Unit 1: Topic 1
Place value
This is a one.This is 12 ones OR 1 ten and 2 ones.
This is 120 ones OR 1 hundred and 2 tens.
This is nga¯ tahi. This is 12 nga¯ tahi OR 1 nga¯ tekau and 2 nga¯ tahi.
Guided practice
1 How many?
2 Write the numbers.
This is 120 nga¯ tahi OR 1 nga¯ rau and 2 nga¯ tekau.
In a 3-digit number, the first digit is hundreds, the second is tens and the third is ones.
1 This is 354.
hundreds
tens ones
2 This is 206.
hundreds tens ones
3 This is 423.
hundreds tens ones
a In 849, the 9 is in the ones place. How many:
b In 347, the 4 is in the tens place. How many: tens? ones?
c In 413, how many: tens? hundreds? hundreds? ones?
d In 508, how many: tens? hundreds? ones? hundreds?
5
a Draw 216.
How many different ways can you rename 216?
b What is a number more than 216?
c What is a number less than 216?
1
Use the digits to make:
a the biggest number.
b the smallest number.
c the biggest number with 8 in the ones place.
d 2-digit numbers.
2 Write a digit on each balloon.
3
Use the digits to make:
a the biggest number.
b the smallest number. 3 8 6
a The smallest number is:
b The numbers bigger than 115 are:
Unit 1: Topic 2
Regrouping and renaming numbers
You can arrange 236 as:
2 hundreds, 3 tens and 6 ones
OR 2 nga¯ rau, 3 nga¯ tekau and 6 nga¯ tahi.
2 hundreds, 2 tens and 16 ones
OR 2 nga¯ rau, 2 nga¯ tekau and 16 nga¯ tahi.
1 hundred, 13 tens and 6 ones
OR 1 nga¯ rau, 13 nga¯ tekau and 6 nga¯ tahi.
Guided practice 1 57 2 324
Write how each number has been regrouped.
1 Regroup each number in a different way. Draw and write how you regrouped them.
a 63
b 245
c 536
2 Circle the number that matches the words.
a Three hundred and two: 302 320 3002
b Five hundred and forty: 50 040 5040 540
c Seven hundred and seven: 777 707 7007
3 Write the numbers on the place value chart.
a 6 hundreds and 15 ones
b 23 tens and 8 ones
c 32 tens
d 8 hundreds and 2 ones
4 Write the number that is:
a 3 tens and 17 ones
b 5 tens and 21 ones
c 2 hundreds and 9 tens
d 6 hundreds and 42 ones
e 45 tens
f 61 tens and 8 ones
How many tens are in three hundred?
1 Rename each number without using hundreds.
For example, 76 4 is 76 tens and 4 ones.
a 527 is tens and ones b 692 is c 302 is
2 Rename each number without using tens.
For example, 764 is 7 hundreds and 64 ones.
a 527 is hundreds and ones
b 692 is c 302 is
3 Use the example to help you make three regrouping addition equations.
729: 729 = 700 + 20 + 9 729 = 720 + 9 729 = 700 + 29
a 832
b 467
c 943
When finding the nearest 10, check a number in units.
If the number in units is 0 to 4, round down.
The nearest 10 to 42 is 40.
If the number in units is 5 to 9, round up.
The nearest 10 to 38 6 is 390.
Guided practice
1 Round the numbers using the number lines.
a
b
The nearest 10 is .
c 537 The nearest 10 is .
The nearest 10 is .
When finding the nearest 100, check a number in tens.
If the number in tens is 0 to 4, round down to the nearest 100.
The nearest 100 to 13 8 is 100.
If the number in tens is 5 to 9, round up to the nearest 100.
The nearest 100 to 3 8 2 is 400.
When rounding to the nearest 100, don’t check a number in units.
d 249 The nearest 100 is .
200210220230240250260270280290300
e 978 The nearest 100 is .
9009109209309409509609709809901000
2 Round each number to the nearest 10 and the nearest 100.
a 75 b 821
c 205 d 555
e 992
Extended practice
Rounding is useful to check if your answer to a calculation is reasonable.
Andy said “158 + 78 = 206”. Does that seem right?
Round each number to the nearest 10.
158 → 160 78 → 80
160 + 80 = 240
So, 158 + 78 is about 240.
Andy’s answer doesn’t look right.
1
Round each number in the number sentence to check if each answer seems right.
a 52 + 79 = 131 Does it seem right? Yes No
Write the number sentence with rounded numbers.
+ =
b 86 + 48 = 114 Does it seem right? Yes No
Write the number sentence with rounded numbers.
+ =
2
a 143 + 32 is about .
b 89 + 2 is about .
c 178 + 205 is about
3
Round each number in the number sentence to estimate an answer.
The south school has roughly 260 students after rounding to the nearest 10.
The north school has roughly 290 students after rounding to the nearest 10.
What would be the largest possible number of students altogether and the fewest possible number of students altogether?
Largest possible number of students Fewest possible number of students
South school
North school
Total:
Unit 2: Topic 1 Addition mental methods
You can learn useful methods to help with adding numbers in your head. Recall these addition facts to 20.
Knowing these pairs of numbers makes addition easier.
practice
What are other number pairs that could go in the squares?
1 Fill in the blanks on the Robostars so that the number pairs add up to 20.
15
2 The numbers in the short boxes bond together to make the whole number in the long box. Fill in the gaps so that the number bonds make 16.
1 a Find different number bonds that make the number on each whole bar. Try to find numbers that match the size of the smaller bars.
b Find as many different number bonds as you can that also make 18. and and and and and and and and
2
2 Write different number bonds in each pair of boxes so that they make the number on each large balloon.
1 Use doubles to help you add. a 8 + 9 = 8 + 8 + = + = 1 6 b 10 + 13 = 10 + 10 + = + = c 15 + 17 = 15 + 15 + =
= d 12 + 13 = 12 + 12 + =
14 + 15 = 14 + 14 + =
1 Add these doubles.
a 7 + 7 = b 11 + 11 =
c 16 + 16 = d 20 + 20 =
2 Add these near doubles.
e 25 + 25 = f 50 + 50 = a 7 + 9 = + + = + =
b 11 + 13 = + + = + = c 16 + 17 =
20 + 23 =
1 Find the missing numbers
a 12 + 7 = 15 + b 0 + 16 = 8 +
c 20 + = 13 + 8 d 6 + = 17 + 2
e 9 + = 18 + 2 f 1 + 3 + = 12 + 4 + 1
2 Use doubles to help you find the answers. a 20 + 22 =
=
3 Use doubling methods to solve these in your head.
a 39 + 38 =
b 40 + 41 =
c 100 + 102 =
Addition written methods
Jump method for addition
Start with the larger number. Add the 10s and then the 1s. 22 + 23
1 Use the jump method to solve. a 16 + 21 =
Where would you start if you were adding 2 hundreds numbers?
a 72 + 19 =
b 38 + 57 =
c 27 + 63 =
d 39 + 26 =
e 25 + 58 =
Vertical addition
When using vertical addition, you have to regroup if the total of a place value column is more than 10.
1 Start with the ones. 7 + 5 = 12
2 Now add the tens.
3 tens + 4 tens = 7 tens. We also need to add the regrouped ten, so we end up with 8 tens.
Guided practice
1 Start with the ones to solve.
Regroup the 12 for 1 ten and 2 ones
1 Rewrite as vertical addition and solve.
a 28 + 31 b 62 + 18 c 46 + 27
Remember to line the numbers up in their place value columns.
58 + 8 e 36 + 64
2 Write a vertical addition and solve.
a Serena counted 34 cars on the way to school and 59 cars on the way home. How many did she count altogether?
b Arjun drove 29 km on Saturday and 37 km on Sunday. How far did he travel on the weekend?
93 + 8
1 Use the jump method to solve.
a 75 + 27 = b 81 + 22 =
2 Use vertical addition to solve.
+ 44
3 Choose a method to find the answer. 34 + 89 =
How are the jump method and vertical addition similar?
+
Find the answers with the number lines.
Use the number lines to find the answers.
1 28 – 7 =
2 25 – 8 =
3 41 – 14 =
4 Solve on the number line and write a matching number sentence.
a There were 34 people on the bus. Six people got off at the library. How many are left?
b Of the 48 ducks flying over the school, 12 landed on the pond. How many were still in the air? – =
1 Show on the number lines and solve.
2 Solve on the number lines. 252627282930313233343536
Addition and subtraction are connected.
If I know 5 + 7 = 12, I also know 12 – 5 = 7 and 12 – 7 = 5.
1 Write two subtraction facts to match the addition fact.
a 6 + 10 = 16
Why do both subtraction equations start with the same number?
– =
– = 6 1 6 0
– =
b 15 + 4 = 19
c 9 + 11 = 20
d 16 + 7 = 23
Doubling helps with additions and halving helps with subtractions.
