Name: measurement. Class: Date: 58 minutes. Time: 58 marks. Marks: Comments: Page 1 of 41

Transcription

1 measurement Name: Class: Date: Time: 58 minutes Marks: 58 marks Comments: Page 1 of 41

2 1 Write these lengths in order, starting with the shortest. 1 mark 2 Two of these sentences could be true. Tick ( ) the two sentences that could be true. Adam s pencil is 12 centimetres long. Leah is 12 metres tall. Jake s glass holds 12 litres of milk. Kate s younger sister weighs 12 kilograms. 1 mark Page 2 of 41

3 3 On a map, 1 cm represents 20 km. The distance between two cities is 250 km. On the map, what is the distance between the two cities? 2 marks 4 Circle the approximate measurement. The length of a banana is about 2 cm 20 cm 2 mm 2 m 20 m The mass of an apple is about 2 g 20 kg 200 kg 200 g 2 kg A glass of fruit juice is about 2 ml 2 l 20 ml 200 ml 20 l 2 marks Page 3 of 41

4 5 Liam has two different sizes of rectangle. He makes this pattern with them. Not actual size Calculate the lengths of A and B. 1 mark 1 mark Page 4 of 41

5 6 This fence has three posts, equally spaced. Each post is 15 centimetres wide. The length of the fence is 153 centimetres. Calculate the length of one gap between two posts. 2 marks Page 5 of 41

6 7 This design has one large square and two identical small squares. The design measures 36 centimetres by 28 centimetres. Calculate the length of a side of the large square. 2 marks Page 6 of 41

7 8 A stack of 20 identical boxes is 140 cm tall. Stefan takes three boxes off the top. How tall is the stack now? 2 marks Page 7 of 41

8 9 Freddie is half as tall as his mother. Freddie is one metre shorter than his father. Freddie s father is 180 centimetres tall. How many centimetres tall is Freddie s mother? 1 mark 10 Kirsty ran a race in one and a half minutes. Mina took 10 seconds longer. How many seconds did Mina take to run the race? 1 mark Page 8 of 41

9 Seb made a jump of two and a half metres. Kirsty s jump was 10 centimetres longer. How long was Kirsty s jump? 1 mark Page 9 of 41

10 11 Rebecca has rectangular tiles like this. Not to scale She makes a larger rectangle using 4 of the tiles. What is the area of the larger rectangle? 1 mark Page 10 of 41

11 12 Jacob cuts 4 metres of ribbon into three pieces. The length of the first piece is 1.28 metres. The length of the second piece is 1.65 metres. Work out the length of the third piece. 2 marks 13 A white square is painted in one corner of a grey square. Each side of the white square is half the length of a side of the grey square. Not actual size Page 11 of 41

12 What is the area of the grey section? 14 A packet contains 1.5 kilograms of guinea pig food. Remi feeds her guinea pig 30 grams of food each day. How many days does the packet of food last? 2 marks Page 12 of 41

13 15 Here are some shapes on a 1cm square grid. What is the perimeter of shape A? 1 mark Write the letter of the shape that has the smallest area. 1 mark Page 13 of 41

14 16 Here is a grid of regular hexagons. The shaded shape has an area of 3 hexagons and a perimeter of 14 cm. Draw another shape on the grid which has an area of 4 hexagons and a perimeter of 14 cm. 1 mark 17 The area of this square is 36 cm 2. Page 14 of 41

15 The square is cut into quarters to create 4 identical rectangles. What is the perimeter of one of the small rectangles? 2 marks Page 15 of 41

16 18 The cube and cuboid have equal volumes. Calculate the height of the cuboid. 2 marks Page 16 of 41

17 19 Emma makes a cuboid using 12 cubes. Write the letter of the cuboid that has a different volume from Emma s cuboid. 1 mark Page 17 of 41

18 20 Cube A and cuboid B have the same volume. Calculate the missing length on cuboid B. 2 marks Page 18 of 41

19 21 Megan wants to fill a bucket with water. A bucket holds 6 litres. A jug holds 500 millilitres. How many jugs of water does Megan need to fill an empty bucket? 2 marks 22 One jug contains water and the other jug contains oil. How much more oil is there than water? 1 mark Page 19 of 41

20 23 A bottle contains 568 millilitres of milk. Jack pours out half a litre. How much milk is left? 1 mark 24 Joe places some apples on a weighing scale. The pointer shows the mass of the apples. Page 20 of 41

