Making Algebra
Accessible
Steve Pardoe, WMCETT
29th June, 2015
“Why do we have to do algebra?
What’s the point?
When will I ever use it?”
What’s your reply?
What is this?
Be specific!
3
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
1st
2nd
2nd
3rd
3rd
Describe 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?
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?
1st
1st
2nd
2nd
3rd
3rd
Describe the 15th and the 100th
pattern
How could you explain how
many holes there’ll be in any
pattern in the sequence?
1st
2nd
3rd
Describe how each of these
What do these three sequences grows
sequences have in common?
Describe how you’d find how
What are the differences
many holes there are in anybetween the sequences?
pattern in each sequence
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 planner
 Assume 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?
1800
1600
1400
1200
1000
800
600
400
200
0
0
2
4
6
8
10
12
Singapore Bar
 https://www.youtube.com/watch?v=Em2y
ERb3Kfs
Singapore Bar
Allan 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
2 units = 180 g
1 unit = 90 g
180 g
110 g
290 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 Bar
According 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 websites
 MEI 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-infocus/mif_model_drawing_lr.pdf?la=en
 Great Maths Teaching Ideas:
http://www.greatmathsteachingideas.com/2014/12/26/barmodelling-a-powerful-visual-approach-for-introducingnumber-topics/