Problem-Solving Strategies & Skills – Number & Algebra: Year 5

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Number and algebra A surveyor used a surveyor’s wheel with a mechanical device to measure a road.

The surveyor pushed the surveyor’s wheel along a straight path. The device recorded every metre the wheel © R. I .

C.Publ i cat i ons travelled and made one beep every ten •f orr evi ew pur posesonl y• metres.

How many metres would the surveyor have travelled when the device beeped for the hundredth time?

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Number and algebra

A surveyor used a surveyor’s wheel with a mechanical device to measure a road.

The surveyor pushed the surveyor’s wheel along a straight path. The device ©wheel R. I .

C. Publ i cat i ons recorded every metre the travelled f orr e vi e w pur posesonl y• and made one beep• every ten metres.

How many times would the device beep if the surveyor travelled ten thousand metres?

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Number and algebra A council kept a record of the number of trees they had planted each week for 5 weeks. In week one, 1203 trees were planted. In week two, 450 more trees were planted than week one. In week three, 1896 trees were planted. In week four, 264 less trees © R. I .

C.Publ i cat i ons were planted than week three. In the final week, they •f orr evi ew pur posesonl y• planted the same number of plants as weeks two and four combined.

How many trees were planted in total in the five weeks?

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Number and algebra A council kept a record of the number of trees they had planted each week for 5 weeks. In week one, 1203 trees were planted. In week two, 450 more trees were planted than week one. In week three, 1896 trees were planted. In week four, 264 © R. I .

C.Publ i cat i ons less trees were planted than week three. In the •f orr evi ew pur posesonl y• final week, they planted the same number of plants as weeks two and four combined.

If the council had 10 000 trees available, how many did they not plant?

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Number and algebra

Farmer Jack owned a farm that had cows, sheep, pigs and horses. A quarter of all the animals on the farm were cows, four-eighths of the animals were sheep, one-sixth of the animals were pigs © R. I .

C.Publ i cat i ons and one-twelfth of the animals were horses.

•f orr evi ew pur posesonl y•

Order the animals and the fractions from the category with the most animals to the category with the least animals.

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Number and algebra

Farmer Jack owned a farm that had cows, sheep, pigs and horses. A quarter of all the animals on the farm were cows, four-eighths of the animals were sheep, one-sixth of the © R. I .

C.Publ i cat i ons animals were pigs and one-twelfth of the •f orr evi ew pur posesonl y• animals were horses.

If Farmer Jack had 84 animals on his farm, how many of each animal did he have?

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Number and algebra Daria was excited about the cabaret she was performing at a local theatre.

The theatre had an audience capacity of 1055 people. There was going to be a matinee and an evening show on Fridays, © R. I .

C.Publ i cat i ons and a morning, matinee and evening show •f orr evi ew pur posesonl y• on Saturdays and Sundays.

If the theatre is full to capacity for each show, how many people will Daria perform to over the three days?

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Number and algebra Daria was excited about the cabaret she was performing at a local theatre. The theatre had an audience capacity of 1055 people. There was going to be a matinee and an evening show on Fridays, © R. I .

C.Publ i cat i ons and a morning, matinee and evening •f orr evi ew pur posesonl y• show on Saturdays and Sundays.

If the theatre is full to capacity for each show, how many people will Daria perform to over four weeks?

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Number and algebra Susan wanted to start a healthy eating plan so that her weight was in the healthy weight range of 65–78 kg for women her height. On day one, Susan recorded her weight at 80.6 kg. On day two, Susan’s © R. I .

C.Publ i cat i ons weight decreased by 0.3 kg. On day three, •0.1 f or r ev i ew pu r pos esonl y• her weight increased kg.

On day four, her weight decreased by 0.3 kg and the pattern repeated. If Susan continued to lose and gain weight in this pattern, how much will she weigh on the tenth day?

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Number and algebra Susan wanted to start a healthy eating plan so that her weight was in the healthy weight range of 65–78 kg for women her height. On day one, Susan recorded her weight at 80.6 kg. On day two, Susan’s weight decreased by 0.3 kg. On day three, © R. I .

C.Publ i cat i ons her weight increased 0.1 kg. On day four, •f orr evi ew pur posesonl y• her weight decreased by 0.3 kg and the pattern repeated.

