Making Algebra Accessible Steve Pardoe, WMCETT 29 th 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?

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!)

1st2nd3rd 1st2nd3rd Describe the 15 th and the 100 th pattern

? ? How do you know how the 15 th pattern and the 100 th pattern look? How do you know how many holes there are in the 15 th and 100 th pattern? How could you explain how many holes there ’ ll be in any pattern in the sequence?

1st2nd3rd 1st2nd3rd How do you know how the 15 th pattern and the 100 th pattern look? How do you know how many holes there are in the 15 th and 100 th pattern? How could you explain how many holes there ’ ll be in any pattern in the sequence? Describe the 15 th and the 100 th 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 1st2nd3rd

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?

Singapore Bar ERb3Kfs 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 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 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 Mathematics Assessment Project Singapore Bar: A Visual Approach to Word Problems /pdf/white-papers/mathematics/elementary/math-in- focus/mif_model_drawing_lr.pdf?la=en /pdf/white-papers/mathematics/elementary/math-in- focus/mif_model_drawing_lr.pdf?la=en Great Maths Teaching Ideas: modelling-a-powerful-visual-approach-for-introducing- number-topics/ modelling-a-powerful-visual-approach-for-introducing- number-topics/