Problem-Solving Strategies & Skills – Measurement & Geometry: Year 6

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Measurement and geometry On Saturday, Susie, Libby, Leisel, Elka and Petria went swimming. Susie swam twice as far as Leisel but 200 m less than Elka. Libby swam the same distance as Leisel and 250 m more than Petria, who swam 850 m.

On Sunday, the total distance swum all. © Rby .

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C Publ i cat i ons girls was 5 km. Petria swam 0.125 km more f o rr e vi ew pur posesonl y• than Leisel, who swam 125• m more than Libby.

Susie swam 0.125 km less than Libby, who swam a kilometre but 125 m more than Elka.

How many kilometres did each girl swim over the weekend? Write the distances in descending order.

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Measurement and geometry

On Saturday, Susie, Libby, Leisel, Elka and Petria went swimming. Susie swam twice as far as Leisel but 200 m less than Elka. Libby swam the same distance as Leisel and 250 m more than Petria, who swam 850 m.

©R .

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C.Publ i cat i ons On Sunday, the total distance swum by all girls was 5 km. Petria swam km more •0.125 f orr ev i ew pur posesonl y• than Leisel, who swam 125 m more than Libby.

Susie swam 0.125 km less than Libby, who swam a kilometre but 125 m more than Elka.

How many metres, more or less, did each girl swim on Sunday than on Saturday?

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Measurement and geometry

Tuesday was Matt’s favourite day for watching television on Channel HP. The scheduled shows are: 4:45 – 5:10 p.m. All things creepy 5:10 – 5:35 p.m. Cartoon capers © R. I .

C.Publ i cat i ons 5:35 – 6:15 p.m. The Celtic wizard 6:15 – 7:15 p.m. Science hour •f orr evi ew pur posesonl y• If Matt arrives home at 16:55 hrs and has to go out for a family dinner at 18:55 hrs, how much time can he spend watching each show?

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Measurement and geometry Tuesday was Matt’s favourite day for watching television. This is one channel’s schedule: 4:45 – 5:10 p.m. All things creepy 5:10 – 5:35 p.m. Cartoon capers 5:35 – 6:15 p.m. The Celtic wizard 6:15 – 7:15 p.m. Science hour © R. I .

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f orthere r evi e r posesonl y• For shows less than half an• hour, isw pu a two and a half minute commercial break; between half and three-quarters of an hour, there are two two-minute breaks. For shows between three-quarters of an hour and one hour, there are three two-minute breaks.

For how long does each show actually last and what would be Matt’s total viewing time be?

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Measurement and geometry From card, Amy has made four 3-D shapes: a triangular and a square prism, and a triangular and a square pyramid. The dimensions of the 2-D rectangular faces of the prisms are 6 cm x 30 cm. All the sides of the 2-D faces of the pyramids measure 8 cm.

What is the perimeter, in metres, of the net of each 3-D shape Amy has made?

© R. I .

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

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Measurement and geometry From card, Amy has made four 3-D shapes: a triangular and a square prism, and a triangular and a square pyramid. The dimensions of the 2-D rectangular faces of the prisms are 6 cm x 30 cm. All the sides of the 2-D faces of the pyramids measure 8 cm.

Amy wants to line every edge of each shape with a decorative strip and add a pompom to every vertex.

How many pompoms and what length of decorative strip, in metres, does Amy need © R. I .

C.Publ i cat i ons for each 3-D shape?

•f orr evi ew pur posesonl y•

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Measurement and geometry

A recipe for chocolate brownies includes 115 g butter, 228 g chocolate, 200 g sugar, 3 eggs, 5 mL vanilla extract, 80 g flour, 11 g cocoa and 180 g chocolate chips.

Sasha bought 500 g butter, 750© g chocolate, R. I .

C.Publ i cat i ons 1 kg sugar, a dozen eggs, a 60 mL bottle •f o rr ev i ew pur posesonl y• of vanilla extract, 1.5 kg flour, 0.5 kg cocoa powder and 500 g chocolate chips.

How many batches of the recipe can Sasha make?

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Measurement and geometry A recipe for chocolate brownies includes 115 g butter, 228 g chocolate, 200 g sugar, 3 eggs, 5 mL vanilla extract, 80 g flour, 11 g cocoa and 180 g chocolate chips.

Sasha bought 0.5k g butter, 750 g chocolate, 1 kg sugar, a dozen eggs, a 60 mL bottle ©R .

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C.Publ i cat i ons of vanilla extract, 1.5 kg flour, 0.5 kg cocoa •f orr evi ew pur posesonl y• powder and 500 g chocolate chips.

