Download Maths Homework Project Y7: Number – RED/BLUE PATHWAY

Maths Homework Project Y7: Number – RED/BLUE
PATHWAY
Name ……………………….….. Tutor ………..
Teaching Group/Class ……. .
Class Teacher ………….
Date set: 9th May Hand it in on: 16th May
Information for Students: Complete all tasks in the order that they are set.
Information for Parents/Guardians: Ways in which you can support your child.
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Helping students to access the internet and Moodle.
Checking that students are progressing through the tasks and understand the
evidence that they are reading.
Read the work that your child has produced and discuss with them how they
have arrived at their conclusions.
Section 2 – Multiples and Factors
A factor is a number which divides EXACTLY into another number.
A multiple of a number is a number which is in the times table of that number.
Example 1
The factors of 12 are 1, 2, 3, 4, 6, 12.
Notice that factors always come in pairs, like 1 and 12, 2 and 6, 3 and 4.
Example 2
Multiples of 6 are 6, 12, 18, 24, 30, … and so on.
Notice that multiples go on forever.
A factor is the opposite of a multiple, for example, a factor of 15 is 5 and a multiple of 5 is
15.
Questions
Answer the following:
1) Find all the factors of the
following:
a) 4
2) Find the first 5 multiples (including
itself) of the following:
a) 7
b) 6
b) 9
c) 14
c) 13
d) 18
d) 22
e) 24
e) 31
f) 32
f) 38
g) 54
g) 64
h) 60
h) 90
i) 144
i) 100
Notice that some numbers have one of the factors the same and some numbers have one of
the multiples the same. There may be more than one the same even.
Highest Common Factor (HCF) and Lowest Common Multiple
The highest common factor (HCF) is the largest factor of two numbers
The lowest common multiple (LCM) is the smallest multiple of two numbers
Example
The highest common factor for 12 and 18 is 6, since the factors of 12 are 1, 2, 3, 4, 6, 12 and
the factors of 18 are 1, 2, 3, 6, 9, 18. So 6 is the HIGHEST factor in both.
Example
The lowest common multiple for 12 and 18 is 36, since the first few multiples of 12 are 12,
24, 36, 48, … and the first few multiples of 18 are 18, 36, 54, … so 36 is the LOWEST
multiple in both.
Questions
Answer the following questions:
1) Find the HCF for:
a) 6 and 12
2) Find the LCM for:
a) 3 and 5
b) 4 and 18
b) 6 and 12
c) 12 and 24
c) 3 and 4
d) 36 and 15
d) 9 and 12
e) 5 and 15
e) 5 and 12
f) 14 and 15
f) 2 and 3
g) 8 and 12
g) 7 and 11
h) 10 and 25
h) 6 and 8
Section 3 – Rounding
To the nearest 10, 100 and 1000
A. Round the following numbers to the nearest 10
1. 13
2. 23
3. 18
4. 98
5. 134
6. 192
7. 372
8. 1243
B. Round the following numbers to the nearest 100
1. 140
2. 260
3. 180
4. 345
5. 352
6. 985
7. 1050
8. 6929
C. Round the following numbers to the nearest 1000
1. 2300
2. 1978
3. 4368
4. 6500
5. 9500
6. 13483
7. 49268
8. 123436
To the nearest decimal place
D. Round the following numbers to 1 decimal place
1. 4.93
2. 5.03
3. 2.68
4. 7.55
5. 3.44
6. 12.09
7. 18.89
8. 44.347
E. Round the following numbers to 2 decimal places
1. 0.273
2. 1.595
3. 6.473
4. 2.571
5. 8.995
6. 5.721
7. 0.425
8. 44.5564
Significant Figures
1. The number 1628 has 4 significant figures.
(a)
Round it to 3 sig. Figs
(b)
Round it to 2 sig. Figs.