We learnt doubling methods to add numbers.
8 + 8 = 16
We know 8 is half of 16.
So, 16 – 8 = 8.
1 Solve the equations using the halving method.
1 Solve the equations using the halving method.
7 + 7 = 14 So, − 7 =
10 + = So, − = c
12 + = So, − =
2 Using the halving method, solve these equations.
a 16 – 8 = 8 and 17 is one more than 16.
So, 17 – 8 =
b 14 – 7 = 7 and 15 is more than 14.
So, 15 – 7 = .
1 Write addition and subtraction facts to match the pictures.
2 Solve on the number lines and use addition to check your answers.
1 Use the jump method to solve.
a 98 – 34 =
b 360 – 43 =
c 798 – 51 =
d 598 – 125 =
e Use different numbers to write a subtraction that has the same answer as question d. – =
Vertical subtraction
In vertical subtraction, you have to regroup when the number you are subtracting is bigger than the number you are taking away from.
2 Now subtract the tens. We regrouped 1 ten from the first number to the ones. That leaves: 6 tens – 2 tens = 4 tens
1 Start with the ones to solve the subtractions.
1 Start with the ones. You can’t do 3 – 6. Regroup 1 ten from the tens column for 10 ones. 13 ones – 6 ones = 7 ones
1 Rewrite as vertical subtraction and solve. a 34 – 17 b 51 – 33 c 86 – 36
Remember to line the numbers up in their place value columns.
72 – 63 e 73 – 49
2 Write as vertical subtraction and solve.
a Bet ty the baker made 98 cup cakes. She sold 59 of them. How many are left?
b Suresh had $45. He spent $28. How much does he have left?
1 Solve using the jump method.
a 102 – 16 = b 132 – 26 =
2 Solve using vertical subtraction. a b c
3 Choose a strategy to find the answer. 62 – 45 =
Write the equation. 1
Show on the number line.
4 3 × 5 =
8 3 × 6 =
the array. 9 4 × 5 = I wonder if 4 × 5 is the same as 5 × 4. 10 Fill in the gaps and complete the times tables chart.
11 Find the cost for each person.
a Anna bought 3 cupcakes. × 3 = $
b Ben bought 7 juices. × = $
c Jack bought 3 sandwiches. × = $
d Shaun bought 1 donut. × = $
e Sarah bought 10 cupcakes. × = $
Extended practice
2 digits × 1 digit multiplication You can split larger numbers to make multiplying easier.
1 Use the ten frames to find the answer.
a 2 × 14 = is the same as 2 × 10 + 2 × 4 = + =
b 3 × 11 is the same as 3 × 10 + 3 × = + =
c 3 × 14 is the same as 10 × 3 + 4 × = + =
2 Solve with the split method. a 3 × 13 = 3 × 10 + 3 × 3 =
2 × 24 = 2 × 20 + 2
Unit 2: Topic 6
How many groups of 2 in 8?
Guided practice
1
8 divided into groups of 2 gives 4 groups OR 8 ÷ 2 = 4
What does “equal groups” mean?
Draw circles to make equal groups of:
12 divided into groups of 4 gives groups. 12 divided by 4 is 12 ÷ 4 = 4
15 divided into groups of 3 gives groups. 15 divided by 3 is 15 ÷ 3 = 3 b Equal or unequal shares?
1 Add more counters to make the shares equal, then solve the equations.
2 Write the equation.
Multiplication undoes division. Division undoes multiplication.
4 people have 3 marbles each. How many marbles altogether? (12 )
12 marbles shared between 4 people. How many does each person have? ( 3)
3 people have 4 marbles each. How many marbles altogether? (12 )
12 marbles shared between 3 people. How many does each person have? (4 )
3 Use multiplication facts to complete the division facts.
4 Fill in the blanks to show the family of multiplication and division facts for
5 Write the multiplication and division families of fact for each triangle.
1 Draw 3 ways to equally share 16.
2 There are 4 students in each row.
3 Circle the groups that can be shared equally between 3.
The numerator tells us how many parts we are dealing with.
The denominator tells us how many parts a whole or group is divided into.
1 Shade the fractions.
Two-fifths or 2 parts out of 5 are shaded.
The numerator is the top number of the fraction. The denominator is the bottom number of the fraction.
1
2 Draw lines to match each fraction with its picture.
Remember that the parts of a fraction need to be equal in size.
3 Divide each rectangle into the fraction shown.
quarters fifths thirds halves
4 Which fraction in question 3 has:
a the most parts?
b the least parts?
c the smallest parts?
d the biggest parts?
Fraction of a quantity
Fractions can show a part of the whole. 1 2 of 4 donuts is 2 donuts.
5 Find the fraction of each quantity.
What is 1 2 of 2 dogs?
What is 1 3 of 12 apples?
What is 1 4 of 8 strawberries?
What is 1 8 of 8 stars?
What is 1 5 of 10 cats?
1 There are two candy jars.
Ben took half of the candies from Jar A, so he now has 12 candies.
a In total, how many candies were in Jar A?
Kai took half of the candies from Jar B. He now has 6 candies.
b In total, how many candies were in Jar B?
c Which is bigger: one quarter of Jar A or half of Jar B?
1 8 of Jar A or one quarter of Jar B?
Jar A Jar B Same
Jar A Jar B Same
2 a Draw a line to divide the square into 2 equal parts.
b What fraction is each part?
c Draw another line to make 4 equal parts. What fraction is each part?
d Draw 2 more lines to make 8 equal parts. What fraction is each part?
e Colour in 5 parts.
f What fraction is coloured in?
g What fraction is not coloured in?
3 Order the fractions from smallest to largest. 1 2 1 8 1 4 5 8
Number lines are useful for counting by and comparing fractions. 1 Fill in the missing fractions.
1 Match the fractions to the correct place on the number line.
2 Which fraction is missing from question 1c?
3 How many:
a eighths in 1? b halves in 1?
c fifths in 1? d thirds in 1?
e quarters in 1?
Equivalent fractions are fractions that show the same value.
Kaia ate half the pizza.
Akona ate two-quarters of the pizza.
The amount of pizza they ate was the same!
4 Shade and show an equivalent fraction for each fraction.
1 Use the fraction wall to decide which fraction is bigger.
2 Use the fraction wall in question 1 to answer these questions.
a How many quarters in one half?
b How many eighths in one quarter?
c How many eighths in one half?
Addition and subtraction with fractions
When you count items,
1 apple + 2 apples = 3 apples BUT
2 apples + 2 oranges cannot be 4 apples or 4 oranges.
When adding fractions, make sure all the fractions have the same denominator.
The name (quarters) always stays the same!
Guided practice
1 Fill in the gaps.
b += 1 eighth1 eighth2 eighths 8 + 8 = 8
c one fifth + one fifth = fifths
+ = 1 fifth1 fifthfifths
Independent practice
1 Write number sentences. + =
2 Check if Akira answered his homework questions correctly. If he didn’t get a question right, show the correct answer in the box. 1 3 + 1 3 = 2 6 1 5 + 1 5 = 1 10 1 4 + 1 4 = 2 4 1 8 + 1 8 = 2 8 a Correct Incorrect b Correct Incorrect c Correct Incorrect d Correct Incorrect
3 Fill in the gaps to complete each subtraction.
1 Draw each story and write a number sentence.
a The cup is 1 3 full of milk. Derek pours another 1 3 into the cup. How much milk altogether?
b There is one quarter of a pizza left on a plate. Anna adds another quarter to the plate. What fraction of pizza is there now?
c There are 10 stars. One fifth of the stars are coloured in yellow. Another fifth of the stars are coloured in red. How many stars are coloured altogether?
1 Circle coins that equal:
$1
20c
2 Circle notes that equal:
$20
$100
$50
$45
3
How much is … ?
Is a $5 note or a 50c coin worth more? Why?
4 Order the totals from smallest to largest.
a $2
b $50
c $25
2 1 Draw 3 different ways to make:
a Find 4 ways to make 50c.
b How many ways can you make $1?
1 Make $1 with:
a 50c coins
b 10c coins
c 20c coins
2 Make $100 with:
a $10 notes
b $20 notes
c $50 notes
3 Rearrange the coins to make them easier to count.
a
How much?
b How much?
c How much? Which coin is worth the most?
1 Draw the least number of coins you could use to make:
$3.50
Number of coins: b $6.80
Number of coins:
2
a How much?
3
a How much?
b How much would you have left over from this amount if you spent:
i $20?
ii $45?
iii $32?
b How much would you have left over from this amount if you spent:
i $20?
ii $45?
iii $32?
