Problem-Solving Strategies & Skills – Number & Algebra: Year 6 by Teacher Superstore

Number and algebra

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• Each of the eight teams in the sports league has its own stadium. They all agree to offer 85% of tickets to home fans and 15% to away fans. The number of seats available at each team’s stadium is: Tigers – 34 593, Lions – 48 264, Panthers – 51 515, Pumas – 53 853, Leopards – 42 798, Cheetahs – 56 347, Jaguars – 43 082 and Cougars – 83 541. How many seats are available to home and away fans at each team’s stadium? R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

Each of the eight teams in the sports league has its own stadium. The number of seats available at each team’s stadium is: Tigers – 34 592, Lions – 48 264, Panthers – 51 516, Pumas – 53 854, Leopards – 42 798, Cheetahs – 56 346, Jaguars – 43 082 and Cougars – 83 542.

In the finals competition, the top four teams of the season (in order: f orr e vi ew pother ur po sonl y• Lions, Leopards, Tigers and• Jaguars) play each ins ae round of matches all held at the three largest venues, where 50% of the available seats are allocated to fans of each team. The top team plays the second team at the largest venue, the third team at the second-largest venue and the fourth team at the third-largest venue. List the matches played at each venue and the number of seats allocated to fans of each team. R.I.C. Publications® Prim-Ed Publishing

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Number and algebra 1 ×

‘Fill the gap’ is a fun way to practise 3 0 long multiplication. Children are given single-digit number cards to place in 1t ©R . I . C.Publ i ca i ons 2 8 each gap to correctly complete the operation. •f orr evi ew pur posesonl y•

Use the cards to complete the operation.

1 6

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

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Number and algebra 9

‘Fill the gap’ is a fun way to practise long multiplication. Children are given single-digit number cards to place in each gap to correctly 9s © R. I . C.Publ i cat i on complete the operation.

3 8

•f orr evi ew pur posesonl y•

Use the cards to complete the operation.

7 2

8 3 4

0 6

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

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Number and algebra

Planet

Diameter in km

Mercury

4800

Venus

12 100

•f orr evi ew pur posesonl y• Earth

12 750

The children in Class 6 are studying the diameter of the planets of our solar system. They know approximately how similar-sized planets compare but they want at more © R. I . C .P ub l i ca i ons accurate figure. How much bigger is the diameter of the first planet in each pair than the diameter of the second? Mars and Mercury

Earth and Venus

Jupiter and Saturn

Uranus and Neptune

Mars

6800

Jupiter

142 800

Saturn

120 660

Uranus

51 800

Neptune

49 500 R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

Planet Mercury The children in Class 6 are studying the planets of our Venus solar system. They know approximately how the planets © R. I . C.P ubl i ca t i ons compare in size but they want to know how the smallest •f orr evi ew pur posesonl y• Earth planet compares with the others. Mars How much bigger in diameter are the four largest planets compared to the smallest?

Diameter in km 4800 12 100 12 750 6800

Jupiter

142 800

Saturn

120 660

Uranus

51 800

Neptune

49 500 R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

A local bookshop donated 100 200 new library books to be distributed equally among 24 primary schools. The genre of the books were 40% fiction, 40% non-fiction and 20% reference. How many books of each genre did each school receive? R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

A local bookshop donated 200 412 new library books to be distributed equally among 36 primary schools. The genre of the books were 35% adventure, 25% fantasy, 15% science fiction, 10% historical, 10% non-fiction and 5% reference. How many of each genre, to the nearest whole book, did each school receive? R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• The children in Class 6 were preparing a special afternoon tea. They had three packets of Chocolate Delights, six packets of Strawberry Creams and four packets of Ginger Crunches. All the packets were opened and divided equally among 12 serving plates. What was the ratio of chocolate to strawberry to ginger biscuits on each plate? R.I.C. Publications® Prim-Ed Publishing

