Problem-Solving Strategies & Skills – Measurement & Geometry: Year 5

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Measurement and geometry

If Davey leaves for work at 7:30 a.m. and comes home © R. I .

C.Publ i cat i on s at 4:30 p.m., what are the •f orr evi ew pur poseso nl y •days and times of the classes he can attend during the week?

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Measurement and geometry

Davey enjoys spin class, boxfit and pump. If he attends every one of these classes, how many © R. I .

C.Publ i cat i ohours ns would Davey at the gym?

•f orr evi ew pur posesspend onl y• What is the latest time he would finish on any night?

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Measurement and geometry

Mrs Tyrell is making biscuits for her local community fundraiser.

She rolls out a sheet of dough that is 15 cm x 21 cm. The symmetrical © R. I .

C.Publ i cat i ons cookie cutter she is using is as •f orr evi ew pur posesonl y• pictured.

What area of dough remains after she cuts 4 cookies?

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Measurement and geometry

Mrs Tyrell is making biscuits for her local community fundraiser. She rolls out a sheet of dough that is 15 cm x 21 cm. The cookie cutter © R. I .

C.Publ i cat i ons she is using is as pictured.

•f orr evi ew pur posesonl y•

How many whole cookies can she cut out of the dough if she keeps rolling out the leftover bits of dough?

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Measurement and geometry

If the ferris wheel starts in the position shown, where © willRthe .

I .

C.Publ i cat i ons boys in positions B• and Hr end f or e vi ew pur posesonl y• up after five 180° turns?

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Measurement and geometry

The ferris wheel starts in the position shown. It makes 4 full turns in a clockwise direction before making 5 half-turns in. an ©R I .

C.Publ i cat i ons anti-clockwise direction.

•f orr evi ew pur posesonl y•

How many degrees in total has the ferris wheel turned and what position did the girl in G end up at?

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Measurement and geometry

It’s nearly Pippa’s birthday and she has spotted some presents wrapped up and hidden away in a cupboard. She can see one present ©four R. I .

C.Publ i cat i ons has one square face and triangles forming an apex, and thepur •f orr e vi ew posesonl y• other present has two pentagon faces and five rectangular faces.

What two 3-D shapes can she see?

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Measurement and geometry It’s nearly Pippa’s birthday and she has spotted some presents wrapped up and hidden away in a cupboard. She can see one present has two circles on either©end and it ubl R. I .

C.P i cat i ons is joined onto a shape that has two •f orr evi ew pur posesonl y• hexagon faces with six rectangle faces.

What two 3-D shapes form the present?

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Measurement and geometry

Milla, Nasir and Cate were comparing their new watches.

Milla’s watch read 1:45, Nasir’s © R. I .

C.Publ i cat i ons watch read 1:30 and Cate’s read 1:20.

•f orr evi ew pur posesonl y• Whose watch showed the hands of the clock at an acute angle?

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Measurement and geometry Milla, Nasir and Cate were comparing their new watches.

Milla’s watch read 1:45, Nasir’s watch read 1:30 and Cate’s read 1:20.

© R. I .

C.Publ i cat i ons One person’s watch the •showed f orr evi ew pur posesonl y• hands at an acute angle from the hour hand to the minute hand.

What was the exact angle, knowing that a circle has 360°?

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Measurement and geometry

Maeve is landscaping her rectangular garden. The whole space of the garden is 12.5 m long and 9.7 m wide. Within that area she wants ©vegetable R. I .

C.Publ i cat i ons to place four equal-sized patches that are 2.6 m 0.9 m •f oby rr e vi ew pur posesonl y• each. She wants the rest of the area grassed.

How much of the area will be grass?

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Measurement and geometry Maeve is landscaping her rectangular garden. The whole space of the garden is 12.5 m long and 9.75 m wide. Within that area she wants to place four equal-sized ©R .

I .

C. i cat i ons vegetable patches that are 2.6 m xPubl 0.9 m each. She wants the rest of pur •f or r e vi ew posesonl y• the area grassed, with the exception of a patio area that is 2.1 m x 3.2 m, which she wants paved.

How much area will be grass?

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Measurement and geometry How many interior angles within the shapes are obtuse, acute, reflex or right angles? Write the total for each.

© R. I .