If Susan continued to lose and gain weight in this pattern, on which day will she weigh exactly 78 kg?

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Number and algebra

Children Females

Males

Females

Males

1 3

1 2

1 2

1 2

0

1 8

?

2 6

6

1 4

2 5

1 12

Bus

1 12

1 16

1 10

?

Other

?

?

0 5

0 2

TOTAL

1

1

1

1

Car

Bicycle © R. I .

C.Publ i cat i ons 3 A primary school conducted a survey •f orr evi ew pur po sesonl y 1 • Walk

of how their children and teachers travel to school.

Which fraction is bigger—female teachers who rode a bicycle or male teachers who took the bus?

Teachers

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Number and algebra

Children Females

Males

Females

Males

1 3

1 2

1 2

1 2

0

1 8

?

2 6

6

1 4

2 5

1 12

Bus

1 12

1 16

1 10

?

Other

?

?

0 5

0 2

TOTAL

1

1

1

1

Car

Bicycle © R. I .

C.Publ i cat i ons 3 A primary school conducted a survey •f orr evi ew pur po sesonl y 1 • Walk

of how their children and teachers travel to school.

What fraction of all children took ‘other’ transport to school? Write the answer in its simplest form.

Teachers

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Number and algebra

Julia was going on an aeroplane that had seven seats in each row—two seats on each window side and three seats in the centre with an aisle down each side of the centre seats. She was to be seated in row 72, which was the third last row in the plane. While waiting for her flight, Julia imagined a whole city being evacuated on these planes.

© R. I .

C.Publ i cat i ons

How many planes would it •f orr evi ew pur posesonl y• take to evacuate a city with a population of 35 742 people?

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Number and algebra

Julia was going on an aeroplane that had seven seats in each row—two seats on each window side and three seats in the centre with an aisle down each side of the centre seats. She was to be seated in row 72, which was the third last row in the plane. While waiting for her flight, Julia imagined a whole city being evacuated on these planes.

© R. I .

C.Publ i cat i ons

How many planes would it •f orr evi ew pur posesonl y• take to evacuate a city with a population of 10 000 people?

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Number and algebra

I am a three-digit even number made using the digits 6, 3 and 1.

I can be divided evenly among eight different numbers, including myself © R. I .

C.Publ i cat i ons and one. The only odd number that f orbesides r evi ew pur posesonl y• I can be divided evenly• into, one, is seventeen.

What number am I and am I a prime or composite number?

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Number and algebra

I am a four-digit number and every number in my family is comprised of the four digits 0, 1, 4 and 8. I am one of only four odd numbers in my family—two of which have eight factors and one of which has factors. © R4.

I .

C.Publ i cat i ons The two with eight factors are both •f orr evi ew pur posesonl y• divisible by 11 and the one with four factors is divisible by 31. I am the only four-digit prime number that can be made in my family.

What number am I? R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

The average heights and weights of players in a school basketball team were recorded in a table.

Player

Height

Weight

Player

Height

Weight

Sam

1.38 m

29.48 kg

Kye

1.3 m

31.06 kg

Nick

1.24 m

Lewis

1.32 m

32.08 kg

Noah

1.33 m

29.99 kg

Sahid

1.35 m

30.49 kg

Duncan

1.41 m

31.76 kg

Alan

1.29 m

31.67 kg

Hafiz

1.39 m

31.48 kg

© R. I .

C.Publ i cat i ons 30.16 kg Shawn 1.27 m 30.01 kg •f orr evi ew pur posesonl y•

Order the heights from tallest to shortest.

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Number and algebra

The average heights and weights of players in a school basketball team were recorded in a table.

Player

Height

Weight

Player

Height

Weight

Sam

1.38 m

29.48 kg

Kye

1.3 m

31.06 kg

Nick

1.24 m

Lewis

1.32 m

32.08 kg

Noah

1.33 m

29.99 kg

Sahid

1.35 m

30.49 kg

Duncan

1.41 m

31.76 kg

Alan

1.29 m

31.67 kg

Hafiz

1.39 m

31.48 kg

© R. I .

