Problem-Solving Strategies & Skills – Number & Algebra: Year 2

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Number and algebra

Julian is three years older than Dan. Julian’s and © R. I .

C.Publ i cat i ons Dan’s ages add together •f orr evi ew pur posesonl y• to equal thirteen.

How old are the boys?

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Number and algebra

Julian is four years older than Dan. Steven is three years older than Julian and R. I .

C .Publ i cat i ons seven years older©than Dan. •f orr e vi ew pur posesonl y• Steven’s and Dan’s ages added together equal 17.

How old are the boys?

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Number and algebra

Casey has lots of toy vehicles. He has twelve more cars than trucks. © R. I .

C.Publ i cat i ons He has nine motorbikes •f orr evi ew pur posesonl y• and 71 vehicles in total.

How many cars and trucks does he have?

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Number and algebra Casey has lots of toy vehicles. He has twentysix more cars than trucks.

He has nineteen less© R. I .

C.Publ i cat i ons motorbikes than• cars. f orr evi ew pur posesonl y• He has 22 motorbikes.

How many toy vehicles does he have altogether?

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra Harry baked cookies at the weekend. Each school day he took two cookies for himself and two for each of his two friends. © R. I .

C.Publ i cat i ons On Saturday, he • had cookies f orsix r evi ew pur posesonl y• left.

How many cookies had he baked?

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra Harry baked cookies at the weekend. Each school day he took two cookies for himself and two for each of his two friends. © R. I .

C.Publ i cat i ons On Saturday, he • had f orenough r evi ew pur posesonl y• cookies left over to give himself and his two brothers six each.

How many cookies had he baked?

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

Mr Wilde bought some new pets for his pet shop. He added twenty-four more goldfish to one tank and six birds to the cage. He bought seven more rabbits, © R. I .

C.Publ i cat i ons three more guinea pigs and fifteen white •f o rr ev i ew pur po sesonl y• mice. After adding the pets to those he already had, he had a total of eighty pets.

How many pets did he have before he bought the new ones?

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Number and algebra

Mr Wilde had forty-seven goldfish, nine birds, eight rabbits, five guinea pigs and twenty-one white mice in his pet shop. © R. I .

C.Publ i cat i ons

In one week 18 goldfish, 2e birds, •f orr vi ew pur posesonl y• 3 rabbits, 1 guinea pig and 15 white mice were sold.

How many of each type of pet were left?

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Number and algebra

Ryan was a skilled tenpin bowler.

In one week, while practising, he bowled seven strikes*, three ‘nines’ and four ‘fives’. © R. I .

C.Publ i cat i ons

f orr evi ew pur osesonl y• How many pins did•he knock overp in total that week? * A strike occurs when all ten pins are knocked down with one ball.

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Number and algebra

Ryan was a skilled tenpin bowler. In one week of practice, Ryan bowled ten ‘fives’, six ‘threes’, nine ‘twos’ and four ‘ones’.

The rest were strikes*.

© R. I .

C.Publ i cat i ons If the total number • off pins he o rr evi ewknocked pur posesonl y•

over that week was 130, how many strikes did he bowl? * A strike occurs when all ten pins are knocked down with one ball.

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Number and algebra

Stephanie drew a crazy creature with three eyes, two heads and ten legs each with©five toes.

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•f orr evi ew pur y• How many eyes, heads, legsposesonl and toes would three crazy creatures have?

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Number and algebra

Stephanie drew some crazy creatures. Each crazy creature had three eyes, two heads and © R. I .

C.Publ i cat i ons ten legs each with five toes.

•f orr evi ew pur posesonl y•

How many crazy creatures did Stephanie draw if there were one hundred and fifty toes?

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Number and algebra

Dylan is twice as old as Jake. Jake is ten times as old as Rob. Rania© isR half of .

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C. Publ i cat i ons Jake’s age. •f orr evi ew pur posesonl y• If Dylan is a young man of 20, how old is Rania?

