Transcript Junior Statistics literacyx - CMA-workshop

“Statistical investigation is part of information gathering and
learning process with is undertaken to seek meaning from and to
learn more about observed phenomena as well as to inform
decisions and actions. The ultimate goal of statistical
investigation is to learn more about a real world situation and to
expand the body of contextual knowledge”
J UNIOR S TATISTICAL L ITERACY
Telling stories from data
P LAYING

Sort your toys…
WITH TOYS
I NTRODUCTION

Grant Ritchie and Dr Michelle Dalrymple

Cashmere High School

Junior Statistics focus

Collated information from variety of resources

Plan
B ACK

I notice…

I wonder…
TO THE TOYS
NZ C URRICULUM
Subject
content
Values
& Key
Comps
NCEA
Junior Probability
NCEA – S TATISTICS
C URRICULUM

LEVELS
Information collated from:

Curriculum AOs

Second tier information: student exemplars

http://nzmaths.co.nz/nzc-and-standards
go to…

Key ideas

http://www.nzmaths.co.nz/key-mathematicalideas?parent_node
go to…
S ECOND TIER INFORMATION …
S ECOND TIER INFORMATION …
S ECOND TIER INFORMATION
C URRICULUM

LEVELS
Information collated from:

Curriculum AOs

Second tier information: student exemplars


http://nzmaths.co.nz/nzc-and-standards
Key ideas

http://www.nzmaths.co.nz/key-mathematicalideas?parent_node
CHS E MPHASIS
Year 9


Introducing PPDAC –
Through Probability
Year 10

PPDAC Statistics
(Making the call)
Statistical Literacy

Theoretical Probability &
Literacy
CHS E MPHASIS
Year 9
Year 10

Introducing PPDAC –
Through Probability

Theoretical Probability &
Literacy

Statistical Literacy

PPDAC Statistics
(Making the call)

Introducing PPDAC

Background article for teachers

“How Kids Learn – The Statistical Enquiry Cycle”

http://www.censusatschool.org.nz/resources/howkids-learn/
T IME

SERIES
Linking into what students have done at Primary

Growing plants etc

Emphasis on scales, comparisons, slope

Activity using whole PPDAC

Reviewing others reports based on time series

Current time series that students can relate to
T IME S ERIES D ATA

I wonder what patterns and trends there are in Cashmere
High Schools power consumption?
T IME S ERIES D ATA

I wonder what patterns and trends there are in Cashmere
High Schools power consumption?
W ORDS TO DESCRIBE
T IME S ERIES DATA

Long-term trend  increasing,
decreasing, stable
Because…

Seasonal patterns  peaks, troughs
Because…

Unusual values
Because…
T IME S ERIES D ATA
I wonder what patterns and trends there are in Cashmere High
Schools power consumption?

What stories can we tell with this data?

What are we hoping to see?

Can we predict/forecast into the future?
B IVARIATE
DATA

Relationships fall naturally out of playing with
data cards or toys

C@S tasks including


Scatterit

The case of the missing cake

Are you a Masterpiece
Leads into 91036 Bivariate data
The case of the missing cake
The case of the missing cake
• It was Sam’s birthday so
his grandmother baked him
a cake to share with his
classmates at lunchtime.
• Everyone was excited.
• All morning the children
could smell the delicious
chocolate cake.
The case of the missing cake
• It made it very difficult to
concentrate.
• Hohepa asked if they could
have lunch early.
• Ying was caught ‘sniffing’
the cake.
• Ms Royal, the teacher
decided everyone should
go outside for a run before
lunch.
The case of the missing cake
• When they got back the
cake was gone. All that
was left were a few
crumbs and a muddy
footprint.
The case of the missing cake
25cm
m
The case of the missing
cake
• Unfortunately the school system only
has the heights of the students.
• Here is the data from the school records
for Ms Royal’s class.
Daisy
Ella
Fay
Gwen
Hazel
Irene
Jess
Kate
Lucy
Mary
Nova
Olivia
Paige
Rose
Sally
12
13
12
13
13
14
14
13
13
14
14
10
9
9
11
Estimat
e
height
153
140
153
160
157
157
160
185
200
183
147
127
140
153
150
Gender
M
M
M
M
M
M
M
M
M
M
M
M
F
F
F
Age
10
10
10
11
11
13
14
15
14
10
9
8
11
11
11
Student
Estimat
e
height
Gender
Alex
Ben
Caleb
Dan
Eddie
Fred
Greg
Harry
Ike
John
Kane
Lewis
Anna
Beth
Cath
Age
Student
The case of the missing
cake
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
173
170
153
160
143
187
163
157
160
153
160
140
133
160
160
The case of the missing
cake
• DATA:
• 25 students randomly selected from
CensusAtSchool: right foot, height, gender.
• Can you predict the foot size from
someone’s height in order to narrow the
list of suspects?
25cm
m
The case of the missing
cake
• Create a scatterplot to see if there is a relationship between
foot length and height.
• I notice that..
– As foot size increases, height….
– I notice some unusual values such as…
– Based on my sample, people with a right foot length of
25cm are probably around ___cm tall.
– Feet are about ____ as long as people’s heights.
The case of the missing
cake
12
13
12
13
13
14
14
13
13
14
14
10
9
9
11
Estimate
height
Daisy
Ella
Fay
Gwen
Hazel
Irene
Jess
Kate
Lucy
Mary
Nova
Olivia
Paige
Rose
Sally
Gender
153
140
153
160
157
157
160
185
200
183
147
127
140
153
150
Age
M
M
M
M
M
M
M
M
M
M
M
M
F
F
F
Student
Estimate
height
10
10
10
11
11
13
14
15
14
10
9
8
11
11
11
Gender
Age
Student
Alex
Ben
Caleb
Dan
Eddie
Fred
Greg
Harry
Ike
John
Kane
Lewis
Anna
Beth
Cath
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
173
170
153
160
143
187
163
157
160
153
160
140
133
160
160
Who are your main
suspects & why?
More Resources
Check them all out and adapt them if you
wish on
http://new.censusatschool.org.nz/resources/
B IVARIATE D ATA

