Basic Facts

Junior Focus Group23 November 2010

Raewyn Carman & Dianne Ogle

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 notunderstanding place value are the two key reasonschildren 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.

Basic Facts – Stage 2-3By stage five instant recall of basic addition facts is required. There is plenty of time to learn them. Aframework for learning basic facts:

Stage 2: Addition and subtraction facts to five

Stage 3: Essential to recall addition and subtraction facts to fiveOptional – Addition and subtraction with sums up to ten,

doubles to ten

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 multiplicationStage 6: Essential- Derive and learn, connect to division

4 times table from 4 x 4 to 4 x 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 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 learnx 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 roteVan 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 - Memorise1. Start with strategies

2. Plenty of Practice

3. Move on to memorise the basic facts

Strategies that help for additionLinks to counting –• Adding nothing leaves the number unchanged• Adding one gives the next number in the

counting sequence• Adding two corresponds to the skip counting

pattern

Strategies that help for subtractionLinks to counting –• Taking off zero (nothing) leaves the number

unchanged• Taking off one gives the previous number in the

counting sequence• Taking off two corresponds to the skip counting

pattern

Strategies - Addition• Doubles and near doubles

plus or minus 1plus or minus 2

• Make a tenNear groupings to ten 6+5, 6+3

• Plus nine – plus 10, take away one

Strategies - Subtraction• Halves

• The opposite of addition – subtraction as counting on from, 8-6 as count on from 6 until reach 8

• Subtract nine – take away 10, add one

• Derived from addition using the family of facts

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 2

6 10

10

64

Triplets – Family of Facts• Introduce triplets

• 10 , 6, 4

• Make chains of number triplets

• Try 2 out of 3

10

6 4

Tens Frames• Hold up a tens frame and have the children

say the 10 facts that go with the card. • Children need to be able to say the four

connected facts that go with each tens frameSeven and three makes tenThree and seven makes tenTen take away seven is threeTen take away three is seven

As children tell the story it is important they see written forms – words and symbols

Add to tenTwo playersDeal all cards out between two players. Take turns to turn over one card - state what else makes 10. Also play by taking number off ten. Modify for younger students – make five (remove some cards, use five frames/tens framesWorking backwards - subtraction is harder. Children need lots of practise with subtraction

1,2,3 Fists - Paper, Scissors, RockTwo playersPlay as for Paper, Scissors, Rock One or two handsCount 1,2,3, put down some fingers - add/multiply together

Make Ten, Two playersDeal out ten cards in a row. First player looks across the row for combinations that make ten. Aim is to collect as many cards as possible, so combinations that require more cards are best.Continue playing until all the cards are used or until there are no more combinations that add to ten.Winner has the most cards.

Make Ten again, Two playersDeal all cards out in 3x3 gridTake turns to make 10 - Continue playing until all the cards are used or until there are no more combinations that add to ten.Winner has the most cards.

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 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 playersDeal all cards out between two players. Place one card in middle. - e.g. 2 (add this number to card that is turned over) 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 multiplication

Grab FiveGrab five sticksPut 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.

• 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

Discussion Time• Share with your table other useful activities

you use to help children learn basic facts.