Basic Facts – one definition ARB – Basic Fact Concept Map “Any number or mathematical fact or idea that can be instantly recalled without having to resort.

Basic Facts – one definition

• ARB – Basic Fact Concept Map

“Any number or mathematical fact or idea that can be instantly recalled without having to

resort to strategy.”

Basic FactsBy 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 five times table- 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 5 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 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.

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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 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 that help for addition

Links 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 1

plus or minus 2

• Make a ten

Near 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

Strategies - Multiplication

• Multiplication facts can be mastered by relating new facts to existing knowledge – important that children understand the commutative property – 2x8 is related to 8x2, (turnaround facts) and should be learned together.

Two times table• The sequence of doubles. • Use work problems where 2 is the number of sets.

Later use problems where 2 is the size of the sets.Five times table• Follows from the 10 times table, the jumps half

way between each ten. • Make the connection to counting in lots of five• Use the slavonic abacus to reinforce lots of five

Strategies for times table3x table• From repeated addition• The 2x table plus one more4x table• Double 2x table6x table• Double 3x table. • 5x plus one more8x table• Double, double, double or double 4x table9x• X10 take away one • The tens digit of the product is always one less than the other factor (the one

other than 9)• The sum of the two digits in the product is always nine

Division Strategy

• What thought processes do you use to recall division facts?

• Learn the turnaround facts – 42÷ 6 = ? As 6 x ? = 42

Assessment

• Once some facts have been learnt regular assessments, both written and oral, help strengthen the learning.

• It is crucial that all errors be corrected immediately then the correct fact practisedIf the student got 6+3=8 the teacher ensures that the child writes 6+3 =9, 3+6=9, 9–6 = 3, 9-3=6. The student should repeat saying, seeing, and writing each fact at least 5 times.

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

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 frame

Seven and three makes tenThree and seven makes ten

Ten 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

Games to help children with basic facts.

Add to tenTwo players

Deal 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 frames

Working backwards - subtraction is harder. Children need lots of practise with subtraction

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 - add/multiply together

Make Ten, Two players

Deal 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 players

Deal all cards out in 3x3 grid

Take 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 players

Deal 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 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

If I know, then I knowTo help children make connections with what they know and how it helps them to solve other problems

Makes links to knowledge they have

Independent and group activity.

Can begin as a whole class warm up.

With a partner - if I know 4 + 3, then I know…

Share with other group at your table.

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