I wonder what the relationship is between mouse body
weight and mouse heart weight?
Body (g)
Heart (mg)
27
118
30
136
37
156
38
150
32
140
36
155
38
144
42
159
36
149
44
170
33
131
38
160
How would we have got
this data?
Why might we want to
find a relationship?
The analysis section is about
exploring the data and
reasoning with it

Investigating the stories in the data

I noticed that…

I wondered if…
The analysis section is about
exploring the data and
reasoning with it

Reading the data


Reading between the data


Interpreting the graph (one step to answer)
Reading beyond the data


Taking information directly off a graph
Extending, predicting or inferring
Reading behind the data

Connecting the data
to the context
W ORDS TO DESCRIBE A
BIVARIATE RELATIONSHIP

Linear
or
Non-linear

Positive
or
Negative
Which means…

Strong or Moderate or Weak
Which means…
B IVARIATE D ATA
Body (g)
27
Heart (mg) 
118
30
136
37
156
38
150
32
140
36
155
38
144
42
159
36
149
44
170
33
131
38
160
I wonder what the relationship is between
mouse body weight and mouse heart weight?
B IVARIATE D ATA
Body (g)
27
Heart (mg) 
118
30
136
37
156
38
150
32
140
36
155
38
144
42
159
36
149
44
170
33
131
38
160
I wonder what a mouse heart would weight if
their body weight was 40grams?
S TATISTICAL L ITERACY

Evaluate statistical investigations undertaken by
others including data collections methods, choice
of measures, and validity of findings

Evaluating effectiveness of data displays and
statements made by others
Eg: Grant says that all girls seem to be quite fit

C@S Chocolicious

Statistics court for extension students
Chocolicious
The following is a paid advertisement for
Dodgycereal Limited.
–
Watch for small print and outrageous claims
Are you gorgeous?
Are you intelligent?
Are bored with old peoples’ cereal?
Dodgycereal Limited
has the cereal for you
Chocolicious
Just peel back the foil and eat it.
A glass and a quarter of milk has already
been mixed into the rich brown
chocolicious block.
You can even
eat it on the
way to school!
After extensive research we found that
(we surveyed the 30 children of the 8 company employees)
 Hardly any teenagers eat breakfast – especially
intelligent males.
 Almost all teenagers don’t eat breakfast because the cereal
their parents buy is for old people.
 Females are also more gorgeous than males
Here’s the proof
Do you eat breakfast?
Yes
No
11.75
• Hardly any teenagers eat
breakfast – especially
intelligent males.
10.75
9.75
• Females are more discerning
than males because more of
them don’t eat breakfast.
8.75
Count
This graph shows
without a doubt that
7.75
6.75
• Females are also more
gorgeous than males (we don’t
need to prove this one)
5.75
4.75
3.75
Female
Male
All 13-15 year old didn’t eat breakfast
because the cereal is for old people.
Reasons why students don't eat breakfast
100%
90%
I am too rushed in
the morning to sit
down and eat
Percentage
of responses
80%
70%
60%
It’s too messy in a
bowl, I would rather
eat a block of cereal
50%
40%
30%
The cereal my
parents buy is for
old people
20%
10%
0%
9
10
11
Almost all teenagers don’t
eat breakfast because the
cereal their parents buy is for
old people.
12
Age
13
15
Younger teenagers are
more disorganised than
older teenagers as they
are too rushed to eat.
Chocolicious
The cereal for intelligent gorgeous teenagers.
Buy some today
Hmm something
smells fishy…
Are Dodgycereal Ltd’s
claims correct?
S TATISTICAL L ITERACY
What parts of a Statistical Investigation
are being challenged here?
S TATISTICAL C OURT

Give an article to students with Statistical claims

Separate the class into Affirmative and Negative

Points are awarded for points made that are
statistically sound

Points are deducted for “hot air”
e.g. “Men drivers are twice as likely to crash as women”
http://nzmaths.co.nz/nzc-and-standards
Key mathematical (and statistical) ideas:
http://www.nzmaths.co.nz/key-mathematical-ideas?parent_node
L INKS WITH USEFUL
INFORMATION …
Census at School
http://www.censusatschool.org.nz/