Does Sasha have enough to make five batches of the recipe? If not, which ingredients does she need more of and how much of each?

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Measurement and geometry Leila invited five friends to her party.

She filled a five-litre capacity punchbowl with home-made fruit juice. Leila and her friends drank from glasses with a capacity of 125 mL.

©remaining R. I .

C.Publ i cat i ons After the party, Mum poured the fruit juice into a measuring jug, •f orwhich r evi ew pur posesonl y• showed there was 0.5 L left over.

If the girls all drank the same amount of juice, filling their glasses to capacity each time, how many glasses did each have and what volume did each drink?

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Measurement and geometry

Leila invited five friends to her party.

She filled a five-litre capacity punchbowl with home-made fruit juice. Leila and her friends drank from glasses with a capacity of 125 mL.

© R. I .

C.Publ i cat i ons If three more friends arrived unexpectedly, •f o rr evi ew pur posesonl y• how much less juice is available per person compared with what Leila had originally planned? Write the answer in litres, to three decimal places.

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Measurement and geometry

Anya helped her grandad place a seed potato at even intervals along the freshly dug drills in the raised garden bed. Forty seed potatoes were evenly planted in the bed,© which R. I .

C.Publ i cat i ons measures 5 metres by 2 metres.

•f orr evi ew pur posesonl y•

What area, in metres, does each seed potato have to itself?

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Measurement and geometry

Anya helped her grandad place a seed potato at even intervals along the freshly dug drills in the raised garden bed.

Forty seed potatoes were planted in the bed, which measures 5 metres by 2 © metres.

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f or r evi ew pur posesonl y• Anya’s grandad wants to • plant 100 more seed potatoes in another garden bed, with the same space for each potato. What area, in square metres, does this garden bed need to be?

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Measurement and geometry

From home, it takes Anna 13 minutes to walk to school, nine minutes and 45 seconds to walk to the leisure centre and six and a half minutes to walk to her aunt and uncle’s house.

Anna always walks to and from© school.

On Saturday R. I .

C .P ubl i cat i ons mornings, she walks to and from the leisure centre.

•f orr evi ew pur posesonl y• After lunch on Sundays, she walks to and from her aunt and uncle’s house.

For how long, in hours, minutes and seconds, does Anna walk each week?

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Measurement and geometry

From home, it takes Anna 13 minutes to walk to school, nine minutes and 45 seconds to walk to the leisure centre and six and a half minutes to walk to her aunt and uncle’s house.

Anna always walks to and from school. On Saturday mornings, she walks to and from© theR leisure centre. .

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C.P ubl i cat i ons After lunch on Sundays, she walks to and from her aunt •f orr evi ew pur posesonl y• and uncle’s house. While she is there, they always take the dogs for a five-kilometre walk around the lake.

This takes them 55 minutes.

Anna always walks at this rate. How far, in kilometres to three decimal places, does Anna walk in one week?

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Measurement and geometry In Kirby’s garden, he has a rotary washing line with a 4 m × 4 m brick paved area underneath.

He wants to create a new paving pattern reusing the old 20-cm square bricks and incorporating some new bricks. He would like to add new rectangular bricks which are half the width of the old square brick, new ©and R. I .

C.Publ i cat i ons small square bricks.

•f orr evi ew pur posesonl y•

They will be repeated in this pattern:

How many old bricks and new bricks will Kirby use?

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Measurement and geometry

In Kirby’s garden, the four perpendicular arms of the rotary washing line each measure one metre. Line is threaded tightly through holes in the arms of the washing line. Each arm has five holes, at 20-cm intervals. The first hole in each arm is. located ©R I .

C.Publ i cat i ons 0.95 m from the centre of the washing line.

•f orr evi ew pur posesonl y•

Viewed from above, how many squares does the threaded washing line make and what is the length, in metres, of the diagonal of each square?

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Measurement and geometry

For her birthday, Josh gives his mum a scented candle sitting in a bowl of washed pebbles.

The candle weighs 341 g and the bowl weighs 971 g. The pebbles came from a large bag © Mum’s R. I .

C. Publ i cat i ons which, unopened, weighed 10 kg. gift weighs 2.792 kg.

•f orr evi ew pur posesonl y• What weight of pebbles, in kg, does Josh use and what weight, in kg, is left in the bag after Josh has made his mum’s present?

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Measurement and geometry For her birthday, Josh gives his mum a scented candle sitting in a bowl of washed pebbles.

