teaching historically higher tier content to foundation
TRANSCRIPT
Teaching historically higher tier content to foundation tier
students
Christian Seager, Trinity High School
List of resources
1. Averages from grouped data – whodunit?
Data sheet and worksheet – use the grouped data to work out who committed the crime.
2. Vectors – whodunit?
Data sheet and worksheet – use the vectors to work out who committed the crime.
3. Expanding brackets
Worksheet – examples, practice questions, exam questions and checklist
4. Scatter graphs
Worksheet – examples, practice questions, exam questions and checklist
5. Ratio
Worksheet – examples, practice questions, exam questions and checklist
6. Stem and leaf diagrams
Worksheet – examples, practice questions, exam questions and checklist
7. Reverse percentages number grid
Worksheet – find the answers to the questions in the number grid
8. Standard form connect 4
Worksheet – tackle the standard form questions to connect four answers on the grid
9. Standard form follow me
Worksheet – use standard and ordinary form to complete the sentence
10. Trigonometry dominos
Worksheet – solve the trig problems to play dominos
11. Functional skills strategies and revision table mat
Problem-solving strategies for multi-step functional questions
12. Revision table mat or poster
Tips for effective revision
Christian has taught at his current school, Trinity High School for nine years. He is Head of
Mathematics after starting at Trinity as an NQT, and has helped Trinity rise from National
Challenge in 2007 to the most improved school in England in the January 2013 league tables.
Christian is supported by a fantastic team, including Melanie. Along with Melanie, Christian
has set up JustMaths, the fantastic support for fellow maths teachers, with loads of resources
available on www.justmaths.co.uk.
www.justmaths.co.uk ©JustMaths 2012
Now you need to work out where and when the crime was committed....
Who, where and when?
Who?
One of the following four people has committed a crime.
The criminal made 4 errors, the victim has made 0
errors and two suspects have made 1, 2 or 3 errors.
The ICT teacher said
- The modal class
of B is
160 < h ≤ 170
- The median of E is
18000 < S ≤ 20000
- The median of D is
4 < h ≤ 6
- The median of B is
140 < h ≤ 150
The music teacher
said:
- The modal class
and median of A
is 20 < t ≤ 30
- The modal class of F is
150 < h ≤ 160
- The median of E is
14000 < S ≤ 16000
- The modal class of B is
150 < h ≤ 160
The English teacher said:
- The modal class
and median of D
are the same
- The median of F is
150 < h ≤ 160
- The median of C is 37 to 39
- The median of E is
18000 < S ≤ 20000
The Maths teacher
said:
- The modal class
and median of B
are the same
- The median of F is
140 < h ≤ 150
- The modal class and median of
C are NOT the same
- The modal class of E is
50000 < S ≤ 100000
www.justmaths.co.uk ©JustMaths 2012
Where? The murder was committed at one of the locations below, but which one?
It happened where ALL the answers are true.
The maths classroom
The total number of girls is 30.
The total number of people in Table A is 40.
The total number of trainers is 4.
The dining hall
The total number of boys is 100.
The total hours using a PS3 is 720.
The total boys’ height is 14,900cm.
The gym
The total time to get to work is 1130 hours.
The total number of boys is 100.
The total salaries are £1,565,000.
The playing fields
The total girls’ height is 4430cm.
The total in table C is 20.
The total number of salaries is 7.