2. Round the following numbers to 3 sig. figs :(a)
4162
(b) 5077
(c) 9125
(e)
29849
(f)
17651
(g) 123 854
3. Round the following to 2 sig. figs :(a)
578
(b) 964
(c) 2365
(d) 18 370
(h) 37 996
(d) 1722
4. The crowd at a World Cup match was 92 847. Round this figure to :
(a)
4 sig. figs
(b) 3 sig. figs
(c) 2 sig. figs (d) 1 sig. fig
5. To find an approximate answer to 379 x 2126, we could round each
number to 1 sig. fig : 379 x 2126
≈ 400 x 2000 = 800 000 (approximate)
By rounding each number to 1 sig. fig, find an approximate answer to :(a)
187 x 196 (b) 315 x 409
(c) 4085 x 394
(d)
5998 ÷ 19
(e) 38 651 ÷ 211 (f) 7686 ÷ 2194
6. Round each of the following to 2 sig. figs :(a)
0.137
(b) 0.896
(c) 0.05771
(d) 0.006031
7. Round each of the following to 1 sig. fig :(a)
0.0781
(b) 0.93265
(c) 0.00473
(d) 0.00097
Section 4 – Multiplying and Dividing
Answer each of the following multiplications
1. 54 x 10 =
7. 735 x 1000 =
2. 78 x 10 =
8. 3547 x 1000 =
3. 543 x 10 =
9. 94 x 1000 =
4. 527 x 100 =
10. 2.5 x 10 =
5. 354 x 100 =
11. 3.35 x 1000 =
6. 87 x 100 =
12. 465.7 x 100 =
Answer each of the following divisions
1. 540 ÷ 10 =
7. 2000 ÷ 1000 =
2. 680 ÷ 10 =
8. 45000 ÷ 1000 =
3. 54680 ÷ 10 =
9. 876000 ÷ 1000 =
4. 8600 ÷ 100 =
10. 687 ÷ 10 =
5. 4500 ÷ 100 =
11. 4536 ÷ 100 =
6. 987800 ÷ 100 =
12. 637468 ÷ 1000 =
Use the column method to answer these questions
Fill in the answers to each of these divisions
Multiplication and Division Problems
1
2
3
4
Section 5 – Prime Numbers and Prime Factors
A prime number is a number which has two factors; one and itself.
1) Colour number 1, because 1 only has one factor.
2) Number 2 is a prime, so we can keep it, but we need to colour all the
multiples of 2 (i.e. even numbers).
3) Number 3 is also a prime, so again we keep it and colour all the multiples of
3.
4) The next number left is 5 (because four has been crossed off), so we keep it
and colour all the multiples of this number.
5) The final number left in the first row is number 7 (it’s prime so keep it), so
colour all the multiples of 7.
6) You have finished. All of the "surviving" numbers which you haven’t
coloured on your grid are prime numbers.
Prime Factor Decomposition
4)
1)
3
Product of prime factors =
………2 x 2 x 3 = 12
Product of prime factors =
…………………………….
5)
2)
Product of prime factors =
…………………………….
Product of prime factors =
…………………………….
3)
6)
Product of prime factors =
…………………………….
Product of prime factors =
…………………………….
Draw a Factor Tree to find the prime factors of:
a) 15
b) 20
c) 24
d) 28
f) 40
g) 80
Prime factors, HCF and LCM Problems
1
Tom, Sam and Matt are counting drum beats.
Tom hits a snare drum every 2 beats.
Sam hits a kettle drum every 5 beats.
Matt hits a bass drum every 8 beats.
Tom, Sam and Matt start by hitting their drums at the same time.
How many beats is it before Tom, Sam and Matt next hit their drums at the
same time?
..................................................................................................................................
..................................................................................................................................
Answer .............................................................. beats
2
Polly Parrot squawks every 12 seconds.
Mr Toad croaks every 21 seconds.
They both make a noise at the same time.
After how many seconds will they next make a noise at the same time?
……………………………………………………………………………………………...
……………………………………………………………………………………………...
Answer …………………………………………… seconds
3
(a)
24 can be written as 24 = 2a × 3
What is the value of a?
........................................................................................................................
Answer a = ...................
(b) A box measues 24 cm by 18 cm by 15 cm.
The box is to be filled with cubes of equal size.
What is the length of the side of the largest cube that could be used to fill
the box?
........................................................................................................................
........................................................................................................................
Answer .................................................... cm
Section 6 – Square, Cubes and Indices
I.
Square Numbers
A square number is a number that is multiplied by itself → 12 = 1× 1 = 1 ; 22 = 2 × 2 = 4 ; etc…..
We call them square numbers because of these numbers can be rearranged to form square
figures.
Shade in all the square numbers on the grid.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
II.
Cube Numbers
A cube number is a number that is multiplied by itself and then multiplied by itself again
→ 13 = 1× 1 × 1 = 1 ; 23 = 2 × 2 × 2 = 8 ; 33 = 3 × 3 × 3 = 27 etc…
Shade in all the square numbers on the grid.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
III.
Square roots
Definition:
The square root of a number is a number which multiplied by itself, gives you the
original number.
