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Do you find students struggle to recall basic math facts or tables? Use a mental strategies approach to equip students with tools to think about the numbers and visualize how they relate to each other. I recommend you start with ten frames, and gradually and systematically build students' knowledge of basic facts in each operation. Go to www.classroomprofessor for more math teaching resources, including free sample worksheets and software license trials. Math PD notes, presented at Queensland Education Resources Expo, 24/25 August 2013 in Brisbane, Australia
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© Classroom Professor, 2013
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,
© Classroom Professor, 2013
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WHY MEMORISE NUMBER FACTS?
3
© Classroom Professor, 2013
Basic facts are part of the foundation needed for algebra, geometry, measurement, probability and statistics
© Classroom Professor, 2013
Using a calculator for basic facts is slower than recalling them
© Classroom Professor, 2013
NAPLAN!
© Classroom Professor, 2013
NAPLAN & number facts
© Classroom Professor, 2013
Human students can think; they are not robots
© Classroom Professor, 2013
Knowing basic facts allows you to answer lots of operations questions without an algorithm
© Classroom Professor, 2013
Allows students to tackle real maths - shopping, helping in the shed, sports, ...
© Classroom Professor, 2013
Knowing one number fact tells you families of other facts
© Classroom Professor, 2013
We will need the next generation to solve the world’s problems
© Classroom Professor, 2013
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THE MENTAL STRATEGIES APPROACH
13
© Classroom Professor, 2013
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
© Classroom Professor, 2013
Visualising and OWNING maths learning
4+4=810=6+41+4=
I love math
I think that 4+4=8
10=6+4
© Classroom Professor, 2013
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
© Classroom Professor, 2013
Early Years: Use Ten Frames
• How many are here?
• How many now?
• Double ten frames:
1 5
© Classroom Professor, 2013
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
© Classroom Professor, 2013
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:
© Classroom Professor, 2013
Nines Patterns
9 x 7 = ?
10 x 7 = 70 70 – 7 = 63
© Classroom Professor, 2013
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
© Classroom Professor, 2013
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].
© Classroom Professor, 2013
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OUR TIMES TABLES SOLUTION
© Classroom Professor, 2013
A Sequenced System for Memorisation of Number Facts
Yr 2
Yr 4Yr 5
Yr 3
Yr 6
© Classroom Professor, 2013
• 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:
© Classroom Professor, 2013
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
© Classroom Professor, 2013
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QUEDREX SPECIAL OFFERS
© Classroom Professor, 2013
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
© Classroom Professor, 2013
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
© Classroom Professor, 2013
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
© Classroom Professor, 2013
More Information?• Free Maths Worksheets, Gadgets software trial:• Sign up at our QUEDREX stand
• Our resources: • store.classroomprofessor.com
• Questions / Comments / Feedback: • [email protected]
• Web: • www.classroomprofessor.com