Measuring stations Set up measuring stations, get them to record their data onto post it notes. Blue for male, pink for female Collect in the post it notes.

Introductions and set up Hand out curriculum AOs sheet. Explain what this is about. The grey is from NZMaths http://www.nzmaths.co.nz/key-mathematical-ideas?parent_nodand describes the big key ideas for each level (4-6). Then there is the achievement objectives for the level (4-6), followed by three blank columns. At times during the day I will give you time to fill these in. This is as much as anything to help you make decisions about activities while they are fresh in your mind. The first column is for deciding where an activity we have done might link to the curriculum (or an adaption of it to make it higher/lower). Other ideas that the activity generates. The last column is for where you might address this idea (year 9-11).

Exploring data collection and information Introduction to CensusAtSchool www.censusatschool.org.nz · New survey every two years (but can be used in in-between years) · Designed to support teaching and learning · Good links to measurement, in fact the measuring could be done during measurement and kept for using in statistics · Brief discussion on questionnaire/survey design – the censusatschool process · Reference to Making measures document · Look at the survey questions posed (handout sets of cards to look at – sets for groups – have a look at the additional information that can be used with this · Why might questions be changed? · Why do we have very specific instructions on the cards? – determining appropriate measures, considering sources of variation...

Working with participant’s data pick a variable to explore – graph using the post it notes. · Look for errors – what might be an error · What is the range of values we might expect for ..., what would be too big, too small?

Explore the year 10 dataset – hand out sets of cards need the questions sheet for 2009 · do the same variable as we did with their data – display using the cards · What do you notice? Any extreme values? Can they/do they need “cleaning”? · Why do you think they are wrong? Can we correct (impute a value). · Use iNZight to show the data. year10foriNZight.xls Reflect where these activities or variations would link to the curriculum.

making-measures-2011.doc measurement station set of cards

Shape sketching · Remove the shape activity without turning it over or unfolding. Try not to look at the next page, it is the one that is sticking out of the folder. · Using the powerpoint run through the activity. Sketching shapes.ppt · Slides 1-26 cover first part – answers to the contexts · · Sketch the shape – slide 27-28 –in folder · Slide 29 finish

Using shape to tell the story · A further activity – take one of the graphs – describe the shape fully – work in pairs. · Hand to another pair and get them to sketch the shape. In folder

Describing populations · If time use iNZight to draw population graphs of variables - describe

Go to student papers – have a look at the last page and their descriptions of shape Reflection time for these activities.

Karekare College · Hand out data sets · Work out the variables – use the 2009 question sheet · Why is it a particular variable? What is the unit? Is it categorical or numerical? What was the survey question asked? · Refer page with info about the college – don’t turn over!

Posing questions · Using A3 paper and pens – pose some questions that could be asked of this data · Decide which are summary, comparison or relationship. · Collect in and pin up

Sorting questions · Using the posed question cards (posed-investigative-questions.pdf) sort the questions in any way you like · Collect reflections from the group about how they grouped the question · Look for good/bad aspects of question posing. · Aspects of a good question. · Reference to posing questions lesson plan

Get out students tests – look at firstly the questions they posed. Look at their comments on good/bad questions.

Back to their questions they have posed · any we would like to change · make the changes together modelling going from incomplete and/or incorrect to complete and correct.

Graphing popliteal lengths What are typical popliteal lengths of students at Karekare College? · Ask students how we might answer this question. · Hopefully they will suggest that they make a graph first. · They also might suggest that they need to find the mean or the median. · Encourage them to make a graph. Get them to use the data cards as they are all the students from Karekare College. · Hopefully someone will suggest that using all the cards will take a long time. · So what can be done instead? Hopefully someone will suggest that they just take some students to get a picture of the school. · Suggest that each group selects a handful students from Karekare College. This is called a sample. Why might a sample be a better idea than using the whole population? · Some reasons for sampling: practicable, takes less time. · How might we sample? · Can a sample tell us about the population? · Sample is good enough to look at the population. Can get general/overall ideas. Not specific. · We take a sample because it tells us about the population.

· Reflection as a class on what they have noticed about all the graphs. Pull together the big ideas from the lesson. · Did the graphs of different samples give the same information? · In what ways were they the same? · In what ways were they different? Reflection on these activities

Investigative questions to explore Within a group of four decide who is doing which questions to explore. Choose from:

Do the heights of Karekare College boys tend to be greater than the heights of Karekare College girls?

