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/
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