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Number and algebra Dylan is three times the age of Rob. Jake is three years older than Rob, but three years younger than Dylan. .

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C.Publ i cat i ons Rania, their sister,©isRone •f orr evi ew pur posesonl y• year older than Rob. If Rania is four years of age, how old are Dylan, Jake and Rob?

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Number and algebra

Each box of fruit at the wholesalers holds 10 rows of apples with eight ©R I .

C.Pu bl i cat i ons apples in each row.

A. fruit shop owner •f o evi ew pur posesonl y• bought 2 boxes ofrr fruit.

How many apples did he have in total?

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Number and algebra

Each box of fruit at the wholesalers holds 10 rows of apples with eight apples in each row.

A. fruit shop owner ©R I .

C.Pu bl i cat i ons bought 2 boxes ofrr fruit. packaged •f o evi ewHe pu r posesonl y• the apples in bags of ten.

How many bags of apples did he have?

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra Heather added three one-digit numbers using a number line. When she was finished, her diagram looked like the one below. © R. I .

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Which three one-digit numbers did she add, what was the addition problem and what was the answer she got?

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Number and algebra

Heather chose a two-digit number on the number line and added ten three times. When she was finished, her diagram looked like the one below.

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20

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90

100

Which two-digit number did she start on, what was the addition problem and what was the answer she got?

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Number and algebra Dave used coloured blocks to solve an addition problem.

© is R. I .

C.Publ i cat i on s one Dave made?

Which row of blocks equivalent to the

ROW 1

•f orr evi ew pur posesonl y•

ROW 2 R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

Dave used coloured blocks to solve an addition problem.

What number goes in the box? i © R. I .

C.Publ cat i ons

•f ew pur posesonl y• ROW 7 +18 + 9 = 7 + 9or +r 8evi

=8+7+9=8+9+7

ROW = 92+ 7 + 8 = 9 + 8 + R.I.C. Publications® Prim-Ed Publishing

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Number and algebra Stuart made up three tricky problems to test his friend.

1. (9 + 6) + 8 = 9 + (6 + 2. 5 + (3 + 3. (

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) = (5©+R3) +.P 8ubl .

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C i cat i ons

orr vi ew pur y• + 1) + 2• =f 8 +e (1 + 2) posesonl

The same number belongs in the box of each problem.

What is the number?

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Number and algebra

Stuart made up some tricky problems to test his friend.

1. (9 + 6) + 8 = 9 + (6 + 2. 5 + (3 + 3. (

)

) = (5©+R3) +.P 8ubl .

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C i cat i ons

orr vi ew pur y• + 1) + 2• =f 8 +e (1 + 2) posesonl

The same number belongs in the box of each problem.

What is the answer for each problem?

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

The book Lisa is reading has 164 pages. She read 28 pages on the first day, 32 pages on the second day and 19 on the third © R. I .

C.Publ i cat i ons day.

•f orr evi ew pur posesonl y•

What is the difference between the number of pages she read on the first day and the number of pages she read on the third day?

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Number and algebra

The book Lisa is reading has 164 pages. She read 28 pages on the first day, © R. I .

C.Publ i cat i ons 32 pages on the second day •f o rr evi ew pur posesonl y• and 19 on the third day.

How many pages does she still have left to read?

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Number and algebra

Joe used the hundred square to work out how many more toy soldiers he needed to make a company* for his battle display.

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11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

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C.Publ i cat i ons 51 52 53 f or r ev i ew pur posesonl y• 61 62 63 If he already has• 69 toy soldiers,

how many more soldiers does he need to make a company?

4

54 55 56 57 58 59 60 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

*His company has 100 soldiers.

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Number and algebra

Joe used the hundred square to work 1 2 3 11 12 13 out how many more toy soldiers he 21 22 23 needed to make a company* for his 31 32 33 battle display. He already has 41 42 43 © R. I .