Do Karekare College students who walk to school tend to get there faster than Karekare College students who take the bus?

Predict and draw the population distributions for the variable in the question. Show one population distribution relative to the other, eg. Heights of boys, heights of girls Give a rough indication of the range of values they expect. What does tend to mean?

· Selecting samples, drawing dot plots and box plots. · Logistically they will have one bag between four people. They will have to take the samples from the same bag. · Between the four they explore the two questions (a pair do one question and then they share information). · Agreement to do about 30 (a handful) not addressing random sampling at this stage.

Descriptions of their graphs. Purpose of descriptions:

Insight comes from looking at the data

Look and notice important things that are going on. Training about what to look at and what to look for

Why? To check assumptions for formal methods for later on.

Looking for anything interesting, unusual or unexpected. This may require further investigation.

Want to become good lookers at data – data detectives

· Describe shape reflecting on earlier session · Shift- position of boxes relative to one another, overlap of the boxes Get egs of descriptions up on the board. Actively reflect on these. That is make them context rich and correct/relevant statements.

Exemplar to give out and Write on sheet to do descriptions.

Compare and contrast samples. What is similar, what is different? Look for same question.

PPT

11:40-11:45

Wrap up. 1.Link between sample and population 2. Students need to experience the need to sample. 3. Describe sample distributions and then think about the population distributions. 4. Predict population distributions. 5. Care with language, these boys, these girls.

PPT

Back of handout workshop1- handout2.

11:45-11:50

Introduction to the session Explore two questions.

Do the heights of Karekare College boys tend to be greater than the heights of Karekare College girls?

Do Karekare College students who walk to school tend to get there faster than Karekare College students who take the bus?

In a previous session “students” have taken samples to answer these two questions, they have drawn dot plots and box plots. They have made descriptive statements and had inferential thoughts about each question. At the end of the session they have transferred the boxes (or signal) information about the two questions onto pre-prepared grids.

Spread out the two sets of graphs. · Taking one set at a time make observations across the set of graphs. What do you notice? What is similar, what is different? · Look at shift, overlap, the medians, what do you notice? · Write descriptive statements about what you notice. · Encourage groups if they don’t automatically to sort the graphs. · Collate back ideas of what groups found on the board. Ask them about the decisions they made when sorting the graphs in each set. Overall message: Situation 1 (heights): in all samples the boxes overlap by a lot Sometimes the boys box is to the right (higher) sometimes the girls box is to the right (higher) Sometimes the boys median is higher, sometimes the girls median is higher, sometimes they are the same, the medians are all within the overlap of the two boxes The message is inconsistent, the samples give different messages and I am not sure what might be happening back in the populations, I can’t say if boys tend to be taller than girls or if girls tend to be taller than boys. Situation 2 (time to school): in all samples the bus box is further to the right than the walk box Sometimes the boxes overlap, sometimes they do not, when they overlap it is only by a small amount The bus median is always higher than the walk median and all but one of the graphs the bus median is outside the box of the walk. In the one situation where it is not, the bus median is equal to the walk median, but the walk median is below the bus box. In all cases at least one of the medians is outside the overlap of the two boxes. The message is consistent, the samples are giving the same message, I am fairly confident that back in the populations the time it takes to get to school by bus will tend to be longer than the time it takes to walk to school.

Sets of height boxes, sets of time to school boxes.

Movies to reinforce the message, including getting teachers to raise their hands to indicate which median is higher and to reinforce the constant changing for situation 1 and minimal if no changing for situation 2.

TimingActivityResourcesSet up measuring stations, get them to record their data onto post it notes. Blue for male, pink for female

Collect in the post it notes.

making-measures-2011.dochttp://www.censusatschool.org.nz/2011/teachers-information-pack/

instruction sheet

WARM UP ACTIVITY.doctapes

rulers

blu tac

post it notes

string

Hand out curriculum AOs sheet. Explain what this is about.

The grey is from NZMaths http://www.nzmaths.co.nz/key-mathematical-ideas?parent_nodand describes the big key ideas for each level (4-6).

Then there is the achievement objectives for the level (4-6), followed by three blank columns. At times during the day I will give you time to fill these in. This is as much as anything to help you make decisions about activities while they are fresh in your mind.