Last digit pattern counting by fives: , 50 0123456789 1011 121314151617181920
1 Find the last digit pattern, then continue the pattern on the number line.
a Counting by twos: , , , , 0123456789 1011 121314151617181920 21 222324252627282930
b Counting by threes: , , , , , , , , ,
c Counting by tens: 02468 10121416182022 242628303234363840 42 44464850 Which number pattern is the longest?
1
a Circle the final digits in the pattern.
b The pattern is counting by:
c Complete the pattern. 48 12 16 20 24
2
a Circle the final digits in the pattern.
b The pattern is counting by:
c Complete the pattern.
3 Find the missing numbers.
4 Join the dots by following the pattern.
5 The double of 1 is 2. The double of 2 is 4. The double of 3 is 6
a Continue the doubles pattern on the chart by circling the next number in the pattern and then circling its double in the same colour.
b Use the same process to finish the pattern.
6 Use the chart in question 5 to help you answer the questions.
a What is double 4?
b What is the answer if you double 4, then double it again?
c What is half of 16?
d What is the answer if you halve 16 and then halve it again?
1
123456789 10
11121314151617181920
21222324252627282930
31323334353637383940
41424344454647484950
51525354555657585960
61626364656667686970
71727374757677787980
81828384858687888990
919293949596979899 100
d What is the last digit pattern?
a Circle the numbers counting by 5 from 3.
b What is the last digit pattern?
c Colour the numbers counting by 3 from 2.
2 What would you be counting by if the last digit pattern was:
a 2, 7, 2, 7, 2, 7?
b 0, 8, 6, 4, 2, 0, 8, 6, 4, 2?
c 7, 7, 7
3
a Use these numbers to make a pattern.
37 57 7 27 47 67 17
b What are you counting by?
I wonder if the patterns are going forwards or backwards?
Word problem
Two monsters went shopping. They met three more monsters. How many altogether?
1 Solve the word problems.
a Rawiri had 3 cars. He was given 4 more for his birthday. How many did he have altogether?
b Abbey had 8 balloons but 3 of them popped. How many did she have left?
Number sentence
Diagram 2 + 3 = 5
Number sentence + =
Number sentence − =
c One scooter has 3 wheels. Draw a diagram and write how many wheels are on four scooters.
1 Draw the problem, then write a number sentence to solve it.
a Tessa has 38 cupcakes. She gives 6 to her friends. How many does she have left?
Number sentence:
b Hamish has 12 pencils and Primrose has 4 pencils. How many more pencils does Hamish have?
Number sentence:
c There are 17 candles on the cake. Linus blows out 7 of them. How many are still lit?
Number sentence:
d Anahera read 10 books in April and 6 books in May. How many did she read altogether?
Number sentence:
2 Write a word problem to match the number sentence.
8 + 4 = 12
3 Decide if each word problem is addition or subtraction.
a Remy scored 14 points on Monday and 17 points on Tuesday. What was his total point score?
b Jay had 17 marbles. He bought another 12. How many does he have now?
c Nina had 16 pairs of shoes. She gave away 14 pairs. How many pairs does she have left?
Addition Subtraction
Addition Subtraction
Addition Subtraction
4 Circle true or false for each equation. Write the correct answer if it is false.
a 42 + 132 = 184 True or False Cor rect answer:
b 743 – 520 = 241 True or False Cor rect answer:
c 2 × 8 = 14 True or False Cor rect answer:
d 30 ÷ 5 = 6
An algorithm is a list of steps (or rules) that are needed to solve a problem. When going out, you put on socks first → then shoes → then tie your shoelaces.
If you don’t follow these steps, then it won’t work. shoe then sock shoelaces then shoes
Creating patterns is also part of an algorithm. 14101316 7
+3+3
These numbers increase by 3. Can you guess what comes after 16?
5 How do you brush your teeth? Put these steps into the correct order.
a Brush your teeth for 2 minutes.
b Rinse your mouth.
c Put some toothpaste on the toothbrush.
d Grab the toothbrush and toothpaste.
6 Draw a diagram and write how many legs are on: a 1 chair. b 2 chairs. c 3 chairs. d 4 chairs.
e Write what you notice about the pattern in the answers.
7 In this pattern the number of circles increases by .
1 The teacher asks you to use the flowchart below to sort paper shapes for the class. Follow the flowchart and write which box each shape should go in.
Metres
We measure the length of long items in metres (m).
1 Use a metre ruler to find:
What are some things we might measure in metres? 4m 3m
a the length of your classroom. b the width of a bookcase.
c the height of the door. d the width of the whiteboard.
1 Find items you think fit the estimates, then check with a metre ruler.
maths book
less than 1 metre less than 1 metre
less than 1 metre about 1 metre more than 1 metre
2 Draw lines to match the items with the estimates.
less than 1 metre about 1 metre more than 1 metre
Centimetres
We measure the length of small things in centimetres (cm).
There are 100 cm in 1 m.
A child that is 3 or 4 years old is about one metre tall.
Guided practice
1 Use a 30 cm ruler to find:
a the length of your pencil.
centimetres
How many centimetres tall do you think I am?
b the width of this book.
centimetres
2 Draw something in your classroom that is about:
a 15 centimetres long.
centimetres b 1 metre long.
centimetres
1 Find items you think fit the estimates, then check with a 30 cm ruler.
2 Draw lines to match the items with the estimates. Item
my eraser
less than 30 cm 5 cm
less than 30 cm about 30 cm more than 30 cm
less than 30 cm about 30 cm more than 30 cm
3 Estimate the length in metres. a car metres b bookshelf metres
0102030405060708090100
c basketball court metres
4 Measure the lines with a ruler and record the length. a cm b cm c cm
Centimetres are a unit that we use to measure the length or height of something smaller, like your finger.
5 Use a ruler to draw a line that is:
a 4 cm.
b 7 cm.
To find the perimeter of a shape, measure all the sides and add them up.
This shape has 6 cm in length and 2 cm in height.
The perimeter is 6 + 6 + 2 + 2 = 16. The perimeter is 16 cm long.
6 Find the perimeter of each shape.
7 Measure the perimeter of each shape and order them from longest to shortest.
1 Would you measure these items in metres or centimetres?
2 Which of the items in question 1 do you estimate is the longest?
3 Which is the shortest?
4 How long might the couch be?
5 How long might the banana be?
Unit 6: Topic 2 Area
This book has an area of 12 sticky notes.
Guided practice
This laptop screen has an area of 12 sticky notes.
a Circle the item with the smallest area in blue.
b Circle the item with the biggest area in red.
2 How many sticky notes do you use to find the area of: a a book? b your table? c another item?
1 Measure the area of each object using sticky notes. Complete the table.
Area to find
EstimateActual area
my pencil case 32 erasers
my writing book
2 Find the area of each shape.
What else could you use to measure area with?
my lunch box my eraser a b squares squares c d squares squares e squares
3 Circle the shape above with the largest area.
4 Draw 1 cm squares on the rectangles. Record the area of each rectangle.
5 Using blocks, draw a shape with an area of:
a 7 squares.
b 12 squares. squares squares
1 Use the grid paper to draw:
a a blue square with an area of 9 squares.
b a red rectangle with an area of 10 squares.
c 2 different green rectangles, each with an area of 12 squares.
d a yellow square with an area of 4 squares.
2 In words, what is the total area of the shapes in question 1?
3 a Estimate the area of the shape below. squares
b Find the area of the blue square. squares
c Find the area of the red rectangle. squares
d What is the total area? squares
Unit 6: Topic 3
Volume and capacity
The volume of this object is 6 blocks.
The volume of this object is 13 blocks.
Volume is how much space an object takes up.
1 What is the volume of each object? a blocks b blocks
2 Is the volume of object A different to object B?
Object A is larger. Both are the same. Object B is larger.
a Write the letters to order these objects by volume.
Smallest volume Largest volume
b Which objects have a bigger volume than E?
c Which objects have a smaller volume than C?
Build a model using the same amount of blocks as object D in question 1. Draw your model and write down how many blocks you have used.
blocks
Capacity (internal volume) is how much a container holds.
A litre (L) is a unit of capacity. This milk cartoon holds 1 litre (1 L).
1 Estimate the capacity of these containers. Then measure the actual capacity using a 1 litre container like a milk bottle. Container
a Number these containers 1 to 6 from smallest to largest capacity.
b Write the letters of the items that hold 1 L or less.
c Write the letters of the items that hold more than 1 L.
d Which item has the largest capacity?
e What is the capacity of the detergent and spray bottle together?
1 What is the volume of each of these objects?
2 Decide whether each story is about volume or capacity. Then, solve the problem.
a Kaia had a full bottle of soft drink. She shared the drink equally into four cups. If the bottle held 2 litres, how much did each person get?
volume capacity Answer:
b Tariq’s water tank has 120 litres in it. If he uses 10 litres per day for one week, how much water will he have left?
volume capacity Answer:
c Nea wants to build a model building with four layers, and 8 blocks in each layer. How many blocks will she need?
volume capacity Answer: blocks blocks blocks
The base unit for measuring mass is the kilogram (kg). Many everyday items are measured in kilograms.