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Extension

Number and algebra

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• The children in Class 6 were preparing a special afternoon tea. They had three packets of Chocolate Delights, six packets of Strawberry Creams and four packets of Ginger Crunches. All the packets were opened and divided equally among 12 serving plates. Write an equation showing, on the left side, the number of packets and biscuits of each type and, on the right side, the number of serving plates and biscuits on each. R.I.C. Publications® Prim-Ed Publishing

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Number and algebra School closes for a two-week holiday on a Friday afternoon and opens again on a Monday morning. Jack and Jill set themselves a challenge to cycle every day of the holiday. They begin gently by cycling 1 km on the first day, 3 km on the second and 6 km on the third. They plan the length ©R . I . C .Publ i cat i ons of each day’s ride by adding one kilometre •f orr evi ew pur posesonl y• to the difference between the rides of the previous two days and adding this to the distance of the previous day’s ride. How far do Jack and Jill cycle on the Thursday of the second week?

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

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Extension

Number and algebra School closes for a two-week holiday on a Friday afternoon and opens again on a Monday morning. Jack and Jill set themselves a challenge to cycle every day of the holiday. They begin gently by cycling just 1 km on the first day, 3 km on the second and 6 km on the third. R. I . C.Publ i cat i ons They plan the length of each© day’s ride •f or r e vi ew pur posesonl y• by adding one kilometre to the difference between the rides of the previous two days and adding this to the distance of the previous day’s ride. How far have Jack and Jill cycled, in total, by the end of the holiday?

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

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Number and algebra Class 6 enjoy playing number games. In this game, each child is given an operation sign and single-digit number cards to place in the correct tens, ones, tenths, hundredths and thousandths columns of two rows to make a given answer. Troy was given these cards to make the answer 86.340.

Troy has already placed some cards. Where must he place the others?

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

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Extension

Number and algebra

Class 6 enjoy playing number games. In this game, each child is given single-digit number cards. They must decide which operation is needed to make the given answer and place the cards in the correct tens, ones, tenths, hundredths and thousandths columns. Troy was given these cards to make the answer 34.475. Troy has already placed one row of cards. What operation can he do and where must he place the other cards?

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

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Number and algebra Population

Area in km2

Santorini

11 400

Capri

12 200

6160

19 726

6304

4696

2465

31 000

Serifos

2625

Vis

3617

Skiathos Fabiola and her family will visit some Ischia Mediterranean and Aegean islands while on holiday in Europe. Before they go, they want Lampedusa © R. I . C.Publ i cat i ons to know how busy each island may be. Skopelos •f orr evi ew pur pose sonl y• List the islands in order from the highest to Tenedos the lowest population density. Gozo

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

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Number and algebra Santorini Capri Fabiola and her family will visit some Skiathos Mediterranean and Aegean islands while on holiday in Europe. In the summer, the Ischia population of islands with an area greater Lampedusa ©average R. I . C.Publ i cat i ons than 50 km2 is increased by an of 23%. The average increase smaller Skopelos •f orfor r ev i ew pur pose sonl y• islands is 37%. Tenedos List the islands in order from the lowest to Gozo the highest summer population density. Serifos Vis

Population

Area in km2

11 400

12 200

6160

19 726

6304

4696

2465

31 000

2625

3617

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

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Number and algebra

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• The children in each class at Palm Primary School were asked if they wanted to visit the local museum. The positive response from each year group was: 1 – 87.5%

2 – 12.5%

3 – 37.5%

4 – 50%

5 – 25%

6 – 62.5%

What fraction of each year group did not want to go to the museum? R.I.C. Publications® Prim-Ed Publishing

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Extension

Number and algebra

The children in each class at Primary School were asked if they wanted to visit the ©Palm R. I . C.Pub l i cat i ons local museum.

