literacy and thinking bivariate data investigations

Anna MartinAvondale College

LITERACY AND THINKING

BIVARIATE DATA INVESTIGATIONS

LITERACY AND THINKING

• Thinking about data• Thinking about relationships• Thinking about sources of variation

• Communicating understanding • Improving literacy

THINKING BEHIND UNIT

• Who were we doing the unit with?• What was there prior knowledge?• What were their identified needs?• What strategies could we use?• What else did we know had worked previously?

LITERACY AND THINKING STRATEGIES

SOLO for levels of thinking – identify features, use features to explain relationships• Structuring paragraphs using TEXT

• T (topic sentence)• E (evidence)• X (explanation)• T (tie up)

SETTING THE CONTEXT

What are people worried about?

What areas might be affected?

How could you get data?

Is this for real?

UNPACKING LEARNING OUTCOMES

• LO: Use the statistical enquiry cycle to investigate multivariate data

• Get students to try to explain what the words enquiry, cycle and multivariate mean

• Share understandings and acknowledge contributions

• Model more than one way to explain something

FROM ONE VARIABLE TO TWO

• Focus on rental prices (one variable)

• Explore what might be affecting/linked/related to rental prices e.g. rugby world cup, suburb, number of bedrooms

• Lots of structure early on to help with writing

FROM ONE VARIABLE TO TWO

• “How much is the typical weekly rent for a house in Kingsland?”

Analysis: Mark on your dot plot the lowest rental price and the highest rental priceConclusion: Complete the sentence “In Kingsland, the rents range from $____ to $_____”Analysis: Mark on your dot plot the middle 50% of house prices (remind them that half of 20 is 10, so where do the middle 10 house sit between).Conclusion: Complete the sentence “The rents are typically between $____ and $____”Analysis: Mark on your dot plot any common rent prices (modes)Conclusion: Complete the sentence “Common rent prices in Kingsland are $___ and $____”

WHY BIVARIATE?

Get the students into the habit of reflecting on their investigation, in particular the dataWhy do the rental prices in Kingsland vary so much? (answers could be: because the condition of houses are different, where they are located is different, how many bedrooms they have etc.)Why are there two common rental prices? (one would be the typical price for 1-bedroom houses, and one would be the typical price for 2-bedroom houses)

COMPLETE ANOTHER CYCLE…..

What happens when you compare the rent by number of bedrooms?Greater shift in rent prices (but still variation)What appears makes more difference to rent – where the house is, or how many bedrooms it has?

King

slan

dSa

ndrin

gham

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Rental data Dot Plot

Area "Kingsland"= Area "Sandringham"= or

THE PAINT BRUSH

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Number_of_bedrooms1 2 3 4 5 6

Rental data Scatter Plot

Area "Mt Eden"=

Houses with fewer bedrooms tend to rent for less than houses with many bedroomsStill variation in rental prices for houses with the same number of bedrooms

THE PAINT BRUSH

THINKING ABOUT RELATIONSHIPS

Get the students to paint pictures e.g. use a paint brush to show the relationship between your age and your heightVery scaffolded at first – put age along the bottom (in years) and put height along the side (in units of 10 cm)Students verbally describe what would happen as you get olderThen try to paint the relationship (direction, type and strength by width of paint brush)Build up ideas of suitable units, scales, ranges for variables, explanatory/response, no relationships

THE ELLIPSE

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Number_of_bedrooms1 2 3 4 5 6

Rental data Scatter Plot

Area "Mt Eden"=

Using for relationships we think are linearNot easy at first but students get thereHelps position line of best fitCan use for informal predictions

LINKING FEATURES AND STATEMENTS

Describe the relationship:• in context• positive/negative• strength/type• does it make

sense?

Use the names of the variablesIt’s a positive relationship because….It’s a strong linear relationship because….

Points are close to the lineOverall the points look like they make a lineThe line slopes upAs one gets bigger the other gets biggerLow goes with low, high goes with high

FORMATIVE ASSESSMENT

Is there a relationship between the size of a family and the number of bedrooms for their house?

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Size_of_family1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

Collection 1 Scatter Plot

Bi-variate investigationLO: Use the relationship between two variables to make a prediction

Relate features of a relationship

Describe the relationshipUse the relationship to make a prediction

LO: Use the relationship between two variables to make a prediction

LO: Use the relationship between two variables to make a prediction

Problem

LO: Use the relationship between two variables to make a prediction

You want to manufacture a 10G memory stick.How much do you charge for it?