When? Find the day where all the estimates of the means are correct:
Monday If table A is 28.25 and table C is 38 (to 1 significant figure)
and table E is £17,388.89 (to 2 decimal places)
Tuesday If table B is 147.7 (to 1 decimal place) and table C is 40
(to 1significant figure) and table D is 6.1 (to 1 significant figure)
Wednesday If table A is 28.3 (to 1 decimal place) and table F is 200 (to 1 significant figure) and table D is 6.1 (to 1 decimal place)
Thursday If table C is 38.15, and table F is 100 (to 1 significant
figure) and table B is 147.7 (to 1 decimal place)
Friday If table F is 149 and table D is 6.1 (to 1 decimal place) and
table B is 150 (to 1 significant figure)
The Accusation
Who
Where
When
Time to get to work (t minutes) Time
Frequency 0 < t ≤ 10 3 10 < t ≤ 20
8 20 < t ≤ 30 11 30 < t ≤ 40 9 40 < t ≤ 50
9
TABLE A
Height of girls
Height
(h, cm(
Frequency
120 < h ≤ 130 3
130 < h ≤ 140 6
140 < h ≤ 150 7
150 < h ≤ 160 8
160 < h ≤ 170 6
Trainer shoe sizes
Shoe size Frequency 34 to 36 4 37 to 39
12 40 to 42 3 43 to 45 1
TABLE B TABLE C
Hours using a PS3
No of hours
(h, hours)
Frequency
0 < h ≤ 2 10
2 < h ≤ 4 15
4 < h ≤ 6 30
6 < h ≤ 8 35
8 < h ≤ 10 25
10 < h ≤ 12 5
Annual Salary
Salary (S, £) No of people 10000 < S ≤ 14000 32 14000 < S ≤ 16000 24 16000 < S ≤ 18000 16 18000 < S ≤ 20000 6 20000 < S ≤ 40000 9 40000 < S ≤ 50000 2
50000 < S ≤ 100000 1
Boys height
Height
(h, cm)
Frequency
120 < h ≤ 130 8
130 < h ≤ 140 16
140 < h ≤ 150 25
150 < h ≤ 160 30
160 < h ≤ 170 21
TABLE D
TABLE E TABLE F
©JustMaths 2012 www.justmaths.co.uk
www.justmaths.co.uk ©JustMaths 2014
Now you need to work out where and when the crime was committed....
Who, where and when?One of the following four people has committed a crime.
The criminal made 2 errors, the victim has made 0errors and the other two suspects have made 1 error.
a = b = c = d = e =
Victor said:
a + b =
c + d =
e = 3a
a + 2b =
The girls said:
a + c =
a + d =
5d =
2c + a =
The minions said:
d + e =
a + b =
a + 2b =
2d + c =
Gru said:
a + e =
d + b =
2e =
½ c =
www.justmaths.co.uk ©JustMaths 2014
Where and when?Use the questions on the accompanying sheet
The murder was committed at one of the locations below, but which one?It happened where the most mistakes have been made.
Gru’s Lab on Monday
Q1. AB = b – aQ2. AP = b - a
Q3. AF = (c – a)
Q4. FA = - b
Vector’s house onWednesday
Q1. BA = a – bQ2. PB = (b – a)
Q3. OF= a + c
Q4. EB = 2b
Miss Hattie’s Home forGirls on Saturday
Q1. CD = 2b – 2aQ2. BA = b - aQ3. OE = c + 2aQ4. AC = b – 2a
Bank of Evil onThursday
Q1. OC = 2aQ2. AB = a + bQ3. AC = c - aQ4. BD = a + b
The AccusationWho
Where &When
A and B are midpoints ofOD and OC respectively.
OB = bOA = a
©JustMaths 2014www.justmaths.co.uk
Q. 1.
A
C D
B
O Q. 2.
P is one third of the wayalong AB
OA = aOB = b
O
A
B
P
OA = AD = CB = BE = a
OC = AB = DE = c
F is one third of the way along AC
Q. 3.
ABCDEF is a regular hexagon
OA = a
OB = b
Q. 4.
O
A
BE
CD
F
O C
A B
D E
F
Now have a go yourself .. . .
How to . . .