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

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Measurement and geometry How many interior angles within the shapes are obtuse, acute, reflex or right angles? Write the total for each.

© R. I .

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

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Measurement and geometry

The golden emperor cicada is an insect that creates a singing sound through vibrations in its wings. It © R. I .

C.Publ i cat i ons creates 226 pulses per second.

•f orr evi ew pur posesonl y•

How many pulses would it create in 35 minutes?

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Measurement and geometry

The golden emperor cicada is an insect that creates a singing sound through vibrations in its© wings.

R. I .

CIt.Publ i cat i ons creates 226 pulses per second.

•f orr evi ew pur posesonl y•

How many pulses would it create in 1.5 hours?

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Measurement and geometry Liam, Kat, Esther and Penelope took their dogs to the vet and had them weighed.

Liam’s dog weighed 27 kg. Kat’s dog ©R .

I .

C.Publ i cat i ons was 2 the mass of Liam’s.

Esther’s 3 dog weighed 9300• gf more than Kat’s orr e vi ew pur posesonl y• dog and Penelope’s dog was 0.15 kg lighter than Esther’s dog.

Whose dog was the heaviest and by how many grams?

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Measurement and geometry Liam, Kat, Esther and Penelope took their dogs to the vet and had them weighed.

Liam’s dog weighed 23 kg. Esther’s dog weighed 10 030 grams more than Liam’s R. I .

C.P bl i cat i ons dog and Penelope’s dog© was 6.15 kgulighter than Esther’s dog. •f orr evi ew pur posesonl y• The combined mass of all dogs was 99 910 grams.

How many kilograms did Kat’s dog weigh?

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Measurement and geometry

Jerry has a fish tank containing 60 litres of water, but it is not quite full to capacity yet. Each day of the week Jerry adds one cup of water, © R. I .

C.Publ i cat i ons which holds 250 millilitres. Each •f or r evi ew pur posesonl y• week one cup of water evaporates.

How many litres of water are in the fish tank after 7 weeks?

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Measurement and geometry Jerry has a fish tank containing 60 litres of water, but it is not quite full to capacity yet. Each day of the week Jerry adds one cup of water, which holds 250 millilitres. Each 20. mL ©day R. I .

C Publ i cat i ons of water evaporates.

•f orr evi ew pur posesonl y•

If Jerry continues at this rate and the evaporation continues, how many weeks and days will it take to reach capacity of 71.5 litres?

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Measurement and geometry

Mitch wants to frame three pictures using lengths of wood. One picture is 11 cm x 22 cm, the other picture ©the R. I .

C.Publ i cat i ons is 13.5 cm x 22.5 cm and last picture is 16.5 cm x cm.

•28 f or r evi ew pur posesonl y• How many metres of wood does he need to purchase?

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Measurement and geometry Mitch wants to frame three pictures using lengths of wood. One picture is 11 cm x 22 cm, the other picture is 13.5 cm x 22.5 cm and the last picture is 16.5 cm x 28 cm.

© R. I .

C.Publ i cat i ons Lengths of wood are sold inv 1.6 mpur •f orr e i ew posesonl y• lengths.

How many lengths will he need to buy, and how many metres will be left over?

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Measurement and geometry Meg has been instructed to design a swimming pool with interior angles that include at least one reflex angle, no right angles, four acute angles and two obtuse angles.

Which pool did she design?

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

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Measurement and geometry Meg has been instructed to design a swimming pool with interior angles that include an equal number of obtuse, reflex and acute angles.

Which pool did she design?

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

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Measurement and geometry Calais

Wilbur is hiring a campervan to travel around France. He collects the van in Paris and then drives 144 km to Reims, before continuing on to Calais for another 256 km.

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C.Publ i cat i ons •f o rr evi ew pur posesonl y• If he drove from Paris to Reims at 90 km per hour, and Reims to Calais at 80 km per hour, how many hours and minutes has he been driving?

BELGIUM

Reims PARIS

Le Mans

Vouvray

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

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Measurement and geometry Wilbur is hiring a campervan to travel around France. He collects the van in Paris and then drives 144.2 km to Reims, before continuing on to Calais for another 272.9 km. The on to © journey R. I .

