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 Facts By stage five instant recall of basic addition facts is
required. There is plenty of time to learn them. A framework for learning basic facts: Stage 2: Addition and subtraction facts to five Stage 3: Essential to recall addition and subtraction facts to five Optional – Addition and subtraction with sums up to ten, doubles to ten
Stage 4 Essential for part-whole reasoning that comes in stage five
is the instant recall of basic addition and subtraction facts with answers no more than ten. Addition and subtraction facts up to ten Doubles – to ten Optional: – Addition and subtraction facts from to 9 + 9 - Derive and learn the two times tables from doubles.
Stage 5 Essential 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 the commutative principle for multiplication Stage 5: Essential – Addition and subtraction facts from 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 6 Instant recall of times tables with 100% reliability is needed for stage 7 so regular teaching and practising of tables 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 the commutative principle for multiplication Stage 6: Essential- Derive and learn, connect to division 4 times table from 4 x 4 to 5 x 9 5 times table from 5 x 5 to 5 x 9 6 times table from 6 x 6 to 6 x 9 7 times table from 7 x 7 to 7 x 9 8 times table from 8 x 8 to 8 x 9 Derive and learn 9 x 9, connect to 81 ÷ 9 Use the 0 and 1 principles
Basic Facts Learning of times tables 0 times or times 0
A principle not a table 1 times or times 1 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 10 12 14 16 18 15 21 24 27 20 28 25 36 30 35 40 45 42 48 54 49 56 63 64 72 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 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
Start with strategies Plenty of Practice 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 subtraction
Links 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
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 table
3x table From repeated addition The 2x table plus one more 4x table Double 2x table 6x table Double 3x table. 5x plus one more 8x table Double, double, double or double 4x table 9x 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 practised If 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 10 4 6 6 2 6 10
Triplets – Family of Facts
Introduce triplets 10 , 6, 4 Make chains of number triplets Try 2 out of 3 10 6 4 4 2
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 ten Three and seven makes ten Ten take away seven is three Ten 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 ten Two 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, Rock
Two 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 Five Grab 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 know To 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
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