•f orr evi ew pur posesonl y•

The positive response from each year group was: 1 – 58.33%

2 – 66.67%

3 – 83.33%

4 – 75%

5 – 12.5%

6 – 50%

There are 576 children in the school, equally divided among the year groups. On all school excursions, there must be a minimum of one adult to every ten children. How many buses, each able to carry 57 passengers, are required for the museum trip? R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

© R. I . C.Publ i cat i ons •f orr evi ew ur po ses onl y • rectangular cake For a family celebration, Mum made fourp large cakes using identical tins. Mum cut the cakes into different-sized pieces. She began by cutting each cake into thirds. She divided the first cake to make ninths, the second to make sixths, the third to make twelf ths and the fourth to make eighteenths. How many pieces of cake in total were created? How many eighteenths in total could be created from all four cakes? R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

For a family celebration, Mum made four different cakes using identical rectangular cake tins. Mum cut the cakes into different-sized pieces. Kane loved his mum’s baking and ate so 1 5 of one cake, 29 of another, 18 of another and 16 of yet much he later felt quite ill. He ate 12 another. If Kane put all the pieces he had eaten into one of his mum’s cake tins, what fraction, in its simplest form, of the tin would they fill? R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

The populations of the Nordic countries Denmark, Finland, Iceland, Iceland Norway and Sweden are 5 695 294, 5 534 474, 331 987, 5 282 160 and 9 867 807 respectively. Erik wants to © R. I . C.Publ i cat i ons know how many more people live f oin rr evi ew pur posesonl y• in the other Nordic countries • than his home country of Iceland.

Finland Norway Sweden

Write the name of the country and its difference in population from Iceland, from least to greatest.

Denmark

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

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Number and algebra

The populations of the Nordic countries Denmark, Finland, Iceland, Norway and Sweden are 5 695 294, Iceland 5 534 474, 331 987, 5 282 160 and 9 867 807 respectively. With the countries listed in descending order© R. I . C.Publ i cat i ons of population, Erik wants to know •f orr evi ew pur posesonl y• the population differences between the countries in first and second, second and third, third and fourth, and fourth and fifth positions. Calculate the answers for Erik.

Finland Norway Sweden

Denmark

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Number and algebra Class 6 enjoy playing number games. In this game, each child is given an operation sign and single-digit number cards to place in the correct tens, ones, tenths, hundredths and thousandths columns of two rows to make a given answer. Tracey was given these cards to make the answer 57.869. Tracey has already placed some cards. Where must she place the others?

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

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Extension

Number and algebra

Class 6 enjoy playing number games. In this game, each child is given single-digit number cards. They must decide which operation is needed to make the given answer and place the cards in the correct tens, ones, tenths, hundredths and thousandths columns. Tracey was given these cards to make the answer 18.407. Tracey has already placed one row of cards. What operation can she do and where must she place the other cards?

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Number and algebra

Belle and Betty like playing the card game ‘500’. The aim of each round is to make as many ‘sets’ or ‘runs’ as possible and to be the first to use up all of your cards. Points are scored for sets and runs made Belle and deducted for any cards left in the hand at the + score – score © R. I . C.Publ i cat i ons end of the round. The winner of the game is the first 157 f orr evuse i ew ur p osesonl y• person to reach 500 or• more, and allp their cards. 139 The table shows the positive and negative scores for each girl. 108 96 What was the final score for each player?

Betty + score

– score

142

178

132 121

148

127

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Extension

Number and algebra

Ava, Bea and Cate like playing the card game ‘500’. The aim of each round is to make as many ‘sets’ or ‘runs’ as possible and to be the first to use up all of your Ava Bea Cate cards. Points are scored for sets and runs + score – score + score – score + score – score made and deducted for any cards left in © R . I . C . P u b l i ca t i ons the hand. The winner of the game is the 78 92 107 84 99 •or f o rr ev i ew pur posesonl y• first person to reach 500 more, and 146 17 86 92 164 use all their cards. The table shows the 179 150 7 123 42 positive and negative scores for each girl. 135

Who won the game and what was the final score for each player?

183

139

113

307

106

217

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Number and algebra

Each child in Miss Winters’ class made a random equation by pulling cards from •f orr evi ew pur posesonl y• two bags; first a number card and then an operation card. They continued pulling cards until they pulled an equals sign from the operations bag. Placing the cards in order, they wrote and solved an equation. The numbers Karl pulled from the bag were: 133, 7, 4, 4 and 3. His operations were: ÷, +, –, × and =. Write and solve Karl’s equation.