The candle weighs 341 g and the bowl weighs 971 g. The pebbles came from a large bag which, unopened, weighed 10 kg. Mum’s gift weighs 2.792 kg.

Rfor .

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C .P ubl i cat i ons Josh decides to make the same© gift his two grandmothers and his three aunts.

He buys bowls •f orr e vi e wp ur posesonl y• that weigh the same as the one he used for his mum’s gift and candles that weigh 11 g more. He uses all the pebbles left in the bag, putting an equal amount in each bowl.

By how much are these gifts more or less in weight than his mum’s gift?

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Measurement and geometry

The children in Mr Bonn’s class are making pancakes in a science lesson on food. The recipe they use, which asks R. I .

C.Publ i cat i ons for 180 mL of milk, makes eight© small pancakes.

•f orr evi ew pur posesonl y• How many dozen pancakes can the class make if they have a 3 L carton of milk?

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Measurement and geometry

The children in Mr Bonn’s class are making pancakes in a science lesson on food. The recipe they use, which asks for 180 mL of milk, makes eight small pancakes.

© R. I .

C.Publ i cat i ons How many 1 L cartons of milk •f ordoes r evi ew pur posesonl y• Mr Bonn need to supply to make enough pancakes for 150 children to have two each, and how much, if any, is left over?

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Measurement and geometry

Ethan cycled 3.45 km to pick up Nathan. The two boys cycled 2.65 km to Kane’s house, then all three cycled 9.35 km to pick up Sam. Together they climbed 6.65 km to reach Joe’s house, where they had lunch. After lunch, the boys cycled home. After 6.25 km, they reached Kane’s house. Ethan was next ©the R. I .

C.Publ i cat i ons to say goodbye, 7.25 km further on. Sam f or r e vi ew pur posesonl y• and Nathan raced the next• 6.35 km to Sam’s house, then Nathan cruised the final 2.5 km on his own.

How far, in kilometres, did each boy cycle?

Write the answers in ascending order.

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Measurement and geometry

Ethan cycled 3.45 km to pick up Nathan. The two boys cycled 2.65 km to Kane’s house, then all three cycled 9.35 km to pick up Sam. Together they climbed 6.65 km to reach Joe’s house, where they had lunch. After lunch, the boys cycled home. After 6.25 km, they reached Kane’s house. Ethan was the next to. say ©R I .

C.Publ i cat i ons goodbye, 7.25 km further on. Sam and Nathan f orr evi ew pur posesonl y• raced the next 6.35 km to• Sam’s house, then Nathan cruised the final 2.5 km on his own.

What percentage, to three decimal places, of the total distance ridden did each boy cycle?

Write the answers in descending order.

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Measurement and geometry

Harry’s swimming club train every day before and after school and on Saturday mornings. Morning sessions are held from 5:30 a.m. to 6:40 a.m. and afternoon sessions from 4:30 p.m. to 5:45 p.m. Every second .

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C.Publ i cat i ons week, time trials are held after © theR Saturday session from 6:55 a.m. to• 7:35 a.m. f or r evi ew pur posesonl y• What is the maximum length of time, in hours and minutes, Harry can train in a two-week cycle?

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Measurement and geometry Harry’s swimming club train every day before and after school and on Saturday mornings.

Morning sessions are held from 5:30 a.m. to 6:40 a.m. and afternoon sessions from 4:30 p.m. to 5:45 p.m.

Harry swims every session he can, but every second Friday his grandparents© pick Rhim .

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Cup .Publ i cat i ons from school and he stays • with them until f orr evi ew pur posesonl y• Saturday afternoon.

When Harry does not go to his grandparents’ house, he attends an extra time trial session on Saturday mornings from 6:55 a.m. to 7:35 a.m.

On average, how much time, in hours, minutes and seconds, does Harry swim each week?

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Measurement and geometry

Jay drew positive x and y axes on 1-cm graph paper and marked each at 1-cm intervals to 15 cm. He marked the following coordinates on the paper: ©ER .

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C.Publ i cat i ons A (3, 4); B (2, 7); C (7, 9); D (9, 7); (8, 3).

Jay then joined the points• inf the order he o rr evi e whad pur posesonl y• marked them, finally joining point E to point A. What is the name of the shape he drew and what is the size of the angle at each point?

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Measurement and geometry

Jay drew positive and negative x and y axes on 1-cm graph paper, making four quadrants.

He marked each axis at 1-cm intervals.

In the positive quadrant, he marked the following coordinates: A (3, 4); B (2, 7); C (7, 9); D (9, 7); E (8, 3).