C.Publ i cat i ons 30.16 kg Shawn 1.27 m 30.01 kg •f orr evi ew pur posesonl y•

Order the weights from lightest to heaviest.

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Number and algebra

Florence is practising for a swimming competition that she wants to enter. She 1 starts her training by swimming 12 of the total distance for three days, then increases the distance by one-twelth of total © the R. I .

C .Publ i cat i ons distance for the next three •f odays. rr evi ew pur posesonl y• If she continues to increase her training 1 distance by 12 of the total distance every three days, how many days will it take her to swim the total distance for the first time?

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Number and algebra

Florence is practising for a swimming competition that she wants to enter. She 3 starts her training by swimming 12 of the total distance for seven days, then increases the distance by three-twelths the total © of R. I .

C. Publ i cat i ons distance for the next seven days.

•f orr evi ew pur posesonl y•

If she continues to increase her training 3 distance by 12 of the total distance every seven days, on what day will she swim the total distance for the first time?

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Number and algebra

Michele compared the sugar content of three different juices. The 1 L carton of orange juice had 80 grams of sugar in total, the 2 L carton of apple juice had R. I .

C.Pthe ubl i cat i ons 0.2 kilograms of sugar in© total and 250 mL carton of pineapple juice •f orr ev i ewhad pur posesonl y• 20 grams of sugar in total.

What fraction of juice is sugar in a 100 mL serving of each type of juice?

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Number and algebra

Michele compared the sugar content of three different juices. The 1 L carton of orange juice had 80 grams of sugar in total, the 2 L carton of apple juice had 0.2 kilograms of sugar in total and the 250 mL carton of ©R I .

C.Pu bl i cat i ons pineapple juice had 20 grams of. sugar in •f orr evi ew pur posesonl y• total.

If all three juices were advertised as having 8% sugar content, which juice was advertised incorrectly and what percentage of sugar is actually in it?

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Number and algebra

Louise bought a garden plot that grew a variety of fruit and vegetables, except tomatoes. She loved tomatoes and instantly made plans to add them to her collection to sell. Louise bought ninety-six tomato seeds © R. I .

C.Publ i cat i ons from the gardening store and cleared an area •f orr evi ew pur posesonl y• to plant them. She wanted to plant them in full rows and columns.

If she had enough space for eight columns of seeds, how many rows did she plant?

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Number and algebra

Louise bought a garden plot that grew a variety of fruit and vegetables, except tomatoes. She loved tomatoes and instantly made plans to add them to her collection to ©R .

I .

C.Pseeds ubl i cat i ons sell. Louise bought ninety-six tomato from the gardening store and cleared an area •f o rr e vi ew p ur p osesonl y• to plant them. She wanted to plant them in full rows and columns.

How many different combinations of rows and columns can she plant her tomato seeds?

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Number and algebra

A dog training school divides its classes into small breed, medium breed and large breed classes. Each day, they have three classes of small breed dogs which have a maximum of 12 dogs in each, four classes medium ©of R. I .

C.Pubbreed l i cat i ons dogs which have a maximum of 10 inoeach •f orr e vi ewdogs pur p sesonl y• and two classes of large breed dogs which have a maximum of 8 dogs in each.

If classes were full to capacity, how many dogs attended this dog training school?

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Number and algebra

A dog training school divides its classes into small breed, medium breed and large breed classes. Each day, they have three classes of small breed dogs which have a maximum of 12 dogs in each, four classes of medium © R. I .

C.Publ i cat i ons breed dogs which have a maximum of 10 dogs •f orr evi ew pur posesonl y• in each and two classes of large breed dogs which have a maximum of 8 dogs in each.

If each class had three dogs not attending one day, how many dogs were there on this day?

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Number and algebra

Leila was cooking pancakes for everyone in her family.

She found a recipe to use and calculated that she would need four batches of I .

C.Publ i cat i ons pancakes to feed her family.© R.

•f orr evi ew pur posesonl y•

How many cups of milk will she need to make pancakes for her family?

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Number and algebra

Leila was cooking pancakes for everyone in her family.

She found a recipe to use and calculated that she would need four batches of I .

C.Publ i cat i ons pancakes to feed her family.© R.

•f orr evi ew pur posesonl y•

How many cups of caster sugar will she need to make four batches of pancakes?