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Extension

Number and algebra

Each child in Miss Winters’ class made a random equation by pulling cards from •f orr evi ew pur posesonl y• two bags; first a number card and then an operation card. They continued pulling cards until they pulled an equals sign from the operations bag. Placing the cards in order, they wrote and solved an equation. The numbers Mirka pulled from the bag were: 36, 2, 32, 2 and 27. Her operations were: ×, ÷, +, – and =. Write and solve Mirka’s equation.

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Number and algebra

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• In the school canteen, fruit was cut into small equal portions to make identical jumbo fruit kebabs. A watermelon was cut into sixty-four pieces and a pineapple into forty-eight pieces. Forty balls were scooped from a honeydew melon. Seventy-two strawberries were cut in half. Twenty-four red grapes were left whole, as were the same number of green grapes. There were three of each coloured grape on each kebab and all kebabs were identical. There were no pieces of fruit left over. How many kebabs were made? How many pieces of each fruit were on each kebab? How many pieces of fruit in total were on each kebab? R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• In the school canteen, five fruits were cut into small equal portions to make identical fruit kebabs. In total, there were 384 pieces of fruit. Each kebab held 4 watermelon pieces; 2 pineapple pieces; 3 honeydew melon pieces; 6 strawberry halves and 1 grape. What is the maximum number of kebabs that can be made and what fraction, in its simplest form, of a whole kebab is each type of fruit? R.I.C. Publications® Prim-Ed Publishing

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Number and algebra 1

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 51 52 53 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 b 82l 83a 84 85 n 86 © R. I . C.Pu i c t i o s87 88 89 90 91 92 93 94 95 96 97 98 99 100 •f orr evi ew p ur posesonl y•

Khalid loves playing with numbers. On a copy of a hundred square, he circled all the prime numbers. He added all the prime numbers in each column. Then he added all the composite numbers in each column, ignoring the columns with no prime numbers. Next, Khalid found the difference between the prime number total and the composite number total for each column, excluding those columns with no prime numbers. Finally, he found the mean of these differences and rounded the answer to the nearest whole number. What was his final number? R.I.C. Publications® Prim-Ed Publishing

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Number and algebra 1

81 b 82l 83a 84 85 n 86 © R. I . C.Pu i c t i o s87 88 89 90 91 92 93 94 95 96 97 98 99 100 •f orr evi ew p ur posesonl y•

Khalid loves playing with numbers. On a copy of a hundred square, he circled all the prime numbers. He added all the prime numbers in each column and then all the composite numbers. He ignored columns with no prime numbers. For each column, Khalid divided the prime number total by the composite number total and gave the answer to three decimal places. Finally, he found the mean of these quotients and gave the answer to three decimal places. What was his final number? R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

75.3

75.5

75.9

76.5

77.3

78.3

79.5

What are the next two numbers in the pattern? R.I.C. Publications® Prim-Ed Publishing

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Extension

Number and algebra

16.0625

16.1875

16.4375

16.5625

16.8125

16.9375

17.1875

What are the next two numbers in the pattern? R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

Input The children in Mr McCarthy’s class were 3 asked to create rules for an ‘Input – Output’ number machine. The table shows the Input © R. I . C.Publ i cat i ons 6 and Output numbers using Zoltan’s rule.

•f orr evi ew pur posesonl y•

If the input number is n, and the output number is m, what is Zoltan’s rule?

Output 19 31

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Extension

Number and algebra

Input The children in Mr McCarthy’s class were 2 asked to create rules for an ‘Input – Output’ number machine. The table shows the Input © R. I . C .Publ i cat i ons and Output numbers using Zoltan’s rule. 3

•f orr evi ew pur posesonl y•

If the input number is n, and the output number is m, what is Zoltan’s rule? (It involves cubed numbers.)