He joined them in the order he had marked them, © R. I .

C.Publ i cat i ons finally joining point E to point A. He called this •f orr ev e wp r posesonl y• shape S1. He then wrote coordinates toi show au reflection of S1 across the positive y axis and called this shape S2. He made another reflection of S1 across the positive x axis and called this shape S3.

Finally, Jay made shape S4 by sliding S2 11 cm down into the negative quadrant.

What coordinates did Jay write for shapes S2, S3 and S4?

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Measurement and geometry

In his shed, Callum’s grandad has two identical backpacks; one contains 58 golf balls, the other 44 tennis balls. With the balls, each bag weighs 3 kg. A single © golf R. I .

C.Publ i cat i ons ball weighs 44 g and a single tennis ball •f orr evi ew pur posesonl y• weighs 58 g.

What is the weight, in kg, of each empty bag?

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Measurement and geometry

In his shed, Callum’s grandad has two identical backpacks, each of which weighs 550 g when empty. One bag contains golf balls, the other tennis balls. A single golf ball weighs 44 g © R. I .

C.Publ i cat i ons and a single tennis ball weighs 58 g. f or r evi ew pur posesonl y• The bag containing golf• balls weighs 3.718 kg and the bag containing tennis balls weighs 4.204 kg.

How many balls are in each bag?

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Measurement and geometry

Jeremy won a goldfish at the fair. Dad found an old round fish bowl which they could use until they set up a proper tank. The bowl has a capacity of 4.8 L. On the first day, Jeremy fills .

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C .Publ i cat i ons the bowl to 75% of its capacity.© OnR the following four days, he changes 50% ofo the water each day.

•f rr e vi ew pu r posesonl y• By the end of the fifth day, how many litres of water, in total, has Jeremy put in the bowl?

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Measurement and geometry

Jeremy won a goldfish at the fair. Dad found an old round fish bowl which they could use until they set up a proper tank.

The bowl has a capacity of 4.8 L. On the first day, Jeremy fills the bowl to 75% of its capacity. On the following four days, ©R .

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C.Publ i cat i ons he replaces 50% of the water each day. To f or r e vi e w pur posesonl y• change the water, Jeremy• uses an old jug with a 500 mL capacity.

To remove the water for four days, what is the minimum number of times Jeremy needs to put the jug into the fish bowl?

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Measurement and geometry

Mira and Ryan are helping their father to paint his office. The room measures 5 by 3 metres and the height of the four walls from floor to ceiling is 2.4 metres.

There are two doors on separate ©walls R. I .

C.Publ i cat i ons which do not need to be painted. One f ordouble r evi ew pur posesonl y• is 2 × 0.85 metres and the• other door is 1.8 metres square.

What is the total area, in square metres, of wall to be painted?

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Measurement and geometry

Mira and Ryan are helping their father to paint his office. The room is a 5 by 3 metre rectangle with walls that are 2.4 metres from floor to ceiling. The patio doors leading to the garden are 1.8 metres squared. The door into © R. I .

C.Publ i cat i ons the room is 2 × 0.85 metres.

•f orr evi ew pur posesonl y•

A 4-litre tin of paint will cover an area of 50 m2 once. If they paint two coats, how many 4-L tins of paint are needed and how many more square metres can they paint with the leftover paint?

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Measurement and geometry

Ferries travel daily to and from Holiday Island. They leave the mainland every hour on the hour from 07:00 hrs until 15:00 hrs, arriving at the island every hour on the three-quarter hour from 07:45 hrs to 15:45 hrs. The ferries leave the island every hour on the half hour from 08:30 hrs to 16:30 hrs, ©arriving R. I .

C.Publ i cat i ons at the mainland every hour on the quarter •f o rr evi ew pur posesonl y• hour from 09:15 hrs to 17:15 hrs.

What is the minimum number of ferries required to operate this ferry service and how many return trips does each make?

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Measurement and geometry

Ferries travel daily to and from Holiday Island. They leave the mainland every hour on the hour from 07:00 hrs until 15:00 hrs, arriving at the island every hour on the three-quarter hour from 07:45 hrs to 15:45 hrs. The ferries leave the island every hour on the half hour from 08:30 hrs to 16:30 hrs, arriving at the mainland every hour on the quarter hour from 09:15 hrs to 17:15 hrs.

© R. I .

C.Publ i cat i ons Wills and his family are going spend •f oto rr evi ew pur posesonl y•

Saturday night on the island. He and his dad take the first ferry on Saturday.

