Problem-Solving Strategies & Skills – Measurement & Geometry: Year 3

1

Measurement and geometry Nikita only likes to use numbers that are symmetrical.

Which of the following number combinations would she choose as a password?

© R. I .

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Measurement and geometry

Extension

Nikita likes to play ScrabbleTM, but only uses tiles that contain I .

C.Publ i cat i ons symmetrical letters. © R.

•f orr evi ew pur posesonl y•

Which of the following words on the board did she make?

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2

Measurement and geometry

I have at least two angles smaller than a right angle.

I have no parallel sides © R. I .

C.Publ i cat i ons and I have less sides than •f orr evi ew pur posesonl y• a pentagon.

What shape am I?

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Measurement and geometry

Extension

My equal angles are greater than a right angle but less than a hexagon’s angles. I have more sides I .

C.Publ i cat i ons than a triangle. I am © R. symmetrical but • have f orno r evi ew pur posesonl y• perpendicular or parallel lines.

What shape am I?

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3

Measurement and geometry

A worm is wriggling around the edge of a vegetable garden patch.

cm

© R. I .

C.Publ i cat i onHow s many centimetres •f orr evi ew pur poseso nl ythe • worm wriggled if it has

18 0

travelled around the whole vegetable patch?

90 cm

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Extension

Measurement and geometry

A worm is wriggling around the edge of a vegetable garden patch. The patch is a rectangle with two sides that are 82 cm long and two sides © R. I .

C.Publ i cat i onthat s are 47 cm wide.

•f orr evi ew pur posesonl y•

How many centimetres has the worm wriggled if it travelled around the vegetable patch twice?

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4

Measurement and geometry At the local hospital, nurses were celebrating the arrival of triplets.

A nurse placed all three babies on the weighing scales, which displayed ©one R. I .

C .Publ i cat i ons 8.4 kg. The nurse removed baby •f or r ev i ew pur posesonl y• and the scales displayed 5.5 kg.

One more baby was removed from the scales and it displayed 2.4 kg.

What is the weight of each baby?

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Measurement and geometry

Extension

At the local hospital, nurses were celebrating the arrival of triplets. A nurse placed all three babies on the weighing scales, which displayed 8.4 kg. The nurse removed one baby and the scales displayed 5.5 kg. One more baby was removed from the scales and itubl © R. I .

C.P i cat i ons displayed 2.4 kg.

•f orr evi ew pur posesonl y• In the next room, two other babies were being weighed. One was 2.8 kg and the other was heavier than this by 0.4 kg.

What are the weights of all five babies in order from lightest to heaviest?

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5

Measurement and geometry Station

Departure times 1st train

2nd train

3rd train

Highland

9:29

10:29

11:29

Coombes

9:41

10:41

11:41

Crestwell

10:05

11:05

12:05

Braxton

© R. I .

C.Publ i cat i ons 9:53 10:53 11:53 w p •f orr evi e ur posesonl y•

Benedict lives in Highland. If he wants to get to Crestwell just before his appointment, which train should he catch and how long is the train ride?

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5

Measurement and geometry

Station

Departure times 1st train

2nd train

3rd train

Highland

9:29

10:29

11:29

Coombes

9:41

10:41

11:41

Crestwell

9:53

Braxton

Extension

©R .

I .

C .Pu bl i cat i ons 10:53 11:53 •f orr evi ew pur posesonl y•

10:05

11:05

12:05

Benedict lives in Coombes. If he wants to get to Braxton with enough time to allow 40 minutes to run some errands, and 15 minutes to have a coffee before his appointment, which train should he catch? How much time will he have spare?

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6

Measurement and geometry Petra painted the walls in her room with a 4-litre can of paint. When she finished 1 she noticed there was exactly 4 of a tin of paint left.

© R. I .

C.Pu bl i cmany at i ons How litres of paint did she use?

•f orr evi ew pur posesonl y•

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Measurement and geometry

Extension

Petra wants to paint the walls in her house using 4-litre cans of paint.

She chooses two colours—yellow and blue—and buys two cans of each colour. She uses one full can and 1250 mL of yellow, and one full can and 2570 mL of blue.

What is the volume, in millilitres,

© R. I .

C. Publ i cat i ons of each colour that remains?

•f orr evi ew pur posesonl y•

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7

Measurement and geometry The animals in the zoo are growing up fast. The giraffe was 120 cm tall as a baby but it grew 33 cm. The elephant was 97 cm tall as a baby but is now 41 cm taller. The bear was 89 cm a. baby ©as R. I C .Publ i cat i ons but is now 55 cm taller.