Expanding Brackets
(a) Expand 3(2 + t)
(b) Expand 3x(2x + 5)
(c) Expand (m + 3)(m + 10)
(5)
Sorted it
a) 2(p + 3) b) 3(p - 3) c) 4(p + q)
d) 3(5 - p) e) 2(2x + y - 3) f) 5(3c + 1)
g) 4(x2 + 1) h) 3(x2 - 2) i) 3(n2 - 2n + 1)
NAILED IT
a) p(p + 2) b) q(q - 3) c) 2p(p + 5)
d) x(4 - x) e) x(y + z) f) d(3d - 4)
g) -2(x + 3) h) -3(2p + 2) i) -2d(d - 4)
MASTERED IT
a) (x + 2)(x + 3) b) (x + 3)(x + 4)
c) (x + 1) (x + 2) d) (y + 2)(y - 5)
e) (x - 2)(x + 3) f) (y + 1) (y - 2)
g) (x - 2)(x - 3) h) (x - 4)(x - 5)
i) (x + 2)2 j) (y + 1)(2y + 1)
k) (x - 1)(3x + 1) l) (2y + 3) (y + 4)
m) (3p + 2)(2p + 5) n) (x - y)(x - 2y)
www.justmaths.co.uk ©JustMaths 2013
Checklist
Ready to be marked ? Expand and Simplify (i) 2(x - 4) + 3(x + 2) (ii) x(x + 3) (iii) y(2y - 3) (iv) (x + 3)(x + 4) (v) (x - 3)(x + 9) (vi) (x - 3)(x - 7)
Answer checked
Working out shown
Keywords
Things to remember ...
What went well ...
Teacher comment ..
Exam Questions
Now have a go yourself .. . .
How to . . .
Scatter Graphs The scatter graph shows information about 10 apartments in a city.
The graph shows the distance from the city and the monthly rent of each apartment
www.justmaths.co.uk ©JustMaths 2013
The table shows the distance from the city centre and the rent of two other apartments
a) On the graph plot these two points.
(2)
Distance
km
Rent
£
2 250
3.2 180
b) Describe the relationship between the distance from the centre and the monthly rent.
(1)
An apartment is 2.8km from the city centre.
c) Find an estimate for the monthly rent for this apartment.
(2)
Every Saturday for 5 weeks in the Autumn the number of centime-tres of rainfall and the percentage of cloud cover were recorded by a group of students. The results are shown in the table:
a) On the graph, draw a scatter diagram of the results . (1)
b) Draw, by eye a line of best fit. (2)
c) Describe the relationship between the percentage of cloud cover and the amount of rain. (1)
d) Find an estimate for the percentage of cloud cover on a day with 0.6
cm of rainfall. (2)
Cloud cover %
Rainfall cm
55 0.48 10 0.24 60 0.52 85 0.84 5 0.10
Checklist
Ready to be marked ?
Answer checked
Points plotted
Line of best fit
Keywords
Things to remember ...
What went well ...
Teacher comment ..
Exam Question The scatter diagram shows the height, in cm, and the weight, in kg, for each of 20 members of a sports club.
a)Write down the height and weight of the heaviest of the 20 members of the sports club.
Weight ....................kg
Height ....................cm
(2)
b) Write down the type of correlation shown in the scatter diagram. (1)
c) Draw, by eye, a line of best fit on the scatter diagram. (1)
d) Estimate the weight of a person of height 155 cm. (2)
e) Is it possible to estimate the weight of a person with a height of 210 cm from the scatter diagram. You must give a reason (1)
Now have a go yourself .. . .
How to . . .
Ratio
5 schools sent some students to a conference. One of the schools sent boys and girls. This school sent 16 boys. The ratio of the number of boys it sent to the number of girls it sent was 1:2 The other 4 schools sent only girls. Each of the 5 schools sent the same number of students. Work out the total number of students sent to the conference by these 5 schools.