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Number and algebra

Jackie wrote a number on a piece of paper using the digits 2, 4, 5 and 6. It was an odd number and had six ‘thousands’, five ‘ones’, two ‘hundreds’ and four ‘tens’.

© R. I .

C.Publ i cat i ons She then performed the •following f orr evi ew pur posesonl y• calculations to form a new number: subtract 1000, add 100, subtract 10, add 500, subtract 1000 and add 50.

What is her new number?

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Number and algebra

Jackie thought of a number in her head.

To that number she performed the following calculations. She added 1000, subtracted 6 ‘tens’, subtracted 10 ‘ones’, © R. I .

C.P ubl i cat i ons added 100, subtracted 2 ’thousands’ and •f orwas r evi e w pur posesonl y• added 10 ‘tens’. The answer 8034.

If Jackie’s original number was made using the digits 0, 4, 8 and 9, what number did Jackie start with?

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Number and algebra

A publishing company published 120 reference books, including atlases and encyclopedias. They published twice as many reference books as picture books, three times as many non-fiction books as picture books and half as many fiction I .

C.Publ i cat i ons books as non-fiction books.© R.

•f orr evi ew pur posesonl y•

How many of each type of book did they publish?

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Number and algebra

A publishing company published 120 reference books, including atlases and encyclopedias. They published twice as many reference books as picture books, three times as many non-fiction books as picture books and half as many fiction books as non-fiction books.© R. I .

C.Publ i cat i ons

•f orr evi ew pur posesonl y•

If they published 500 books overall, how many books were classified in the ‘other’ category?

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Number and algebra

A children’s cycling club organised a long distance race for its 11-yearolds. The first leg of the race was 0.75 km, the second leg of the race was 0.9 km, the third leg of the ©leg R. I .

C.Publ i cat i ons race was 1.22 km, the fourth of •f o rr e vi ew pur posesonl y• the race was 1.45 km and the fifth leg of the race was 1.08 km.

What was the difference between the longest leg of the race and the shortest leg of the race?

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Number and algebra

A children’s cycling club organised a long distance race for its 11-yearolds. The first leg of the race was 0.75 km, the second leg of the race was 0.9 km, the third leg of the © R. I .

C.Publ i cat i ons race was 1.22 km, the fourth leg of •f orr evi ew pur posesonl y• the race was 1.45 km and the fifth leg of the race was 1.08 km.

How many kilometres was the race in total?

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Number and algebra

Frederick loved solving tricky mathematics equations. He especially loved equations that had unknown quantities marked with letters.

(144 ÷ 6) – 4 = a

© R. I .

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

(a + 16) ÷ 3 = b bx4+2=c Help Frederick find the value of a, b and c.

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Number and algebra

Frederick loved solving tricky mathematics equations. He especially loved equations that had unknown quantities marked with letters.

(3 x 3 + 1) x 15 = a (200 – a) ÷ 2 = b bx

4 5

© R. I .

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

÷ 10 = c

Help Frederick find the value of a, b and c.

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Number and algebra

Miley and Cole made cookies for a cake sale at school. Miley baked her chocolate-chip cookies in batches of 7 cookies. Cole baked his chocolate cookies in batches © R. I .

C.Publ i cat i ons of 11 cookies. Both children •f orr evi ew pur posesonl y• baked less than 100 cookies each.

If both children baked the same number of cookies, how many cookies did they each bake?

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Number and algebra

Miley and Cole made cookies for a cake sale at school. Miley baked her chocolate-chip cookies in batches of 7 cookies. Cole baked his chocolate cookies in batches of 11 cookies.

Both © R. I .

C.Publ i cat i ons children baked less than 100 cookies •f orr evi ew pur posesonl y• each.

If both children baked the same number of cookies, how many batches did they each bake?

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Number and algebra

Cakes in a shop are sold as a whole cake, half a cake, a quarter of a cake or one slice, equalling an eighth of a cake.

The sales of chocolate cake for the day ©4R .

I .

C.Publ i cat i ons were: 11 quarters, 15 halves, whole •f orr evi ew pur posesonl y• cakes and 19 slices.

Write the total amount of chocolate cake sold as a mixed fraction in eighths.