•f orr evi ew pur posesonl y• Which is the tallest animal and by how many more centimetres is it taller than the second tallest animal?

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Measurement and geometry

Extension

The animals in the zoo are growing up fast. The giraffe was 1.3 m tall as a baby but it grew 37 cm. The elephant started at 990 mm tall as a baby but is now 42 cm taller. The bear was cm ©89 R. I .

C.Publ i cat i ons as a baby but is now• 650 taller. f ormm r evi ew pur posesonl y• Which is the shortest animal and by how many more centimetres is it shorter than the second shortest animal?

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Measurement and geometry

What number am I? (The number of edges of a cube) – Professor Pi told his class that (the number of surfaces of he was thinking of a number and a sphere) + (the number wrote the following clues of triangular faces of a on the board. square-based pyramid) © R. I .

C.Publ i c at i ons

•f orr ev i ew pur posesonl y• What number was he thinking of?

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Measurement and geometry

Extension

What number am I? (The number of edges of a cube) x (the number of circular faces of a Professor Pi told his class that cylinder) + (the number he was thinking of a number of edges of a sphere) + and wrote the following clues (the number © R. I .

C.Publ i c at i o ns of vertices of a triangular prism) on the board.

•f orr evi ew pur po sesonl y •

What number was he thinking of?

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Measurement and geometry

A car drives down a one-way street that runs parallel to Main Street. Then it turns left into the second street that runs © R. I .

C.Publ i cat i ons perpendicular to Main Street.

•f orr evi ew pur posesonl y• Which street is the car on?

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Measurement and geometry

Extension

A jogger starts his course on a horizontal street. He turns onto a street that is perpendicular to the street he was just on.

He then turns onto another street ©R .

I .

C.Publ i cat i ons that is perpendicular to that street.

•f orr evi ew pur posesonl y•

Is he jogging on a vertical or horizontal path now?

Is it parallel or perpendicular to the street he started on?

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10

Measurement and geometry

Kellie is making a cake for her grandmother.

She adds 250 grams of flour to 125 grams of butter and 10 grams of baking powder. © R. I .

C .Pmixture. ubl i cat i ons She also needs to add sugar to the

•f orr evi ew pur posesonl y•

If the total weight of the ingredients is 415 grams, how many grams of sugar did she add?

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Measurement and geometry

Extension

Kellie is making a cake for her grandmother.

She adds 250 grams of flour to 125 grams of butter and 10 grams of baking powder.

She also needs to add sugar and walnuts © R. I .

C.Publ i cat i ons to the mixture. There are 50 grams more •f orr evi ew pur posesonl y• of walnuts than sugar.

If the total weight of the cake is 485 grams, how many grams of sugar was added?

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Measurement and geometry

On a clock, what are the two R. I .

C .Publ i cat i ons times that show the hour©hand at •f orr e vi ew pur posesonl y• a right angle to the minute hand?

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Measurement and geometry

Extension

Which time shows the minute and hour hands in a position that © R. I .

C.Publ i cat i ons forms two angles greater than •f orr evi ew pur posesonl y• a right angle?

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Measurement and geometry Hennie is trying to pick the largest muffin from the tray. She decides the best way to do it is to weigh each muffin. Muffin A weighs 51 grams. Muffin B weighs I .

C.Publ i cat i ons 3 grams less than Muffin©A.R. •f orr evi ew pur posesonl y• Muffin C weighs 2 grams more than Muffin B. Muffin D weighs 5 grams more than Muffin B. Which muffin should Hennie pick, and how many grams heavier is it than the lightest muffin?

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Measurement and geometry

Extension

Hennie is trying to pick the largest muffin from the tray. She decides the best way to do it is to weigh each muffin. Muffin A weighs 51 grams. Muffin B weighs 2 grams less than Muffin© A.R. I .

C.Publ i cat i ons Muffin C weighs 3 grams than •f ormore r evi ew pur posesonl y• Muffin D. Muffin D weighs 6 grams more than Muffin B. What is the weight difference between the heaviest and lightest muffins?

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13

Measurement and geometry

Kimo wants to create a tile pattern by tessellating two different-shaped tiles together.

Which two shapes should he use so there are no gaps?

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

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Measurement and geometry

Extension

Kimo wants to create a tile pattern by tessellating three different-shaped tiles together.

Which three shapes should he use so that there are no gaps?