Output 6 25

123

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Number and algebra

Every Friday afternoon for eight weeks, Mr Jacobs gives the class a 20-question quiz. Children record their scores and then convert them to percentages. Goran and Novak are competing to have the best overall score. Their respective results for the eight weeks are:

©R . I . C.–P75%, ubl i cat i ons 1 – 70%, 40%; 2 – 80%, 50%; 3 – 65%, 65%; 4 40%;

•f orr evi ew pur posesonl y•

5 – 50%, 60%; 6 – 45%, 55%; 7 – 20%, 45%; 8 – 35%, 65%

How many questions out of 20 did each boy get correct each week? Who averaged the best score for correct answers and what was it? R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

1 – 70%, 40%; 2 – 80%, 50%; 3 – 65%, 65%; 4 – 75%, 40%; 5 – 50%, 60%; 6 – 45%, 55%; 7 – 20%, 45%; 8 – 35%, 65%

If three points are given for each correct answer and one point deducted for an incorrect answer, what is the total final score for each boy?

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Number and algebra

Kevin dropped a box of fraction cards on the floor. To make the task of picking them •f or r ev i ewtoppick ur pup os esof on l y• cards. The cards up more fun, the children were asked sets equivalent that fell were: 2 12

3 18

2 8

3 6

1 2 2 10

4 16

2 14

2 20

1 9

1 3 1 4

4 8 2 16

2 6 3 9

1 8

3 15

2 4

1 6

1 10

3 12

1 5

4 12

2 18

1 7

Write the cards in their equivalent sets. R.I.C. Publications® Prim-Ed Publishing

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Extension

Number and algebra

© and R. I . C.Pu bl i cat i ons Kevin dropped a box of mixed proper fraction cards on the floor. To make the task of picking them up more fun, were to pick up pairs of •f or r ev i ewthepchildren ur pose soasked nl y• equivalent cards. The cards that fell were:

16 5

7 4

9 9

11 8

7 3

34 7

22 9

17 6

1 34

3 45

2 19

4 67

37 10

19 5

19 9

2 56

7 3 10

1 38

2 49

3 15

4 4

2 13

Write the cards in their equivalent sets. R.I.C. Publications® Prim-Ed Publishing

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Number and algebra For the local football match, parents provide 10-L containers of water for both teams and their coaches. There are 16 players in each squad and each team has two coaches. The capacity of the cups used by the players is 0.375 L and © R. I . C.Publ i cat i ons for the coaches, 0.5 L. Everyone drinks orr evi ew pur posesonl y• about four cups each. •f How many 10-L containers do the parents need to bring to the nearest whole container?

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

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Extension

Number and algebra For the local football match, parents usually bring 10-L containers of water for both teams and their coaches. There are 16 players in each squad and each team has two coaches. The capacity of the cups used by the players is 0.375 R. I . C.Publ i cat i ons L and for the coaches, 0.5 L.© Everyone drinks about four cups• each. One week, f orr evi ew pur posesonl y• someone donates a dozen 0.6-L bottles and four 1.5-L bottles of water. How many less 10-L containers do the parents need to bring that week?

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

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Number and algebra

228, 6, 45, 9, 8

÷, +, –, ×, =

Write and solve the equation using the numbers and signs in the orders given. R.I.C. Publications® Prim-Ed Publishing

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Extension

Number and algebra

×, +, ÷, –, =

Write and solve the equation using the numbers and signs in the orders given. R.I.C. Publications® Prim-Ed Publishing

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Number and algebra Population City Current year

Previous year

4 920 000

4 837 836

4 268 997

The table shows the population of some Australian state capital cities for the current and previous year.

Sydney

showing the least to the greatest increase in population.

Brisbane

2 200 000

2 164 360

Perth

1 943 750

1 913 427

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

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Extension

Number and algebra

Population City Current year

Previous year

4 920 000

4 837 836

4 268 997

The table shows the population of some Australian state capital cities for the current and previous year.

Sydney

population, to two decimal places, for each city?

