Students Struggling with Times Tables? Develop Mental Strategies

Subtraction
• How many times can you
subtract 7 from 83, and what is
left afterwards?
• You can subtract it as many
times as you want, and it leaves
76 every time.
• (The Quote Garden)
© Classroom Professor, 2013

the Key to Fluency
Dr Peter Price
Classroom Professor
QUEDREX 2013
Students Struggling
with Number Facts?
Develop Mental
Strategies,

0 1 2 3 4 5
WHY MEMORISE NUMBER
FACTS?
2

Basic facts are part of the
foundation needed for
algebra, geometry, measu
rement, probability and
statistics

Using a calculator for
basic facts is slower than
recalling them

NAPLAN!

NAPLAN & number facts

Human
students
can think;
they are
not robots

Knowing basic facts
allows you to answer lots
of operations questions
without an algorithm

Allows students to tackle
real maths -
shopping, helping in the
shed, sports, ...

Knowing one number fact
tells you families of other
facts

We will need the next
generation to solve
the world’s problems

0 1 2 3 4 5
THE MENTAL STRATEGIES
APPROACH
12

What are we aiming for?
• We want students to understand what they are
doing.
• Rote learning is based on repetition, and cannot
lead to understanding
• Once you forget something learned by
rote, there is little to fall back on
• If you understand and can visualise the
numbers, if you forget you can figure it out
again

Visualising and OWNING
maths learning
4+4=8
10=6+4
1+4=
I love
math
I think that
4+4=8
10=6+4

Early Years:
Use Ten Frames
• Ten frames are the best resource for
representing numbers up to 20
• Aim is to subitise patterns for each number

Early Years:
Use Ten Frames
• How many are here?
• How many now?
• Double ten frames:
1 5

Addition & Subtraction
Strategies
• Count on +1, +2, +3
• Doubles, doubles +1
• Rainbow facts
• Near 10
• Remaining facts
0 1 2 3 4 5 6 7 8 9 10

Multiplication Strategies
• 2x: doubles
• 10x, 5x: place value
• 3x: double + one more
• 4x: double double
• 0x, squ nos: special cases
• 9x: think of tens
• 8x: double double double
• 6x: build from known facts
• 7x: build from known facts
6 x 2 = double 6 = 12
6 x 4 = double 12 = 24
6 x 8 = double 24 = 48
DOUBLING strategies:

Nines Patterns
9 x 7 = ?
10 x 7 = 70 70 – 7 = 63

Nines Patterns
• 9 x 1 = 9
• 9 x 2 = 18
• 9 x 3 = 27
• 9 x 4 = 36
• 9 x 5 = 45
• 9 x 6 = 54
• 9 x 7 = 63
• 9 x 8 = 72
• 9 x 9 = 81
• 9 x 10 = 90
0
1
2
3
4
5
6
7
8
9
+
+
+
+
+
+
+
+
+
+
=
=
=
=
=
=
=
=
=
=
9
8
7
6
5
4
3
2
1
0
9
9
9
9
9
9
9
9
9
9
9 x 7 =
1 less
than 7
9 – 6 = 3
6 3

Nines Patterns
1
2
3
4
5 6
7
8
9
10
9 x 7 = ?
6 3

References
• Child’s drawing copied with permission from Aviva Dunsiger:
http://missd.commons.hwdsb.on.ca/2012/05/11/school-point-of-view/
• All other graphics from Flickr, copied under Creative Commons License:
• Question & ladder:StockMonkeys.com http://www.flickr.com/photos/86530412@N02/8231156853/sizes/o/
• Calculator:jakeandlindsay http://www.flickr.com/photos/jakeandlindsay/5639214967/sizes/o/
• Little skier: The U.S. Military Academy at West Point http://www.flickr.com/photos/west_point/4425431834/sizes/o/
• Exam room: Z17R0 http://www.flickr.com/photos/42319778@N02/4923775302/sizes/o/
• Sale notice: Danny Nicholson http://www.flickr.com/photos/dannynic/6363183821/sizes/l/
• Duck family: kiwinz http://www.flickr.com/photos/kiwinz/4012597779/sizes/o/
• Polluted beach: Vince Alongi http://www.flickr.com/photos/vincealongi/306696455/sizes/o/
• Making Bubbles: Maxmroz http://www.flickr.com/photos/maxmroz/5758445169/sizes/o/
• Robot 1: geishaboy500 http://www.flickr.com/photos/geishaboy500/108824992/sizes/o/
• Math Sculpture: NMC Second Life http://www.flickr.com/photos/nmc-campus/249565400/sizes/o/
• Highway sign: quinn.anya http://www.flickr.com/photos/quinnanya/5798114796/sizes/o/
• Climbing :Mathematical Association of America http://www.flickr.com/photos/maaorg/6348838232/sizes/l/
• Toy Ducks: pterjan http://www.flickr.com/photos/cmoi/46192785/sizes/o/
• The Quote Garden 2013, Quotations about Math, http://www.quotegarden.com/math.html
[Accessed 13 August 2013].

0 1 2 3 4 5
OUR TIMES TABLES SOLUTION

A Sequenced System for
Memorisation of Number
Facts
Yr 3

• Year 2:
• Lets Go!
• Year 3:
• 10 Minutes a Day, Level 1
• Year 4:
• Year 5:
• Year 6-7:
• Bring It On!
“Developing Number Fluency” eBook series:

Classroom Professor Gadgets Software
• Five modules:
• Fraction Counter
• Equivalent Fractions
• Fraction Converter
• Fraction Addition & Subtraction
• Number Fact Exploration
• Designed for IWB use
• Cross-platform (works on iPads)
• Follow-up worksheets eBook for
each module
• Unlimited 12-month licenses
QUEDREX PD SESSION:
Fractions are Tough to
Teach, and Difficult to Learn!
Saturday 12:45
Sunday 10:45
Right here

0 1 2 3 4 5
QUEDREX SPECIAL OFFERS

QUEDREX-only Bundle #1
• Early Years (P-2) Bundle:
• Ten Frames Bundle:
• Flash Cards
• Worksheets
• Games
• Let’s Go! eBook series (4 eBooks)
• Introducing Fractions 1 & 2
Normally:
$205

• Year 3-7 Bundle:
• Your choice of a 10 Minutes a
Day or Bring It On! eBook
series (4 eBooks)
• Gadgets Software
• cross-platform interactive
• 5 titles + eBooks
• 12-month classroom license
Normally:
$270

• School Bundle:
• Entire Developing Number
Fluency series (20 eBooks)
• Gadgets Software
• cross-platform interactive
• 5 titles + worksheets
eBooks
• 12-month school site
license

More Information?
• Free Maths Worksheets, Gadgets software trial:
• Sign up at our QUEDREX stand
• Our resources:
• store.classroomprofessor.com
• Questions / Comments / Feedback:
• peter@classroomprofessor.com
• Web:
• www.classroomprofessor.com

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