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

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Measurement and geometry

Three friends are going on separate holidays. Jill is spending 23 days in Hawaii. Jackson is spending 2 weeks in Texas. Miram is going to Paris for © R. I .

C.Publ i cat i ons 1 week and 13 days.

•f orr evi ew pur posesonl y•

Who is going to be away the longest, and by how many days longer will they be away than the next closest person?

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Measurement and geometry

Extension

Three friends are going on separate holidays. Jill is spending 1 week in Sydney, a fortnight in Melbourne and 3 days travelling around Tasmania.

Jackson is spending two weeks and .

I .

C.to Publ i cat i ons 5 days in Florida. Miram © is R going •f o rr evi e w pur posesonl y• Prague for 1 week and Vienna for 13 days.

Who is going to be away the longest, and by how many days longer will they be away than the next closest person?

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Measurement and geometry

Trang and Lacey are playing with their water pistols. They can fit 500 mL of water in each pistol.

They continue playing until © R. I .

C.Publ i cat i ons they have filled their pistols orr evi ew pur posesonl y• three times each. •f How many litres of water did they use altogether?

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Measurement and geometry

Extension

Trang and Lacey are playing with their water pistols. The pistol canisters take 500 mL of water each. The girls have a full 5-litre © R. I .

C.Publ i cat i ons bucket of water to fill up their •f orr evi ew pur posesonl y• canisters with.

How many times can each of the girls refill their pistols?

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Measurement and geometry

What number am I? (The number of sides of a hexagon) x (the number of corners of triangle) +l ©aR .

I .

C.Pub i cat i ons (degrees of one angle of ar rectangle) –pos •f or e vi ew pur esonl y• (the number of lines of symmetry of a square)

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Measurement and geometry

Extension

What number am I? (The number of lines of symmetry of a rectangle) x (the number of sides © R. I .

C. Publ i cat i ons of an octagon) – (the•number of lines f orr evi ew pur posesonl y• of symmetry of a hexagon) + (the sum of angles of a square)

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Measurement and geometry

Mira wants to make her own dice by cutting out and folding a cardboard template.

Which template should she NOT choose?

A

B

D

C

© R. I .

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

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Extension

Measurement and geometry

Mira wants to make her own dice by cutting out and folding a cardboard template.

Which templates cannot be used to make a cube?

A

B

C

D

© R. I .

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

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Measurement and geometry

At the Silly Olympics, many countries competed for the title of ‘Fastest person to blow up a balloon with their nose’. Canada finished in 183 seconds, Australia took © R. I .

C.Publ i cat i ons 2 minutes and 14 seconds, •f orr evi ew pur posesonl y• Great Britain completed the task in 1 minute and 79 seconds, and Ireland finished in 142 seconds.

Which country was the fastest?

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Measurement and geometry

Extension

At the Silly Olympics, many countries competed for the title of ‘Fastest person to blow up a balloon with their nose’.

Canada finished in 183 seconds, Australia took 2 minutes and R. I .

C.Publ i cat i ons 14 seconds, Great Britain©completed f or r e vi ew pur posesonl y• the task in 1 minute • and 79 seconds, and Ireland finished in 142 seconds.

How many seconds difference was there between the fastest and slowest competitors?

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Measurement and geometry

Tom the bricklayer is building a wall 1.2 metres long. He can use either of two lengths of brick.

© R. I .

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

20 cm

15 cm

How many bricks of each size will make up the first row of the wall?

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Extension

Measurement and geometry

Tom the bricklayer is building a wall 1.2 metres long. He can use either of two lengths of brick.

© R. I .

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

25 cm

15 cm

Which length brick will not have any leftover pieces in the first row?

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Measurement and geometry

The scales show the mass (weight) of a case of apples compared to bowling balls.

© R. I .

C.Publ i cat i ons If the mass (weight) • off ar case o r evi ew pur posesonl y• of bananas is twice as much as the mass (weight) of the apples, how many bowling balls does that equal?

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Measurement and geometry

Extension

The scales show the mass (weight) of a case of apples compared to bowling balls.

© R. I .

C.Publ i cat i ons If the mass (weight)• off ar case of o r evi ew pur posesonl y• bananas is equal to 6 bowling balls, how many cases of apples does that equal?

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Measurement and geometry

Which coloured car is parked in a space that is parallel© R. I .

C.Publ i cat i ons to the yellow car and also •f orr evi ew pur posesonl y• perpendicular to the red car?

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Measurement and geometry

Extension

Which coloured cars are parked parallel to the orange © R. I .

C.Publ i cat i ons car, and are not perpendicular f orr evi ew pur posesonl y• to the red car or in a• vertical line?