The first column is for deciding where an activity we have done might link to the curriculum (or an adaption of it to make it higher/lower). Other ideas that the activity generates. The last column is for where you might address this idea (year 9-11).

statisticsinfotest.docstatisticsinfotest.docstatsL4-6summarysheet.docstatsL4-6summarysheet.doc

Introduction to CensusAtSchool

www.censusatschool.org.nz

· New survey every two years (but can be used in in-between years)

· Designed to support teaching and learning

· Good links to measurement, in fact the measuring could be done during measurement and kept for using in statistics

· Brief discussion on questionnaire/survey design – the censusatschool process

· Reference to

Making measuresdocument· Look at the survey questions posed (handout sets of cards to look at – sets for groups – have a look at the additional information that can be used with this

· Why might questions be changed?

· Why do we have very specific instructions on the cards? – determining appropriate measures, considering sources of variation...

Working with participant’s data pick a variable to explore – graph using the post it notes.

· Look for errors – what might be an error

· What is the range of values we might expect for ..., what would be too big, too small?

Explore the year 10 dataset – hand out sets of cards

need the

questions sheetfor 2009· do the same variable as we did with their data – display using the cards

· What do you notice? Any extreme values? Can they/do they need “cleaning”?

· Why do you think they are wrong? Can we correct (impute a value).

· Use iNZight to show the data.

year10foriNZight.xlsReflect where these activities or variations would link to the curriculum.

making-measures-2011.docmeasurement station set of cards

http://www.censusatschool.org.nz/2011/teachers-information-pack/

post it notes completed

datacards – 8 sets

http://www.censusatschool.org.nz/2009/teachers-day/unit/1/

year10-datacards.pdf2009-questions.pdfyear10foriNZight.xlsyear10foriNZight.xls

down load iNZight

http://www.stat.auckland.ac.nz/~wild/iNZight/

· Remove the shape activity without turning it over or unfolding. Try not to look at the next page, it is the one that is sticking out of the folder.

· Using the powerpoint run through the activity.

Sketching shapes.ppt· Slides 1-26 cover first part – answers to the contexts

·

· Sketch the shape – slide 27-28 –in folder

· Slide 29 finish

Using shape to tell the story

· A further activity – take one of the graphs – describe the shape fully – work in pairs.

· Hand to another pair and get them to sketch the shape. In folder

Describing populations

· If time use iNZight to draw population graphs of variables - describe

Go to student papers – have a look at the last page and their descriptions of shape

Reflection time for these activities.

Sketching shapes.pptSketching shapes.pptSHAPE ACTIVITY.docSHAPE ACTIVITY.docSHAPE ACTIVITY-context.docSHAPE ACTIVITY-context.docdrawing popgraphs.docdrawing popgraphs.docfulldescriptionshape.docfulldescriptionshape.docyear10foriNZight.xls· Hand out data sets

· Work out the variables – use the 2009 question sheet

· Why is it a particular variable? What is the unit? Is it categorical or numerical? What was the survey question asked?

· Refer page with info about the college – don’t turn over!

Posing questions

· Using A3 paper and pens – pose some questions that could be asked of this data

· Decide which are summary, comparison or relationship.

· Collect in and pin up

Sorting questions

· Using the posed question cards (

posed-investigative-questions.pdf) sort the questions in any way you like· Collect reflections from the group about how they grouped the question

· Look for good/bad aspects of question posing.

· Aspects of a good question.

· Reference to posing questions lesson plan

Get out students tests – look at firstly the questions they posed.

Look at their comments on good/bad questions.

Back to their questions they have posed

· any we would like to change

· make the changes together modelling going from incomplete and/or incorrect to complete and correct.

http://www.censusatschool.org.nz/2009/teachers-day/unit/1/

· posed-investigative-questions.pdf

· variable-list.pdf

· year10-datacards.pdf

· Lesson Plan (lesson 2)What are typical popliteal lengths of students at Karekare College?· Ask students how we might answer this question.

· Hopefully they will suggest that they make a graph first.

· They also might suggest that they need to find the mean or the median.

· Encourage them to make a graph. Get them to use the data cards as they are all the students from Karekare College.

· Hopefully someone will suggest that using all the cards will take a long time.

· So what can be done instead? Hopefully someone will suggest that they just take some students to get a picture of the school.

· Suggest that each group selects a handful students from Karekare College. This is called a sample. Why might a sample be a better idea than using the whole population?

· Some reasons for sampling: practicable, takes less time.

· How might we sample?

· Can a sample tell us about the population?

