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MENTAL COMPUTATION. Why Focus on Mental Mathematics?. It is the form of calculation used by numerate people. It makes sense. It develops number sense. It promotes thinking and reasoning skills. It provides an insight into student’s thinking and understanding.
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Why Focus on Mental Mathematics? • It is the form of calculation used by numerate people. • It makes sense. • It develops number sense. • It promotes thinking and reasoning skills. • It provides an insight into student’s thinking and understanding. • When students use the written algorithm they often get the wrong answer.
MENTAL COMPUTATION Develops from: Focused discussions to introduce and reinforce mental strategies using: 1) Visual aides and models 2) Number Sense Activities 3) Contextual Problem 4) Relevant games Practicing mental strategies with: 1) Appropriate oral work 2) Appropriate written work 3) Relevant games
NUMBER FACTS ARE IMPORTANT 1) Knowledge of the facts is essential for mental computation 2) The thinking strategies that we use to establish the facts are great starting points for mental computation. The strategies are NO longer JUST the vehicle for learning the FACTS. The strategies are the beginning for MEMTAL COMPUTATION.
What strategies are likely to be extended beyond the number fact range? ADDITION Count-on 0, 1, 2, 10 Doubles and use doubles Use combinations equal to 10 MULTIPLICATION Use counting (5’s and 10’s) Think real-world (0’s and 1’s) Use doubles (2’s, 4’s and 8’s) Build up/down (9’s, 6’s and 3’s)
$19.00 STRATEGY vs TABLES A ‘strategy’ approach to learning number facts provides a better foundation for mental computation than a ‘tables’ approach. What is the cost of 3 shirts at $ 19.00 each? The traditional teaching of ‘tables’ DOES NOT emphasize THINKING.
ADDITION STRATEGIES for 69 + 27 Make a ten 69 + 27 is the same as 70 + 26 Add the parts 69 + 27 is the same as 69 + 20 + 7 Use place-value 69 + 27 is the same as 60 + 20 + 9 + 7 Round or Adjust 69 + 27 is the same as 69 + 30 - 3
SUBTRACTION STRATEGIES for 75 - 29 Use a ten 75 - 29 is the same as 76 - 30 Round or Adjust 75 - 29 is the same as 75 - 30 + 1 Subtract the parts 75 - 29 is the same as 75 - 20 - 9 Count on 75 - 29 is the same as 29 + 1 + 40 + 5 = 75
MULTIPLICATION STRATEGIES for 8 x 15 Double and Halve 8 x 15 is the same as 4 x 30 Use doubles 8 x 15 is the same as double, double, double 15 Multiply the parts 8 x 15 is the same as (8 x 10)+(8 x 5) Use factors 8 x 15 is the same as 8 x 5 x 3
DIVISION STRATEGIES for 328 ÷ 8 Halve (Related to Double) 328 ÷ 8 is the same as having 328, then halving that and halving again. Divide the parts 328÷8 is the same as (320 ÷ 8)+(8 ÷ 8)
NUMBER SENSE Complete the story using each of these numbers only once. 1.95 10 7.80 2.20 4 Jamie bought ______ ice cream cones. She paid $ _____ each. The total cost was $ _____ . She received $ _____ change from $ ______ .
NUMBER SENSE Examine the number line. 0 If the arrow is pointed to 50, mark where you think these numbers are located. a) 65 b) 25 c) 10 d) 45 e) 100 f) 110
CONSIDER the CONDITIONS Complete this square by ADDING 19 ACROSS the square and 29 up the square. +29 +19
The method used by numerate people (Survey of 200 individuals—Northcote & McIntosh, 1999) • 84.6% of all calculations involved some form of mental mathematics • 11.1% involved written mathematics • 6.8% involed the use of calculators • 19.6% used other physical objects (Total is not 100% because some instances used more than one method.)
GOOD NUMBER SENSE activities possess one or more of the following Provide open input Encourage visual thinking Establish connections Foster a search for patterns Encourage student’s language Involve estimation Support mental computation Use multiple models for number (counting, relative position, place-value, etc.
