105. Opening Minds Maths: QK, UK, The World!

8/6/2019 105. Opening Minds Maths: QK, UK, The World!

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QK, UK, The World Maths Learning JourneyKey Vocabulary Learning Journey QK, UK, The World!

Key OM Objectives

Children should learn:

To relate individual statistical techniques to a wider problem

To use charts and graphs to calculate mode and median from them

To think analytically about a statistical problem

To apply a variety of techniques to solve a problem

Key Activities

Class, group and paired discussion

Data collection

Drawing charts and graphs, calculating median, mode and percentages

Drawing conclusions from charts and results as well as using them as supporting evidence for a conclusion

Writing a report for the school council

Improving the School Environment: Wheres worst?

This task uses a Problem-Solving Approach and is interspersed with skills based lesson blocks.

Students will be shown how to select areas of the school environment to improve. As a group they will decide on the characteristics to use to judge the environment using a technique fromgeography (EQI).

Pupils will collect data on their own school environment to help them suggest an area to improve. This involves a qualitative survey (Environmental Quality Indexing) andprocessing throughthe use of stem-and-leaf diagrams. The pupils task is to produce a written report for the school council giving details and supporting evidence about the area they think should be improved.

Note: The Objectives in green relate directly to the Power point Wheres worst. You will need to read through the power point carefully at the beginning of delivering this section as it will be

interspersed with specific skills based lessons so the children can meet the above objectives.

PLTs and Subject Specific

Learning Objectives

Activity no.

Mental/oral starter Main Activity Activity

Outcomes/

Assessment for

Learning

Resources-

please highlight

those you feel

we will have toorder

1

Children should learn:

The context of the problem

That peoples opinions can

vary greatly

The importance of everyone

feeling like they have a say

Discussion: Why are schools currently a priority?

What improvements could be necessary in a new school?

Which schools are likely to get funding first?

Discussion: What is a fair decision?

Discussion: Which area of the school would you renovate?

What reasons are there to renovate an area?

The expected

outcome of the

work: a report


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QK, UK, The World Maths Learning JourneyWhat reasons would the school council appreciate?

You could highlight the importance of everyone feeling like they are being heard by

priming a pupil

to keep putting their hand up and trying to contribute and you making a point of

ignoring their view

asking them how they felt afterwards could add to this

2

To distinguish between

qualitative and quantitative

measurement

To appreciate the value in

the different types of

measurement

That people use various

methods to try to quantifyqualitative judgements

To appreciate that fair

judgements depend on

everyone being represented.

Discussion: Can you think of some examples of each type of measurement?

When might qualitative judgement be more useful than quantitative judgement?

What are the problems associated with qualitative measurements?

Points to note

In this resource we will go on to use a qualitative measurement to gain peoples

opinions about the school.

Points to note

The use of EQI will mean that students will decide on certain factors to score an

environment

Hostile/Welcoming on a scale of 1 to 5 for example. Several different factors will beused and then scores will be allocated to each environment by totalling the score for

each factor. This total will be the index for that environment and these numbers will be

used for comparison purposes.

3

What factors/criteria are

How Environmental

Quality Indexing works

Activities

Get students to score the scene before it appears on the slide.

Discussion: Does everyone agree? What do you think about the criteria? Are they

important?

Appropriate? Discussion: What scores would suggest a negative feeling?


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QK, UK, The World Maths Learning Journeyconclusions and identify

further questions to ask

Construct and interpretfrequency tables, bar charts

with grouped discrete data,

and line graphs Interpret piecharts

Whats different about the two charts? Why do you think they are different? What do

you think a chart like this would look like for our village/town/city/estate?

Roughly how many people live in Little Steignton? How can you tell? Approximately

how many more people are in the 61-70 age bracket than over 80?Approximately how many people are there aged 40 or less in each place? And over?

Agree answers with a partner.

Group of 4-5 childrenLaunch the ITP Data handling, choose your own data, enter age ranges as opposite and

enter numbers for people watching a childrens film. Click on the vertical bar chart

icon, enter a title, and also click on the far right bar to display percentages.

What sort of film do you think these people might be watching? Why do you think that?

Make a list of films currently showing. What do you think the age profile might be foreach of these? Modify the numbers on the graph to show this.

How might the age profile be different at different times of day? Would this be the same

every day? Why not? Discuss the differences between weekends, working days, school

holidays, any cheap deal evenings/matinees etc.

Some Ask children to sketch a bar chart for different scenarios.