His mum and sisters follow on the midday ferry. On Sunday, his mum and sisters arrive back on the mainland at 14:15 hrs, while Wills and his dad return on the last ferry on Sunday.

How much longer do Wills and his dad spend on the island than his mum and sisters?

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Measurement and geometry

Sasha used a single type of four-sided 2-D shape to draw a new 2-D shape. The internal angles of the shape she used were opposing pairs of 60º and 120º; and the sides all measure 2.5 cm. Sasha positioned the shape so one edge was sitting parallel to the base of the page and the lower-left angle was acute. © R. I .

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•f or e vi ew pur posesonl y• Sasha drew around the shape sixr times, following these instructions: ‘draw, reflect up, draw, translate to the right, draw, reflect down, draw, translate to the right, draw, reflect up, draw’.

What is the perimeter, in metres, and how many sides does the new shape have?

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Measurement and geometry

Sasha is making a bracelet out of differentshaped stones and gems. She wants to arrange the 3-D shapes in a chain, starting with a cube, and so that each shape shares a face with the following shape. The faces do not have to beu ©R .

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C .P bl i cat i ons the same size.

•f orr evi ew pur posesonl y•

She wants to join the chain and close the loop so the last shape has to join back to the cube.

List the possible ways she can make her bracelet.

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Measurement and geometry

Postman Pete has just put five parcels in his van, ready for delivery. Parcel A weighs 3.765 kg. Parcel B weighs twice as much as Parcel C. Parcel C weighs one third of the weight of Parcel E. © R. I .

C.Publ i cat i ons Parcel D weighs 2.985 kg more than f orkg r e vi ew pur posesonl y• Parcel A. Parcel E weighs• 0.375 less than Parcel D. Write the parcels and their weights, in ascending order of weight.

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Measurement and geometry From Monday to Friday for four weeks, Postman Pete loads five parcels into his van. On each day, the individual parcels are delivered to the same five addresses. Parcel A weighs 3.765 kg.

Parcel B weighs twice as much as R. I .

C.Publ i cat i ons Parcel C. Parcel C weighs one © third of the weight of Parcel E. Parcel Dr weighs •f or evi ew pur posesonl y• 2.985 kg more than Parcel A. Parcel E weighs 0.375 kg less than Parcel D. In descending order, what is the total parcel weight, to one decimal place, delivered to each address?

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Measurement and geometry

Over the winter and spring, Miss Cooper’s class used an old 240-L barrel to collect rainwater from a downpipe on the school shed. By early summer, the barrel was full and the children were able to water their vegetable patch R. I .

C.Publ i cat i ons during the drier months. From © Monday to Friday, they filled a 4-L• watering f orr evi ew pur posesonl y• can to its capacity and watered the vegetables each day.

If no more rain is collected in the barrel, for how many weeks will the supply last?

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Measurement and geometry

Over the winter and spring, Miss Cooper’s class used an old 240-L barrel to collect rainwater from a downpipe on the school shed. By early summer, the barrel was full and the children were able to water their vegetable patch during the drier months.

From Monday to Friday, they filled a 4-L R. I .

C.Publ i cat i ons watering can to its capacity and© watered the vegetables each day. •f orr evi ew pur posesonl y• After four weeks, there was a storm and the equivalent of 25% of the barrel’s capacity of rainwater was added to the barrel.

How much water is now in the barrel and for how many weeks will it last?

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Measurement and geometry

Dad is making a big square cushion for each member of the family: himself, Mum, George, Lily and Spot, the dog. The sides of each cushion are 60 cm.

© R. I .

C.Publ i cat i ons The material he wants to • buy cm wide. f oisr150 r ev i ew pur posesonl y• What length, in metres, does he need, and what area of material, in square metres, will be left over after the cushions have been made?

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Measurement and geometry

Dad is making a big square cushion for each member of the family: himself, Mum, George, Lily and Spot, the dog. The sides of each cushion are 60 cm.

© R. I .

C.Publ i cat i ons

Cushion fabric can be bought by the metre and •f orr evi ew pur posesonl y• comes in two different widths: 90 cm and 150 cm.

What lengths of 90-cm and 150-cm material, in metres, would he need and what area of material, in square metres, would be left over from each?

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Measurement and geometry

The theatre is advertising performance times for its new production. From Thursday to Sunday, there is an evening performance at 20:00 hrs, and on Saturday and Sunday there is also a matinee performance at 15:00 hrs.

The performance lasts for two hours and © R. I .

C.Publ i cat i ons 15 minutes, and there is a 25-minute interval •f orr evi ew pur posesonl y• halfway through.