The mass of the dog is 15 kg. The mass of the laptop is 1 kg.
1
a Estimate whether each item has a mass of less than 1 kg, about 1 kg or more than 1 kg. Draw lines to show your answers.
Less than 1 kg
About 1 kg
More than 1 kg
b Which item do you estimate has the heaviest mass?
1 Many everyday items, such as groceries, are labelled in kilograms. Find and draw three items that are packaged and labelled in kilograms.
2
a Estimate first, then find the mass of these items to the nearest kilogram. You may need to use scales.
Stapler
5 textbooks Your lunchbox
1 litre of water Rugby ball
b Which item is the heaviest?
c Which item is the lightest?
d Write the items in order from lightest to heaviest.
1 How many of each item could be packed in a box that holds 24 kg?
Unit 6: Topic 5
Time
Guided practice
1 What number is the minute hand pointing to at: 2 o’clock a b c Why do we say “quarter past” and “quarter to”?
2 Draw a line to match the clocks to the times. quarter past 2 half past 2 quarter to 3
5 o’clock? quarter to 6?quarter past 11? half past 8?
1 Draw in the minute hands.
a half past 3 b quarter past 1 c 7 o’clock
d quarter past 12 e quarter to 7 f half past 6
2 Draw in the hour hands.
a quarter past 3 b 8 o’clock c quarter to 10
d half past 5 e quarter to 9 f 12 o’clock
Why do you think it is called the “hour hand”?
3 Draw the times on the clocks.
quarter to 5 b quarter past 8
half past 1
quarter past 10 e 6 o’clock f half past 11
4 Write in the times.
What’s another way of saying “half past”?
a 1 hour?
b half an hour?
c quarter of an hour?
d 2 hours?
2 Fill in the missing times.
1 What time will it be in: 2:15 a b c d e f : 3 o’clock 3:45 quarter to 12:00 :15 quarter past 7
:
1
2
The first day of January was a Monday.
The first Sunday in January was the 7th.
The last day of January was a Wednesday.
a What is the first day of February?
b What date is the first Sunday in February?
c What is the last day in February?
a How many Sundays are in November?
b How many Saturdays?
c What day is the 13th of November?
d What date is the last day in November?
1 a How many days are in each month?
Days b On this calendar, circle the following important dates: Waitangi Day 6th February New Years Eve 31st December Your birthday c Highlight the Term 1 and 2 school holidays you have this year. Check the duration of each holiday. Ter m 1 holiday: days Ter m 2 holiday: days
a If today is the 4th, what will be the day and date in 2 weeks?
b What day is 9 days after the 13th of May?
c Which days are there 5 of in the month?
d If you went on holidays on the 3rd of May for 11 days, on which day would you get back?
e How many days is it from the 17th to the 23rd of May?
f If today is the 23rd of May, how many days are left in the year?
Use the calendar on the previous page to help you.
Show how you worked out the answer.
Does May always start on a Wednesday?
a Fill in the name of the current month.
b Fill in the dates on the correct days.
c What day does the month start on?
d How many days are in the month?
2 This calendar shows one month of the year.
a Could it be February?
b Which months could it be?
c How many full weeks are there?
d What date is the third Thursday of the month?
Unit 7: Topic 1 2D shapes
1 A hexagon has:
2 A pentagon has: corner side a corners b sides a corners b sides
The shape has 4 corners and 4 sides. The opposite sides are straight lines.
How else could you describe this shape?
3 An octagon has: a corners b sides
1
a Colour the shapes with 4 corners and 4 straight sides blue.
b Colour the shapes with at least one curved side pink.
2 Match the shapes to their names and descriptions.
6 sides and 6 corners
4 sides all the same length, 2 sets of parallel lines 4 corners, opposite sides are the same length 3 straight sides
3 Draw the following shapes. Then circle the word “regular” or “ir regular” to show what each shape is.
a 3 sides and 3 corners b no corners
c at least 2 straight sides and 1 curved side d 5 cor ners and 5 sides
e 4 straight sides with 2 sides the same length
f 4 straight sides of different lengths
Splitting shapes
This is a square.
If we draw a line like this, it makes two triangles.
Combining shapes
If we draw two lines like this, it makes four triangles.
We can join these two triangles ... ... and this trapezium ... ... to make a rectangle.
practice
1 Draw the lines to split these shapes.
a Draw 1 line to make 2 smaller triangles.
b Draw 2 lines to make 2 triangles and a rectangle.
c Draw 2 lines to make 4 triangles.
2 Draw lines to show how these 4 triangles can join together to make the white shape.
3 Draw and name the shape that would be made if you slid the triangle across to join the trapezium.
The shape is a .
5 Which of the shapes from question 1: has 4 corners? has two pairs of parallel opposite lines? is irregular? has no corners?
Unit 7: Topic 2
Lines of symmetry
A shape is called “symmetrical” if one side is a mirror image of the other.
The square is symmetrical. The left side of the black line is exactly the same as the right side. This line is called a line of symmetry.
Guided practice
1 Draw 1 line of symmetry on each shape.
2 Circle the shapes that have a line of symmetry.
1 Reflect these shapes across a line of symmetry. Use the dot on each shape as a starting point.
1 Use the squares and lines of symmetry below to create symmetrical pictures.
An angle is the amount of turn between 2 arms.
A square corner angle is known as a right angle. A right angle is a quarter of a full turn. This angle is smaller than a right angle. This angle is larger than a right angle.
The lines that make up an angle are called arms. The point where the 2 arms meet is the vertex. If the arms are at right angles, they called called perpendicular.
1 Tick whether each angle is smaller or larger than a right angle.
1 Find and draw 3 things in your classroom that have a right angle.
2 Circle the shapes that have right angles.
3 How many right angles?
4
Look at the angles marked between the clock hands.
a At what times do the hands make a right angle?
b Which clocks show angles smaller than a right angle?
c Which clocks show angles larger than a right angle?
5 a Draw your own times on the clocks below. b Draw a clockwise arrow to show the angle.
c Tick a box to classify each angle.
Smaller than a right angle A right angle Larger than a right angle
Smaller than a right angle A right angle Larger than a right angle
What would the angle look like if it were 6 o’clock?
Smaller than a right angle A right angle Larger than a right angle
1
a Find and draw 4 angles in the classroom.
b Write a description to classify your angle compared to a right angle.
Angle 1
Angle 2
Angle 3
Angle 4
2 Draw lines to match the angles that are the same size.
7: Topic 4 3D shapes
corner/vertex edge face
1
A cube has:
• 6 faces
• 12 edges
• 8 cor ners.
Faces of 3D shapes can be different shapes, such as circles, triangles or squares.
A rectangular prism has:
a faces
b edges
c corners.
2
a faces
b edges
c corners. A cylinder has:
3 a faces
A triangular pyramid has:
b edges
c corners.
1 How many of each shape do you need to make the 3D shape?
2 triangles rectangles
Write the letter of the 3D shape with:
a at least one curved face.
b only one corner.
c more than 5 edges.
d faces that are all the same shape.
e at least one triangular face. a b circles rectangles squares triangles c d squares circles
3 Draw lines to match the shapes with their names and descriptions.
sphere square pyramid cylinder triangular prism
6 corners and 9 edges 1 curved face
3 faces and 2 edges 5 corners, 1 square face and 4 triangular faces
A prism has two parallel bases that are the same shape, and the other faces are rectangles.
4
a Colour the cubes blue.
b Colour the other prisms green.
c Colour the pyramids red.
1 Join the dots to make 3D shapes.
2 Name each shape from question 1.
3 Who am I?
a My faces are rectangles.
I have 8 corners.
I am not a cube.
I am a .
b I have 2 edges but no corners.
I have 3 faces.
I am a . Draw Draw
Guided practice
1
The dog is to the right of the clock.
The photo is on the middle shelf.
The train is below the piggy bank.
The clock is above the photo and between the dog and the dinosaur.
What other words can you use to describe where something is?
a What is above the picnic?
b What is between the slide and the bin?
c Where is the picnic basket?
d What is to the right of the dog?
e What is on the slide?
1 Where is:
2
a the computer?
b the whiteboard?
c the teacher?
d the water bottle?
a Draw a clock on the shelf.
c Draw a chair next to the bed.
e Draw a bookcase in the bottom right corner.
b Draw a mat in front of the door.
d Draw a desk in the top left corner.
f Draw a TV to the left of the bookcase.
3 Fill in the gaps.
Why do shopping centres have maps?
a The shoe shop is the hairdresser.
b The book shop is the toy shop and the toilets.
c The food court is the department store.
d The play area is the food court.