C.P ub l i cat i ons Le Mans is another 511.1 km, and onto •f orr evi ew pur posesonl y• Vouvray is another 56.2 km. The last leg back to Reims is 298.1 km.

Which town has he arrived at if he has travelled at 95 km per hour for 13.5 hrs?

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Measurement and geometry

Tex works at the local chicken shop. He roasts his chickens on a rotisserie placed over hot coals.

Each chicken slowly makes one full © R. I .

C.Publ i cat i ons rotation 150 times.

•f orr evi ew pur posesonl y•

How many degrees has each chicken rotated by the time it has finished cooking?

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Measurement and geometry Tex works at the local chicken shop. He roasts his chickens on a rotisserie placed over hot coals.

Each chicken slowly makes one full rotation 100 times, before he bastes it with his special sauce© every half R. I .

C .Publ i cat i ons rotation a further 20 times. He then •f orr evi ew pur posesonl y• sprinkles some herbs every quarter rotation 5 times.

How many degrees has each chicken rotated by the time it has finished cooking?

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Measurement and geometry

One small bucket holds 4 litres. One large bucket holds 6 litres. One trough holds 10 litres.

Pool 1 requires 2600 troughs of water to fill it.

Pool 2 requires 3100 © R. I .

C.Publ i cat i ons large buckets of water to •f orr evi ew pur posesonl y• fill it.

Pool 3 requires 3700 small buckets of water to fill it.

Which pool holds the most water?

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Measurement and geometry

One small bucket holds 5000 millilitres. One large bucket holds 6 litres. One trough holds 12 litres.

Pool 1 requires 2571 troughs of water to fill it.

Pool 2 requires 3101 © R. I .

C.Publ i cat i ons large buckets of water to •f orr evi ew pur posesonl y• fill it.

Pool 3 requires 2964 small buckets of water to fill it.

Write the volume of the pools, in litres, in ascending order.

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Measurement and geometry If this tile is tessellated as shown, what colours will be in the corners A, B and C?

© R. I .

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

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Measurement and geometry

Which letters correspond to the coloured angles in the © R. I .

C.Publ i cat i on stessellation shown?

•f orr evi ew pur posesDescribe onl y• the movement made to arrive at the location.

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Measurement and geometry Which gemstone has more obtuse angles in the facets shown?

Diamond

Emerald

© R. I .

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

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Measurement and geometry Which gemstone has more obtuse angles in the facets shown?

Amethyst

Diamond

Emerald

© R. I .

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

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Measurement and geometry

Montoya Island is 1264 km2 and Kuta Island has an area of 1319 km2.

© R. I .

C.Publ i cat i ons Which island is Aloha Island •f o rr evi ew pur posesonl y• closest to in approximate area if each square has an area of 100 km2?

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Measurement and geometry

Montoya Island is 1264 km2 and Kuta Island has an area of © R. I .

C.Publ i cat i ons 1319 km2.

•f orr evi ew pur posesonl y•

Which island is Aloha Island closest to in approximate area?

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Measurement and geometry Petra, Iva, Evie and Hans all think they have broken the world record for the longest distance travelled on rollerblades. Petra achieved a distance of 0.89 km, Iva came in © R. I .

C.Publ i cat i ons at 89 900 cm, Evie travelled for 892 000 mm and Hans went •f or r evfor i ew pur posesonl y• 891 metres.

Write the names in order of who travelled the furthest to shortest distance.

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Measurement and geometry Petra, Iva, Evie and Hans all think they have broken the world record of 3.55 kilometres for the longest relay on rollerblades. Petra achieved a distance of 0.89 km, Iva continued for 89 900 cm, Evie © R. I .

C.Publ i cat i ons travelled for 892 000 mm and Hans •f orr evi ew pur posesonl y• finished the final leg of the relay with 891 metres.

Did Petra, Iva, Evie and Hans beat the world record, and what was the difference in metres?

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Measurement and geometry

A baker sliced his freshly baked apple pie into three pieces. He cut the largest piece at an angle of 195° and topped it with cream. He sprinkled on ©cinnamon R. I .

C.Pu bl i cat i ons 1 the second part, which was of •f or r ev3i e wthe pur posesonl y• size of the cream portion.

At what angle did he cut the last piece?