C.Publ i cat i ons 51 52 53 52 infantrymen and 34ev officers.

•f orr i ew pur posesonl y•

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6

7

8

9

10

14 15 16 17 18 19 20 24 25 26 27 28 29 30 34 35 36 37 38 39 40 44 45 46 47 48 49 50 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

How many more soldiers does he need to make a company?

71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

* His company has 100 soldiers.

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Number and algebra

The children were working hard to gain merit points. They needed 200 points to receive an hour of free time on Friday © R. I .

C.Pu bl i c at i ons afternoon. They already had 185 points, f orr evi ew pur pos esonl y• but, when Trevor•misbehaved on Thursday afternoon, the teacher deducted 25 points.

How many merit points did they still have?

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Number and algebra

The children were working hard to gain merit points.

They needed 200 points to receive an hour of free time on Friday afternoon. They already had 185 points but Trevor misbehaved, so the teacher deducted 15 points. Then forgot © RDallas .

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C.Pub l i cat i oto nsbring her homework so the teacher another •f o rr evi ewdeducted pur poseso nl y• 10 points.

How many merit points did they still have?

How many more did they need to reach their target?

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Number and algebra

Mr Brown chose children in the class to count numbers in a sequence. Jade counted in 3s from 33 to 69. © R. I .

C.Publ i cat i ons

•f orr evi ew pur posesonl y• How many two-digit numbers were there in the number sequence she counted (including the first and last numbers)?

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Number and algebra

Mr Brown chose children in the class to count numbers in a sequence. Jade counted in 3s from 33 to 69. © R. I .

C.Publ i cat i ons

f orr evi ew pur posesonl y• How many of the•two-digit numbers in the sequence she counted had an odd number as the last digit?

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Number and algebra Brad and Jack each made three-digit numbers using a simple abacus.

BRAD

JACK

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• HUNDREDS

TENS

ONES

HUNDREDS TENS

ONES

How many more ‘hundreds’, ‘tens’ and ‘ones’ does Jack need to have the same number as Brad?

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Number and algebra

Brad and Jack each made three-digit numbers using a simple abacus.

BRAD

JACK

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• HUNDREDS

TENS

ONES

HUNDREDS TENS

ONES

If Brad adds 4 ‘hundreds’, no ‘tens’ and two ‘ones’ to his abacus, and Jack adds 5 ‘hundreds’, 3 ‘tens’ and no ‘ones’, who has the larger number?

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Number and algebra

Martin split two numbers into hundreds, tens and H ones to make them easier to subtract. He wrote them in © R. I .

C.Publ i cat i ons5 a table, then he subtracted •f orr evi ew pur posesonl y• them and wrote his answer.

2

What number did he subtract from 567?

T 6

O 7

3

3

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Number and algebra

Martin split two numbers into hundreds, tens and H ones to make them easier to subtract. He wrote them in © R. I .

C.Publ i cat i ons a table, then he subtracted •f orr evi ew pur poseson l y• 3 them and wrote his answer.

4

What number is missing from the table?

T

O

7 7

2 7

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Number and algebra

Silvia and her mum were searching for a house on Double Street. Silvia’s cousin had just moved and they were paying their first visit.

‘The house numbers go in twos’, said Mum. R. I .

C. Pub l i cat i o ns ‘The even numbers © are on the right.

We’re •f or r evi ew pur posesonl y• looking for number 74!’

‘There’s 98!’ shouted Silvia.

How many houses after 98 do Silvia and her mum need to pass before reaching the one they want?

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Number and algebra

Silvia and her mum were searching for a house on Double Street. Silvia’s cousin had just moved and they were paying their first visit.

‘The house numbers go in twos’, said Mum. R. I .

C. Pub l i cat i o ns ‘The even numbers © are on the right.

We’re •f or r evi ew pur posesonl y• looking for number 74!’

‘There’s 98!’ shouted Silvia.