21 He takes away one apple. The mass goes down by 120 grams. Draw the pointer in its new position on the scale below. 1 mark Page 21 of 41

22 25 Every 100 g of brown bread contains 6 g of fibre. A loaf of bread weighs 800 g and has 20 equal slices. How much fibre is there in one slice? 2 marks 26 Amir has three parcels. Parcels A and B together weigh the same as parcel C. Page 22 of 41

23 The three parcels weigh 800 grams altogether. Parcel A weighs 250 g. How much does parcel B weigh? 2 marks 27 Here is part of a centimetre scale, with two points marked. What is the distance between point A and point B? 1 mark Point C is twice as far from point A as it is from point B. On the scale above, mark one place where point C could be. 1 mark Page 23 of 41

24 28 This scale shows how much Chen weighs. How much does Chen weigh? 1 mark 29 Chen is cooking some pasta. The recipe says he needs 350 grams of pasta for 4 people. How many kilograms of pasta does he need for 12 people? 2 marks Page 24 of 41

25 30 (a) 1 kilogram of grapes costs 5.80 Megan buys 700 grams of grapes. How much does she pay? 1 mark (b) 1 kilogram of cheese costs Megan buys a piece of cheese costing 2.49 What is the mass of the cheese to the nearest 100 grams? 2 marks Page 25 of 41

26 31 One toffee apple needs: 1 stick, 100 g of sugar, 1 apple. Page 26 of 41

27 Children buy just enough sticks, sugar and apples to make 100 toffee apples. They sell all 100 toffee apples for 1 each. The profit goes to charity. Work out how much money goes to charity. 3 marks 32 Lin has five blocks which are all the same. She balances them on the scale with two weights. Page 27 of 41

28 Calculate the weight of one block. 2 marks 33 A cuboid has a square base. It is twice as tall as it is wide. Its volume is 250 cubic centimetres. Page 28 of 41

29 Calculate the width of the cuboid. 2 mark Page 29 of 41

30 Mark schemes 1 Lengths written in correct order as shown: Accept use of equivalent units, eg 2.5 cm Accept answers with missing or incorrect units. [1] 2 Two sentences ticked as shown: Adam s pencil is 12 centimetres long. Leah is 12 metres tall. Jake s glass holds 12 litres of milk. Kate s younger sister weights 12 kilograms. Both answers must be ticked for the award of the mark. Accept any other clear way of indicating the correct sentences, such as yes. [1] 3 Award TWO marks for the correct answer of 12.5 If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g OR 20 km is 1 cm 100 km is 5 cm 50 km is 2.5 cm 5 cm + 5 cm cm Answer need not be obtained for the award of ONE mark. Do not accept incorrect proportions in any step without evidence of the calculation performed. Up to 2m Page 30 of 41

31 4 Award TWO marks for all three values correct as shown: banana 2cm 2mm 2m 20m apple fruit juice 2g 20kg 200kg 2kg 2ml 2l 20ml 20l If the answer is incorrect, award ONE mark for two correct measurements. Accept alternative unambiguous indications, eg correct value filled in. Up to 2m 5 (a) 5 1 (b) 15 If the answer is incorrect, award the mark if the answers to (a) and (b) total 20 U1 6 Award TWO marks for the correct answer of 54 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 153 (3 15) = Answer need not be obtained for the award of ONE mark. Up to 2 (U1) Page 31 of 41

32 7 Award TWO marks for the correct answer of 20 If the answer is incorrect, award ONE mark for evidence of appropriate working, eg Small square = = 8 Large square = 28 8 = wrong answer Working must be carried through to reach an answer for the award of ONE mark. Up to 2 (U1) 8 Award TWO marks for the correct answer of 119. If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g = = OR = = Answer need not be obtained for the award of ONE mark. Up to 2m U1 [1] 10 (a) 100 seconds Answer must be in seconds. Do not accept 1 minute 40 seconds. 1 (b) 260 cm OR 2.6 m Accept 260 OR 2.6 OR 2 m 60 cm [1] Page 32 of 41

33 12 Award TWO marks for the correct answer of If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g = OR = OR = Accept for ONE mark an answer of 107 metres as evidence of an appropriate method. Answer need not be obtained for the award of ONE mark. Up to 2m 13 Award TWO marks for the correct answer of 108 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg = 144 of 144 OR (12 12) (6 6) OR (12 12) + (6 6) OR (6 6) 3 Answer need not be obtained for the award of ONE mark. Up to 2 (U1) Page 33 of 41

