
D
B
55
9781380050687__text.indb 55
03/05/2022 10:18
E
Give a friend instructions to help them draw a rectangle accurately. Use these words to help you:
quarter turn right angle straight line horizontal
vertical
turn right angle straight line horizontal
vertical
Solid shapes (three-dimensional shapes)
Here are some everyday objects. Can you match the 3D shapes and their names?
56
9781380050687__text.indb 56
03/05/2022 10:18
Unit 4 – Lines and shapes
1 Solid shapes are three-dimensional (3D). We can pick them up. Here is a cube and a cuboid. Both the cube and cuboid have the same number of faces, edges and vertices. What is different about the shape of their faces and the length of their edges? 8 vertices 6 faces 12 edges
Here is a cone and a cylinder.
2
curved face
flat face
They both have a curved face. They both have at least one flat circular face. What else is the same about them? What is different about them?
1 What information is missing from the table? Name of shape Number of flat faces Number of curved faces
Number of straight edges
Number of vertices
Cube
0
Cuboid Sphere Cylinder
0
0
57
9781380050687__text.indb 57
03/05/2022 10:18
What shape am I? (a) I have no edges, no flat faces and no vertices. (b) I have 12 edges, 8 vertices and 6 square faces. (c) I have 2 flat circular faces, 1 curved face and no vertices.
2
Write the names of these 3D shapes. (a) (b) (c)
1
(d)
(e)
Copy and complete the table. Name of shape How many curved faces?
2
How many faces are squares?
How many faces are circles?
Sphere Cube
0
Cone Cylinder
Which shape is being described each time?
3
58
9781380050687__text.indb 58
03/05/2022 10:18
Unit 4 – Lines and shapes
E
Work with a partner to design a poster to help others identify the differences between cubes and cuboids, and between cones and cylinders. What do you need to tell them about?
Each group will need a camera to take photographs or a notebook and pencil for sketching. Go for a ‘shape walk’ outside. Sketch or photograph all the shapes you can see in the environment. Did you see any of these 2D or 3D shapes?
circles semicircles squares rectangles
pentagons hexagons octagons
cubes spheres cuboids
cones cylinders
Photograph or sketch some of the shapes you see. Work together in the classroom to make a presentation to show others. You can use your sketches, print out your photographs or make a presentation on the computer.
59
9781380050687__text.indb 59
03/05/2022 10:18
5 Multiplication Multiplication and division
60
9781380050687__text.indb 60
03/05/2022 10:18
KEY words
Which of these words can you use to describe what you see in the picture?
Multiply
Divide Total
Groups of
Array
Double
KEY questions
How does the picture show multiplication and division? What different number sentences can you make up?
61
9781380050687__text.indb 61
03/05/2022 10:18
Representing multiplication
Here is a 100 square. Start by counting by twos. What do you notice about the numbers you say? Now count by fives. What do you notice this time? Finally count by tens. Where are all these numbers on the square? Which numbers appear in all the counts you made?
10 20 30 40 50 60 70 80 90 100
9 19 29 39 49 59 69 79 89 99
8 18 28 38 48 58 68 78 88 98
7 17 27 37 47 57 67 77 87 97
6 16 26 36 46 56 66 76 86 96
5 15 25 35 45 55 65 75 85 95
4 14 24 34 44 54 64 74 84 94
3 13 23 33 43 53 63 73 83 93
2 12 22 32 42 52 62 72 82 92
1 11 21 31 41 51 61 71 81 91
How many different ways can you arrange 12 coconuts into equal rows? Use counters or other small objects to help you. What do you notice?
1 We can show the multiplication sentence 6 × 2 in different ways. (a) There are 2 pineapples in each group. There are 6 groups of pineapples.
62
9781380050687__text.indb 62
03/05/2022 10:18
Unit 5 – Multiplication and division
(b) The number line shows 6 jumps of 2
+2 +2 +2
+2
+2
+2
0
2
4
6
8 10 12
(c) The array shows 6 columns of 2 counters.
(d) The repeated addition number sentence 2 + 2 + 2 + 2 + 2 + 2 = 12 shows there are 6 twos to be added.
What do you see? Write a repeated addition sentence and a multiplication sentence to match. (a)
1
There are
cherries in each group.
There are
groups of cherries.
