Half-Term Test 1 Pupil Book 3(Chapters 1, 2, 3) Mark Scheme

Half-Term Test 1 Pupil Book 3 Mark Scheme1

Half-Term Test 1 Pupil Book 3(Chapters 1, 2, 3) Mark Scheme

Question / Answer / Mark / Comment / Objective / Reference to Pupil Book 3
1
(a)
(b) / 5
0.5 / 1
1 / Express simple functions in words, then using symbols; represent them in mappings / Exercise 1D
2 / 37
260
10
195 / 1
1
1
1 / Classify and visualise properties and patterns; generalise in simple cases by working logically; draw simple conclusions and explain reasoning / Exercise 2F
3 / A: 4, 6, 4
B: 6, 12, 8 / 2 / Deduct 1 for each error / Use 2-D representations to visualise 3-D shapes and deduce some of their properties / Exercise 3C
4
(a)
(b)
(c)
(d) / 0, +6, –7
–2, +2
+9
–7 / 1
1
1
1 / Understand negative numbers as positions on a number line; order, add and subtract integers in context / Exercise 2C
5
(a)
(b)
(c) / 646.8
646800
6.468 / 1
1
1 / Classify and visualise properties and patterns; generalise in simple cases by working logically; draw simple conclusions and explain reasoning / Exercise 2F
6
(a)
(b) / x – 2
6, 15, 9 / 1
2 / Award 1 mark for any two correct / Use letter symbols to represent unknown numbers or variables / Exercise 1E
7
(a)
(b)
(c)
(d) / 4
20
48
24 / 1
1
1
2 / Award 1 mark if attempt is made to divide 99 by 4 / Generate sequences from patterns or practical contexts and describe the general term in simple cases / Exercise 1C
8
(a)
(b)
(c) / Check cuboid is drawn correctly (no horizontal lines)
8 cm3
28 cm2 / 2
1
2 / Deduct 1 mark for any incorrect dimension
Correct answer must include correct units
Award 1 mark if 8 + 4 + 2 is seen in working / Use 2-D representations to visualise 3-D shapes and deduce some of their properties; calculate the surface area of cubes and cuboids; know and use the formula for the volume of a cuboid / Exercise 3C, 3D
9 / –12, 20
6, –10 / 2 / Award 1 mark for any two correct / Understand negative numbers as positions on a number line; order, add and subtract integers in context / Exercise 2C
10 / 17, 21
add 4
8, –1 / 1
1
1 / Both correct for 1 mark
Both correct for 1 mark / Describe integer sequences; generate terms of a simple sequence, given a rule (for example, finding a term from the previous term, finding a term given its position in the sequence) / Exercise 1A, 1B
11 / 3.4 m, 350 cm, 3700 mm, 0.036 km / 2 / Award 1 mark if attempt has been made to change to same units / Compare and order decimals in different contexts; know that when comparing measurements, the units must be the same / Exercise 2B
12
(a)
(b) / 31.8(18...)
3.9(2857..) / 1
2 / Allow rounded or truncated
Allow rounded or truncated
Award 1 mark if 55 or 2.2 × 25 is seen in working / Express simple functions in words, then using symbols; represent them in mappings / Exercise 1D
13
(a)
(b) / 9 cm
1 and 36 or
2 and 18 or
3 and 12 in either order / 1
1 / Know and use the formula for the area of a rectangle; calculate the perimeter and area of shapes made from rectangles / Exercise 3A
14 / 2.25 m / 2 / Award 1 mark if correct method seen or if 7.8 m is seen / Use efficient written methods to add and subtract whole numbers and decimals with up to two places; extend to multiplying decimals with one or two places by single-digit whole numbers / Exercise 2E
15 / 4.44 cm2 / 3 / Award 1 mark if either 2.28 or 2.88 is seen; award 1 mark if 2.16 or 1.56 is seen; award 1 mark for units / Know and use the formula for the area of a rectangle; calculate the perimeter and area of shapes made from rectangles / Exercise 3A
16
(a)
(b) / 3n + 2
4n + 1 / 1
1 / Generate sequences from patterns or practical contexts and describe the general term in simple cases / Exercise 1C
17
(a)
(b) / 3.36 m2
/ 1
2 / Award 1 mark if 0.84 ÷ 4.2 is seen / Calculate the perimeter and area of shapes made from rectangles / Exercise 3A

Mark Boundaries

Level 4b0–12

Level 4a13–18

Level 5c19–24

Level 5b25–30

Level 5a31–37

Level 6c38–43

Level 6b44–50

Investigation Answers/Suggestions

This investigation covers the following skills:

Creative thinkers – ask questions to extend their thinking
Reflective learners – evaluate experiences and learning to inform future progress

Students may try out different pairs of 2-digit numbers, for example, 24 + 31, until they find that either 42 + 31 or 41 + 32 make the biggest total of 73. Some students may be able to deduce that the higher digits must be used as the tens digits.

By similar reasoning, students should then find that 24 + 13 or 23 + 14 make the smallest total of 37.

The difference is 36.

Repeating this for the digits 2, 3, 4 and 5 gives 52 + 43 = 95 and 25 + 34 = 59. The difference between the totals is again 36.

This can be repeated for any four consecutive digits (e.g. 5, 6, 7, 8) with the same result.

The investigation could be extended using digits 1, 2, 3, 4, 5, 6, for example. Students may be able to deduce that the two highest digits must be used as the hundreds digits and the two lowest digits as the units.