How many houses between the numbers 98 and 74 have a zero in them?

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Number and algebra Mrs Baker uses a star chart to reward each child for good behaviour and good class work. Each star that goes on the chart has five points.

© R. I .

C.Publ i cat i ons •f orr ev i ew pur pos esonl y•

By Friday afternoon, Stephanie had

collected twenty-seven stars.

If she counted every star point on her stars, how many would there be?

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Number and algebra

Mrs Baker uses a star chart to reward each child for good behaviour and good class work. Each star that goes on the chart has five points. There are twenty-four children in the class. © R. I .

C.Publ i cat i ons •f orr evi ew children pur poses onl y•

By Friday afternoon, eighteen had

collected five stars each.

If the children worked out the number of star points they had in total, what would the answer be?

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Number and algebra

The fisherman scooped up a group of large shrimp* in his net. He placed some in each of the two buckets he had. The first bucket contained R. I .

C .Pu bl i cat i ons seventy shrimp legs© and the second f orr evi e w pur posesonl y• bucket held forty•shrimp legs.

How many shrimp did he catch altogether? * A shrimp has ten legs.

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Number and algebra

The fisherman scooped up a group of large shrimp* in his net.

He placed some in each of the two buckets he had.

The first bucket contained seventy shrimp legs and the second bucket held forty shrimp legs. © R. I .

C.Publ i cat i ons f orr ev i ew p ur p os esonl y• How many shrimp • would need to be added

to the second bucket to have equivalent numbers of shrimp legs in each bucket? * A shrimp has ten legs.

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Number and algebra

Chris used a number line divided into 5s to solve this problem: ‘At the car show there were 5 sections of cars and each section had 17 cars. What was the total number of cars at the car © R. I .

C.Publ i cat i ons show?’

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0

5

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

What number on the line is the answer to Chris’s problem?

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Number and algebra

Chris used a number line divided into 5s to solve this problem: ‘At the car show there were 5 sections of cars and each section had cars. What was the total number of cars at the car © R. I .

C.Publ i cat i ons show?’

•f orr evi ew pur posesonl y•

If Chris’s answer is shown below, how many cars are in each section?

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10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

Mr Cash asked the children to write some problems and to use the symbol < (is less than) or > (is greater than) to make them correct.

© R. I .

C.Publ i cat i ons Nina wrote: 51• +f 0r>r 50. o e vi ew pur posesonl y•

Henry wrote: 97 – 40 < 50.

Who used the symbol correctly?

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Extension

Number and algebra

Mr Cash asked the children to write some problems and to use the symbol < (is less than) or > (is greater than) to make them correct.

© R. I .

C.Publ i cat i ons Nina wrote: 31• +f 0r>r 31 –w0.pur o e vi e posesonl y•

Henry wrote: 97 – 60 < 50 – 12.

Whose problem is correct?

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Number and algebra

Sasha received a new bookshelf on which to place her collection of favourite books. The bookshelf had © R. I .

C.Pu bl i cat i ons four shelves and each shelf held five •f or r evi e w pur posesonl y• 1 books. She filled ⁄2 of the shelves.

How many books did she place?

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Number and algebra

Sasha received a new bookshelf on which to place her favourite books.

The bookshelf had four shelves and © R. I .

C.Publ i cat i ons each shelf held five books.

•f orr evi ew pur posesonl y•

How many books did she still need to place to fill the shelves after she had placed 1⁄4 of them?

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

The local cinema had three large sections of seats. Each section had ten rows with ten seats in © R. I .

Ctook .Publ i cat i ons each row. The school group orr evi ew pur posesonl y• up half of the seats.•f How many seats in the cinema did the school group take up?

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Number and algebra

The local cinema had three large sections of seats. Each section had ten rows with ten seats in each row. The school group took up half © R. I .

C. Publ i cat i ons of the seats. The residents of the •f o rr e ewthe pur posesonl y• 2v ⁄4 i of aged care home took up remaining seats.