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Number and algebra

Cakes in a shop are sold as a whole cake, half a cake, a quarter of a cake or one slice, equalling an eighth of a cake.

The sales for the day of one particular flavoured cake were: 11 quarters, © R. I .

C.Publ i cat i ons 15 halves, 4 whole cakes and 19vi slices.

•f orr e ew pur posesonl y• If each of the cakes were cut into eight pieces regardless of the size the customer bought, how many slices of cake did they sell in total?

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Number and algebra

A flower shop owner recorded the number of bouquets she sold in six-month periods over the course of three years.

2013 January– June

July– December

12 492

12 602

2014 ©R .

I .

C.Publ i cat i ons 2015 January– July– January– July– •f orr evi ew pur poses onl y•December June December June 13 958

14 703

15 097

15 998

Which year had the greatest increase from the first half of the year to the second half of the year?

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Number and algebra

A flower shop owner recorded the number of bouquets she sold in six-month periods over the course of three years.

2013 January– June

July– December

12 492

12 602

2014 ©R .

I .

C.Publ i cat i ons 2015 January– July– January– July– •f o rr evi ew pur poses onl y•December June December June 13 958

14 703

15 097

15 998

What is the difference between the year with the most total sales and that with the least total sales?

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Number and algebra

Alexi was combining three different types of chocolate into one bowl to melt. To the bowl she added half a kilogram of milk chocolate buttons. Next she added 0.4 of a kilogram of white chocolate buttons © R. I .

C.Publ i cat i ons 1 and then added 10 of a• kilogram ofwdark f orr evi e pur posesonl y• chocolate buttons to the bowl and mixed them all thoroughly.

What percentage of total chocolate is white chocolate?

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Number and algebra

Alexi was combining three different types of chocolate into one bowl to melt. To the bowl she added half a kilogram of milk chocolate buttons. Next she added 0.4 of a kilogram of 1 white chocolate buttons and added ©then R. I .

C .Publ i cat i ons 10 of a kilogram of dark chocolate buttons to •f orr ev i ew pur posesonl y• the bowl and mixed them all thoroughly.

What percentage of chocolate is milk and dark chocolate combined?

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Number and algebra

While on holidays, Shanique and Carlos wanted to experience lots of adventure activities. Shanique booked into a scuba-diving course on the day that Carlos booked into a mountain-climbing tour. Shanique dived as far as 17 metres below sea level to see turtles, fish and coral. Carlos © R. I .

C .Pwas ubl i cat i ons climbed to the top of a mountain that •f orr evi ew pur posesonl y• 1.25 km in height.

On a number line with zero as ‘sea level’, what numbers represent the positions of each person at their furthest distance (in metres) from sea level?

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Number and algebra

While on holidays, Shanique and Carlos wanted to experience lots of adventure activities. Shanique booked into a scuba-diving course on the day that Carlos booked into a mountain-climbing tour. Shanique dived as far as 17 metres below sea level to see turtles, fish and coral. .

I .

C.Pub l i cat i ons Carlos climbed to the top of© aR mountain that orr evi ew pur posesonl y• was 1.25 km in height. •f What is the total distance between Carlos’ position and Shanique’s position at their furthest distance (in metres) from sea level?

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Number and algebra

Sammy has a rectangular backyard that measures 12 m long by 8 m wide. He wants to pave a square alfresco area for entertaining his guests. He wants a garden bed with a one-metre width © R. I .

C.Publ i cat i ons around the perimeter of his alfresco area.

•f orr evi ew pur posesonl y• What is the largest sized area that Sammy can have his alfresco area and what will be the length and width of his alfresco area?

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Number and algebra

Sammy was comparing square blocks of land to buy so he could build a new house. The first block had an area of 441 m2 with a nice view of the park across the road. The second block had an area of 529 m2 and faced a national park. .

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Cm .P bl i c at i ons 2 u The third block had an area© ofR 324 and was f othe rr e vi ew pur posesonl y• within walking distance•of beach.

If Sammy wanted the length of his block to be less than 20 m, which block should he buy and what is the length of the block?

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

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Number and algebra

Lila and Demetri counted the jelly beans in a bag and worked out the fraction of each coloured jelly bean in the bag. The results 1 were: 16 of the jelly beans were green, 18 of the ©R .