(4)
MUST - share the following in the ratio shown
a) £40 in the ratio 3:2 b) £35 in the ratio 4:1
c) £54 in the ratio 5:1 d) £35 in the ratio 4:3
e) £42 in the ratio 2:5 f) £65 in the ratio 2:3
SHOULD - share the following in the ratio shown
a) £30 in the ratio 2:2:1 b) £84 in the ratio 3:3:1
c) £990 in the ratio 7:2:2 d) £64 in the ratio 5:2:1
e) £240 in the ratio 5:3:2 f) £140 in the ratio 6:3:1
COULD
a) Mr A, Mr B and Mr C own 2, 3, and 6 parts of a busi-ness. They share the profit according to how many parts of the business they own. If Mr C gets £132 how much profit did the business make?
b) To make suet you need fat to flour in the ratio 1: 3. Jane has 180 g of flour. How much fat does she need to make the suet?
c) The sides of a triangle are in the ratio 2 : 4 : 5. The middle sized side is 28 cm.
a). Find the length of the other two sides.
b). Find the perimeter of the triangle.
www.justmaths.co.uk ©JustMaths 2013
Checklist
Ready to be marked ? Q1. Last year Kerry’s take home pay was £15 000 She spent 40% of her take home pay on rent. She used the rest of her take home pay for living expenses, clothes and entertainment in the ratio 3 : 1 : 2 How much did Kerry spend on entertainment last year?
Q2. Talil is going to make some concrete mix. He needs to mix cement, sand and gravel in the ratio 1 : 3 : 5 by weight. Talil wants to make 180 kg of concrete mix. He has:
15 kg of cement 85 kg of sand
100 kg of gravel Does Talil have enough cement, sand and gravel to make the concrete mix?
Answer checked
Working out shown
Keywords
Things to remember ...
What went well ...
Teacher comment ..
Exam Questions
Now have a go yourself .. . .
How to . . .
Stem and Leaf
Sixteen babies are born in a hospital.
Here are the weights of the babies in kilograms.
2.4 2.7 3.5 4.4 4.5 4.1 4.4 2.8
4.1 3.8 3.8 4.2 3.3 3.0 3.7 3.3
Show this information in an ordered stem and leaf diagram.
(3)
Q1. Here are the times, in minutes, taken to solve a puzzle.
5 10 15 12 8 7 20 35 24 15
20 33 15 24 10 8 10 20 16 10
In the space below, draw a stem and leaf diagram to show these times.
Find the median time to solve this puzzle.
Q2. Jim did a survey on the lengths of caterpillars.
Information about the lengths is given in the stem and leaf dia-gram.
a) Work out the median. ............ cm b) Work out the range. ............ cm c) Work out the mode. ............ cm d) Work out the inter-quartile range ............ cm
www.justmaths.co.uk ©JustMaths 2013
Key:
1 3 5 7 7
2 0 6 8 8 8 9
3 1 5 5 5 5 6 8 9
4 1 5
5 2
Key: 5│2 means 5.2cm
Checklist
Ready to be marked ? .The numbers below list the ages of the members of a tennis club.
71 39 40 16 57 12 63 34 41 45 65
27 16 59 40 60 14 22 48 43 38 52
35 23 25 52 36 38 26 31 27 17 16
a) Construct a stem and leaf diagram with these ages.
b) Use it to find the following:
How many members the club has.
The modal age of the members.
Their median age.
The range of their ages.
The fraction of members who are over 40.
(8)
Order correct
Key included
Keywords
Things to remember ...
What went well ...
Teacher comment ..
Exam Questions
www.justmaths.co.uk ©JustMaths 2014
esreveR segatnecreP (!)
Work out the answers to the questions then search for the answers in the grid
(Ignore any decimal points e.g. 42.7 becomes 427)
1. In a sale, all prices are reduced by 30%. The sale price of a jacket is £33.60
Work out the original price of the jacket.
2. The price of a new washing machine is £376 which includes Value Added Tax (VAT) at 17.5% Work out the cost of the washing machine before VAT was
added.
3. Employees at a firm get a pay increase of 4% After the pay increase, Mel earns £24,960 How much did Mel earn before the pay increase?
4. Top Shop is having a 20% off sale and I have treated myself to a new handbag
– it cost £40, how much was it before the sale?