34 14 Award TWO marks for the correct answer of 50 If the answer is incorrect, award ONE mark for evidence of appropriate working using common units, eg = wrong answer Calculation must be performed for the award of ONE mark. Do not accept as evidence of appropriate working. Up to 2 15 (a) 14 1 (b) C Accept Shape drawn on grid as shown: Accept: shape in any position or orientation. Accept: slight inaccuracies in drawing provided the intention is clear. Accept: alternative unambiguous indications of the correct shape provided the intention is clear. Accept: mathematically correct answers involving fractions of a hexagon. Shape need not be shaded. [1] or 6(cm) and 1.5(cm) seen (the dimensions of the rectangle) 2 Page 34 of 41

35 OR Shows or implies a complete correct method, eg: = 8 (error) 8 4 = 2 2 (8 + 2) 6 6 = = 1.2 (error) Do not accept confusion between area and perimeter, ie: side of square is 36 4 = 9 (error) 2 ( ) or 1728 seen (the volume of the cube/cuboid) or Shows or implies a complete correct method, eg: = 1440 (error) 1440 = 16 6 height height = 1440 (16 6) = ! Measures See guidance 1 19 C Accept 18. [1] Page 35 of 41

36 20 Award TWO marks for the correct answer of 9 If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g = = OR Answer need not be obtained for the award of ONE mark. Up to 2m 21 Award TWO marks for the correct answer of 12 If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg 6 litres = 6000 ml 6000 ml 500 ml Answer need not be obtained for the award of ONE mark. Up to (ml) OR (l) [1] Do not accept incorrect units, e.g. 68 l OR ml. [1] Page 36 of 41

37 24 Arrow drawn to 640, as shown: Arrow should be closer to 640 than to 620 or 660 Accept any unambiguous indication of the correct point on the scale, including an arrow not originating from the centre of the dial. Accept answer given on upper diagram provided no answer is given on lower diagram. [1] 25 Award TWO marks for the correct answer of 2.4 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 6 8 = 48 (48 g fibre in one loaf) OR = 40 (one slice weighs 40 g) 6% of 40 Answer need not be obtained for the award of ONE mark. Up to 2 26 Award TWO marks for the correct answer of 150 If the answer is incorrect, award ONE mark for evidence of appropriate working, eg = = wrong answer Working must be carried through to reach an answer for the award of ONE mark. Up to 2 (U1) 27 (a) 4½ OR Page 37 of 41

38 (b) A point marked on the line at either 17cm OR 11cm, ie OR The mark need not touch the line provided the intention is clear. The marked point need not be labelled. U [1] 29 Award TWO marks for the correct answer of 1.05 kg. If the answer is incorrect, award ONE mark for evidence of appropriate working, eg: 12 4 = = = wrong answer Do not accept 1050 g Accept for ONE mark 10.5 or 105 as evidence of appropriate working. Working must be carried through to reach an answer for the award of ONE mark. Up to 2m 30 (a) 4.06! Money See guidance 1 Page 38 of 41

39 (b) 200 or! Measures See guidance 2 Gives an answer of 180 or 184 or 184.4( ) OR Shows or implies a complete correct method, eg: = = = = 200! Inconsistent units Within an otherwise correct method, condone eg, for 1 mark accept: ( ) = 1.35(p) ( ) (p) ( ) = ( ) (p) ( ) [3] Page 39 of 41

40 31 Award THREE marks for the correct answer of Award TWO marks for a complete correct method with one arithmetic error, eg Sticks Sugar 9.99 (error) Apples Total OR Profit If the answer is incorrect, award TWO marks for evidence of a correct total for all the ingredients, eg Sticks Sugar 9.90 Apples Total OR Award ONE mark for sight of and 9.90 Up to 3 [3] 32 Award TWO marks for the correct answer of 60 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg = Answer need not be obtained for the award of ONE mark. Up to 2 (U1) Page 40 of 41

41 33 Award TWO marks for the correct answer of 5 cm If the answer is incorrect award ONE mark for evidence of an appropriate method, eg 2n n n = 250 so n n n = 125 The calculation need not be completed for the award of the mark, but n n n = 125 OR n = 125 must be reached. 3 Up to 2 Page 41 of 41