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COMPUTATION STRATEGIES Presentation for Parents March 2013 Flexible Thinking There are many ways to solve problems. The more ways we solve a problem, the deeper our understanding of the mathematics. When we ask "How would you do that?" or "Can you show me another way?" we are helping children understand math better. Encourage children to use what they know to solve problems. Traditional algorithms involving lining up columns rely heavily on memorizing procedures and can work against developing number sense. 85% of all calculations we do involve mental math. Addition and Subtraction Facts Grades 1, 2 and 3 Students will learn mental mathematics strategies to determine basic addition and related subtraction facts to 18. Doubles 3+3=6 One More One Less 3+1=4 3-1=2 Making 10 8+5= 8+2+3= 10+3= Friendly Numbers 7+3= 6 +4= 5+5= Commutative Property (Flip) 3+9= 9+3= Think Addition for subtraction 15-6= 6+?=15 Counting back 7-2= Think 7 6, 5 Number families 3+4=7 7+3=7 7-4=3 7-3=4 Counting on 7+2= Think 7 8, 9 Zero Property 7-0=7 5+0=5 Doubles 1+1=2 2+2=4 3+3=6 4+4=8 5+5=10 6+6=12 7+7=14 8+8=16 9+9=18 DOUBLES +1 DOUBLES -1 THINK SO…. 5+6= 5+5 = 10 5+6 = 11 FOR THINK SO…. 4+5= 5+5 = 10 4+5 = 9 FOR Commutative Property (Flip) FOR THINK SO…. 3+9= 9+3 = 12 3+9 = 12 Friendly Number 10 1+9 2+8 3+7 4+6 9+1 8+2 7+3 6+4 5+5 Make 10 When 1 of the numbers you are adding is 7,8 or 9 Go to 10 And add the rest For Think So… 8+5 8+2+3 10 + 3 = 13 8+5 = 13 Counting on For 6+2 = Start at the largest number and count forwards: 6…7,8 So 6+2 = 8 ______________________ 6 7 8 Counting Back For 6-2 = Start at the largest number and count backwards: 6…5,4 So 6-2 = 4 ___________ 4 5 6 Think Addition for Subtraction For 12- 5= Think 5 + __ = 12 So 12 – 5 = 7 ______________________ 5 10 12 Zero Property Any number + 0 or -0 Remains the same 5+0=5 9-0=9 Number Families If I know that 3+4=7 I also know that 4+3=7 7-4=3 7-3=4 0,1,2/Doubles/ Near Doubles/Make 10 0 1 2 3 4 5 6 7 8 9 0 0 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 10 2 2 3 4 5 6 7 8 9 10 11 3 3 4 5 6 7 8 9 10 11 12 4 4 5 6 7 8 9 10 11 12 13 5 5 6 7 8 9 10 11 12 13 14 6 6 7 8 9 10 11 12 13 14 15 7 7 8 9 10 11 12 13 14 15 16 8 8 9 10 11 12 13 14 15 16 17 9 9 10 11 12 13 14 15 16 17 18 + Computation Strategies for Addition and Subtraction of Large Numbers Students will use personal strategies to add and subtract numbers in problem solving situations. Blank Number Lines 24+8= +4 +4 __________________ 24 28 32 Place Value (decomposing numbers) 24+15= 20+10=30 4+5=9 30+9=39 Think Addition for Subtraction 52-23= 23+?=52 +20 +7 +2 _____________________ 23 43 50 52 Place Value (Left to Right) 425 +368 700 80 13 795 Place Value Decomposing Numbers 334 + 419 = (300 + 400) + (30 + 10) + (4 + 9) 700 + 40 + 13 753 Place Value Place Value Left to Right 334 + 419 Add the 100s 700 Add the 10s 40 Add the 1s + 13 753 Blank Number Line Number Line 334 + 419 = +300 419 +30 719 +1 +3 749 750 753 Think Addition for Subtraction 828 - 729 = 70+28+1=99 +1 +70 729 730 800 +28 828 Multiplication and Divison Facts Grades 3-6 Students will demonstrate and apply different mental mathematical strategies to develop recall of basic multiplication facts to 9 x 9 and related division facts. Use a fact you know: I know 5x8=40 so… 5x9=45 Distributive Property 7x6= (5x6) + (2x6) Think Multiplication for Division: 20÷5= Think how many groups of 5 are in 20? Or 5x?=20 Doubling/ Halving 6x4= Visualize Arrays 3x2= 6÷3=2 think 12x2= Fact families 3x4=12 4x3=12 12÷4=3 12÷3=4 Commutative Property 3x9= 9x3= Doubling and Halving Doubling and Halving *halve one number and double the other number 15 x 4 = 30 x 2= So 30 x 2 = 60 Skip Counting from a Known Number Skip Counting from a Known Number 6X7= I know that 5 X 7 = 35 So…6 X 7 = 35 + 7 = 42 Distributive Property 6X7 (6 X 5 =)+(6 X 2 =) 30 + 12 42 Commutative Property 6 X 7= 7x6= Arrays 3x2= 2x3= 6÷3=2 6÷2=3 Fact Families 6 X 7=42 7x6=42 42÷6=7 42÷7=6 Think Multiplication for Division 20÷5= Think how many groups of 5 are in 20? Or 5x?=20 Computation Strategies for Multiplication Students will demonstrate an understanding of multiplication by using different strategies to determine answers. Distributive Property: 4 x 86 = (4 x 80) + (4 x 6) 320 + 24=344 Repeated Addition 25x4= 25+25+25+25= Traditional Algorithm (Left to Right) 26 X8 160 + 12 172 62x21=1302 x 20 1 60 1200 60 2 40 2 Repeated Addition 15 x 6 = Add 15 six times 15 + 15 + 15 + 15 + 15 + 15 = 30 + 30 + 90 30 Place Value (Distributive Property) 15 x 6 (10 x 6) + (5 x 6) 60 + 30 = x 10 5 6 60 30 90 Place Value (Left to Right) Place Value Left to Right 15 x 6 60 +30 90 Computation Strategies for Division Students will demonstrate an understanding of division by using different strategies to determine answers. Fair Sharing 92 ÷4 = 92 20 20 20 20 3 3 3 3 Algorithm Division Place Value 4 136 -120 16 -16 0 30 + 4 34 For More information Pembina Trails School Division http://www.pembinatrails.ca/program/earlyyears/Li nk%205/Numeracy.html Manitoba Education and Literacy http://www.edu.gov.mb.ca/k12/parents/index.html A Star and A Wish I appreciated learning……. I wish I could lean more about…..