After the matinee, it takes the cast and crew one and a half hours to prepare for the evening performance. How much time do they have to relax between performances?

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Measurement and geometry

The theatre is advertising performance times for its new production. From Thursday to Sunday, there is an evening performance at 20:00 hrs, and on Saturday and Sunday there is also a matinee performance at 15:00 hrs.

The performance lasts for two hours and © Rduring .

I .

C.Publ i cat i ons 15 minutes, and there is an interval which the cafe opens for • light refreshments. f or r evi ew pur posesonl y• The lights come on at the end of the evening performance at 22:35 hrs and at 17:45 hrs at the end of the matinee. For how long is the cafe open over the Thursday to Sunday period?

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Measurement and geometry

A class was playing some old-fashioned games. Robert brought in a sack of his dad’s prized marbles. To make sure none were lost during the day, Miss Adams weighed the sack of marbles. It weighed 508.3 g. She also R. I .

C.Publ i cat i ons weighed a random selection of© individual marbles and they each weighed 5.255 g.w pu •f orr evi e r posesonl y• The marbles were shared equally among 6 groups, then Miss Adams weighed the empty sack and found it weighed 35.35 g.

How many marbles did each group have?

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Measurement and geometry

A class was playing some old-fashioned games.

Robert brought in a sack of his dad’s prized marbles. To make sure none were lost during the day, Miss Adams weighed the sack of marbles. It weighed 508.3 g. She also weighed a random selection of individual marbles and they each weighed 5.255 g. The© marbles were R. I .

C. Publ i cat i ons shared equally among 6 groups, then Miss •f orr evi ew p r posesonl y• Adams weighed the empty sack and found itu weighed 35.35 g.

At the end of the day when the sack of marbles was reweighed, it weighed 471.515 g.

How many marbles were missing?

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Measurement and geometry

The instructions on a one-litre bottle of cordial concentrate suggest using one part cordial to four parts water to make the best strength of cordial. © R. I .

C.Publ i cat i ons

•could f orr ev i ewifp ur posesonl y• How many 250 mL glasses be filled the whole bottle of concentrate is used and the instructions followed exactly?

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Measurement and geometry

The instructions on a one-litre bottle of cordial concentrate suggest using one part cordial to four parts water to make single-strength cordial.

© R. I .

C.Publ i cat i ons

How many litres of cordial are made using one bottle of •f orr evi ew pur posesonl y• concentrate if 0.5 L is used to make half-strength cordial, 0.25 L is used following the instructions on the bottle and 0.25 L is used to make double-strength cordial?

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Measurement and geometry

The world is divided into several time zones. The local time of any place in the world relates to its position on the globe compared with Greenwich in London. Times can be the same as, ahead or behind Greenwich. © R. I .

C.Publ i cat i ons

f o rr evi e wp ur pin os eso nl y• and Grandpa Ned lives Daniel lives in New Zealand.• His Grandpa John lives Perth, Australia, in Ireland. He has three uncles: James lives in Switzerland, Alex lives in Chile and Jake lives in Alaska in the USA. His grandpa in Ireland lives in the same time zone as Greenwich. Switzerland, in Western Europe, is one hour ahead. Perth, in Western Australia, is seven hours ahead and New Zealand is twelve hours ahead. Chile, in South America, is five hours behind Greenwich and Alaska is nine hours behind.

When it is midday on a Tuesday in New Zealand, what time and day is it for the people in Daniel’s family who live in other parts of the world?

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Measurement and geometry

The world is divided into several time zones. The local time of any place in the world relates to its position on the globe compared with Greenwich in London. Times can be the same as, ahead or behind Greenwich.

© R. I .

C.Publ i cat i ons Daniel lives in New Zealand.

His Grandpa lives in Perth, Australia, and Grandpa Ned •f o rr evi ewJohn pur pos es onl y•

lives in Ireland. He has three uncles: James lives in Switzerland, Alex lives in Chile and Jake lives in Alaska in the USA. His grandpa in Ireland lives in the same time zone as Greenwich.

Switzerland, in Western Europe, is one hour ahead. Perth, in Western Australia, is seven hours ahead and New Zealand is twelve hours ahead. Chile, in South America, is five hours behind Greenwich and Alaska is nine hours behind.

If Daniel wants to call his family who live in other parts of the world when it is midday their time, at what time in New Zealand must he make each call?

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Measurement and geometry

The table shows the area of some islands of the world. Australia and Greenland are by far the biggest islands. © R. I .