Brisbane

2 200 000

2 164 360

Perth

1 943 750

1 913 427

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

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Number and algebra

Kurt dropped a box of fraction, decimal and percentage cards on the floor. To make the •f or r e vi e w pur pos esoto nl y• task of picking them up more fun, the children were asked find sets of equivalent number cards. The cards that fell were: 1 2

5 8

0.5

0.1 70%

12.5% 0.125

0.375 3 4

50%

0.3

1 4

3 10

0.7

62.5%

10% 75%

1 8

37.5%

7 10

0.25

1 10

0.625

0.75

30%

25%

3 8

In order from smallest to largest, write the first, middle and last set of equivalent cards. R.I.C. Publications® Prim-Ed Publishing

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Extension

Number and algebra

Kurt dropped a box of fraction, decimal and percentage cards on the floor. As they picked them up, the children were asked to put the cards in order of value from the smallest to the largest. The cards that fell were: 0.2

1 9

75%

3 18

0.7

4 12

12.5%

9 10

0.1

1 7

0.8

25%

Write the cards in order of value from the smallest to the largest. R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• A survey was taken to discover the favourite reading genres of a group of children. The results were: Mystery – 36; Science fiction – 24; Fantasy – 18; History – 12; Biography – 9 and Reference – 9. What fraction on a pie chart would represent each genre? R.I.C. Publications® Prim-Ed Publishing

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Extension

Number and algebra

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• A pie chart showed the favourite reading genres of each child in a group. The results were: Mystery – 48; Science fiction – 40; Fantasy – 30; History – 20; Biography – 15; Reference – 15 and Poetry – 12. For each genre, what is the angle at the centre of the pie chart? R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

There are 90 children in total in Year 6. Their birthdays are spread quite evenly across the year. The same number were born in May, August and October as were born in January. Twice as many were born in February as were born in December. Three less were born in July than were born in May. Two more were born in November than © R. I . C.Publ i cat i ons were born in April. The same number were born •f or r ev i ew pur posesonl y• in June as were born in September. Nine were born in January. The same number were born in March as in November. Two more were born in February than in July. The same number were born in April as in July. One more was born in March than were born in June and September. How many children were born in June? R.I.C. Publications® Prim-Ed Publishing

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Extension

Number and algebra

There are 90 children in total in Year 6. Three times as many were born in the months beginning with the letter J than in those beginning with the letter M. Half as many were born in the months beginning with the letter A than in those beginning with ©second R. I . C.Publ i cat i ons the letter J. Seven were born in the month of the year. Three times asr many •f o r evi ew pur posesonl y• were born in September than in August. Four times as many were born in January than in October. One quarter as many were born in November than in May. How many children were born in December?

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

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Number and algebra

The printer began to run out of ink as Mr Garston was printing the answer sheets for his class’ mathematics test.

3 +

5 7 3 7

7 2

5 9 6 9

3 7

0 5

8 3 1 2 1

9 5

9 2 0

8 6 6

Help Mr Garston by working out the missing numbers in each calculation.

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

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Extension

Number and algebra

The printer began to run out of ink as Mr Garston was printing the answer sheets for his class’ mathematics test.

3 9 6

4 6 2 +

7 6

8 3 6 4

8 9 5 9

5 9 +

0 3

7 9 5

1 4 6 3

7 8 6

8 9

7 7

3 4

Help Mr Garston by working out the missing numbers in each calculation.

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

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Number and algebra The table shows some of the Cereal Energy nutritional values of 100 mL of 100 g kJ milk and 100-g portions of four A 1490 breakfast cereals. Breakfast cereals are Sofia’s favourite snack. She B 1560 eats one 50-g measure of each © R . I . C . P u b l i c a t i o n s cereal every day with 100 mL of C 1580 •f orr evi ew pur posesonl y• milk each time. D 1640 How many kilojoules of energy do Milk Sofia’s bowls of cereal provide each 267 100 mL day and what is her daily intake, in grams, of sugar and salt?

Sugar g

Salt mg

3.30

270

1.50

27.00

18.90

260

5.00

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

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Extension

Number and algebra The table shows some of the nutritional values of 100 mL of milk Cereal Energy and 100-g portions of four breakfast 100 g kJ cereals. Breakfast cereals are Sofia’s A 1490 favourite snack. She eats one 250-g measure of each cereal every B 1560 day with 150 mL of milk each time. © R . I . C . P u b l i c a t i o n s Average recommended daily intake C 1580 •f o rr evi ew pur posesonl y• values are: energy – 8700 kJ; D 1640 sugar – 90 g and salt – 2.3 g. Milk 100 mL

To two decimal places, how much more or less energy, sugar and salt is Sofia consuming compared with the recommended daily intake of each?

