students struggling with times tables? develop mental strategies

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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)

the Key to FluencyDr Peter PriceClassroom ProfessorQUEDREX 2013

Students Struggling with Number Facts? Develop Mental Strategies,

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WHY MEMORISE NUMBER FACTS?

3

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

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Using a calculator for basic facts is slower than recalling them

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NAPLAN!

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NAPLAN & number facts

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Human students can think; they are not robots

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

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

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Knowing one number fact tells you families of other facts

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

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THE MENTAL STRATEGIES APPROACH

13

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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

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Visualising and OWNING maths learning

4+4=810=6+41+4=

I love math

I think that 4+4=8

10=6+4

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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

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Early Years: Use Ten Frames

• How many are here?

• How many now?

• Double ten frames:

1 5

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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

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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:

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Nines Patterns

9 x 7 = ?

10 x 7 = 70 70 – 7 = 63

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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

0123456789

++++++++++

==========

9876543210

9999999999

9 x 7 =

1 less than

7

9 – 6 = 3

63

© Classroom Professor, 2013

Nines Patterns

1

23

4

5 6

78

9

10

9 x 7 = ?

6 3

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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].

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OUR TIMES TABLES SOLUTION

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A Sequenced System for Memorisation of Number Facts

Yr 2

Yr 4Yr 5

Yr 3

Yr 6

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• Year 2:

• Lets Go!

• Year 3: • 10 Minutes a Day, Level 1

• Year 4: • 10 Minutes a Day, Level 2

• Year 5:

• 10 Minutes a Day, Level 3• Year 6-7:

• Bring It On!

“Developing Number Fluency” eBook series:

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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 12:45Sunday 10:45

Right here

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QUEDREX SPECIAL OFFERS

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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 $109

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QUEDREX-only Bundle #2

• 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 $145

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QUEDREX-only Bundle #3

• School Bundle:• Entire Developing Number

Fluency series (20 eBooks)

• Gadgets Software• cross-platform interactive• 5 titles + worksheets eBooks• 12-month school site license

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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