C.Publ i cat i ons

•f orr evi ew pur posesonl y•

How many times could each of the five smallest islands fit into Australia and Greenland?

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Measurement and geometry

The table shows the area of some islands of the world.

Although classed as a continent; Australia is the biggest island in the world by area. The other islands could fit into it many times over. ©R .

I .

C.Publ i cat i ons

•f o rr evi ew pur posesonl y• What area of Australia would remain if: – Greenland fitted into it as many times as possible.

– Iceland fitted into it ten times and Java fitted into it once?

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Measurement and geometry

The table shows the height above sea level of some mountains of the world. Use the information to find the missing height, in kilometres, in each equation.

Mont Blanc + Ben Nevis = Denali © R–.

I .

C.Publ i cat i ons

•f o r evi ew+ pur posesonl y• Kilimanjaro – Monte Rosa =r Snowdon

Aconcagua +

= Jungfrau + Matterhorn

2(Eiger) = Everest –

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Measurement and geometry

The table shows the height above sea level of some mountains of the world. Experienced climbers can climb at an average rate of: 250 m/hr for peaks between 1000 and 2000 m 200 m/hr for peaks between 3000 and 4000 m ©and R. I .

C.P bl i cat i ons 175 m/hr for peaks between 4000 5000 mu 150 m/hr for peaks between 5000 and 6000 mu •f orr evi ew p r posesonl y• 125 m/hr for peaks between 6000 and 7000 m 100 m/hr for peaks between 7000 and 8000 m To the nearest whole hour, which peaks would take the same number of hours to climb?

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Measurement and geometry

The table shows the approximate dates of different empires and civilisations in world history.

Write the empires and civilisations in order from the earliest to the latest beginning.

© R. I .

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

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Measurement and geometry

The table shows the approximate dates of different empires and civilisations in world history.

Write the empires and civilisations in descending order of duration.

© R. I .

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

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Measurement and geometry

On average, a small car weighs 1.354 tonnes; a medium car, 1.590 tonnes; and a large car, 1.985 tonnes. A small car can comfortably carry four people; a medium car, five people; and a large car, six people. If the average adult weighs 80 kg, the average teenager 65 kg, and the average child 30 kg, calculate the total weight, in tonnes, of each car load.

© R. I .

C.Publ i cat i ons

A large car carrying two adults, two teenagers •f orr evi ew pur posesonl y• and two children.

A medium car carrying two adults, one teenager and two children.

A small car carrying one adult and three children.

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Measurement and geometry

On average, a small car weighs 1354 kg; a medium car, 1590 kg and a large car, 1985 kg.

The average adult weighs 85 kg; the average teenager, 70 kg; and the average child, 45 kg.

The weight limit of a small river bridge is 2 tonnes.

Which cars would be able to cross the bridge and who could remain in the car as it was crossing?

© R. I .

C.Publ i cat i ons A large car carrying two adults, two teenagers •f or r ev i ew pur posesonl y• and two children.

A medium car carrying five adults.

A small car carrying one adult and three children.

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Measurement and geometry

After a severe winter and very wet spring, all the reservoirs in the country were at full capacity, but after a hot summer and dry autumn they all lost a significant volume © R. I .

C.Publ i cat i ons of water.

•f orr evi ew pur posesonl y•

Which reservoirs require the greatest and least amounts of water to bring them back to full capacity?

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Measurement and geometry

After a severe winter and very wet spring, all the reservoirs in the country were at full capacity, but after a hot summer and dry ©volume R. I .

C.Publ i cat i ons autumn they all lost a significant of water.

•f orr evi ew pur posesonl y• The total water lost could fill which reservoir, and with how much left over?

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

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Measurement and geometry – Answers Elka – 3.150 km Susie – 3.075 km Leisel – 2.225 km Libby and Petria – 2.1 km Extension Susie – 1325 m less

Libby – 100 m less

Leisel – 25 m more

Elka – 1650 m less

Petria – 400 m more Card 1

Card 2 2 hrs Extension All things creepy –

22 m 30 s

Cartoon capers –

22 m 30 s

The Celtic wizard –

36 m

Science hour –

54 m

Total viewing time –

135 m or 2 h 15 m

triangular prism – 1.08 m square prism – 1.32 m triangular pyramid – 0.48 m

square pyramid –

0.64 m Extension triangular prism – 6 pompoms, 1.26 m strip

square prism – 8 pompoms, 1.68 m strip

triangular pyramid – 4 pompoms, 0.48 m strip

square pyramid – 5 pompoms, 0.64 m strip Card 3

Card 5 6 glasses, 750 mL each Extension 0.278 L Card 6 0.25 m2 Extension 25 m2 Card 7 2 h 42 m 30 s Extension 19.773 km Card 8 400 rectangular bricks

400 little square bricks

100 old square bricks Extension 5 squares

1 – 1.90 m

2 – 1.50 m

3 – 1.10 m

4 – 0.70 m

5 – 0.30 m

© R. I .