267

Sugar g

Salt mg

3.30

270

1.50

27.00

18.90

260

5.00

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

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Number and algebra Eve was helping her dad sort a box of loose photographs. They organised them into three piles: family, friends and holidays. They put the photographs into albums in the ratio of 6:3:1. They filled five © R. I . C.Publ i cat i ons albums using the same ratio for f orr evi ew pur posesonl y• each. The albums held• different numbers of photographs: 360, 250, 120, 100 and 80. How many photographs from each pile did they put in each album?

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

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Extension

Number and algebra

Eve was helping her dad sort a box of loose photographs. They organised them into five piles: family, friends, holidays, school and sports. They wanted to put the photographs into albums in the ratio of © R. I . C.Publ i cat i ons 4:3:3:1:1. The empty albums they had held f o80 rr evi ew pur posesonl y• 360, 250, 180, 120, 100• and photographs. Which of the six albums would Eve and her dad be able to use to store their photographs in the required ratio?

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

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Number and algebra

Felix’s Uncle Klaus likes to set him maths puzzles to solve. What would be the numbers I . C.Publ i cat i ons for positions 17, 29 and 43? © R.

•f orr evi ew pur posesonl y•

Position

Number

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

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Extension

Number and algebra Felix’s Uncle Klaus likes to set him maths puzzles to solve. The clue to solve this puzzle is ‘square numbers’. Find the pattern for the © R. I . C.Publ i cat i ons sequence of numbers in positions 1 to 7. •f orr evi ew pur posesonl y•

Position

Number

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

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Number and algebra – Answers Card 1

TEAM Tigers Lions Panthers Pumas Leopards Cheetahs Jaguars Cougars

Extension

HOME AWAY 29 404 5189 41 024 7240 43 788 7727 45 775 8078 36 378 6420 47 895 8452 36 620 6462 71 010 12 531

Lions v. Leopards @ Cougars – 41 771 Lions v. Tigers @ Cheetahs – 28 173 Lions v. Jaguars @ Pumas – 26 927 Leopards v. Tigers @ Pumas – 26 927 Leopards v. Jaguars @ Cheetahs – 28 173 Tigers v. Jaguars @ Cougars – 41 771

Card 2

0 2 3

7 8 5

8 5 4

9 3 3

× 1 1

Extension

3 2 5

× 2 3

6 9 6

4 2 1 6 7

3 5 5 0 5

4 3 2 8 0

6 7 2 0 2

Card 4 Extension

Fiction – 1670 Non-fiction – 1670 Reference – 835 Adventure – 1948 Fantasy – 1392 Science fiction – 835 Historical – 557 Non-fiction – 557 Reference – 278

Card 5

3:8:5

Card 3 Extension

Mars 2000 km Earth 650 km Jupiter 22 140 km Uranus 2300 km Mercury, the smallest Jupiter – 30 x bigger Saturn – 25 x bigger Uranus – 11 x bigger Neptune – 10 x bigger

Card 6 Extension

91 km 816 km

Card 7 Extension

63.929 + 22.411 86.340 24.368 + 10.107 34.475

Card 8

Extension

Card 9

Capri, Gozo, Ischia, Lampedusa, Skiathos, Santorini, Tenedos, Skopelos, Vis, Serifos Serifos, Tenedos, Vis, Skopelos, Skiathos, Lampedusa, Santorini, Capri, Ischia, Gozo 1–

1;2– 8 1;5– 2

7;3– 8 3;6– 4

5; 8 3 8

4–

Extension

7 buses

Card 10

45 servings; 72 eighteenths

Extension

3 4

Card 11

Norway – 4 950 173 Finland – 5 202 487 Denmark – 5 363 307 Sweden – 9 535 820

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

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Number and algebra – Answers Extension

