p7 numeracy remote learning pack term 3 week 7...arsenal watford 1-0 chelsea bolton wanderers 2-2...
TRANSCRIPT
P DUNBAR
P7 NUMERACY REMOTE LEARNING PACK
TERM 3 WEEK 7
Numeracy Remote Learning Overview WEEK 15th June
Learning
Intention
Pupil
Tasks
Teaching
Resources
Lesson
1
Using
Timetables
a) Train timetable sheet
(basic level)
b) Train timetable/London
Eye (middle level)
c) Train timetable (higher
level)
d) Extension Activity:
Video link – using timetables.
https://corbettmathsprimary.com/2018/07/21/timetables-video/
Lesson
2
Understand
probability in
terms of
outcomes of
real events.
a) (higher level)
b) (middle level)
c) (basic level)
d) Extension
Activity:online wheel
spinner
BBC- bitesize web page explaining probability.
https://www.bbc.co.uk/bitesize/topics/zx9k7ty/articles/zqpxmnb
Link to extension activity.
https://pickrandom.com/random-wheel/
Lesson
3
Understand
probability in
terms of
outcomes of
real events
a. (higher level)
b. (middle level)
c. (basic level)
d. Extension Activity:
online wheel spinner
Extension activity link. https://pickrandom.com/random-wheel/
Lesson
4 & 5
Investigate
probability
a) List of investigations
(higher/middle level)
b) Guided investigation
sheet (basic level)
c) Football league
investigation Extension
Activity:
EXPLANATION NOTES:
This lesson builds on using timelines to solve
duration problems. This is focused on timetables
which is a useful life skill. Use the links in the
contents page to help explain how to read
timetables and calculate the durations. Knowing
the language and style of timetables is a skill in
itself.
H M B
B
Ramsgate 9.55 10.40 11.15 11.55
Canterbury West 10.30 11.15 11.50 12.30
Ashford Int 10.55 11.40 12.15 12.55
St Pancras Int 11.35 - 12.55 13.35
Waterloo 11.50 12.05 13.10 13.50
1. How long does the first train from Ramsgate take to travel to Waterloo?
2. How much later does the second train from Ramsgate leave than the first?
3. If I catch the 10.40 train from Ramsgate, how many stops are there until I reach Waterloo?
4. How many trains pass through Canterbury West between 11.00 and 12.00?
5. I arrive at Ashford Int at 12.00. I want to travel to Waterloo. I catch the next train. What
time will I arrive at Waterloo?
6. I want to be in Waterloo by 13.00. What is the time of the latest train I can take from
Canterbury West?
7. I want to go to Waterloo. If it faster to catch the 10.30 train from Canterbury West or the
11.15 train from Canterbury West?
Opening Times for the London Eye
Monday Closed
Tuesday to Friday 10am to 7.30pm
Saturday 8.15 am to 9.00pm
Sunday 11am to 4.45pm
8. How many hours is the London Eye open on Wednesdays?
9. If I arrived at the London Eye at 6.15 on a Thursday, how long have I got before it closes?
10. Which day of the week is the London Eye open the longest?
11. I get the train to London on Sunday. My train arrives at the station at 9.15. How long have I
got to wait before the London Eye opens?
12. Which day has the latest closing time?
M M
Here is part of a train timetable
Ramsgate 10.05 10.40 11.15 11.55 12.05 12.20 12.30
Canterbury
West 10.40 11.15 11.50 12.30 - 12.55 -
Ashford Int 11.05 11.40 12.15 12.55 13.05 13.20 13.30
St Pancras Int 11.40 - 12.55 13.35 - 14.00 -
Waterloo 12.10 12.55 13.10 13.50 14.00 14.15 14.25
1. How long does the first train from Ramsgate take to travel to Waterloo?
2. How much later does the second train from Ramsgate leave than the first?
3. If I catch the 10.40 train from Ramsgate, how many stops are there until I reach Waterloo?
4. How many trains pass through Ashford Int between 11.30 and 13.00?
5. I arrive at Ashford Int at 12.00. I want to travel to Waterloo. I catch the next train. What
time will I arrive at Waterloo?
6. I want to be in Waterloo by twenty past two. What is the time of the latest train I can take
from Canterbury West?
