Making Algebra Accessible

Steve Pardoe, WMCETT29th June, 2015

“Why do we have to do algebra?

What’s the point?

When will I ever use it?”

What’s your reply?

3

Be specific!

What is this?

What is this?

3x + 1

Be specific!

Is this algebra?

There are to be 8 guests per table

3 tables are needed for serving food from

How many tables are needed?

Workshops aims

To explore how algebra can be made more accessible by:

Making it visual

Making links to real-life applications

(… with lots of pictures & no x, y or n!)

1st 2nd 3rd

1st 2nd 3rdDescribe the 15th and the 100th pattern

? ?

How do you know how the 15th pattern and the 100th pattern look?

How do you know how many holes there are in the 15th and 100th pattern?

How could you explain how many holes there’ll be in any pattern in the sequence?

1st 2nd 3rd

1st 2nd 3rd

How do you know how the 15th pattern and the 100th pattern look?

How do you know how many holes there are in the 15th and 100th pattern?

How could you explain how many holes there’ll be in any pattern in the sequence?

Describe the 15th and the 100th pattern

What do these three sequences have in common?

What are the differences between the sequences?

Describe how each of these sequences grows

Describe how you’d find how many holes there are in any pattern in each sequence

1st 2nd 3rd

Is this algebra?Did you use algebraic thinking?

Where in the slides did you begin using algebraic thinking?

Did you use any algebraic notation?

Where did you start using it?

How might you use this with learners in context?

The wedding planner

There are to be 8 guests per table

3 tables are needed for serving food from

How many tables are needed?

The wedding planner

What if there are 64 guests?

What if 80 guests?

What if there are 10 guests per table?

What if 4 tables are needed for serving?

The wedding plannerAssume 8 guests per table & 3 serving tables

Form an equation to show how the number of tables required varies with the number of guests

Try substituting different numbers of guests & seeing how many tables are required

Construct a table of possible values

Plot a graph to show the relationship

What questions can you ask about the graph?

Is there algebra here?

Real-life graphs & equations

Work in groups of 2 or 3

Match the different cards – making clear your justification

Answer the question cards

What might this represent?

0 2 4 6 8 10 120

200

400

600

800

1000

1200

1400

1600

1800

Singapore Bar

https://www.youtube.com/watch?v=Em2yERb3Kfs

Singapore BarAllan puts some brown sugar on a dish.

The total weight of the brown sugar and the dish is 110 g.

Bella puts three times the amount of brown sugar that Allan puts on an identical dish, and the total weight of the brown sugar and the dish is 290 g.

Find the weight of the brown sugar that Bella puts on the dish.

110 g

290 g

110 g180 g

2 units = 180 g

1 unit = 90 g

3 units = 270 g

Singapore Bar

On a package holiday, two adults and one child can go for £1135.

Similarly, the fare for two adult and three children is £1485.

How much does it cost for one adult and a child?

Singapore Bar

£1135

£1485

Singapore BarAccording to US psychologist Jerome Bruner, people learn in 3 basic stages:

1. By handling real objects

2. Through pictures

3. Through symbols

Symbols are “clearly the most mysterious of the three.”

Singapore based its maths on the ideas of Bruner.

Why study algebra?

“Our world is increasingly automated and programmed and if you want any kind of active participation in that world, you’re going to need to understand variable representation and manipulation. That’s Algebra. Without it, you’ll still be able to clothe and feed yourself, but that’s a pretty low bar for an education.”

Dan Meyer

Some useful websitesMEI Contextualisation Toolkit http

://www.mei.org.uk/contextualisation-toolkit

Mathematics Assessment Project http://map.mathshell.org

Singapore Bar: A Visual Approach to Word Problems http://www.hmhco.com/~/media/sites/home/education/global/pdf/white-papers/mathematics/elementary/math-in-focus/mif_model_drawing_lr.pdf?la=en

Great Maths Teaching Ideas: http://www.greatmathsteachingideas.com/2014/12/26/bar-modelling-a-powerful-visual-approach-for-introducing-number-topics/