How many seats did the residents of the aged care home occupy?

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Number and algebra Farmer Fred planned his vegetable garden. He wanted two sections. In each section, he wanted five rows with ten © Rin .

I .

C .Publ i cat i ons vegetable seedlings each •f orr evi ehe wp ur posesonl y• row. By the afternoon, had planted 3⁄4 of the seedlings.

How many vegetable seedlings had he planted?

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Number and algebra

Farmer Fred planned his vegetable garden. He wanted two sections. In each section, he wanted five rows with ten vegetable seedlings in © R. I .

C.Pu bl i cat i ons each row. He bought 25 seedlings •f orr evi ew pur posesonl y• to plant out the first section.

What fraction of the first section will he be able to plant out?

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Number and algebra

When Julio and Pedro received their pizzas, they each cut them into a different number of slices.

Julio cut his into 8 pieces and © R. I .

C.Publ i cat i ons Pedro cut his into 4 pieces.

•f orr evi ew pur posesonl y•

Julio ate 1⁄4 of his pizza and Pedro ate two pieces.

Who ate the most pizza?

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Number and algebra

When Julio and Pedro received their pizzas, they each cut them into a different number of slices. Julio cut his into 8 pieces and Pedro cut his into © R. I .

C.Publ i cat i ons 4 pieces.

•f orr evi ew pur posesonl y•

Julio ate 6 pieces of his pizza.

If they each ate the same fraction of their pizza, how many pieces did Pedro eat?

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Number and algebra

Tom used his knowledge of equivalent fractions on a number line to solve this problem:

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0 ‘Monster A lost three of his four © R. I .

C.Publ i cat i ons limbs in a battle. Monster B lost •f orr evi ew pur poseso nl y•1 0 five of his eight limbs in a battle.

4 Who lost the larger fraction of their 0 1 2 limbs?’

8

What is Tom’s answer?

8

1 2

2 2

2 4 3 8

4 8

3 4 5 8

6 8

4 4 7 8

8 8

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Number and algebra

Tom used his knowledge of equivalent fractions on a number line to solve this problem:

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‘Monster A lost one of his two 0 © R. I .

C .Publ i cat i ons limbs in a battle. Monster B lost •f o i ew pur poseso nl y•1 two of his four limbs inrr aev battle.

0 4 Monster C, who has 8 limbs, lost the same fraction of limbs. How 0 1 2 many limbs did Monster C lose?’

8 8

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2 2

2 4 3 8

4 8

3 4 5 8

6 8

4 4 7 8

8 8

What is Tom’s answer?

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

1 2 ‘Ben, can you count in threes 11 12 from 33?’ said his teacher, 21 22 Mr Brown. ‘Stop on the first 31 32 number greater than©50.’

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What number did he say last?

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51n 52 •f orr evi ew pur poseso l y53 • 54

Ben used the hundred square and counted in threes.

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55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

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Extension

Number and algebra

‘Ben, can you count in threes from 33?’ said his teacher, Mr Brown. ‘Stop on the first number greater than 50.’

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45 46 47 48 49 50 55 56 57 58 59 60

and counted in threes.

61 62 63 64 65 66 67 68 69 70

How many odd numbers and even numbers did Ben say?

81 82 83 84 85 86 87 88 89 90

71 72 73 74 75 76 77 78 79 80 91 92 93 94 95 96 97 98 99 100

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Number and algebra Bruce added the same number each time to make up a number sequence. He wrote these problems to show what he had done: 65 +

© R. I .

C. l i c at i o ns+ = 69, 69 +Pub= 73, 73

= 77,

= 81, 81 +

= 89

•f orr evi ew pur posesonl y•

77 +

= 85, 85 +

What number goes in the box and what is the next number in the sequence?

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

Bruce added the same number each time to make up a number sequence. The first problem he wrote = 69. Bruce made up a sequence down was 65 + © R. I .