7. I want to go to Waterloo. If it faster to catch the 10.40 train from Canterbury West or the
11.15 train from Canterbury West?
:
H
EXTENSION
H H
ANSWERS (higher level extension)
EXPLANATION NOTES:
The sheets for the lessons 2 & 3 are based on probability. The key to probability is
to place the outcome somewhere on the probability line. (see below) the probability
lines can be labelled with statements in the case of ‘life events’ or with fractions,
decimals or percentages which are all different types of fraction. Some of the links
will provide further detail. P7 have done probability earlier in the year. This recap
builds upon previous skills and leads in well to the investigations in lesson 4 & 5.
These investigations are varied in outcome and show pupils probability is not always
exact maths. We have all rolled 2 sixes in a row and the probability states we should
not. Key to this is that every throw the probability goes back to 1/6.
REMEMBER : look for the fraction + place the fraction on the probability line.
Read the thought bubble on the next page to revise some of the language of
probability. Use the links to the BBC bitesize website and have a go at some of the
quizzes. Read the information to help revise the way probability works.
Frequency- how often an outcome occurs
Outcome- what happens/the result
Predict- to try to guess using knowledge and
facts what will happen
Likelihood- what are the chances of
something happening
SYNONMS FOR PROBABILITY: chance.
likelihood. odds. possibility. prospect. The ‘mode’ of the result (outcome) that
appears most often (frequent)
M
A: answers may vary ( valid arguments accepted)
1. unlikely 2. Unlikely 3. Even 4. Likely
5. unlikely 6. Varies 7. Impossible/unlikely
8. unlikely
H
Write out the events and write one of the words from the
scale of probability below that you think is the best word to
describe the chances of the event really happening.
B
ANSWERS
EXPLANATION NOTES:
The sheets for the next 2 lessons are based on probability. The
key to probability is to place the outcome somewhere on the
probability line. (see below) the probability lines can be labelled
with statements in the case of ‘life events’ or with fractions,
decimals or percentages which are all different types of fraction.
Some of the links will provide further detail. P7 have done
probability earlier in the year. This recap builds upon previous
skills and leads in well to the investigations in lesson 4 & 5. These
investigations are varied in outcome and show pupils probability
is not always exact maths. We have all rolled 2 sixes in a row and
the probability states we should not. Key to this is that every
throw the probability goes back to 1/6.
REMEMBER : look for the fraction + place the fraction on the
probability line.
V
H
H
H
M
M
M
‘/
B
EXTENSION ACTIVITY
(all groups could have a go) Follow the link in the contents table and use the online spinner to
create a wheel of your choice. You could put prizes on; colours;
names etc. Try and make a wheel with a variety of different
fractions like the one below (They may have to use this to decide
the ‘League’) Then use a tally chart to test the probability of each
of the items in the wheel. Spin the wheel a set number of times.
If you spin the wheel a multiple of the denominator then the
predictions are easier. E.g. in my wheel the denominator is 24. So I
could spin it 48 times.
Spinner TOPIC
Football teams likely to win the Premiership
Items on wheel
Fraction
Prediction
Tally
Result
EXPLANATION NOTES:
The following sheets have a series of investigations
of probability.
The middle/higher level focus should be
completing a few of these over 2 days. Select an
investigation; get the equipment ready; decide
how to record it in numeracy book; make a
prediction of what the outcomes should be if
probability is perfect. Then carry out the
investigation and see if it was close. The outcomes
will almost certainly not be the exact % or fraction
you would expect for perfect probability. E.g if you
toss a coin 20 times the outcome most likely not 10
heads and 10 tails. The more times you repeat the
closer to perfection the result becomes.
BASIC LEVEL- this task involves testing 4 spinners.
Two each day for lesson 4 & 5. The instructions are
in the sheets below.
Probability Experiments
Carry out some of the following probability experiments. Try and predict what
should happen if probability is perfect.
1. Toss a coin 20 times.
2. Roll a dice numbered 1-6 thirty times.
3. Test the 4 spinners below . Stick on card, cut out and stick a pencil
through centre. The edge that lands on the floor after a spin is the
recorded outcome. Spin each one 30 times and record your results. Look
at the outcomes. What did you expect?
4. Toss TWO coins 30 times. Record the number of tails you get each time
(0, 1 or 2).