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Measurement and geometry A baker sliced his freshly baked apple pie into four pieces. The first piece was 1 of the whole pie, and 8 the second piece was cut at an angle 27° larger than the ©first.

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C.Publ i cat i ons

•f orr evi ew pur posesonl y•

The third piece was 2 the size of 3 the angle of the second piece.

At what angle was the cut for the fourth piece?

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Measurement and geometry

Kane attends dance lessons from 15:45 until 17:00. Kim attends tennis practice from 15:30 until 16:45. Mabel goes to her karate class from 5:30 p.m. until 6:30 p.m. © R. I .

C .P ub l i cat i on s Angus has swimming lessons for 45 minutes, starting a half hour after Kane finishes class.

•f o rr evi edance w pur posesonl y• In which order should their parents pick them up after their classes?

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Measurement and geometry

Kane attends dance lessons from 16:30 for an hour and 15 minutes. Kim attends tennis practice for 75 minutes from 15:45. Mabel goes to her karate class for 60 minutes from © R. I .

Clessons .Publ i cat i ons 5:15 p.m. Angus has swimming for 50 minutes, starting half hour after Kim •af o rr e vi ew pu r posesonl y• finishes tennis class.

In which order should their parents pick them up after their classes?

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Measurement and geometry A helicopter is tracking a suspicious boat from above.

The boat starts at (A,1). Which coordinates did the boat arrive atat ifi it n made © R. I .

C.Publ i c o s the following movements?

•f orr evi ew pur posesonl y•

0° 3 spaces, 90° 2 spaces, 180° 1 space, 270° 1 space, 0° 3 spaces.

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Measurement and geometry A helicopter is tracking a suspicious boat from above.

The boat starts at (B,3) and makes the following movements.

2

© R. I .

C.Publ i c at i ons 90° 4 spaces, 0° 2 spaces, •f orr evi ew pur posesonl y•

270° 2 spaces, 180° 3 spaces.

Which direction and distance was the boat’s final move if it ends up at (A,2)?

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Measurement and geometry

Which two pieces join together to make a triangular pyramid (tetrahedron)?

© R. I .

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

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Measurement and geometry

There are eight 3-D shapes cut in two pieces. What are the shapes and which pieces join together to make them?

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Measurement and geometry

© R. I .

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

How many kilometres of rope is needed to secure the perimeter of this farmland if the farmer uses two rows of rope?

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Measurement and geometry

© R. I .

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

How many kilometres of rope is needed to secure the perimeter of this farmland if the farmer uses four rows of rope?

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Measurement and geometry

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• If the sum of angles in a rectangle is the same as the sum of angles in all quadrilaterals, what is the difference between angles A and B, without using a protractor?

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Measurement and geometry

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• The sum of angles in a rectangle is the same as the sum of angles in all quadrilaterals, but is double the sum of angles in all triangles.

What are the angles A, B and C, without using a protractor?

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Measurement and geometry

Harold went on a 6-week fitness blitz.

Each week he recorded his weight.

At the end of the 6 weeks Harold © R. I .

C.Publ i cat i ons weighed 93 kilograms.

•f orr evi ew pur posesonl y•

How much did Harold weigh at the end of week 3?

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Measurement and geometry

Harold went on a 6-week fitness blitz. Each week he recorded his weight. At the end of the weeks ©6R .

I .

C.Publ i cat i ons Harold weighed 93 kilograms.

•f orr evi ew pur posesonl y•

How much did Harold weigh to begin with?

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Measurement and geometry

The school is planning to add a rectangular playing field to the school grounds, so they will require additional fencing. First they need © R. I .

C .Publ i cat i ons to remove the existing portion of fencing that is no longer needed •f orr evi ewand pur posesonl y• use it for the new fence.

How many additional metres does the school need to buy?

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Measurement and geometry

A new school is being built and requires fencing for the surrounding area. There is also © R. I .

C.Publ i cat i ons a pool area which will require additional fencing.•f orr evi ew pur posesonl y• How many metres of fencing does the school need to buy?

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Measurement and geometry The military academy has a strict daily schedule. The troops rise at 06:00 and attend breakfast for half an hour, followed by weight training for 45 minutes. For the next 3 hours they ©R .

I .

C.P ubl i cat i ons attend boot camp training before it’s time to hit the books and attend •f o rr evi ewclasses pur posesonl y• for an hour and a half. Then everyone gathers for lunch.