Children work in pairs to shuffle two packs of 1-10 cards (in two different piles). They

take one off each pile and find the product. They record the results in a grouped

frequency table, first predicting which range will have the highest frequency:

Product Tally Frequency

1-20

21-40

41-60

61-80

81-100

They stop when one group has reached 20. They draw a bar chart to show their results.

All Children use a multiplication table if they struggle with finding some products (see

resources). They stop when one range has reached 10.

Most Children construct their own frequency table, choosing their own ranges.

y Packs of 1-10 cards

Multiplication

table (see

resources)

8 Draw a vertical axis from 0 to 50 labelled product in steps of 2 and horizontal axisfrom 0 to 15 labelled multiplier. Write the title A line graph to show multiples of 3.y

Temperaturedata (see


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QK, UK, The World Maths Learning Journey15-19

20-24

25-29

Ask students to count up how many letters they have in their name (the total of those in

their first and last names).Instead of writing how many people have each number of

letters in their names, were going to see how many people have the number of letters

in a range, so for example the number of people with 0, 1, 2, 3, or 4 letters in their

name. Do you think there will be many? Which group of numbers do you think will be

most common?

Put up your hand if you have 5, 6, 7, 8 or 9 letters in your name. If any, record the

number of people on the table.Put up your hand if you have 10, 11, 12, 13 or 14 letters in your name.

Which group of numbers was the most common? So names with these numbers of letters

occur most frequently in our class.

Write the following names on the board:

Eva, Matthew, Harry, Sandip, James, Lucy and Jasminder.

What is the length of the shortest name? And the longest name? So the range of

numbers of letters is from 3 to 9, this a range of 6, the difference between the shortest

name and the longest name. Was there one number which occurred more than once? If

so which number of letters occurred most? We call this the mode, so for these chns

names the mode is 5. Mode means it occurs the most number of times, that is the most

common length of name in this group.Group of 4-5 children

Were going to throw two dice and write down the product. Whats the minimum

product we could get? And the maximum? So the range is? What product do you think

might come up most often? Were going to draw a graph to show the results. We could

draw a bar for every product from 1 to 36, but thats a lot of bars! What else could we

do? Draw out that you could use grouped data. Agree a sensible group size and together

record a frequency table, e.g.

Product range Tally Frequency

1-6

7-12

13-1819-24

25-30

31-36

Which rows do you think will have the highest number and why? And the least?

Students take it in turns to roll the two dice, find the product and record a tally on the

correct row.

When the total on one row reaches 10, stop and discuss the frequency table. Which row

has the highest number of tallies? And the least? How do you think this might change if

we carried on rolling the two dice and finding the product?

Ask students to draw a bar graph to show the results.


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QK, UK, The World Maths Learning Journey

Were going to find the angle between the distance to the top of the tree and a line

horizontal with our eyes. Demonstrate how to look through the astrolabe to the top of

the tree, and then hold the plumb line against the card whilst you lower the card to read

the angle.

Explain that the angle from the line of sight to the tree and the vertical is 90 more than

needed, and so the astrolabe is designed to take 90 off the total angle.Ask a child to measure the distance you are standing from the tree. (It is helpful to stand

a distance of whole metres to make the drawing easier.) Now we need to draw the sametriangle to scale. Take chn back inside and discuss what scale should be used, e.g. one

centimetre on paper to 50cm outside. Draw the base line, and then a vertical line to

represent the tree. Remind chn how to use the protractor to draw the angle from the

point to represent where you were standing to the top of the tree. Continue this line

until it crosses the vertical line of the tree. So how can we now work out how tall the

tree was? Help students to interpret the scale to find out. Point out that you also need to

add the height of your eyes to the height of the tree! Does this height seem about right?

And we managed to find the height without climbing up the tree!Students make their own astrolabes and use them to work out the height of the school

building, trees or whatever tall structures to which you can measure the distance.

All: Suggest students stand 5 or 10m away from the object they are measuring to make

the scale drawing easier.Most/some Encourage students to measure two angles at two different distances from

the tree/building and check the two results against one another.

15 Show students how to take their pulse. Ask them to count the beats, and stop after 30

seconds.Double your count to find your heart rate that is the number of beats per

minute, and write it down. Explain that you are going to ask students to run as fast as

y Stop watches

y Whistle

y Graph paper

Equal angles


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QK, UK, The World Maths Learning JourneyA more complete list of definitions can be found on internet at CrimeStatistics.org.uk

Activities

Setting the context of the problem

DiscussionIt is possible to get data for individual crimes, however, data is more easily available on

the six key crimes (particularly over the last few years). For this reason the resources

for this project tend to concentrate onBurglary, Robbery, Sexual offences, Theft of a vehicle, Theft from a vehicle and

Violence.