+
+
=
×
=
(b)
+3
+3
0
2
6
9
12
×
=
63
9781380050687__text.indb 63
03/05/2022 10:18
2 Use counters to make the arrays. How many counters in total
each time? (a) 3 × 2
(b) 4 × 2 (c) 5 × 2 Can you predict how many counters will be in a 10 × 2 array? Why will you also need 8 counters for a 2 × 4 array?
1 Draw number lines to show these repeated additions. Then write the multiplication sentences. (a) 2 + 2 + 2 + 2 + 2 + 2 + 2 = (b) 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = (c) 3 + 3 + 3 + 3 =
(d) 3 + 3 + 3 + 3 + 3 =
2 Leon wants to use counters to show each of these multiplication sentences as arrays. (a) Which of the arrays will have the same totals? Think first.
(b) Use counters to check.
E
How many bananas in total? Use what you know to show this in at least three different ways.
64
9781380050687__text.indb 64
03/05/2022 10:18
Unit 5 – Multiplication and division
Multiplying by 2 and 4
Winston knows that multiplying by two is the same as doubling but he is stuck when doubling all the numbers to 20. What strategies could you show him?
Look at the towers of cubes.
1
How many cubes in total in each set of 3 towers? First set: 2 + 2 + 2 = 6 and 3 × 2 = 6 Second set: 4 + 4 + 4 = 12 and 3 × 4 = 12
2
Each tower of four cubes is made up of 2 towers of two cubes.
1 How many cubes will we need to make the following towers?
(b)
(a)
+
+
+
+
=
+
+
+
=
×
=
×
=
2 How many cubes will we need to make these towers? 4 towers of 4 cubes + + + = × = 5 towers of 4 cubes + + + + = × =
65
9781380050687__text.indb 65
03/05/2022 10:18
Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Page 7 Page 8 Page 9 Page 10 Page 11 Page 12 Page 13 Page 14 Page 15 Page 16 Page 17 Page 18 Page 19 Page 20 Page 21 Page 22 Page 23 Page 24 Page 25 Page 26 Page 27 Page 28 Page 29 Page 30 Page 31 Page 32 Page 33 Page 34 Page 35 Page 36 Page 37 Page 38 Page 39 Page 40 Page 41 Page 42 Page 43 Page 44 Page 45 Page 46 Page 47 Page 48 Page 49 Page 50 Page 51 Page 52 Page 53 Page 54 Page 55 Page 56 Page 57 Page 58 Page 59 Page 60 Page 61 Page 62 Page 63 Page 64 Page 65 Page 66 Page 67 Page 68 Page 69 Page 70 Page 71 Page 72 Page 73 Page 74 Page 75 Page 76 Page 77 Page 78 Page 79 Page 80 Page 81 Page 82 Page 83 Page 84 Page 85 Page 86 Page 87 Page 88 Page 89 Page 90 Page 91 Page 92 Page 93 Page 94 Page 95 Page 96 Page 97 Page 98 Page 99 Page 100 Page 101 Page 102 Page 103 Page 104 Page 105 Page 106 Page 107 Page 108 Page 109 Page 110 Page 111 Page 112 Page 113 Page 114 Page 115 Page 116 Page 117 Page 118 Page 119 Page 120 Page 121 Page 122 Page 123 Page 124 Page 125 Page 126 Page 127 Page 128 Page 129 Page 130 Page 131 Page 132 Page 133 Page 134 Page 135 Page 136 Page 137 Page 138 Page 139 Page 140 Page 141 Page 142 Page 143 Page 144 Page 145 Page 146 Page 147 Page 148 Page 149 Page 150 Page 151 Page 152 Page 153 Page 154 Page 155 Page 156 Page 157 Page 158 Page 159 Page 160 Page 161 Page 162 Page 163 Page 164 Page 165 Page 166 Page 167 Page 168 Page 169 Page 170 Page 171 Page 172 Page 173 Page 174 Page 175 Page 176 Page 177 Page 178 Page 179 Page 180 Page 181 Page 182 Page 183 Page 184 Page 185 Page 186 Page 187 Page 188 Page 189 Page 190 Page 191 Page 192 Page 193 Page 194 Page 195 Page 196 Page 197 Page 198 Page 199 Page 200Made with FlippingBook Learn more on our blog