5. Select 20 cards at random from a pack of playing cards.
Discuss the probability of:
(a) red / black card
(b) different suits
(c) picture /non-picture cards
6. Throw THREE dice simultaneously. Record the totals for 30
throws.
7. A game for 3 players. Each player chooses a position (side-up, bottom-up
or top-up). Toss a yoghurt pot in the air 20 times. Record the outcome :
side-up, bottom-up, top-up.
Who wins? Is the game fair?
H M
Experimenting with Football Results.
There are only four possible results in a football match. These are a home win (team playing
at home scores more goals), an away win (team playing away from home scores more
goals), a score draw (both teams score the same amount of goals) and a no score draw
(both teams fail to score). The team first in the match list is the home team.
From the football scores given, (actual results from 18-9-99), copy and complete the tally
chart below.
Result Tally Total
Home Win
Away Win
Score Draw
No Score Draw
Total Number of Games = 34
It could be argued that the probability for anyone of these results is one chance in four, that
is P = = (0.25). Calculate the probability as a fraction out of 34 and convert to a decimal.
(using a calculator) divide the numerator by the denominator and round to 2 decimal
places Use the decimal probability line as a guide. (see bottom of page)
H H
• Calculate the experimental probability for home win.
• Calculate the experimental probability for an away win.
• Calculate the experimental probability for a score draw.
• Calculate the experimental probability for a no score draw.
Comment on any differences found between these results and the probability of (0.25).
List any reasons why there should be such differences.
Aston Villa
1-0
Bradford City
Derby County
0-5
Sunderland
Leicester City
2-2
Liverpool
Manchester United
1-1
Wimbledon
Southampton 0-1
Arsenal Watford
1-0
Chelsea
Bolton Wanderers
2-2
Barnsley
Crewe Alexandra
2-1
Swindon Town Crystal Palace
3-0
Grimsby Town
Fulham
1-0
Queens Park Rangers
Huddersfield Town
1-0
Norwich City
Ipswich Town
0-1
Birmingham City
Sheffield United
1-2
Charlton Athletic
Stockport County
1-0
Port Vale
Tranmere Rovers
2-4
Portsmouth
Walsall
0-1
Manchester City
West Bromwich
2-2
Blackburn Rovers
Blackpool
0-0
Bournemouth
Brentford
2-0
Luton Town
Bristol Rovers
3-2
Oldham Athletic
Burnley
3-0
Colchester United
Bury
2-0
Wycombe Wanderers
Cardiff City
2-1
Notts County
Gillingham
0-2
Preston North End
Millwall
2-1
Cambridge United Reading
1-0
Chesterfield
Scunthorpe United
1-2
Bristol City
Stoke City
1-1
Wigan Athletic
Wrexham
1-0
Oxford United
Barnet
2-1
Northampton Town
Brighton 2-3
Chester City
Darlington
0-0
Mansfield Town
Exeter City
2-1
York City Hartlepool United
3-0
Plymouth Argyle
Hull City
2-0
Swansea City
Leyton Orient
0-2
Torquay United Lincoln City
1-1
Macclesfield Town
Peterborough United
1-0
Cheltenham
Rotherham United
0-1
Rochdale
Shrewsbury Town
4-1
Carlisle United
ANSWER to discussion: it is a proven fact that teams play better at home. They
are urged on by the home fans; they don’t have a long journey on match day and
they are familiar with the pitch. These things appear to create an advantage to
probability it altered slightly. Apart from Liverpool of course as they win nearly all
their matches , home and away.
SPINNER PROBABILITY INVESTIGATION
Cut out the spinners and push a short pencil through the centre.
Use the table below to record your results.
Make a prediction first.
Spin the top 2 spinners 24 times. Spin the bottom 2 spinners 30 times.
Fill in all the columns in the tables below. An example using the first
spinner has been given to let you see what to do.
EXAMPLE Spinner shape
Hexagon divided into rhombi
Colours orange blue purple
Fraction 1/3 1/3 1/3
Prediction 12 12 12
Tally
Result
B
Spinner shape
Colours
Fraction
Prediction
Tally
Result
Spinner shape
Colours
Fraction
Prediction
Tally
Result
Spinner shape
Colours
Fraction
Prediction
Tally
Result
Spinner shape
Colours
Fraction
Prediction
Tally
Result