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

Card 4 2 Extension No, she would need:

75 g butter, 390 g chocolate, 3 eggs, 400 g chocolate chips

1.48 kg pebbles, 8.52 kg left over Extension 0.235 kg more Card 9

Card 10 10 dozen pancakes Extension 7 1-L cartons, 0.25 L left over Card 11 Kane – 22.25 km

Sam – 26.5 km

Ethan – 35.6 km

Nathan – 41 km Extension Nathan – 92.238%

Ethan – 80.090%

Sam – 59.618%

Kane – 50.056% Card 12 27 h 10 m Extension 12 h 22 m 30 s

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Measurement and geometry – Answers Card 13 irregular pentagon

A – 120º

B – 94º

C – 113º

D – 120º

E – 93º Extension S2: A (–3, 4); B (–2, 7);

C (–7, 9); D (–9, 7); E (–8, 3)

S3: A (3, –4); B (2, –7);

C (7, –9); D (9, –7); E (8, –3)

S4: A (–3, –7); B (–2, –4); C (–7, –2); D (–9, –4); E (–8, –8) Card 14 0.448 kg Extension 72 golf balls 63 tennis balls

Card 15 10.8 L Extension 16 times Card 16 33.46 m2 Extension two 4-L tins, 33.08 m2 Card 17 3 ferries, 3 trips each Extension 8 hours Card 18 perimeter – 0.25 m

six sides Extension 1. A, D, H, C, G, B, E, F

2. A, D, H, E, B, G, C, F

3. A, F, E, B, G, C, H, D

4. A, F, C, G, B, E, H, D

Card 19 Parcel C – 2.125 kg

Parcel A – 3.765 kg

Parcel B – 4.250 kg

Parcel E – 6.375 kg

Parcel D – 6.750 kg Extension Parcel D – 135.0 kg

Parcel E – 127.5 kg

Parcel B – 85.0 kg

Parcel A – 75.3 kg

Parcel C – 42.5 kg

Card 22 50 minutes Extension 2 h 20 m Card 23 15 marbles per group Extension 7 marbles missing Card 24 20 glasses Extension 6.5 L

© R. I .

C.Pub l i c t i o ns Card 20 a 12 weeks Extension 220 L in the tank, •f orr evi ew pu r pose sonl y• 11 weeks 3 m of material, 0.9 m2 left over Extension 90 cm – 6 m with 1.8 m2 left over,

150 cm – 3 m with 0.9 m2 left over Card 21

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Measurement and geometry – Answers Grandpa John in Perth – 7 a.m. on Tuesday

Uncle James in Switzerland – 1 a.m. on Tuesday

Grandpa Ned in Ireland – midnight between Monday and Tuesday

Uncle Alex in Chile – 7 p.m. on Monday

Uncle Jake in Alaska– 3 p.m. on Monday Extension to Perth – 5 p.m.

to Switzerland – 11 p.m.

to Ireland – midnight

to Chile – 5 a.m.

to Alaska – 9 a.m.

Card 25

Card 26

Australia Greenland

Honshu

33

9

Iceland

74

21

Ireland

91

25

Java

58

16

Madagascar

13

3

Extension 2200 km

2

Mont Blanc + Ben Nevis = Denali – 0.042 km

Kilimanjaro – Monte Rosa = Snowdon + 0.176 km

Aconcagua + 1.675 km = Jungfrau + Matterhorn

2 x Eiger = Everest – 0.908 km Extension Matterhorn and Monte Rosa – 26 hours Card 27

Egyptian, Mayan, Satavahanan, Han, Roman, Khmer, Incan, Aztec Extension Mayan, Egyptian, Khmer, Roman, Satavahanan, Han, Incan, Aztec Card 28

Brianne requires the most:

4 508 000 m 3

Pitsford requires the least:

526 350 m 3 Extension Talybont with 3 600 300 m 3 left over Card 30

large car: 2.335 tonnes medium car: 1.875 tonnes

small car: 1.524 tonnes Extension small car: everyone could remain in the car

medium car: only four adults can remain in the car

large car: could not cross the bridge Card 29

© R. I .

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

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

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© R. I .

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

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

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