Its symbol is called a radical and looks like this: √
eg.
√100 =
√16 =
√81 =
√9 =
√64 =
√4 =
√49 =
√1 =
√36 =
√10 =
√25 =
√2 =
IV. Cube roots
Definition:
The cube root of a number is a number which multiplied by itself three times, gives
you the original number.
3
Its symbol is called a radical and looks like this: √
Eg.
3
√1000 =
3
3
√729 =
3
3
√512 =
3
3
√343 =
3
3
√216 =
3
3
3
√125 =
√64 =
√27 =
√8 =
√1 =
√100 =
√81 =
Index Laws
Multiplication
1.
2.
3.
4.
5.
27 x 25 =
95 x 93 =
a7 x a-3 =
b-8 x b4 =
2a3 x 7a4 =
6. 3s8 x 9s2 =
7. 6n5 x 8n10 =
8. 7h2 x -3h4 =
9. -12h-7 x -2h9 =
10. 8h3 x 4h-5 =
Division
1. 27 ÷ 25 =
7. 70a13 ÷ 7a4 =
2. 95 ÷ 93 =
8. 27s8 ÷ 3s2 =
3. a7 ÷ a-3 =
9. 6n5 ÷ 8n10 =
4. b-8 ÷ b4 =
5.
6.
𝑑2
𝑑3
𝑗 14
𝑗9
=
10.
11.
2𝑗 10
8𝑗 9
3𝑡 7
18𝑡 4
=
=
=
Powers
1. (𝑥 2 )4 =
6. (𝑟 6 )10 =
2. (𝑓 6 )7 =
7. (3𝑐 5 )2 =
3. (𝑔9 )−2 =
8. (2𝑎4 )5 =
4. (𝑡 −5 )−5 =
9. (6𝑏 9 )2 =
5. (198 )0.5 =
10. (2𝑥 −6 )3 =
Section 7 – Written Task
There is a famous mathematical sequence called the ‘Fibonacci Sequence’. Your task
is to use the internet to research the Fibonacci Sequence and write about your
findings. Ensure to answer the following questions.
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What is the Fibonacci Sequence?
What are the first 12 terms of the Fibonacci Sequence?
How does the Fibonacci Sequence relate to nature?
What is the ‘Golden Spiral’?
Who invented the Fibonacci Sequence?
Can you find any fun facts about the Fibonacci Sequence?
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STEP
1
2
3
4
5
6
7
8
Teacher feedback:
P
E
N
Whole School Literacy- Assessing Extended Writing
STEP 1
STEP 2
STEP 3
STEP 4
STEP 5
STEP 6
STEP 7
STEP 8
Students can
- Form and write basic words
Students can
- Write words of one or more syllable
- Spell simple words correctly
- Use a full stop at the end of a sentence
Students can
- Spell words with an –ed or –ing ending
- Write in simple sentences
- Use some interesting words
- Organise ideas into a sensible order
Students can
- Spell common words with general accuracy
- Organise ideas into simple paragraphs
- Write simple and compound sentences
- Use a suitable vocabulary for a given purpose
Students can
- Use common and complex words with general accuracy
- Join paragraphs together with a connective word or phrase
- Use a range of punctuation and sentence types
- Vary vocabulary for effect
Students can
- Spell complex words with a high degree of accuracy
- Write and connect a variety of paragraphs with clear cohesion
- Use a full range of punctuation including apostrophes, colons and semi colons
- Use imaginative and attention grabbing vocabulary
Students can
- Spell all words, including uncommon and ambitious words, with a high degree of
accuracy
- Use a full range of punctuation with assurance and control
- Connect a range of paragraphs with assurance to create a well-controlled text
- Use a complete range of vocabulary, including technical vocabulary, to create an
intended effect
Students can
- Use a full range of punctuation with maturity and style, completing written tasks with
exceptional technical accuracy
- Ensure extended texts are structured with style and fluency, completing written tasks
that are highly engaging
- Use an excellent range of vocabulary with flair and maturity
Student Reflection
Q1. What skills or knowledge do you now have because you have completed this
homework tasks?
Q2. How could you do this type of work better in the future?
Q3. What resources did you use to complete these tasks?
Q4. Can you think of any better resources you would like to use in the future?
Q5. Which parts of this homework did you find hardest?
How were you resilient in completing the hardest task?
Parent Comment
Parent Signature …………………………………………..
Teacher Comment
Overall Effort Grade = E1
E2 E3 E4 E5