Presentation on theme: "Basic Facts – one definition"— Presentation transcript:
1 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.”
2 Basic Facts By 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 fiveStage 3:Essential to recall addition and subtraction facts to fiveOptional – Addition and subtraction with sums up to ten, doubles to ten
3 Stage 4 Essential for part-whole reasoning that comes in stage five is the instant recall of basic addition and subtraction factswith answers no more than ten.Addition and subtraction facts up to tenDoubles – to tenOptional:– Addition and subtraction facts from to 9 + 9- Derive and learn the two times tables from doubles.
4 Stage 5 Essential for advanced additive thinking in stage six is the instant recall of all addition and related subtraction facts1 + 1 to 9 + 9Recall of multiplication facts can begin with a focus on thecommutative principle for multiplicationStage 5: Essential– Addition and subtraction facts from to 9 + 9Derive and learn the two times tables from doubles.Derive and learn the five times tableDerive and learn the three times tables from 3 x 3 to3 x 9 using repeated addition and the reverse facts.Optional:- Four and Five times table
5 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 childrenever 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 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
6 Basic Facts Learning of times tables 0 times or times 0 A principle not a table1 times or times 110 times or times 10An English language issue, not a table
7 Basic Facts – only 36 facts to learn x234567891012141618152124272028253630354045424854495663647281
8 Basic Facts – from understanding to rote Van de WalleMastery 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
9 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 countingGuided 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
10 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 soonDon’t use facts as a barrier to good mathematics – mathematics is about reasoning, give children real mathematical experiences.
11 Strategise – Practice - Memorise Start with strategiesPlenty of PracticeMove on to memorise the basic facts
12 Strategies that help for addition Links to counting –Adding nothing leaves the number unchangedAdding one gives the next number in the counting sequenceAdding two corresponds to the skip counting pattern
13 Strategies that help for subtraction Links to counting –Taking off zero (nothing) leaves the number unchangedTaking off one gives the previous number in the counting sequenceTaking off two corresponds to the skip counting pattern
14 Strategies - Addition Doubles and near doubles plus or minus 1 Make a tenNear groupings to ten 6+5, 6+3Plus nine – plus 10, take away one
15 Strategies - Subtraction HalvesThe opposite of addition – subtraction as counting on from, 8-6 as count on from 6 until reach 8Subtract nine – take away 10, add oneDerived from addition using the family of facts
16 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.
17 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 tableFollows from the 10 times table, the jumps half way between each ten.Make the connection to counting in lots of fiveUse the slavonic abacus to reinforce lots of five
18 Strategies for times table 3x tableFrom repeated additionThe 2x table plus one more4x tableDouble 2x table6x tableDouble 3x table.5x plus one more8x tableDouble, double, double or double 4x table9xX10 take away oneThe 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
19 Division StrategyWhat thought processes do you use to recall division facts?Learn the turnaround facts – 42÷ 6 = ?As 6 x ? = 42
20 AssessmentOnce 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.
21 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
22 Missing Number worksheet Begin with circles and ask children what they notice about the numbersTeach the children the circle always has the answerFill in sheet with two numbers children have to find missing number104662610
23 Triplets – Family of Facts Introduce triplets10 , 6, 4Make chains of number tripletsTry 2 out of 3106442
24 Tens FramesHold 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 sevenAs children tell the story it is important they see written forms – words and symbols
26 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 framesWorking backwards - subtraction is harder. Children need lots of practise with subtraction
27 1,2,3 Fists - Paper, Scissors, Rock Two playersPlay as for Paper, Scissors, RockOne or two handsCount 1,2,3, put down some fingers - add/multiply together
28 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.
29 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.
30 Salute You need three players A pack of playing cards (take out 10s and colour cardsTwo 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 cardsThe 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.Variations10 more or ten less/ one more or one lessMultiplyDoubles
31 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
32 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
33 If I know, then I knowTo help children make connections with what they know and how it helps them to solve other problemsMakes links to knowledge they haveIndependent 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.
34 Circle a FactPlace 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 canAdd the two numbers togetherDouble the numbersAdd 10, double plus or minus one or twoMultiply the numbersFind the difference of the two numbers