4
a What would you go past to get from the pet shop to the department store?
b Which way would you turn to get from the surf shop to the muff in shop?
1 Where are you?
a Start at the kiwi. Travel 3 squares to the right. Turn left and travel 3 squares.
b Start at the entrance. Walk 1 square straight ahead. Turn right. Walk 3 more squares.
2 Write directions to walk along the path from:
a the entrance to the morepork.
b the pigeon to the takahe.
c the sheep to the tı¯eke.
Unit 8: Topic 2 Measures of turn
When we turn something around to the right, this is also known as clockwise, as it’s the same direction that the hands go around a clock. quarter turn to the right quarter turn to the left three quarter turn to the right
1 Identify each turn.
1 Decide whether the pattern is showing half turns or quarter turns, then continue the pattern.
a Half turn Quarter turn
b Half turn Quarter turn
2 Write the name of each turn – quarter turn, half turn, three-quarter turn or full turn.
3
Draw what happens if you do a: a half turn. b three-quarter turn to the left.
c quarter turn to the right. d full turn.
4 Draw the shapes after a: a b half turn quarter turn three-quarter turn to the right full turn
1 a Describe the turn used to make the pattern.
b Continue the pattern.
2 a Describe the turns used to make the pattern.
b Continue the pattern.
3 Circle the shapes that show a quarter turn.
What did you have for dinner?
Dinner Students
Chicken Caleb, Serena, Nikau
Pizza Ava, Zac, Josh, Emily, Tayla, Hannah, Sophia, Joseph, Jessie, Aria, Casey
Pasta Riley, Ethan, Toni, Kyle, Matt, Demi, Mason, Darlean
practice
1 What are the favourite ice-cream flavours for your class? Complete the table below.
Ice-cream flavour Student names
2 Use the data from question 1 to fill in the table below.
3 Collect data from 12 students in your class.
Do you have a sister?
What problems or errors do you have when collecting data? Why do you think that is? 4 Record the favourite sport of 12 people in your class.
What question did you ask to get the data in question 4?
What do you notice about the data in question 4?
1 Write a yes/no question to ask your classmates.
2 What do you think the data will show?
3 Ask 12 people your question and record their answers.
4 Record the results another way. Yes No
What do you notice? What is the most common answer?
Guided practice
1 Count the tally marks.
2 Use tally marks to record the colours.
1
a Choose a way to sort the shapes into 4 different groups. Record your categories in the table.
Categories:
Total
b Use tally marks to count the items in each of your categories and add the totals.
c The most common category is .
d There are more than .
a Choose 4 sports that are popular in your class and record them in the table.
Sports: Tally
Totals
b Survey at least 10 people in your class and keep a tally of their answers.
c Total the tallies.
3 Answer these questions about your results.
a Which sport was the most popular?
Did anyone change their answer to match the options in the table?
b Which sport was the least popular?
c What other sports could you have included?
a List 3 different ways you could sort the animals.
b Choose one way to sort the data, and then create a table and make a tally for each category.
c What is one improvement you would do to the above?
What did you do on Saturday afternoon?
Three people went to the movies.
Seven people played sport.
Three more people went shopping than read. Sport was the most popular activity.
Seventeen people were surveyed.
Bugs in the school garden
a Ants are the most common bug. Agree Disagree
b Slugs are the least common bug.
Agree Disagree
c There were 4 more snails than slugs found. Agree Disagree
d There were 25 bugs found in total. Agree Disagree
1
a
Number of hours watching TV last night
b Which 2 people watched the same amount of TV last night?
c Who watched the most?
d Who watched the least? 2 Hair colour in a Year 3 class
a Ask 10 students in your class if they take swimming lessons. Record the results in a list (yes/no).
b Make a tally table using the results. Answer TallyTotal
c Use ticks to show the results.
d Write one statement about the results. Which method of displaying the data do you f ind the easiest to understand?
Yes No
1
a Make a table using the data in the graph.
b What is the most common transport?
c Why might the bus be least common?
d How many more people walk than ride bikes?
e When analysing this data, what information did you find missing?
Unit 10: Topic 1
Chance
Red has a four out of eight ( 4 8 ) chance of being spun. It is the most likely colour to be spun.
Orange has a 2 8 chance of being spun, and green has a 1 8 chance. The spinner is more likely to spin orange than green.
Purple has a 0 8 chance of being spun. It is impossible to spin purple.
1 Answer true or false for the spinner at the top of the page.
a Blue is the most likely colour to be spun.
b The spinner is more likely to spin red than green.
c It is possible to spin orange.
d The spinner is unlikely to spin green.
e It is impossible to spin red.
2 List or draw all the possible outcomes for the spinner at the top of the page.
1 What are 2 possible outcomes if you toss a coin?
Outcome 1:
Outcome 2:
2 When you toss a coin once, what is the chance of getting each outcome?
Outcome 1:
Outcome 2:
3 When you toss a coin 10 times, how many times do you think you ge t outcomes 1 and 2?
Outcome 1:
Outcome 2:
4 Now toss your coin 10 times and record the result using a tally. You could use an online coin tosser.
Outcome 1
Outcome 2
5 Show how many times you get each outcome in words and fractions.
Outcome 1: out of times Fraction:
Outcome 2: out of times Fraction:
6
Compare your results with your classmates. Did they have similar or different results?
1 Wiremu wants to conduct his own chance investigation using lollies. He will close his eyes and pick out a lolly.
a How many lollies are there altogether?
b Which colour do you think Wiremu will pick first? Why?
c Complete the table by working out the numbers and fractions for the lolly colours.
d Which colours have the same chance as each other of being picked?
e Which colour is unlikely to be picked?
addition The joining or adding of two numbers together to find the total. Also known as adding, plus and sum.
Example:
3 and 2 is 5
anticlockwise Moving in the opposite direction to the hands on a clock.
base The bottom edge of a 2D shape or the bottom face of a 3D shape.
area The size of an object’s surface.
Example: It takes 12 tiles to cover this placemat.
array An arrangement of items into even columns and rows that make them easier to count.
balance scale Equipment that balances items of equal mass – used to compare the mass of different items. Also called a pan balance or equal arm balance. base
calendar A chart or table showing the days, dates, weeks and months in a year.
Date
capacity The amount that a container can hold.
Example: The jug has a capacity of 4 cups.
category A group of people or things sharing the same characteristics.
centimetre A unit for measuring the length of smaller items.
Example: Length is 80 cm. 80cm
circle A 2D shape with a continuous curved line that is always the same distance from the centre point.
data Information gathered through methods such as questioning, surveys or observation.
day A period of time that lasts 24 hours.
clockwise Moving in the same direction as the hands on a clock.
cone A 3D shape with a circular base that tapers to a point.
corner The point where two edges of a 2D shape or 3D shape meet. Also called a vertex.
cube A rectangular prism where all six faces are squares of equal size. corner
difference (between) A form of subtraction or take away.
Example: The difference between 11 and 8 is 3.
digit The single numerals from 0 to 9. They can be combined to make larger numbers.
Example: 24 is a 2-digit number. 378 is a 3-digit number.
division/dividing Sharing into equal groups.
Example: 9 divided by 3 is 3
cylinder A 3D shape with 2 parallel circular bases and one curved surface.
double/doubles Adding two identical numbers or multiplying a number by 2.
Example: 4 + 4 = 8 2 × 4 = 8
duration How long something lasts.
Example: The school week lasts for 5 days.
edge The side of a shape or the line where two faces of a 3D shape meet.
eighth One part of a whole or group divided into eight equal parts. edge edge
1 8
Eighth of a whole
Eighth of a group
equal Having the same number or value.
Example:
Equal size
Equal numbers
face The flat surface of a 3D shape.
f lip
To turn a shape over horizontally or vertically. Also known as reflect.
equation A written mathematical problem where both sides are equal.
Example: 4 + 5 = 6 + 3
face vertical flip horizontal flip
fraction An equal part of a whole or group.
Example: One out of two parts or 1 2 is shaded. =
estimate A thinking guess.
friendly numbers Numbers that are easier to add to or subtract from.
Example: 10, 20 or 100
half One part of a whole or group divided into two equal parts. Also used in time for 30 minutes.
Example:
Half of a whole
Half of a group
Half past 4
hexagon A 2D shape with 6 sides.
method A way to solve a problem. In maths you can often use more than one method to get the correct answer.
Example: 32 + 27 = 59
Jump method
horizontal Parallel with the horizon or going straight across.
horizontal line
irregular shape A shape in which the sides are not all the same length and the angles are not all the same size.
jump method A way to solve number problems that uses place value to “jump” along a number line by hundreds, tens and ones.
Example: 16 + 22 = 38
length How long an object is from end to end.