I .

C. Publ i cat i ons jelly beans were blue, 14 of the jelly beans were 6 •f orwere r evi e w pu r po sesonl y• pink and the yellow, 16 of the jelly beans rest were black and white. There were twice as many white jelly beans as black jelly beans.

What fraction of the bag is white jelly beans?

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

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Number and algebra

Lila and Demetri counted the jelly beans in a bag and worked out the fraction of each coloured jelly bean in the bag. The results 1 were: 16 of the jelly beans were green, 18 of the jelly beans were blue, 14 of the jelly beans were ©R .

I .

C. Publ i cat i ons 6 pink and the yellow, 16 of the jelly beans •f orwere r evi e w pu r po sesonl y• rest were black and white. There were twice as many white jelly beans as black jelly beans.

Order the colours of the jelly beans from least to most in the packet.

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

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Number and algebra

A school was ordering new stationery and craft supplies for the term. The company they purchase from sells: craft sticks in packs of 50 or boxes of 250 packs, paper in reams of 500 sheets or boxes of 4 reams © and pencils inl packs R. I .

C.Pub i cat i ons of 30 or boxes of 50 packs.

•f orr evi ew pur posesonl y• If the school ordered two boxes of each stationery item, how many packs/reams of each item did they purchase?

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

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Number and algebra

A school was ordering new stationery and craft supplies for the term. The company they purchase from sells: craft sticks in packs of 50 or boxes of 250 packs, paper in reams of 500 sheets or boxes of 4 reams and pencils int © R. I .

C. Publ i ca i ons packs of 30 or boxes of• 50 packs. f orr evi ew pur posesonl y• If the school ordered two boxes of each stationery item, how many individual craft sticks, sheets of paper and pencils did they purchase?

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27

Number and algebra

The Moosa family were travelling between two cities that are 3600 km apart. On the first day, they drove 15 of the total distance. On R. I .

Cthe .Pu bl i cat i ons the second day, they drove © 10% of total f orfourth r evi ew pur posesonl y• distance. Over the third•and day, they 4 drove 10 of the total distance and on the fifth day they drove 20% of the total distance. They finished the drive on the sixth day.

What fraction of the total distance did they have left to drive on the sixth day?

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

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Number and algebra

The Moosa family were travelling between two cities that are 3600 km apart. On the first 1 day, they drove 5 of the total distance. On the second day, they drove © 10% of total R. I .

Cthe .Pu bl i cat i ons distance. Over the third•and day, they f orfourth r evi ew pur posesonl y• 4

drove 10 of the total distance and on the fifth day they drove 20% of the total distance. They finished the drive on the sixth day.

If they drove three times as far on the fourth day as they did on the third day, what percentage of the total distance did they drive on the fourth day?

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28

Number and algebra

Three children were asked to estimate the answer to 1679 + 4934. Jerita rounded both numbers up to the nearest hundred to give her estimate.

Marcus rounded the first number up and second number down to the nearest hundred to get his estimate, © R. I .

C.Publ i cat i ons and Sheena rounded both numbers •f orr e ew pur posesonl y• down to the nearest hundred tovi give her estimate.

Whose estimate was closest to the correct answer and how far off the correct answer was the estimate?

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Number and algebra

Three children were asked to estimate the answer to 12 269 + 45 099. Jerita rounded both numbers up to the nearest thousand to give her estimate.

Marcus rounded the first number up and second number down to the nearest thousand to get his estimate, © R. I .

C.Publ i cat i ons and Sheena rounded both numbers orr evi ew pur posesonl y• down to the nearest •f thousand to give her estimate.

Whose estimate was closest to the correct answer and how far off the correct answer was the estimate?

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

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Number and algebra

In a fictional story, scientists were recording the population of aliens living on a planet.

The population had been increasing by 23 095 each month since the first recording at the end of January. Between June and July the © R. I .

C.Publ i cat i ons population increased from 577 375 at the end •f orr e ew pur posesonl y• of June to 646 660 at the end ofvi July.

From August to December, the population decreased by 26 347 each month.

What was the population of aliens at the end of January?

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Number and algebra

In a fictional story, scientists were recording the population of aliens living on a planet.