0 9 3 1 7 2
2 2 1 8 5 0
5 7 4 7 0 9
5 3 0 0 0 7
1 3 2 6 0 2
2 1 9 3 2 0
3 5 8 7 4 9
www.justmaths.co.uk ©JustMaths 2014
5. A limited edition version of perfume contains 10% more than the normal bottle. The special bottle contains 88 ml. How much does the normal bottle contain?
6. The recent advert for Jaffa cakes makes the claim that the boxes are 24%
bigger. The new boxes contain 31 biscuits, how many did it have before?
7. I want to sell vegetable boxes at a farmers market - the vegetables will cost me £7.60. How much would I need to sell them for to get 15% profit?
8. Christian invests some money in a bank account. Interest is paid at a rate of 8% per annum. After 1 year, there is £291.60 in the bank account. How much
did Christian invest?
9. A new car drops in value by 30% in its first year. After a year, it is worth £8,400 what was the cost of the car?
10. Christian has bought some shares. The value of the shares fell by 4% since he
purchased them and they are now worth £5200. What was their original value?
11. Fize has just reduced his personal best for the 100 m by 25% to 12.9 seconds. What was his previous personal best?
THINK YOU’VE NAILED IT? .....
How can you check your answers?
1. In a class there are 9 people out on a school trip to the Museum of Maths. This
is 20% of the class.
o How many are there in the class when no one is off ill?
o How many are in the class today?
2. If 35% of an amount is £70 what is 100%?
3. On the 1st May the Museum of Maths increased it prices by 25% to £9 and visitors in May dropped by 8% to 55,476
o What was the price in April?
o How many visitors were there in April?
o Their costs haven’t changed but the museum made 30% profit in May.
How much profit did they make in May?
o How much profit did they make in April?
o Was it a good idea to raise the prices?
Write 47,500,000 in standard form.
Write 4.56 x 104 as
an ordinary number
Write 8.43 x 10-4 as
an ordinary number0.000803 4.56 x 10
41.6 x 10
-5 0.0000456 4.7 x 10-3
Write 5.6 x 10-4 as an
ordinary number
Write 16 x 106 in standard form
Write 5 x 107 as an ordinary number
Write 45,600 in standard form.
0.002047 45,600 1.6 x 108
4.56 x 105
Write 0.0047 in standard form
Write 50,000,000 in standard form.
Write 160 x 106 in standard form
Write 2.047 x 10-3 as
an ordinary number1.6 x 10
-49.87 x 10
-1 47,500,000 0.000843
Write 4.56 x 105 as
an ordinary number
Write 4.56 x 10-5 as
an ordinary number
Write 0.0023 in standard form
Write
0.0016x10-1 in standard form
50,000,000 4.75 x 107
8.03 x 10-4
1.6 x 107
Write
0.016x10-3 in standard form
Write 0.987 in standard form
Write 456,000 in standard form.
Write 4.75 x 107 as
an ordinary number2.3 x 10
-3 0.00056 5 x 107 456,000
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STANDARD FORM (1) - Connect 4
© JustMaths 2013
Answer GridQuestion Grid
Working in pairs – each person takes it in turns to choose a question from the question grid to answer. The correct solution will be found in the answer grid (if your solution is not in the grid, you need to reconsider your answer), and you can colour that box on the answer grid. To win, you need to connect four answers in a line (horizontally, vertically or
diagonally) on the answer grid.
... ever wondered why?
