Basic Facts

Middle Focus Group

Raewyn Carman & Dianne Ogle24 November 2010

Basic FactsThe place value system is universally adopted because allcalculations can be performed by knowing correctprocedures and the basic number facts.

Knowing the addition facts from 1 + 1 to 9 + 9 will enableaddition and subtraction problems to be solved, including decimal fractions.

Knowing the multiplication facts from 2 x 2 to 9 x 9 will enable all multiplication and division problems to besolved, including decimal fractions.

A lack of instant recall of basic facts, along with not

understanding place value are the two key reasons

children are not making progress in number.

• It is important that children are learning their basic facts when they need to be using them.

• Addition and subtraction facts learned first

• Times tables follow, when children are using multiplicative strategies.

Definitions of basic facts

• ARB Concept map“Any number or mathematical fact or idea that can be instantly recalled without having to resort to a strategy to derive it.”

• Van de Walle“Basic fact for addition and multiplication refer to combinations where both addends or both factors are less than 10. Subtraction and division facts correspond to addition and multiplication facts.”

Stage 4Essential for part-whole reasoning that comes in stage fiveis the instant recall of basic addition and subtraction factswith answers no more than ten.

Addition and subtraction facts up to tenDoubles – to ten

Optional:– Addition and subtraction facts from 1 + 1 to 9 + 9- Derive and learn the two times tables from doubles.

Stage 5Essential for advanced additive thinking in stage six is the instant recall of all addition and related subtraction facts 1 + 1 to 9 + 9 Recall of multiplication facts can begin with a focus on thecommutative principle for multiplicationStage 5: Essential – Addition and subtraction facts from 1 + 1 to 9 + 9- Derive and learn the two times tables from doubles.- Derive and learn the three times tables from 3 x 3 to 3 x 9 using repeated addition and the reverse facts.Optional:- Four and Five times table

Basic Facts – Stage 6Instant recall of times tables with 100% reliability isneeded for stage 7 so regular teaching and practising oftables must occur at this level. Failure to know times tables is a major obstacle in children ever becoming multiplicative in their thinking. Recall of multiplication facts can begin with a focus on thecommutative principle for multiplication

Stage 6: Essential- Derive and learn, connect to division4 times table from 4 x 4 to 4x 95 times table from 5 x 5 to 5 x 96 times table from 6 x 6 to 6 x 97 times table from 7 x 7 to 7 x 98 times table from 8 x 8 to 8 x 9Derive and learn 9 x 9, connect to 81 ÷ 9Use the 0 and 1 principles

Basic Facts – Stage 7

Essential division strategy:

Use table to work out divisions with remainders e.g. 58÷7 = 8 remainder 2.

Basic FactsLearning of times tables

• 0 times or times 0– A principle not a table

• 1 times or times 1– A principle not a table

• 10 times or times 10– An English language issue, not a table

Basic Facts – only 36 facts to learn

x 2 3 4 5 6 7 8 9

2 4 6 8 10 12 14 16 18

3 9 12 15 18 21 24 27

4 16 20 24 28 25 36

5 25 30 35 40 45

6 36 42 48 54

7 49 56 63

8 64 72

9 81

Basic Facts – from understanding to rote

Van de Walle Mastery of the basic facts is a developmental

process, students move through stages, starting with counting, then to more efficient reasoning strategies, and eventually to quick recall. Instruction must help students move through these phases, without rushing them to memorisation.

Page 167 , 2010

Approaches to fact mastery• Explicit strategy instruction – designed to support

student thinking – show students possibilities and let them choose strategies that help them get the solution without counting

• Guided invention – using strategies children have, guiding them to the efficient ones. Teacher’s job is to design tasks and problems that will promote the invention of efficient strategies

What not to do• Don’t use lengthy timed tests• Don’t use public comparison of mastery• Don’t proceed through facts in order – (knock

out the ones you know)• Don’t move to memorization too soon• Don’t use facts as a barrier to good

mathematics – mathematics is about reasoning, give children real mathematical experiences.

Strategise – Practice - Memorise

1. Start with strategies

2. Plenty of Practice

3. Move on to memorise the basic facts

Strategies - Multiplication

• Two times table - doubles• Three times table – doubles plus one or repeated

addition• Four times table – double double• Six times table – five plus one• Seven times table – five plus two • Eight times table – double four

Strategies - Multiplication

• Nifty nines – the tens digit of the product is always one less than the other factor, add that to make nine.

9 x 7 = 63

• Investigate the patterns! – How can we do this? Discuss ideas.

one less

add to 9

Strategies - Multiplication

• Investigate the patterns!

• How can we do this? Discuss ideas. What do you do now?

• Maths Games Workshop

Strategies - Multiplication• Relate to a known fact or a helping fact

6 x 7Relate to

5 x 7 (five sevens and 7 more)3 x 7 (double 3 x 7)

Children must be able to add on the 7 or double 21 using a part-whole method.

Strategies - Division• Connect to multiplication – reversibility

56÷ 8 = ? As 8 x ? = 56

• Continually make connections with Family of Facts (Triplets)

• Halve and halve e.g. 40 ÷ 8 is the same as 20 ÷ 4 or 10 ÷ 2

Missing Number worksheet

• Begin with circles and ask children what they notice about the numbers

• Teach the children the circle always has the answer

• Fill in sheet with two numbers children have to find missing number

6 4

6 24

24

64

Triplets – Family of Facts

• Introduce triplets

• 24 , 6, 4

• Make chains of number triplets

• Try 2 out of 3

24

6 4

1,2,3 Fists - Paper, Scissors, RockTwo players

Play as for Paper, Scissors, Rock

One or two hands

Count 1,2,3, put down some fingers - multiply together

Salute• You need three players• A pack of playing cards (take out 10s and colour cards

• Two players collect one card each. Without looking at the card they put it on their forehead.

• The third player calls out the sum or product of the two cards• The two players then call out what card they hold on their forehead by

looking at the other player’s cards.• The player who calls out first wins those cards. • Continue playing until all the cards are used.

Variations• 10 more or ten less/ one more or one less• Multiply • Doubles

Speed (War)Two players

Deal all cards out between two players.

Place one card in middle. - e.g. 2 (multiply by two)

Take turns to turn over one card - both players call out answer. First to call wins both cards.

If a tie, turn over another card. Highest card gets to keep all three cards.

Also for addition

Grab FiveGrab five sticks

Put them in order from smallest to biggest.

Winner is the first one to grab the object from the centre of the table. Must have sticks in the right order.

Can be made to fit children from Year 1 - 8

Circle a Fact• Place a set of A4 numeral cards zero to nine in a circle on the

floor. • Children form a circle around cards or make two teams either

side of the circle. • Two people walk around the outside of the circle, on stop place

their toe on a card. • Winner is the person who calls out answer first. They can

– Add the two numbers together– Double the numbers– Add 10, double plus or minus one or two– Multiply the numbers– Find the difference of the two numbers

Connecting oral to written

• Important that children are given opportunities to practise often.

• Practise must be correct. (MEI resource)

• Take one or two facts to memorisation at a time.

• Oral connection to basic facts is important for the brain

Don’t forget

• Number Facts and Wheels• Thinkboards• Online practise – Digital Learning Objects• If I know, then I know• Plenty of opportunities to apply basic facts to

real life problems

Discussion Time

• Share with your table other useful activities you use to help children learn basic facts.