Example: This poster is 3 pens long.
How heavy an object is.
Split method
metre A unit for measuring the length or height of larger objects.
month The time it takes the moon to orbit the Earth. There are 12 months in a year.
3 m
near doubles A way to add two nearly identical numbers by using known doubles facts.
Example: 4 + 5 = 4 + 4 + 1 = 9
number line A line on which numbers can be placed to show their order in our number system or to help with calculations.
number sentence A way to record calculations using numbers and mathematical symbols.
Example: 23 + 7 = 30
numeral A figure or symbol used to represent a number.
Example: 1 – one 2 – two 3 – three
octagon A 2D shape with 8 sides.
pair Two items that go together.
Example: Pairs that make 4
ordinal numbers Numbers that show the order or position of something in relation to others. Pair
parallel lines Straight lines that are the same distance apart and so will never cross.
parallelparallelnot parallel
partitioning Dividing or separating an amount into parts.
Example: Some of the ways 10 can be partitioned are: 5 and 5 4 and 6 9 and 1
pattern A repeating design or sequence of numbers.
Example: Shape pattern Number pattern 2, 4, 6, 8, 10, 12
pentagon A 2D shape with 5 sides.
picture graph A way of representing data using pictures to make it easy to understand.
Example: Favourite juices in our class
place value The value of a digit depending on its place in a number.
position Where something is in relation to other items.
Example: The boy is under the tree that is next to the house.
prism A 3D shape with parallel bases of the same shape and rectangular side faces.
triangular prism rectangular prism
pyramid A 3D shape with a 2D shape as a base and triangular faces meeting at a point.
rectangle A 2D shape with four sides and four right angles. The opposite sides are parallel and equal in length.
quadrilateral Any 2D shape with four sides.
quarter One part of a whole or group divided into four equal parts. Also used in time for 15 minutes.
Example:
right angle Quarter of a whole Quarter of a group Quarter past 4 1
regular shape A shape in which all the sides are the same length and all the angles are the same size.
rhombus A 2D shape with four sides, all of the same length and opposite sides parallel.
skip counting Counting forwards or backwards by the same number each time.
Example: Skip counting by 5s: 5, 10, 15, 20, 25, 30
Skip counting by 2s: 1, 3, 5, 7, 9, 11, 13
slide To move a shape to a new position without f lipping or turning it. Also known as translate.
sphere A 3D shape that is perfectly round.
split method A way to solve number problems that involves splitting numbers up using place value to make them easier to work with.
Example: 21 + 14 = 35
square A 2D shape with four sides of equal length and four right angles. A square is a type of rectangle.
right angle
subtraction The taking away of one number from another number. Also known as subtracting, take away, difference between and minus
Example: 5 take away 2 is 3
survey A way of collecting data or information by asking questions.
Strongly agree Agree Disagree
Strongly disagree
table A way to organise information that uses columns and rows.
tally marks A way of keeping count that uses single lines with every fifth line crossed to make a group.
three-dimensional or 3D A shape that has three dimensions – length, width and depth. 3D shapes are not f lat.
depth
trapezium A 2D shape with four sides and only one set of parallel lines.
triangle A 2D shape with three sides.
turn Rotate around a point.
two-dimensional or 2D A f lat shape that has two dimensions – length and width.
unequal Not having the same size or value.
Example:
Unequal sizeUnequal numbers
value How much something is worth.
Example:
This coin is worth 10c. This coin is worth $1.
vertical At a right angle to the horizon or straight up and down.
week A period of time that lasts 7 days.
whole All of an item or group.
Example: A whole shapeA whole group
width How wide an object is from one side to the other.
Example: This poster is 2 pens wide. vertical line
volume How much space an object takes up.
Example: This 3D shape has a volume of 4 cubes.
year The time it takes the Earth to orbit the Sun, which is approximately 365 days.
Guided practice
1 a 10 b 24 c 100 d 135
2 a 125 b 262
Independent practice
1 3 hundreds, 5 tens, 4 ones
2 2 hundreds, 0 tens, 6 ones
3 4 hundreds, 2 tens, 3 ones
4 a 4 tens 8 hundreds
b 7 ones 3 hundreds
c 4 hundreds 1 ten 3 ones
d 0 tens 5 hundreds 8 ones
5 a Teacher to check. Look for answers that show students’ ability to correctly interpret and represent hundreds, tens and ones with base-10 materials, an abacus or any other simplified means that doesn’t involve drawing each separate one.
b–c Teacher to check students have correctly written a number that is more than and less than 216.
Extended practice
1 a 863 b 368 c 638
d 38, 36, 86, 83, 68, 63
2 Teacher to check. Look for answers that show students’ ability to manipulate their chosen digits to make the biggest and smallest 3-digit numbers possible.
3 a 97 b 141, 207, 279, 297
Guided practice
1 5 tens and 7 ones; 4 tens and 17 ones; 3 tens and 27 ones
2 3 hundreds, 2 tens and 4 ones; 3 hundreds, 1 ten and 14 ones; 2 hundreds, 12 tens and 4 ones
Independent practice
1 Teacher to check. Look for students who can accurately regroup numbers using their knowledge of place value in their drawings and rewrite the numbers correctly.
a 6 tens and 3 ones
b 2 hundreds, 4 tens and 5 ones
c 4 hundreds, 13 tens and 6 ones
4 a 47 b 71 c 290 d 642 e
Extended practice
1 a 52 tens and 7 ones
b 69 tens and 2 ones or 692 ones
c 30 tens and 2 ones or 302 ones
2 a 5 hundreds and 27 ones
b 6 hundreds and 92 ones or 692 ones
c 3 hundreds and 2 ones or 302 ones
3 a 832 = 800 + 30 + 2
832 = 830 + 2
832 = 800 + 32
b 467 = 400 + 60 + 7
467 = 460 + 7
467 = 400 + 67
c 943 = 900 + 40 + 3
943 = 940 + 3 943 = 900 + 43
Guided practice
Independent
Extended practice
1 a Yes
50 + 80= 130
b No
70 + 50 = 120
2 a 170 b 90 c 380
3 South school Largest: 264 Fewest: 255
North school Largest: 294 Fewest: 285
Total largest: 558 Total fewest: 540
Guided practice
Independent practice
1 a–b Teacher to check that the number bonds total 15 and 18.
2 Teacher to check that the number bonds total 14 and 16.
Guided practice
Independent practice 1
Extended practice
123 Teacher to check methods. Look for students who choose an appropriate method, and can follow the steps sequentially to find the correct answer.
Extended practice
1 Teachers to check number lines. Look for answers that show students’ ability to accurately space their numbers and correctly represent the subtraction sum. Students may also use skip counting or partitioning to show the steps taken to get the answer.
Guided practice
2 a 17 − 8 = 9
b 15 is one more than 14. So, 15 − 7 = 8.
Extended practice
1 a 7 + 11 = 18 18 – 7 = 11 11 + 7 = 18 18 – 11 = 7
b 15 + 19 = 34 34 – 15 = 19 19 + 15 = 34 34 – 19 = 15
2 Teacher to check. Look for answers that show students’ ability to correctly represent the equation on the number line using single steps, skip counting or partitioning.
a 24 – 5 = 19 19 + 5 = 24 OR 5 + 19 = 24
b 35 – 12 = 23 23 + 12 = 35 OR 12 + 23 = 35
17 Teacher to check method. Look for students who choose an appropriate method and can follow the steps sequentially to find the correct answer.
Extended practice
1 a 2 × 10 + 2 × 4 = 20 + 8 = 28
b 3 × 10 + 3 × 1 = 30 + 1 = 31
c 10 × 3 + 4 × 3 = 30 + 12 = 42
2 a 3 × 13 = 3 × 10 + 3 × 3 = 30 + 9 = 39
b 2 × 24 = 2 × 20 + 2 × 4 = 40 + 8 = 48
c 10 × 15 = 10 × 10 + 10 × 5 = 100 + 50 = 150
Guided practice
1 a 12 divided into groups of 4 gives 3 groups.
12 divided by 4 is 3 12 ÷ 4 = 3
b 15 divided into groups of 3 gives 5 groups.
15 divided by 3 is 5 15 ÷ 3 = 5
2 a unequal b equal
Independent practice
1 a
12 ÷ 4 = 3
b
25 ÷ 5 = 5
c
24 ÷ 6 = 4
2 a 9 ÷ 3 = 3
b 20 ÷ 4 = 5
3 a 20 shared between 4 is 5.
5 × 4 = 20
20 ÷ 5 = 4
b 18 shared between 6 is 3.