Sweden/Denmark – 4 172 513; Denmark/ Finland – 160 820; Finland/Norway – 252 314; Norway/ Iceland – 4 950 173

12 65.090 Card – 7.221 57.869 Extension 43.586 – 25.179 18.407 Card 13 Extension Card 14 Extension

Belle (winner) – 517; Betty – 481 Ava – 401; Bea (winner) – 511; Cate – 485 (133 ÷ 7) + 4 – (4 × 3) = 11 (36 × 2) ÷ 3 2 + 2 – 27 = –17

Problem solving cards yr6 Blue NandA.indd 62

Extension

8 kebabs; watermelon – 8 pineapple – 6 honeydew melon – 5 strawberry halves – 18 red grapes – 3 green grapes – 3; 43 pieces per kebab 24 kebabs maximum watermelon – 14 pineapple – 18 3 honeydew melon – 16 3 strawberry – 8 1 grape – 16

Card 16 Extension

187 0.762

Card 17 Extension

Add 1.4 = 80.9 Add 1.6 = 82.5 Add 0.125 = 17.3125 Add 0.25 = 17.5625

Card 15

Card 18 Extension

m = 4n + 7 m = n3 – 2

Extension

Card 19

Goran: 14, 16, 13, 15, 10, 9, 4, 7; Novak: 8, 10, 13, 8, 12, 11, 9, 13; Goran – 11 correct answers Goran – 192 Novak – 176

Extension

14 7 2, 3, 1 12 18 6 1, 3, 4, 2 6 8 1, 2, 3, 3 6 9 2, 3, 1 10 15 5 2, 1 20 10 1, 2 9 18 2, 1 16 8

2 4 4 12

16 = 3 1 7 =13 5 5 4 4 9 = 4 11 = 1 3 9 4 8 8 7 = 2 1 3 4 = 19 3 3 5 5 19 = 2 1 4 67 = 34 7 9 9 7 = 37 2 56 = 17 3 6 10 10 22 = 2 4 9 9

Card 21 Extension

six one less container

Card 22

(228 ÷ 6) + 45 – (9 × 8) = 11 (9 2 × 2 3) + (96÷ 4 2) – 5 3 = 529

Extension Card 23

Perth, Brisbane, Sydney, Melbourne

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

19/01/2017 10:32 am

Number and algebra – Answers Extension

Sydney – 1.67% Melbourne – 2.13% Brisbane – 1.62% Perth – 1.56%

Card 24

1 , 10%, 0.1 10 3 , 37.5%, 0.375 8 3 , 75%, 0.75 4 3, 0.1, 19 , 12.5%, 17 , 18 4 , 0.7, 0.2, 25%, 12 9 75%, 0.8, 10

Extension

1 3

Card 25

Mystery –

Science fiction –

Fantasy – 16 History – 19

Biography –

Reference –

Problem solving cards yr6 Blue NandA.indd 63

1 12 1 12

2 9

Extension

Mystery – 96º

Science fiction – 80º

Fantasy – 60º

History – 40º

Biography – 30º

Reference – 30º

Poetry – 24º

Card 26 Extension

Seven 5

Extension 2

7 4 8 1

8 6 9 4

3 2 5 2

9 1 9 0

6 0 7 3

5 8 6 1

9 5 8 4

8 9 7 6

7 6 9 3

6 7 5 8

8 5 8 3

3 9 9 3

6 7 9 4

4 8 7 0

1 6 7 4

5 + 2 8

9 3 3

6 4 1

9 2 2

3 8 1

3 + 4 8

7 9 6

3 2 6

9 0 0

5 7 2

Card 28 Extension

Energy – 4203 kJ Sugar – 45.35 g Salt – 0.4545 g Energy – 8577.00 kJ more Sugar – 66.75 g more Salt – 629.50 mg less

Card 29 Album

Family

Friends

Holidays

360

216

108

250

150

120

100

Extension

360, 180, 120

Card 30 Extension

17 – 289 29 – 841 43 – 1849 n = p2 + p

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

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

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