Modelling Tasks Lessons Assessment Reflecting

Lessons

Modelling Tasks Lessons Assessment Reflecting

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CompetenciesMethods ICT

In this sub-module you will consider how you can use a modelling approach to teach with a focus on specific mathematical content.

Objectives

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CompetenciesMethods ICT

You will have considered how to devise tasks that lead to lessons where you can use a modelling approach to allow students to learn specific mathematical content.

This module therefore recognises the pressure that teachers often feel to be “covering” the curriculum.

Outcomes

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CompetenciesMethods ICT

You wish to focus on a particular area of the curriculum.

How might you use a mathematical modelling task to ensure learners engage with this?

One way is to develop a task that attempts this – perhaps from an already existing problem that you adapt into a more open modelling task.

Focussing on curriculum content

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AreaPositive & negative numbers

Algebra Handling information/

data

Examples

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Example: Introducing algebra

Imagine…..

You are asked to introduce algebra

Small task: in groups consider what approaches you may have used to do this in the past.

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Introducing algebra

An important aspect of algebra is understanding “letters as variables”Initially students often engage with solving equations at an early stage such as3 + = 12How does this encourage understanding of letters as variables?

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Introducing algebra

This text book encourages students to consider letters as variables.

How can some of these ideas be introduced in such a way that students explore “variable”?

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A class at school decide to raise money for charity by selling refreshments at break-time.

They plan to make 20p profit on each cup of fruit juice they sell.

If they sell c cups, how much will they make in total?

Introducing algebra

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The class also plans to make 15p profit on each fruit bar they sell.

If they sell b bars, how much will they make in total?

What if they combine sales of fruit juice and cereal bars?

Introducing algebra

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12

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Task:

1 Rewrite this idea as an open modelling task.

2. Discuss how you could encourage students working on the task to use an algebraic approach when presenting their work.

Introducing algebra

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CompetenciesMethods ICT

Example: Introducing area

Imagine…..

You are asked to introduce ideas of area

Small task: in groups consider what approaches you may have used to do this in the past.

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Introducing area

The way surface area is introduced in books usually refers to covering a specific area (e.g. rectangle) with smaller squares.

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CompetenciesMethods ICT

How many red and how many blue tiles are needed to cover a kitchen’s (yellow) floor?

Introducing area

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A family wants to refurbish their kitchen floor.

They decided to use blue and red tiles. How many different combinations and patterns can you suggest to them using the two types of tiles?

Introducing area

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Task:

1 Rewrite this idea as an open modelling task.

2. Discuss how you could encourage students working on the task to use understanding of area.

Introducing area

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Introducing area

A family wants to refurbish the floor of the house they use for their weekend holidays. A tiler suggests using three different tile sizes.

The medium size is twice as big as the small tile and the large one is twice as big as the medium size tile.

How much would it cost to cover the floor?

€2

€3

€4

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CompetenciesMethods ICT

Example: adding and subtracting negative numbers

Imagine…..

You are asked to introduce adding and subtracting positive and negative numbers

Small task: in groups consider what approaches you may have used to do this in the past.

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CompetenciesMethods ICT

It is important that students gain an understanding of negative numbers and how they should be added and subtracted – they need plenty of opportunities to practise.

Text books often include exercises like this:

The challenge is to have a task that allows students an opportunity to explore a mathematical model whilst practising lots of addition and subtraction……..

Example: adding and subtracting negative numbers

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CompetenciesMethods ICT

A possible context:

In TV game shows contestants are sometimes awarded negative points if they get a question incorrect.

Investigate different ways of awarding points.

Example: adding and subtracting negative numbers

Images: Thanks to John Oneill, Kamal Sellehuddin at Wikimedia Commons.Files licensed under Creative Commons Attribution 2.0 License.

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You could try simulating contestants in the quiz using coins, dice, spinners.

Thanks to Ptkgfs, published at Wikimedia Commons

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Discuss how you could encourage students working on the task to learn about positive and negative numbers.

Have you any other ideas about how you might take a modelling approach to introducing this topic?

Example: adding and subtracting negative numbers

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Example: Handling information / data

A sample problem:

Alex wants to watch the “Cat Riddle” movie. The movie starts at 8.30 pm. Alex has a guitar lesson which starts at 7.30 pm and last for 45 minutes. If he needs 25 minutes to walk from his music lesson to the cinema, will he be there on time?

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Example: Handling information / data

Programme

Internet Journeys (113 minutes) 7.00 9.00 (Mon, Fri)

The Ship (92 minutes) 7.15 8.30 (Sat, Sun)

Blue Fish (85 minutes) 7.30 9.00 (Tues, Thur)

Cat Riddle (104 minutes) 6.45 8.45 (Sun)

Nick wants to go to the cinema with two friends. He asks them when they can go.

When could the friends visit the cinema?

Mary

On Wednesdays and Mondays I

have guitar lessons

John

I visit my grandma every

Sunday

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Can you develop the task further as a modelling task?

Example: Handling information / data

Thanks to Heidas, published at Wikimedia Commons

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Task:

Choose an area of the curriculum that you will work on with a class in the near future.

Consider how you might take a modelling approach to this.

Activity 1

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CompetenciesMethods ICT

In this sub-module you will consider how you can use a modelling approach to teach with a focus on specific mathematical content.

Objectives

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Content

29

CompetenciesMethods ICT

You will have considered how to devise tasks that lead to lessons where you can use a modelling approach to allow students to learn specific mathematical content.

This module therefore recognises the pressure that teachers often feel to be “covering” the curriculum.

Outcomes

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30

CompetenciesMethods ICT

Use your Teacher diary to: Plan a modelling lesson that will focus on a specific topic

in mathematics Reflect on how this went: in particular how successful it

was in covering the curriculum content.

Teacher diaries