START 1.44 x 104 9.9 x 10-1 6.4 x 10-2 20.4 64000 990 17.6 320 203.6
T I R S N H Y I U H6.4 X 104 1.24 x 10 3.2 X 100 9.9 x102 3.56 x 101 3.2 X 103 3.2 X 10-2 6.4 x 103 324 0.036
3.6 x 10-2 144 1.44 x 10-2 1760 3.6 3.6 x 101 176 14.4 0.0124 2.036 x10-2
T D K S A U S R N A6.4 x 102 3.60 x 100 0.0324 0.0036 1.76 x 10-1 0.99 1.76 X 10-2 0.144 0.064 0.0124
0.02036 64 1.79 x 103 3.24 x 102 1.76 x 10 1.24 x10-2 0.176 3.6 x 10-3 3.24 x 10-2 3200
R B N T O I R Y E E6.4 x 101 3.2 X 102 1.76 X 103 1.44 x 102 6.4 x 10-2 2.036 x10-2 0.0144 17.6 1.24 x10-2 1.76 X 102
0.0176 640 0.032 1.44 x 10-1 6400 3.2 0.064 35.6 3.6 x 102 12.4
U E O H G S U L K N2.04 x 101 1790 36 0.02036 2.036 x102 360 1.44 x 101 1.76 x 101 (1.2 x 102)2 FINISH
www.justmaths.co.uk ©JustMaths 2012
© JustM
aths 2013
START
17 cm
31o
x
8.76 3.72 40.24
22.65 47.46 y
19 m
33o
31.01 18 cm
FIN
ISH
49.06
In triangle ABC
BAC = 90o
AB = 11 cm
AC = 13 cm
Find angle ACB
7 m ladder leans
against a house mak-
ing an angle of 63o
with the floor. How
far up the house does
the ladder reach?
17o
40.37 6.24
Find angle BCA
y
13
.8 c
m
28o
Find the area
x
15m
70.41
7
x
x
41o
29.39
A
C
B
21 cm
16
cm
6
11
22o
19 cm
14
m
x
28o
NOTE: the maths involved is
not always difficult. The problem is work-
ing out what is being asked, deciding what
maths you need to use and remembering to
explain your answer. Pro
ble
m-s
olvin
g
strate
gie
s f
or
MU
LTI—
STE
P
fu
nc
tio
nal
qu
es
tio
ns
Read the question
Extract the key information
Always look at diagrams
Decide what the question is
Underline the key bits
Sounds obvious I know!!
Pick the maths to use
Link your working
Allow for different maths skills
Now do the work...
Work must be organised
One sentence at the end
Re-read the question
Kalculations must be shown
Think of a rough estimate
Is your answer sensible?
Check your answer
Korrect units used?
The question will
probably include
aspects of several
different maths
topics Try to get the spelling
right! ... Oops!
/
REVISING
MATHS
Practising
Know what
topics to
focus on
To revise maths you need to DO maths!
Make sure you
have and USE a
recommended
revision guide
BUT do g
et
them
marke
d
using a
mark-
schem
e
Do a little bit
of “practice”
every day
Study with a friend - teach them a topic & vice versa
Make a
timetable
Ask for
help if
unsure
Wo
rk t
hro
ugh
past
pap
ers
Find a
quiet
worksp
ace
Its no good just ownin
g
a guide ... USE IT!
Take regular
breaks
Follow
@ReviseJustMaths Make a list and update it regularly
Know the formula you need to remember & what is in the paper
Use or make revision cards, a popplet or a prezi
Watch the tutorials or revision clips your teacher suggests
Google it! Work through past papers
/
REVISING
MATHS
Practising
Know what
topics to
focus on
To revise maths you need to DO maths!
Make sure you
have and USE a
recommended
revision guide
BUT do g
et
them
marke
d
using a
mark-
schem
e
Do a little bit
of “practice”
every day
Study with a friend - teach them a topic & vice versa
Make a
timetable
Ask for
help if
unsure
Wo
rk t
hro
ugh
past
pap
ers
Find a
quiet
worksp
ace
Its no good just ownin
g
a guide ... USE IT!
Take regular
breaks
Follow
@ReviseJustMaths Make a list and update it regularly
Know the formula you need to remember & what is in the paper
Use or make revision cards, a popplet or a prezi
Watch the tutorials or revision clips your teacher suggests
Google it! Work through past papers