What time did they stop for lunch, in 12 hour time?

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Measurement and geometry The military academy has a strict daily schedule. The troops rise at 06:00 and attend breakfast for half an hour, followed by weight training for 45 minutes. For the next 3 hours they attend boot camp training before it’s time © to R hit. the and I .

C.books Publ i c at i ons attend classes for an hour and a half. Then •f orr evi ew pur posesonl y• everyone gathers for lunch. The day ends at 17:15.

What time is it at the end of the day in 12 hour time, and how many hours are between lunch and the end of the day?

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Measurement and geometry Handy Harry left his measuring equipment at home, but he has some of the measurements of the area he needs to pave. What are angles A and B, and what is the total area of bricks he will need?

© R. I .

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

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Measurement and geometry Handy Harry left his measuring equipment at home, but he has some of the measurements of the area he needs to pave.

What is angle A, and what is the total area of bricks he will need?

© R. I .

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

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Measurement and geometry

If angle ABD is 85°, angle CBE is 105° and © R. I .

C.Publ i cat i onsangle DBE is 40°, what •f orr evi ew pur posesonl • without using a isyABC protractor?

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Measurement and geometry

If angle ABD is 85°, angle ABE is 135° and angle DBE © R. I .

C.Publ i cat i onis sdouble angle ABC, what •f orr evi ew pur poseso l y• CBD without using isnangle a protractor?

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

03 GREEN YR5 PS Measurement and geometry.indd 60

3/01/2017 10:51 am

Measurement and geometry – Answers Card 1

Extension

Mon 06:00, Mon 17:30, Tue 18:00, Thurs 06:00, Fri 17:30 8 hours; 19:00 or 7 p.m.

Card 2 Extension

261 cm2 23 cookies

Card 3

B ends up at F, H ends up at D 2340°; position C

Extension Card 4

Extension

Square based pyramid and pentagonal prism Cylinder and hexagonal prism

Card 5 Extension

Cate 80°

Card 6 Extension

111.89 m2 105.795 m2

Card 7

9 obtuse, 8 acute, 2 reflex, 12 right

Card 14 Extension

54 000° 40 050°

Card 20 Extension

100° 195°

Extension

9 obtuse, 15 acute, 3 reflex, 12 right

Card 15 Extension

Card 21

Card 8 Extension

474 600 1 220 400

Pool 1 14 820 L, 18 606 L, 30 852 L

Card 16

Card 9 Extension

Esther’s dog by 150 g 17 kg

Extension

A: red, B: blue, C: green light blue: A, dark blue: B, green: C, yellow: D, red: E. Reflected and rotated.

Kim, Kane, Angus, Mabel Kim, Kane, Mabel, Angus

Extension Card 22 Extension

(B,6) 270° 3 spaces

© R. I .

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

Card 10 Extension

70.5 L 7 weeks, 1 day

Card 11 Extension

2.27 m 2 lengths; 0.93 m left over

Card 17 Extension

Diamond Diamond

Card 12 Extension

B C

Card 18 Extension

Montoya Island Montoya Island

Card 13 Extension

4 hours, 48 minutes Reims

Card 19 Extension

Iva, Evie, Hans, Petra Yes; 22 m R.I.C. Publications® Prim-Ed Publishing

03 GREEN YR5 PS Measurement and geometry.indd 61

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Measurement and geometry – Answers Card 23 Extension

E and F A and E = rectangular prism/cuboid; B and F = pentagonal pyramid; C and N = triangular prism; D and I = tetrahedron/ triangular pyramid; G and H = squarebased pyramid; J and M = hexagonal pyramid; K and L = pentagonal prism

Card 24 Extension

32.2 km 90.4 km

Card 25 Extension

44° A=97°, B=34°, C=129°

Card 26 Extension

95 kg 96.6 kg

Card 27 Extension

1310 m 5400 m

Card 28 Extension

11.45 a.m.

5.15 p.m.; 5.5 hours

Card 29 Extension

A = 135°, B = 135°, 29.75 m2 A = 79°, 27.75 m2

Card 30 Extension

20° 60°

© R. I .

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

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

03 GREEN YR5 PS Measurement and geometry.indd 62

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