Plan

LO: Use the relationship between two variables to make a prediction

Collect data about what other USB sticks cost.On the next few pages are USB sticks being sold by Dick Smith Electronics. For each one, record in a table how many GB they are, and their selling price.

Data (example of table)

LO: Use the relationship between two variables to make a prediction

Memory (GB) Price ($)

DataLO: Use the relationship between two variables to make a prediction

Data

LO: Use the relationship between two variables to make a prediction

Analysis

LO: Use the relationship between two variables to make a prediction

There are no USB drives that are 10GB currently advertised.How do we work out how much we should charge?

Problem: Is there a relationship between the GB of a memory stick, and how much is costs?

Analysis

LO: Use the relationship between two variables to make a prediction

Draw a scatter plot of the data.

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GB2 4 6 8 10 12 14 16 18

DSE USB stick data Scatter Plot

Conclusion (relationship)

LO: Use the relationship between two variables to make a prediction

Describe the relationship between GB and price for the USB sticks.

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DSE USB stick data Scatter Plot Is it a linear relationship?Positive/negative?

Strength?

Amount?

Unusual?

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GB2 4 6 8 10 12 14 16 18

DSE USB stick data Scatter Plot

Conclusion (prediction)

LO: Use the relationship between two variables to make a prediction

Use the relationship to make a prediction for 10GB.

Try to imagine painting across the values, draw the ellipse, add the line

Use the line to see how much a 10GB memory stick might cost

Answer the problem!!

Reflection

LO: Use the relationship between two variables to make a prediction

Think about where the data came from, what else might effect the price of a USB memory stick, what you could do to extend the investigation.

Write two “I wonder….” statements for this investigation.

Bivariate investigationLO: Write a plan for a bivariate investigation

List the steps for a method

Identify variables for the investigationDescribe how the variables will be measuredExplain how the data will be collectedDecide how much data to collect

LO: Write a plan for a bivariate investigation

LO: Write a plan for a bivariate investigation

Problem

LO: Write a plan for a bivariate investigation

What is the relationship between the size of the hard-drive memory and the selling price for laptops?

What variables will you investigate?

LO: Write a plan for a bivariate investigation

What is the relationship between the size of the hard-drive memory and the selling price for laptops?

WRITE: The variables I will investigate are……

WRITE: The explanatory variable will be ……

WRITE: The response variable will be ……

The size of the hard-drive memory and the selling price for different laptops

Hard-drive memory (because I think this will explain the selling price of the laptop)

Selling price (because I think this will change/respond to different sizes of hard-drives)

How will you collect data for the investigation?

LO: Write a plan for a bivariate investigation

What is the relationship between the size of the hard-drive memory and the selling price for laptops?

THINK: Are the variables things I can measure myself or can I find measures for the variables from somewhere?

WRITE: I can collect data for this investigation by ……

These variables have already been measured by stores or people selling laptops

Getting ads for laptops being sold that say how big the hard-drive memory is and what price the laptop is being sold for from advertising pamphlets.

How will you measure these variables?

LO: Write a plan for a bivariate investigation

What is the relationship between the size of the hard-drive memory and the selling price for laptops?

THINK: What units should I use? How accurate do I need to be? What equipment do I need?

WRITE: I will measure the variables by using…..

GB for the hard-drive memory and rounding the selling price to the nearest $100.

What things might affect the measures you take?

LO: Write a plan for a bivariate investigation

What is the relationship between the size of the hard-drive memory and the selling price for laptops?

THINK: Does it matter where I get my data from? Do I need to be careful about getting a range of data? Should I focus my investigation more?

WRITE: I wonder if things like…………. might also affect the selling price for laptops

the screen size, the processing speed, how the laptop looks

How many measures will you collect?

LO: Write a plan for a bivariate investigation

What is the relationship between the size of the hard-drive memory and the selling price for laptops?

THINK: How much data do I need? If I am working in a group, how much should each of us collect?

WRITE: I will collect data about ______ different laptops. We will make sure __________________

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we each collect around 10 values each

How will you record your results?

LO: Write a plan for a bivariate investigation

What is the relationship between the size of the hard-drive memory and the selling price for laptops?

THINK: What things should I write down for each laptop? How will I organise this data?

WRITE: I will use a ________ to record my results. I will use ______ columns for each of the two variables.

table

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Group work!

LO: Write a plan for a bivariate investigation

What is the relationship between the size of the hard-drive memory and the selling price for laptops?

In your group, discuss how you will each contribute to the development of a plan for the assessment. Make a commitment to each person that you will attend each day of the assessment and that you will not let them down. Write down how you will demonstrate to your teacher that each person has contributed to the writing of the plan.