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Measurement and geometry

Three friends are fixing the tyres on their bicycles. All of their wheels start in the position shown. Rico finds a hole in his tyre after turning his wheel one half turn.

R. I .

C. Pub l i cat i ons Kyla’s wheel needs to be© turned one quarter •f orr e vi ew pur posesonl y• turn. Dudley turns his tyre three-quarters of the way around to get to the hole.

Who turned their wheel the most number of right angles?

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Measurement and geometry

Extension

Three friends are fixing the tyres on their bicycles. All of their wheels start in the position shown. Rico finds a hole in his tyre after turning his wheel one half turn.

R. I .

C. Pub l i cat i ons Kyla’s wheel needs to be© turned one quarter •f orr e vi ew pur posesonl y• turn. Dudley turns his tyre three-quarters of the way around to get to the hole.

How many more or less right angles did Dudley turn his wheel compared to Kyla?

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23

Measurement and geometry

Kelsey decided it was time to clean out the bowl of her pet fish Flossie.

The bowl holds two litres of water and Kelsey used a cup that holds ©R .

I .

C.Publ i cat i ons 250 millilitres.

•f orr evi ew pur posesonl y• After she pours out the dirty water, how many cups will it take to refill the bowl with fresh water?

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23

Measurement and geometry

Extension

Kelsey decided it was time to clean out the bowl of her pet fish Flossie.

The bowl holds two litres of water and Kelsey used a cup that holds 250 millilitres. © R. I .

C.Publ i cat i ons

•f or r evi ewthe pur posesonl y• If Kelsey uses the cup to remove dirty water, and then refills the bowl with fresh water using the cup again, how many cups in total would the process take?

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24

Measurement and geometry

Tony the carpenter drills 4 holes in a straight line in a plank of wood. The distance between Hole 1 and Hole 4 is 45 mm. The distance between Hole 2 and Hole 3 is 23 mm. © R. I .

C.Publ i cat i ons The distance between Hole 3 and Hole 4 •f orr evi ew pur posesonl y• is the same as the distance between Hole 1 and Hole 2.

How many mm apart are Hole 1 and Hole 2?

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24

Measurement and geometry

Extension

Tony the carpenter drills 4 holes in a straight line in a plank of wood. The distance between Hole 1 and Hole 4 is 69 mm. The distance between Hole 2 and Hole 3 is 35 mm. © R. I .

C.Publ i cat i ons The distance between Hole 3 and Hole 4 •f orr evi ew pur posesonl y• is the same as the distance between Hole 1 and Hole 2.

How many mm apart are Hole 1 and Hole 3?

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25

Measurement and geometry

Albie decided to go for a long walk in the sunshine. He walked for 20 minutes until he reached a playground in the park. He stopped there to play for 15 minutes, before continuing on to R. I .

C .Publ i cat i ons his grandfather’s house,© which took f or r evi ew pu r posesonl y• 25 minutes to reach.• He stayed with him for 30 minutes until they both realised it was noon, which meant lunchtime!

For how many hours and minutes was Albie out and about?

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25

Measurement and geometry

Extension

Albie decided to go for a long walk in the sunshine. He walked to his best friend’s house, which took 20 minutes, and continued walking to his grandfather’s house, which ©He R. I .

C.Publ i cat i ons took 25 minutes to reach. stayed f or e vi ew pur posesonl y• with his grandfather• for 30r minutes until they both realised it was noon, which meant lunchtime!

What time did Albie set off on his long walk?

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26

Measurement and geometry

13

A

pentagon

Each row and each column adds up to the total number of straight sides ©8R. I .

C.Pu bl i cat i othe nspurple box. shown in

•f orr evi ew pur posesonl y•

B

12

9

What shapes should be in A and B?

11

square

11

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26

Measurement and geometry

octagon

A

pentagon

Extension

13

Each row and each column adds up to the total number of straight sides shown in ©14 R. I .

C.Pu bl i cat i othe nspurple box.

•f orr evi ew p ur pos eson l y• A be, and what What shape should

oval

semicircle

number should B be?

5

square

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27

Measurement and geometry

Harrison is a very disorganised chef.

He wants to make a sauce but doesn’t know which pot to use. He has a 1-litre pot, a 2-litre pot and a 4-litre pot.

The sauce requires 900 millilitres R. I .

C. Publ i cat i ons of water, 200 millilitres of©cream and •f or r evi ew pur posesonl y• 300 millilitres of chicken stock.

