Tricks and Tips
Methods for explaining
mathematical concepts
Jo Morgan
@mathsjem
resourceaholic.com
Aims
• Share, discuss and assess alternative
approaches for explaining mathematical
concepts
• Reflect on the importance of subject
knowledge and clarity of explanation
What determines the way we
choose to explain things?
Methods, tricks, shortcuts
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Source: missbsresources.com
Easy to explain?
Easy to remember?
Conceptual understanding?
Common misconceptions?
Activity
Find the Highest Common Factor of the following:
60 and 72
60 and 225
128 and 320
Methods for Finding a Highest Common Factor
The Euclidean Algorithm
Try a new method?
Listing outcomes
Venn method
Pairing method
Indian Method
Euclidean
Algorithm
Use a different method to
find the Highest Common
Factor of the following:
•60 and 72
•60 and 225
•128 and 320
Discuss preferences, pros
and cons.
Tips
For factors, think of a factory
(where separate parts are put
together).
For multiples, think of multipacks eg if cokes are sold in
multi-packs of 6 then I can buy
6, 12, 18 etc.
Activity
Sketch the function y = x2 - 6x + 10,
labelling the coordinates of the turning point.
Turning points in the new GCSE
Turning points
1. ‘Vertex Form’
Complete the square
Graph transformations
2. Formula -b/2a
3. Calculus
4. Symmetry
Source: jamestanton.comm
Vertex Form
Transformations
Formula
Calculus
Symmetry
Activity
Factorise these expressions:
a) 2x 2 + 7x + 6
b) 4x 2 + 5x − 9
c) 6x 2 + 17x + 12
A fine line between a ‘trick’ and a ‘method’
Three methods… plus any others you want to share
• Guess and check
• Grouping
• Slide and divide
Many more here:
http://www.resourceaholic.com/2014/05/fact
orising-harder-quadratics.html
Source: nixthetricks.com
Source: nixthetricks.com
Source: nixthetricks.com
Source: nixthetricks.com
Try a new method?
Factorise these expressions:
a) 2x 2 + 7x + 6
b) 4x 2 + 5x − 9
c) 6x 2 + 17x + 12
Activity
Find the nth term of the following sequences:
a) 9, 12, 15, 18, 21, …
a) -3, 5, 13, 21, 29, …
a) 42, 34, 26, 18, 10, …
Linear sequences: finding the nth term
Tools for ‘Shifting Times Tables’
• http://nrich.maths.org/6713
• http://www.mathspad.co.uk/interactives/sequenc
es/sequences.php
Resources for ‘Zeroth Term’
http://donsteward.blogspot.co.uk/2015/01/jumpingalong-line.html
Try a new method?
Zeroth term
Shifting tables
n=1
Formula
Use a different method to
find the nth term of the
following sequences:
a) 9, 12, 15, 18, 21, …
b) -3, 5, 13, 21, 29, …
c) 42, 34, 26, 18, 10, …
Discuss preferences, pros
and cons.
The Formula Triangles Debate
Units are helpful!
Formula triangles: your opinion?
• http://www.flyingcoloursmaths.co.uk/mathematic
al-pirate-formula-triangle/
• https://cavmaths.wordpress.com/2014/10/12/for
mula-triangles/
The dangers of shortcuts
Key Messages
• If your students 'don't get it', can you find a
different way to explain it? What's confusing
them?
• For teachers, strong subject knowledge and
clarity of explanation are vital.
• Talk to your colleagues! Watch them teach!
Learn from each other.
Inspiration
• Posts on resourceaholic.com tagged
‘methods’. Includes surds, linear graphs,
algebraic division and matrices.
• nixthetricks.com, betterexplained.com,
jamestanton.com
• solvemymaths.com (complements)
• Twitter Lesson Planning #mathsTLP - Sundays
at 7pm - hosted by @mathsjem and
@solvemymaths
About MEI
• Registered charity committed to improving
mathematics education
• Independent UK curriculum development body
• We offer continuing professional development
courses, provide specialist tuition for students
and work with industry to enhance mathematical
skills in the workplace
• We also pioneer the development of innovative
teaching and learning resources