C.P ubl i caa t i o ns of ten numbers. Then he found pattern in the •f orr evi ew pur posesonl y• answers.

What is the pattern of the final digits in Bruce’s answers?

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Number and algebra Bethany counted in sixes from 6 and coloured each number in the sequence on the hundred square.

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11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Which statement © is R correct?

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orr ur posesonl y• 6f + 6e +vi 6ew is p the (a) 6 + 6 + 6 +• 61 62 63 71 72 73 same as 6 × 6.

51 52 53 54 55 56 57 58 59 60

(b) There are both odd and even numbers in the sequence.

64 65 66 67 68 69 70 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

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Number and algebra

1 Bethany counted in sixes from 11 6 and coloured each number in 21 the sequence on the hundred 31 41 © R. I .

C.Publ i cat i ons square.

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12 13 14 15 16 17 18 19 20 22 23 24 25 26 27 28 29 30 32 33 34 35 36 37 38 39 40 42 43 44 45 46 47 48 49 50

51l 52• 53 •f orr evi ew pur poseson y

What is the pattern of the final digits of all the numbers in the sequence?

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54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

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Number and algebra – Answers Card 1 Extension Card 2 Extension Card 3 Extension Card 4 Extension

Julian is 8; Dan is 5.

Julian is 9; Steven is 12; Dan is 5.

There are 37 cars and 25 trucks.

There are 78 vehicles altogether.

Harry had baked 36 cookies.

Harry had baked 48 cookies.

Mr Wilde had 25 pets.

There were 29 goldfish, 7 birds, 5 rabbits, 4 guinea pigs and 6 white mice left.

Card 5

Extension Card 6

Extension

Ryan knocked over 117 pins in total that week.

Ryan made 4 strikes.

Three crazy creatures would have 9 eyes, 6 heads, 30 legs and 150 toes.

Stephanie drew 3 crazy creatures.

Card 9 Extension

7, 8 and 9; 7 + 8 + 9; 24 45; 45 + 10 + 10 + 10; The answer is 75.

Card 16 Extension

one ‘hundred’, one ‘ten’ and one ‘one’ Jack

Card 10 Extension

Row 1 7

Card 17 Extension

334 849

Card 11 Extension

8 1—23, 2—16, 3—11

Card 18 Extension

11 houses 2 houses

Card 12 Extension

9 pages 85 pages

Card 19 Extension

135 star points 450 star points

Card 20

There were 11 shrimp altogether.

3 shrimp would be needed.

© R. I .

C.Publ i cat i ons Card 13 31 soldiers •f orr evi ew pu r poses onl y• Extension 14 soldiers

Card 7 Extension

Rania is 5.

Dylan is 9, Jake is 6 and Rob is 3.

Card 8

The fruit shop owner had 160 apples in total.

The fruit shop owner had 16 bags of apples.

Extension

Card 14 Extension

160 merit points 160 merit points, 40 merit points

Card 15 Extension

13 numbers 7 numbers

Extension Card 21 Extension

85 13 cars

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Number and algebra – Answers Card 22 Extension

Nina Henry’s problem is correct.

Card 27

Card 23

Sasha placed 10 books.

Sasha still had 15 books to place.

Card 28 Extension

51 4 odd numbers and 3 even numbers

Card 29 Extension

4; 93 The pattern is 9, 3, 7, 1, 5; 9, 3, 7, 1, 5, ...

Extension Card 24 Extension

Card 25 Extension

Card 26 Extension

The school group took up 150 seats.

The aged care residents occupied 75 seats.

Extension

Tom’s answer is Monster A. 4 limbs

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

Card 30 Extension

Farmer Fred planted 75 seedlings.

Farmer Fred will be able to plant out 1⁄2 of the first section.

(a) is correct 6, 2, 8, 4, 0; 6, 2, 8, 4, 0, ...

Pedro ate the most pizza.

Pedro ate 3 pieces.

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