Which pot best fits the ingredients with the least remaining volume?

How much capacity, in millilitres, is left in the pot?

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27

Measurement and geometry

Extension

Harrison is a very disorganised chef.

He wants to make a sauce but doesn’t know which pot to use. He has a 1-litre pot, a 2-litre pot and a 4-litre pot.

The sauce requires 700 millilitres R. I .

C.Publ i cat i ons of water, 200 millilitres of© cream, •f or r evi e w pur posesonl y• 250 millilitres of chicken stock and 175 millilitres of coconut milk.

If he uses the 4-litre pot and doubles the recipe, how many more millilitres until the pot reaches its maximum capacity?

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28

Measurement and geometry

The workers at a chair factory make 49 chairs a day. Each day the factory ships the chairs to the nearest city.

© R. I .

C.Publ i cat i ons If the total weight of• af daily shipment orr e vi ew pur posesonl y• is 147 kilograms, how many kilograms does each chair weigh?

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28

Measurement and geometry

Extension

One worker at a chair factory makes 49 chairs a day. Each day the factory ships the chairs to the nearest city.

R. I .

C .Publ i cat i ons At the end of a day, if the©total weight •workers f orr evi e w pur posesonl y• of the chairs that five made is 490 kilograms, how many kilograms does each chair weigh?

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29

Measurement and geometry

These are the houses in Nina’s street.

Are there more of, less of, or the same number of symmetrical houses compared to asymmetrical houses?

© R. I .

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

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29

Measurement and geometry

Extension

These are the houses in Nina’s street.

Are there more of, less of, or the same number of symmetrical houses compared to asymmetrical houses?

© R. I .

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

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30

Measurement and geometry

On Saturday, Kim ran 858 metres.

On Sunday, Kyle ran half of the distance Kim ran plus 345 metres.

On Monday, Lana ran one third of the distance Kyle ran as © well R. I .

Cas .Publ i cat i ons another 230 metres.•f orr evi ew pur posesonl y• What is the difference, in metres, between the distance Kim ran and the distance Lana ran?

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30

Measurement and geometry

Extension

On Saturday, Kim ran 858 metres.

On Sunday, Kyle ran half of the distance Kim ran plus 345 metres.

On Monday, Lana ran one third of the distance Kyle ran as as © well R. I .

C .Publ i cat i ons another 230 metres.•f orr evi ew pur posesonl y• What is the total distance, in metres, ran by Kim, Kyle and Lana?

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Measurement and geometry – Answers Card 1 Extension

308, 803, 333, 080 coda, tax, by, aye, back, awe, be

Card 2 Extension

Triangle Pentagon

Card 3 Extension

540 cm 516 cm

Card 4

2.4 kg, 3.1 kg and 2.9 kg 2.4 kg, 2.8 kg, 2.9 kg, 3.1 kg, 3.2 kg

Extension Card 5 Extension

2nd train; 24 minutes 2nd train; 25 minutes

Card 6 Extension

3 litres 2750 mL yellow and 1430 mL blue

Card 7 Extension

Giraffe by 9 cm Elephant by 13 cm

Card 8 Extension

15 18

Card 16 Extension

104 370

Card 23 Extension

8 cups 16 cups

Card 9 Extension

South Road Horizontal; parallel

Card 17 Extension

E A, B and E

Card 24 Extension

11 mm 52 mm

Card 10 Extension

30 g of sugar 25 g of sugar

Card 18 Extension

Australia 49 seconds

Card 25 Extension

1 hour and 30 minutes 10:45 a.m.

Card 11

Card 19

6 of the 20-cm bricks,or 8 of the 15-cm bricks 15-cm brick

Card 26

Extension

3 o’clock and 9 o’clock 1:30

A is a triangle; B is a hexagon A is a triangle; B is 9

Extension

9 grams

Card 13 Extension

B and D A, B and C

Extension

3 cases of apples

Extension

2-litre pot; 600 mL left 1350 mL

Card 14 Extension

Jill by 3 days Jill by 4 days

Card 21 Extension

Green Black car and white car

Card 28 Extension

3 kg 2 kg

Card 15 Extension

3 litres 5 times each

Card 22 Extension

Dudley two more right angles

© R. I .

C.Publ i cat i ons Extension Muffin Card 12 •f D by 5e grams orr e vi w pu r poses onl y• 4 bowling balls Card 20

Extension Card 27

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Measurement and geometry – Answers Card 29 Extension

Same 2 more symmetrical houses

Card 30 Extension

370 m 2120 m

© R. I .

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

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