6 × 3 = 18
18 ÷ 3 = 6
4 2 × 5 = 10
5 × 2 = 10
10 ÷ 2 = 5
10 ÷ 5 = 2
5 a 2 × 7 = 14
7 × 2 = 14
14 ÷ 7 = 2
14 ÷ 2 = 7
b 3 × 8 = 24
8 × 3 = 24
24 ÷ 8 = 3
24 ÷ 3 = 8
Extended practice
1 Teacher to check. Look for answers that show students’ ability to match their diagrams to the equations successfully.
The possibilities are 16 ÷ 1 = 16, 16 ÷ 2 = 8, 16 ÷ 4 = 4, 16 ÷ 8 = 2 or 16 ÷ 16 = 1.
2 How many rows of students in a class of:
Guided practice
1 a Three of the five parts should be shaded.
b One of the three parts should be shaded.
c One of the two parts should be shaded.
d Three of the four parts should be shaded.
e Four of the five parts should be shaded.
f Two of the three parts should be shaded.
practice
3 a–d Teacher to check. Look for students who can divide the shapes into the correct number of parts and who show an understanding of the need to make the parts equal in size.
4 a fifths b halves
c fifths d halves
5 a 1 dog
b 2 strawberries
c 4 apples
d 1 star
e 2 cats
Extended practice
1 a 24 candies
b 12 candies
c Jar B Same
2 a, c & e Teacher to check. Look for students who can draw lines to divide the square into the correct number of parts and who show an understanding that fractions are made up of parts of equal size.
b 1 2 or a half
c 1 4 or a quarter
Guided practice
3
4 a Students should shade 2 parts. 2 4
b Students should shade 4 parts. 4 8
c Students should shade 2 parts. 2 8
practice
1 a 1 2 b 1 5 c 1 3
d 2 4 e 2 3 f 4 5
2 a 2 b 2 c 4
1
1
to circle notes that correctly make the designated total and demonstrate that they have a strong grasp of counting with money.
3 a $2.70 or two dollars and seventy cents
b $105 or one hundred and five dollars
c $21.60 or twenty-one dollars and sixty cents
d $35 or thirty-five dollars
4 a $55 b $20
c $30.45 d $23.40
Order from smallest to largest: b, d, c, a
+ 20c + 20c + 20c + 20c = $1 OR 5 × 20c = $1
Extended practice
1 Teacher to check. Look for answers that show students’ ability to accurately make the given total each time and to use different combinations of numbers.
2 a Possible answers are: 20c, 20c and 10c; 10c, 10c, 10c and 20c; 10c, 10c, 10c, 10c and 10c; 50c
b Possible answers are: $1; 50c and 50c; 20c, 20c, 20c, 20c and 20c; 10c, 10c, 10c, 10c, 10c, 10c, 10c, 10, 10c and 10c; 50c, 20c, 20c and 10c
$10 + $10 + $10 + $10 + $10 = $50 OR 5 × $10 = $50
$50 + $50 = $100 OR 2 × $50 = $100
2 a Incorrect, 2 3 or 4 6
b Correct
c Incorrect, 2 5 or 4
d Correct
3
$5 + $5 + $5 + $5 = $20 OR 4 × $5 = $20
1 a–d Teacher to check. Look for answers that show students’ ability to circle coins that correctly make the designated total and demonstrate that they have a strong grasp of counting with money.
2 a–d Teacher to check. Look for answers that show students’ ability
1 50c 2 40c 3 20c 4
5 $1.50 6 70c
Independent practice
1 Students may draw, write or use equations to show their answers.
a 2 × 50c coins
b 10 × 10c coins
c 5 × 20c coins
2 Students may draw, write or use equations to show their answers.
a 10 × $10 notes
b 5 × $20 notes
c 2 × $50 notes
3 Teacher to check. Look for answers that show students’ ability to group coins of the same denomination and use skip counting to find the total, or to group coins in easier-to-count groupings, such as $1.
a $4.30 b $1.20 c $12
practice
1 a $2, $1 and 50c
Number of coins: 3
b 3 × $2, 50c, 20c and 10c
Number of coins: 6
2 a $55
b i $35 ii $10 iii $23
3 a $75.80
b i $55.80 ii $30.80 iii $43.80
Guided practice
1 a 0, 2, 4, 6, 8 OR 2, 4, 6, 8, 0
b 0, 3, 6, 9, 2, 5, 8, 1, 4, 7 OR 3, 6, 9, 2, 5, 8, 1, 4, 7, 0 c 0
Independent practice
1 a and c
Extended practice
1 a and c
123456789 10
11121314151617181920
21222324252627282930
31323334353637383940
41424344454647484950
51525354555657585960
61626364656667686970
71727374757677787980
81828384858687888990
919293949596979899 100
b 3, 8, 3, 8
d 2, 5, 8, 1, 4, 7, 0 3, 6, 9
2 a 5s b 2s c 10s
3 a 7, 17, 27, 37, 47, 57, 67 OR 67, 57, 47, 37, 27, 17, 7 b 10s
Guided practice
1 a 3 + 4 = 7 b 8 – 3 = 5
c Teacher to check diagram. Look for students who draw four scooters with three wheels on each. Students should write 12 as the answer.
Independent practice
1 a–d Teacher to check. Look for answers that show students’ ability to accurately depict the number sentence in a drawing, using the correct number of items and identifying the operation required.
Number sentences
a 38 – 6 = 32
5 D, C, A, B
6 a–d Teacher to check diagrams. Answers are:
a 4 b 8 c 12 d 16
e Teacher to check. Look for students who show an awareness of the pattern made by linking it to counting by 4.
7 1
Extended practice
1 B, A, D, A, C, D
b 12 – 4 = 8 OR 4 + 8 = 12
c 17 – 7 = 10
d 10 + 6 = 16
27 24 21 18 15 12 963
4 Teacher to check. Look for students who have followed the numbers in the correct sequence.
5
2 Teacher to check. Look for answers that show students’ ability to correctly identify the operation required and to think of situations that logically demonstrate the operation. Also check for appropriate language to match addition and subtraction.
3 a Addition b Addition
c Subtraction
4 a False, 174
b False, 223
c False, 16
d True
1 a–d Teacher to check. Look for answers that show students’ ability to correctly use a ruler starting at 0 and to record reasonable measurements in metres for the given items.
Independent practice
1 Teacher to check. Look for answers that show students’ ability to make a reasonable estimate of lengths in comparison to a metre, and to then accurately measure their chosen items to check their answers.
2
1 a and b Teacher to check. Look for answers that show students’ ability to correctly use a ruler starting at 0 and to record reasonable measurements in centimetres for the given items.
2 Teacher to check.
Independent practice
1 Teacher to check. Look for answers that show students’ ability to make a reasonable estimate of lengths in comparison to 30 centimetres, and then accurately measure their chosen items to check their answers. less than 1 metre about 1 metre more than 1 metre
3 a 3 m b 2 m c 28 m
4 a 3 cm b 6 cm c 2 cm
5 a and b Teacher to check. Look for answers that show students’ ability to correctly measure and draw the required lines.
6 a 14 cm
b 9 cm
c 16 cm
d 14 cm
7 B, C, A
Extended practice
1 a m b cm c m
d m e cm f cm
2 swimming pool
3 glass
4 about 2 metres
5 about 20 centimetres
Guided practice
1 a The phone should be circled.
b The pillow should be circled.
2 Teacher to check.
Independent practice
3 Figure with area of 10 squares is the largest and should be circled.
4 Teacher to check.
5 Teacher to check.
Extended practice
1 a–d Teacher to check. Look for students who can accurately make the shapes based on the specifications and who show an awareness of the basic concept of area – e.g. the squares that make up each shape must have at least one joining edge.
2 forty-seven centimetres square
3 a Teacher to check.
b 36 cm2
c 6 cm2
d 42 cm2
Guided practice
1 a 6 blocks b 8 blocks
2 Both are the same.
Independent practice
1 a B, E, A, C, D
b A, C and D
c A, B and E
2 Teacher to check.
Guided practice
1 Teacher to check.
Independent practice
1 a A-4, B-2, C-6, D-1, E-5, F-3
b B, D
c A, C, E, F
Guided practice
1 a
Less than 1 kg About 1 kgMore than 1 kg
1 Teacher to check. Look for answers that show students’ ability to choose appropriate uniform units of area that will completely cover surfaces without gaps. Also check that students are not overlapping the units when they are measuring area.
2 a 9 squares
b 6 squares
c 7 squares
d 10 squares
e 7 squares
d C
e 2 L
Extended practice
1 12 blocks; 11 blocks; 5 blocks
2 a capacity, 1 2 L each
b capacity, 50 L
c volume, 32 blocks
b chair or bike
Independent practice
1 Teacher to check.
2 a Teacher to check.
b 5 textbooks
c stapler
d Teacher to check.