· Sample is good enough to look at the population. Can get general/overall ideas. Not specific.

· We take a sample because it tells us about the population.

· Reflection as a class on what they have noticed about all the graphs. Pull together the big ideas from the lesson.

· Did the graphs of different samples give the same information?

· In what ways were they the same?

· In what ways were they different?

Reflection on these activities

Data cards – Karekare College

http://www.censusatschool.org.nz/2009/teachers-day/unit/2/

Lesson Plan (lesson 5)

Within a group of four decide who is doing which questions to explore.

Choose from:

- Do the heights of Karekare College boys tend to be greater than the heights of Karekare College girls?
- Do Karekare College students who walk to school tend to get there faster than Karekare College students who take the bus?

Predict and draw the population distributions for the variable in the question. Show one population distribution relative to the other, eg. Heights of boys, heights of girlsGive a rough indication of the range of values they expect.

What does tend to mean?

· Logistically they will have one bag between four people. They will have to take the samples from the same bag.

· Between the four they explore the two questions (a pair do one question and then they share information).

· Agreement to do about 30 (a handful) not addressing random sampling at this stage.

* W1graphblank.doc

PPT

Purpose of descriptions:

- Insight comes from looking at the data
- Look and notice important things that are going on. Training about what to look at and what to look for
- Why? To check assumptions for formal methods for later on.
- Looking for anything interesting, unusual or unexpected. This may require further investigation.
- Want to become good lookers at data – data detectives

· Describe shape reflecting on earlier session· Shift- position of boxes relative to one another, overlap of the boxes

Get egs of descriptions up on the board. Actively reflect on these. That is make them context rich and correct/relevant statements.

Workshop1- handout2

* W1Handout2.pdf

1.Link between sample and population

2. Students need to experience the need to sample.

3. Describe sample distributions and then think about the population distributions.

4. Predict population distributions.

5. Care with language, these boys, these girls.

Back of handout workshop1- handout2.

Explore two questions.

Do the heights of Karekare College boys tend to be greater than the heights of Karekare College girls?Do Karekare College students who walk to school tend to get there faster than Karekare College students who take the bus?In a previous session “students” have taken samples to answer these two questions, they have drawn dot plots and box plots. They have made descriptive statements and had inferential thoughts about each question. At the end of the session they have transferred the boxes (or signal) information about the two questions onto pre-prepared grids.

· Taking one set at a time make observations across the set of graphs. What do you notice? What is similar, what is different?

· Look at shift, overlap, the medians, what do you notice?

· Write descriptive statements about what you notice.

· Encourage groups if they don’t automatically to sort the graphs.

· Collate back ideas of what groups found on the board. Ask them about the decisions they made when sorting the graphs in each set.

Overall message:

Situation 1(heights): in all samples the boxes overlap by a lotSometimes the boys box is to the right (higher) sometimes the girls box is to the right (higher)

Sometimes the boys median is higher, sometimes the girls median is higher, sometimes they are the same, the medians are all within the overlap of the two boxes

The message is inconsistent, the samples give different messages and I am not sure what might be happening back in the populations, I can’t say if boys tend to be taller than girls or if girls tend to be taller than boys.

Situation 2(time to school): in all samples the bus box is further to the right than the walk boxSometimes the boxes overlap, sometimes they do not, when they overlap it is only by a small amount

The bus median is always higher than the walk median and all but one of the graphs the bus median is outside the box of the walk. In the one situation where it is not, the bus median is equal to the walk median, but the walk median is below the bus box. In all cases at least one of the medians is outside the overlap of the two boxes.

The message is consistent, the samples are giving the same message, I am fairly confident that back in the populations the time it takes to get to school by bus will tend to be longer than the time it takes to walk to school.

- boysgirls1.jpg
- boysgirls2.jpg
- boysgirls3.jpg
- buswalk1.jpg
- buswalk2.jpg
- buswalk3.jpg

PPTheights_2samp_dots_30.pdf

http://www.censusatschool.org.nz/2009/informal-inference/teachers/workshop2/heights_2samp_dots_30.pdf

times_2samp_dots_30.pdf

* times_2samp_dots_30.pdf

- W2Handout2.pdf

Workshop2 – handout2keepinghealthy.doc

data_tables_graphs_formulae.doc

world_local_issues.doc

shortthemes.doc

LPlevel5-6.doc

LPlevel5.doc

LPlevel4-5.doc

LPlevel6.doc