Why do pupils think that these have been chosen by the government askey crimes?

The term key crimes might suggest that the number of these types of crimes are either

large or increasing. This is useful point as it could form the basis of an investigation

predicting if these are the most common.

The students will now have specific lessons on Probability, Fractions and percentages.

Describe and predict

outcomes from data using the

language of chance andlikelihood

Place five red cubes and 10 blue cubes in a bag, showing students as you do so. Ask a

child to close their eyes and draw out a cube. If its red you win a point, if its blue I win

a point. Replace the cube and repeat another 19 times. Draw a tally chart on the boardto keep a record of the results.

Oh look, I win!

Lets play again. What colour do you want to be? Why? Discuss how the game isnt

fair. There were more blue cubes than red cubes in the bag, so there was a greaterchance of drawing out a blue cube, which is why I won!

How many of each should we have to play a fair game? Take up one of the students

suggestions and repeat.If we carried on going until wed drawn 100 cubes, what do you

think the results would be? What if we did this 1000 times? Discuss how the results are

unlikely to be exactly 50:50 but that the more the game is played, the more the results

might even out.

Group of 4-5 students

Place five red cubes, three blue cubes and two yellow cubes in a bag.

Write the following events in Post-it notes:

Yellow,

Blue,

Red,

Yellow or red

Blue or yellow

Blue or red

Black

Blue, red or yellow.

Ask Students to help you to arrange the Post-it notes in order of likelihood.

Give each pair a bag and cubes as above. Ask them to draw out a cube & replace it 20times, recording the results in a tally chart. Collate the group's results and use them to

y Red, blueand yellow

cubes, bagsPost-it

notes


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QK, UK, The World Maths Learning Journey

To think about where they

can get relevant data from

To consider sample size and

data collection methods

That sometimes it is sensible

to collect additional

information that may help

later.

Where their current task fits

within the whole problemsolving approach

This is the first screen, from a series of similar screens, which shows which stage in the

Problem Solving Approach we have reached.We have specified our key questions:

How many crimes occur where you live?

What are the most occurring crimes where you live?

Is where you live a high or low crime area?

Crime statistics are available for various areas. These start with regions (eg North

West), subdivided into main Police Forces (eg Merseyside) and then into smallergroups (eg Wirrall) called CDRPs.

CDRPs are Crime and Disorder Reduction Partnerships and involve the police, local

authorities and primary care trusts (in England).

To find out the name of your local CDPRgo to www. crimestatistics.org.uk

Type in your postcode in the search bar.

Your nearest CDRP will appear on screen

(with a list of the other CDRPs in the same

Police Force).


within the whole problem

solving approach

Now that we have collected (enough) data we need to process it to put it into format

that will help answer our questions :

How many crimes occur where you live?

What are the most occurring crimes where you live?Is where you live a high or low crime area?

To think about variables and

the best way to process them

Appropriate methods for

displaying their data

To relate their investigations

back to the original problem

That investigating a problem

Slide 32 Since this path through the investigation is fairly straightforward pupils should

find success with most, if not all, of the questions here.

When judging whether or not they live in a high or low crime area, how appropriate are

the crimes they have used. Did they use the six key crimes or are they ones that they


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QK, UK, The World Maths Learning Journeyoften leads to new questions

being asked

considered were interesting to them. Are the crimes, they have used, really suitabl e for

judging their area? Would using a different set of crimes change their ranking compared

to the national average?

By asking these additional questions the investigation can be continued or extendedSlide 33 This slide suggests some additional areas which could be investigated in a

second pass of the Problem Solving cycle.


within the whole problemsolving approach

To review their prior work.

To plan what data they willneed to address their question

To think about where they

can get relevant data from

To consider sample size and

data collection methods

That sometimes it is sensible

to collect additionalinformation that may help

later.

Having discussed our findings we could now start the whole cycle again.

Possible extensions could be to see if the perception of crime matches actual crime figures to see how age or gender influences the perception of crime; to see if crime rates are increasing or decreasing;

The questions how worried are you about having property stolen, being mugged,being attacked and being assulted

Very Fairly Not very Not at all

Collecting gender will allow additional research to see if, for example, boys and girls

worry in different ways.

A 4-page Word document with 10 questionnaires per page is available in the shared

area. Cut up and hand out randomly the questionnaires (numbered 1 to 40). Once pupils

have anonymously entered their responses the summary sheet could be handed out to

collate the questionnaires (either called out by you bingo style(!) or shared in smallhandfuls per table and passed at regular intervals on to neighbouring tables).

105. Opening Minds Maths: QK, UK, The World!

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