Extended practice
1 Rice: 12, A4 paper: 8, Watering can: 6, Paint can: 4, TV: 2
Guided practice
1 a 12 b 9 c 3 d 6
2 a 9 o’clock b half past 4
c quarter past 6 d quarter to 11
Independent practice
1 a b
4 a half past 4
b quarter to 6
c 11 o’clock
d quarter past 9
e half past 12
f quarter past 6
Extended practice
1 a half past 8 b 8 o’clock
c quarter to 8 d half past 9
2 a b 2:15 3:00 quarter past 2 3 o’clock OR two fifteen
d 3:45 12:00 quarter to 4 12 o’clock
2 a Saturday 18 May
b Wednesday 22 May
c Wednesday, Thursday and Friday
d Tuesday 14 May
e 6
f Teacher to check working out. Number of days left is 222.
Extended practice
1 a–d Teacher to check. Look for answers that show students’ ability to correctly identify and write the current month and to accurately label the dates. Also check that students can use the information they have provided to correctly identify the first day of the month and the number of days in the month.
or seven fifteen
1 a Tuesday b 6 February
2 a no
b April, June, September or November
c 3
d 17th May
Guided practice
1 a 6 corners b 6 sides
2 a 5 corners b 5 sides
3 a 8 corners b 8 sides
Independent practice
1 a and b 2 rectangle hexagon rhombus triangle
6 sides and 6 corners 4 sides all the same length, 2 sets of parallel lines 4 corners, opposite sides are the same length 3 straight sides
b Teacher to check students have circled the correct dates.
c Answers will vary.
3 Teacher to check. Look for answers that show students’ ability to use the descriptions to accurately draw a shape that matches the criteria.
a Teacher to check if shape is regular or irregular. Will depend on student drawing.
b irregular
c irregular
d Teacher to check if shape is regular or irregular. Will depend on student drawing.
e irregular
f irregular
Extended practice
1 a b c
2
3 The shape is a pentagon.
4 Note that many shapes have a number of possible classifications.
a kite, quadrilateral
Guided practice
Guided practice
1 a smaller b smaller
b square, quadrilateral, rhombus, parallelogram
c pentagon
d parallelogram, quadrilateral, rhombus
e circle
f octagon
5 has 4 corners? has two pairs of parallel opposite lines? is irregular? has no corners?
a, b, d b, d a, d, e, fe
2 Students should circle the kite, octagon and rectangle.
Independent practice
1 a–f Teacher to check.
Extended practice
1 a
c larger d smaller
e larger f larger
Independent practice
1 Teacher to check. Look for students who show an understanding of right angles by finding and accurately representing items in the classroom that include them.
2 The following shapes should be circled: a, e, f
3 a 4 b 1 c 0
4 a 3 o’clock, 9 o’clock b C, D
c B, F
5 Teacher to check. Look for students who understand how to indicate an angle, and who can accurately classify the size of the angle in relation to a right angle.
Extended practice
1 Teacher to check. Look for students who can apply their knowledge of angle sizes to successfully select and classify angles within the classroom.
2
Guided practice
1 a 6 faces b 12 edges
c 8 corners
2 a 3 faces b 2 edges
c 0 corners
3 a 4 faces b 6 edges
c 4 corners
Independent practice
1 a 2 triangles 3 rectangles
b 2 circles 1 rectangle
c 1 square 4 triangles
d 6 squares 0 circles
2 a A, E b E
Guided practice
1 a the tree b the dog
c below the tree OR on the picnic blanket, or similar
d the bin e the cat
Independent practice
1 a–d Teacher to check. Look for answers that show students have a strong grasp of the vocabulary of location and are able to accurately identify where each item is in relation to other items in the room.
2 Item placement is approximately as follows:
Independent practice
1 a quarter turn
b half turn
2 a three-quarter turn
b half turn
c full turn
d quarter turn 3 a b
c B, C, D d C, D e C 3 4
6 corners and 9 edges 1 curved face 3 faces and 2 edges 5 corners, 1 square face and 4 triangular faces sphere square pyramid cylinder triangular prism
3 a–d Teacher to check. Look for answers that show students’ ability to accurately use terms such as “next to”, “to the left of”, “between” and “opposite”.
Extended practice
1 and 2 a b cone cube
c d triangular triangular pyramid prism
3 a rectangular prism
b cylinder
Teacher to check drawings. Look for answers that show students’ ability to accurately represent the given 3D shapes with the correct shapes in the faces that are visible.
4 a Either the toy shop, book shop, toilets and play area OR the food court, muffin shop, jewellery shop and hairdresser depending on route chosen. b left
Extended practice
1 a the seal b the pigeon
2 a–c Teacher to check. Look for answers that show students’ ability to use locational language to accurately describe the route and directions that can be followed.
Guided practice
1 a half turn b quarter turn
c three-quarter d quarter turn
e full turn f quarter turn
c d
4 a half turn quarter turn
b three-quarter full turn turn to right
Extended practice
1 a quarter turn
2 a half turn, then quarter turn to the right
3 a The third and fifth shapes should be circled.
b The first and second shapes should be circled. OR
1 a Teacher to check. Look for answers that show students’ ability to identify variables that match the pictures – for example, number of legs, animals that can/cannot fly, colours of animals or animals that live in the water/on land.
b
Independent practice
1 Teacher to check.
2 Teacher to check. Look for answers that show students’ ability to accurately tally their data.
3 Teacher to check. Look for answers that show students’ ability to accurately record 12 answers using either the tick method or by writing down students’ names.
4 Teacher to check. Look for answers that show students’ ability to accurately record 12 answers using an appropriate method.
5 Teacher to check. Look for answers that show students’ ability to ask an open-ended question that will get the responses listed in the table – for example, “What is your favourite sport?”
6 Teacher to check. Answers will vary depending on student data. Look for answers that show students are able to interpret their data accurately.
Extended practice
1 Teacher to check. Look for answers that show students’ ability to choose a question that can only have “yes” or “no” as the answer.
2 Teacher to check. Look for students’ ability to make reasonable estimates.
3 Teacher to check. Look for accurate recording of both the question and the results in the table.
4 Teacher to check. Look for recording strategies such as ticks or tally marks. Ensure the results match the results that students recorded in question 2.
practice
1 a Teacher to check. Look for answers that show students’ ability to choose appropriate categories, such as shape or colour, and who can identify variables that match – for example, circles and rectangles for shape and blue and green for colour.
b Teacher to check. Look for answers that show students’ ability to make an accurate tally and to use tally mark groupings correctly.
c Teacher to check. Look for answers that show students’ ability to accurately count their tally marks.
d Teacher to check. Look for students who are able to draw simple conclusions from their data.
2 a Teacher to check. Look for answers that show students’ ability to choose appropriate variables that are likely to appeal to the classmates being surveyed – for example, basketball, netball, football, cricket – and to record the variables in the correct section of the table.
b Teacher to check. Look for answers that show students can use tally marks correctly to track of responses.
c Teacher to check. Look for answers showing totals that match the tally marks they recorded.
3 a and b Teacher to check for answers that show students’ ability to correctly identify the most and least popular options using the data they collected.
c Teacher to check. Look for answers that show students’ ability to find plausible options that their classmates are likely to choose, such as rugby.
b Teacher to check. Look for answers that show students’ ability to construct a table with the correct number of columns and rows to record their variables and results. Check students are able to make an accurate tally that matches the data based on their chosen categories.
c Teacher to check. Look for answers that show students’ ability to critically think about data.
3 a Teacher to check. Look for answers that show students’ ability to understand how to record data in a list and that have 10 pieces of data recorded.
b Teacher to check. Look for answers that show students’ ability to correctly label the table, whose tally marks match the data in their list and whose total matches the tally marks.
c Teacher to check. Look for answers that show students’ ability to match the representations in their picture graphs to those in their tally tables.
d Teacher to check. Look for answers that show students’ ability to make a statement that accurately matches the data, such as identifying the category with the greatest or least number of responses, or comparing the numbers in both categories.
Extended practice
1 a
b car
c Ans wers will vary. At this age, maybe students are too young to catch the bus on their own, so are driven to school by their parent/ guardian or walk and ride their bike to school with their parent/guardian.
d 2 people
e Teacher to check. Answers will vary, but it could be the number of people who answered, the year level of the students that were interviewed, etc.
1
2 red: 4 out of 8, orange: 2 out of 8, green: 1 out of 8, blue: 1 out of 8
Independent practice
1 Outcome 1: heads
Outcome 2: tails
2 Outcome 1: 1 out of 2
Outcome 2: 1 out of 2
3 Ans wers will vary.
4 Ans wers will vary.
5 Teacher to check.
6 Ans wers will vary.
Extended practice
1 a 10
b Ans wers will vary. For example, green because there are more green lollies than any other colour.
d blue, yellow and red
e Pink because there is only one pink lolly.
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Acknowledgements
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