Statistics

Based on work by Pip Arnold, TEAM Solutions

Objectives:

• Become familiar with Statistics in the new Curriculum document and Standards

• Use the Statistical Enquiry Cycle

• Know the ‘census at school’ website and other resources.

Mathematics Statistics

Exploration of and use of patterns and relationships in… quantities, space and time

Set answer

Exploration of and use of patterns and relationships in… data

No definitive answer

How is Statistics different in the new curriculum?

•Data is still key•Verbs •Specific graphsnot mentioned•Enquiry cycle

(www.wordle.net)

Statistics in the NZC and Standards

Highlight the difference in progression from Y1 to Y8

Circle any vocabulary that you are unsure of.

Problem

• Statistical investigation cycle has at its heart a starting point based on a problem (best linked into topic of interest)

• Data driven or Question driven

Problem Question Types• Summary (Years 1- 8)

– A description of the data, usually a single data set“What is the most common birth month in our class”

• Comparison (Y5 onwards)– Comparing two (or more) sets of data across a common

variable, e.g. “Do females typically live longer than males?”

• Relationship (Y7 onwards)– Interrelationship between two paired variables,e.g.“Does watching a lot of TV increase your IQ?”

Plan

– What variables do we need to collect?– How shall we pose the survey questions.– Who shall we ask / how many?– How will we know when we have asked

everyone?– How are we going to record and collect the data?

Collecting dataWhat are these data types?

• Category data (Y1 onwards)

• Number data - Whole number, e.g. 7 years (Y3 onwards)- Measurement, e.g.1.35m, (Y7 onwards)

• Time-series data (Y6 onwards)

• Multivariate data (Y6 onwards)

PAT Question (time-series data)

Emma went for a run from home. She stopped for a while and then walked home. Which graph shows how far from home she was during her journey?

Collecting Category data

(birth month)

August

Postits / stickers

Pictures / drawings

cubes

Real things

Collecting multivariate data using post it notes

What school subject do you most enjoy teaching?

Bed-Time

What school subject did you most enjoy at school as a child?

Birth month

Analysis

• Make a display / graph to help you to answer your question.

• Describe the display / graph and identify patterns and trends in context.

• Remember the context. If I cover any labels can I still tell what the display /graphs are showing?

Numerical Data

Real things, cubes, pictures, stickers

Category Data

• used to detect patterns and relationships, not just communicate the patterns at the end of an investigation.

• Drawing graphs is helpful for issues of scale and creating titles, axes, and keys etc……

Statistical Displays

• however ICT plays a critical role in allowing students to view and analyse multiple displays of the same data rapidly.

• Experience how one type of category data graph can be transformed into another.

• Choose critically about how best to display data for the purposes of analysis and communication.

Statistical Displays

Analysis: Use I notice… as a starter for statements

Describing Number Data, e.g. bed times

Shape Middle Spread

Clump(s)

Gap (s)

symmetrical,

most of the data is.. a few points are..

Same/different

The middle of the data is …..

about..,

between,

higher/lower

Close together, spread out,

evenly spread, mostly between,

less/more spread out than…

Describing Category Data, e.g. colour

Most (N.B. “most” must be more than half), most typical, least typical, most common, least common least, some, all, more than, less than, more than half, about half, roughly a quarter, a lot, not many, a few, most popular, least popular,

“What are typical birth months in our class?”

I notice…

( )count

1

2

3

4

5

6

Birth_monthFebruary March April May June July August September October December

• I notice that the most common birth month is August with 5 people in the group.

• I notice the least common birth months are January and November with no one in the group born in these months.

• I notice that four months have four people born in them, they are May, June, October and December.

• I notice that the Winter months have the most people born in them, 12 people. Spring has the least number of people born with only 5 people born then.

( )count

1

2

3

4

5

6

Birth_monthFebruary March April May June July August September October December

I wonder……?

Conclusion– Answer the question.– Provide supporting evidence from your analysis.

“What are the typical birth months in our class?”

Birth months in our class are generally in the winter. August has highest number of people born in it, 5 people. June has 4 people and July has 3 people. Altogether from the group of 30 people, 12 were born in winter. May, October and December have 4 people born in them. The other seasons, spring, summer and autumn have 5, 6 and 7 people born respectively.

Let’s Investigate!

Write some questions generated from our data.

summative comparison relationship

How many years you’ve been a numeracy lead teacher?

What school subject you most enjoy teaching?

Which country you were born in

Superpower you would choose to have

Complete the investigation sheet for one of our problems.

Useful Statistics Resourcesnzmaths BSM

Figure It Out

ARBs

Book 9

www.censusatschool.org.nz

CensusAtSchool

http:///

www.censusatschool.org.nz (Y5 -8)

Effective Teaching Cycle

Assessing

Analysing data

Planning

Teaching

Practicing /Applying

So what assessment data will you use to start your teaching?

Could you use a task?

www.babynamewizard.com

2nd Tier Support on nzmaths

BSM Statistic Units on nzmaths

Figure It Out (incl. Teachers Notes)

Level 1 L1 exemplar one See booklet

Greedy CatMatch ups (literacy)

-

Level 2 L2 exemplar three Party Party PartyTrue or False (literacy)Data Squares Level 2

FIO 2-3 Statisticsp.1 Choice Squaresp.13 Where on Earth

Level 3 L3 exemplar one Data Squares Level 3Paper PlanesWhich Graph (literacy)

FIO L3 Statisticsp.13 Lapping up Numbersp.5 Television Times

Level 4 L4 exemplar two FIO L3-4 Statisticsp.1 Sorting Statistics

• Look at topic/enquiry work for the rest of the year or next year – where could a statistics unit be integrated?

• Explore resources for Levels 1, 2 or 3

e.g. (FIO, Statistics units on nzmaths, 2nd tier support exemplars).

Possible Follow up Syndicate Meetings

Concluding thought…

98% of all statistics are made up.

Additional Slides

Workshop MaterialsHandout Workshop Resources

•NZC and Statistics with 2nd tier support info.•Data Cards•Investigation Sheet•Data Displays

•Powerpoint handout•A3 NZC and Statistics•Highlighters•PPDAC poster•Postits – pink and blue•A3 Data Displays ?•PAT question?

Follow up Workshop resources:•2nd tier support Levels 1-4•FIO books•nzmaths units•2nd tier exemplars

Write some questions generated from our data

summative comparison relationship

What school subject do you most enjoy teaching?

What time did you go to bed last night? (to the nearest half hour?)

What school subject did you most enjoy at school as a child?

Which country you were born in

How might data be sorted and displayed?

answer the question answer and compare

Level 1Are there more boys or girls in the class?

Patterned sets

Thinking Routines

PROCESSJUSTIFICATIONS

IMPROVEMENTS

EMOTIONS

INFORMATION

I notice….

I used to think… now I think….

What limitations does this data havefor my question?.

I wonder….

I conclude that….

What data? How shall I collect it? What do I think might happen?