The population had been increasing by 23 095 since the first recording at the end of January.

Between June and July the population increased © R. I .

C.Publ i cat i ons from 577 375 at the end of June to 646 660 at •f orr evi ew pur posesonl y• the end of July. From July to December, the population decreased by 26 347 each month.

Did the overall population increase or decrease from January to December and by how much?

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

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Number and algebra

Houlio was making a rainbow pom-pom with different coloured wool. He started with 0.68 m of violet wool, then added 0.60 m of blue wool, 0.55 m of indigo wool, 0.5 m of © wool, R. I .

C. Pubm l i c at i ons green wool, 0.43 m of yellow 0.39 of •f or r ev i ew pur posesonl y• orange wool and 0.33 m of red wool.

How many metres of wool did he use in total?

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

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Number and algebra

Houlio was making a rainbow pom-pom with different coloured wool. He started with 0.68 m of violet wool, then added 0.60 m of blue wool, 0.55 m of indigo wool, 0.5 m of green wool, 0.43 m of yellow wool, 0.39 m .

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C .Pub l i cdecided at i ons of orange wool and 0.33 m © of R red wool.

He •f orr evi ewsopu r poadded seson l y• to make his pom-pom symmetrical then the same lengths of each coloured wool in the reverse order, starting and finishing with violet wool.

How many metres of wool did he use in total?

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

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Number and algebra – Answers Card 1 Extension

1000 metres 1000 times

Card 8 Extension

136, composite 4801

Card 12 Extension

12 rows 12 combinations

Card 2 Extension

9669 trees 331 trees

Card 9

Card 13 Extension

92 dogs 65 dogs

Card 3

Sheep 8 , cows 4 , 1 1 pigs 6 , horses 12 21 cows, 42 sheep, 14 pigs, 7 horses

1.41 m, 1.39 m, 1.38 m, 1.35 m, 1.33 m, 1.32 m, 1.3 m, 1.29 m, 1.27 m, 1.24 m 29.48 kg, 29.99 kg, 30.01 kg, 30.16 kg, 30.49 kg, 31.06 kg, 31.48 kg, 31.67 kg, 31.76 kg, 32.08 kg

Card 14

6 cups of milk

Extension

1 3 cups caster sugar

Card 15 Extension

4885 8904

Extension

4

1

Card 4 Extension

8440 people 33 760 people

Card 5 Extension

79.5 kilograms Day 27

Card 6

Male teachers who took the bus

Extension

23 48

Card 7 Extension

69 aeroplanes 20 aeroplanes

Extension

1

© R. I .

C.Pub l i c t i o s books, reference Card 16 a 120n 60 o picture books, or r evi ew pur poses nl y • 180 Card 10 •f days 34 non-fiction books Extension

Day 22

Card 11

Orange juice

Extension

and 90 fiction books 50 books

apple juice pineapple juice

Card 17 Extension

0.7 kilometres 5.4 kilometres

Card 18 Extension

a = 20, b = 12, c = 50 a = 150, b = 25, c = 2

children

8g 100 mL , 10 g 100 mL ,

8g 100 mL

Extension

Apple juice, 10% sugar

Card 19 Extension

77 cookies Miley baked 11 batches, Cole baked 7 batches

Card 20 Extension

16 8 133

Card 21 Extension

2011 6001 sales

Card 22 Extension

40% 60%

Card 23

Shanique – 17 metres, Carlos – 1250 metres 1267 metres

Extension

5

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Number and algebra – Answers Card 24

Extension

Area = 36 m2 , length = 6 m, width = 6 m The third block— 324 m2 ; length is 18 m 2 16

1

Card 25 Extension

or 8 Black/green, white/ blue, yellow, pink

Card 26

500 packs of craft sticks, 8 reams of paper, 100 packs of pencils 2500 craft sticks, 4000 sheets of paper, 3000 pencils

Extension

Card 27 Extension

Card 28 Extension

Marcus’ estimate, 13 Sheena’s estimate, 368

Card 29 Extension

461 900 Increase, 53 025

Card 30 Extension

3.48 m of wool 6.96 m of wool

© R. I .

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

1 10

of the total distance 30% of the total distance R.I.C. Publications® Prim-Ed Publishing

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