Computation STRATEGIES Introductions 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. The goal is for students to have a variety of strategies and to be able to choose one, the most efficient one, when solving problems.

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. Commutative Property (Flip) 3+9= 9+3= Counting back 7-2= Think 7 6, 5 Counting on 7+2= Think 7 8, 9 One More One Less 3+1=4 3-1=2 Doubles 3+3=6 A focus in grades 1-3 is on learning addition and subtraction facts. By the end of grade 3 children should know their facts. There are many ways that teachers help children learn these facts. Making 10 8+5= 8+2+3= 10+3= Friendly Numbers 7+3= 6 +4= 5+5= Think Addition for subtraction 15-6= 6+?=15 Number families 3+4=7 7+3=7 7-4=3 7-3=4 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 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 One of the first strategies kids learn is doubles. Kids learn this fairly quickly. There are many examples of doubles in everyday life and up to 5+5 children can use their fingers.

THINK 5+5 = 10 SO…. 5+6 = 11 FOR 4+5= SO…. 4+5 = 9 FOR 5+6= DOUBLES +1 DOUBLES -1 FOR 5+6= THINK 5+5 = 10 SO…. 5+6 = 11 FOR 4+5= SO…. 4+5 = 9 Once kids know double we can build on that to teach them doubles +/- 1 and doubles +/- 2.

Commutative Property (Flip) FOR 3+9= THINK 9+3 = 12 SO…. 3+9 = 12 Another strategy we want kids to learn is the commutative property which means that changing the order of the numbers you are adding does not change the answer.

2+8 8+2 3+7 7+3 4+6 6+4 5+5 Friendly Number 10 1+9 9+1 1+9 9+1 2+8 8+2 3+7 7+3 4+6 6+4  5+5 Another important concept kids learn is the numbers that you can combine together to make 10. Adding numbers to 10 is easy therefore we want kids to be able identify the numbers that can be combined to make 10. When adding 7+8+3= we want children to be able to see that 7+3=10 and 10+8=18

When 1 of the numbers you are adding is Make 10  When 1 of the numbers you are adding is 7,8 or 9 Go to 10 And add the rest For 8+5 Think 8 + 2 + 3 10 + 3 = 13 So… 8+5 = 13 When kids know the friendly numbers that combine to make 10 they are able to use this information to add other numbers.

Counting on For 6+2 = Start at the largest number and count forwards: 6…7,8 So 6+2 = 8 ______________________ 6 7 8 Counting on an efficient strategy for adding 1, 2 and maybe 3 to a number.

Start at the largest number and count backwards: Counting Back For 6-2 = Start at the largest number and count backwards: 6…5,4 So 6-2 = 4 ___________ 4 5 6 Counting back is an efficient strategy for subtraction 1, 2 or 3 from a number.

Think Addition for Subtraction 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 This is one of the most efficient strategies for teaching subtraction facts. Once children have learned addition facts we want to be link them to subtraction facts by using the number family strategy.

0,1,2/Doubles/ Near Doubles/Make 10 + 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 When children know Zero property, +/-1 and 2, doubles, near doubles, how to make 10 and add the rest they know all but 6 addition facts. 44/50=88/100

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 Place Value (Left to Right) 425 +368 700 80 13 795 As with addition and subtraction facts, we want to equip children with different strategies for solving problems with large numbers. The goal is that they will be able to choose an efficient strategy for solving a particular problem. Think Addition for Subtraction 52-23= 23+?=52 +20 +7 +2 _____________________ 23 43 50 52

753 Place Value Decomposing Numbers 334 + 419 = (300 + 400) + (30 + 10) + (4 + 9) 700 + 40 + 13 753 This strategy uses place value to add the numbers. We look at the value of each of the digits and we add them.

Place Value Left to Right 334 + 419 Add the 100s 700 Add the 10s 40 Add the 1s + 13 753 This is a similar process to the previous one we practiced however it is presented in a traditional format.

Blank Number Line Number Line 334 + 419 = +300 +30 +1 +3 419 719 749 750 753 Another way children are learning to add and subtract is through the use of a blank number line. In this example we are adding 334 to 419. It’s important to start with larger number.

Think Addition for Subtraction 828 - 729 = 70+28+1=99 +1 +70 +28 729 730 800 828 One of the most efficient strategies for teaching subtraction is having kids think addition. Instead of trying to count back kids use a number line to count forward. When using a number line efficiently you should be able to solve the problem with the fewest jumps. Another way to solve this problem might be to add 100-729-829 and then to subtract 1.

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) Doubling/Halving 6x4= think 12x2= Visualize Arrays 3x2= 6÷3=2 There are many strategies teacher use to teach children multiplication and division facts. Fact families 3x4=12 4x3=12 12÷4=3 12÷3=4 Think Multiplication for Division: 20÷5= Think how many groups of 5 are in 20? Or 5x?=20 Commutative Property 3x9= 9x3=

*halve one number and double the other number 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 6 X 7 = I know that 5 X 7 = 35 So…6 X 7 = 35 + 7 = 42

Distributive Property 6 X 7 (6 X 5 =)+(6 X 2 =) 30 + 12 42 If multiplying by 7 is hard for me but I know my 2 and 5 times tables I might use this strategy. I know that 7 =5 and 2 so I can multiply 6x5 and 6x2 and then add the answers.

Commutative Property 6 X 7= 7x6=

Arrays 3x2= 2x3= 6÷3=2 6÷2=3

6 X 7=42 7x6=42 42÷6=7 42÷7=6 Fact Families This is an important strategy for teaching division facts. As children are learning their multiplication facts we want to link that knowledge to division.

Think Multiplication for Division 20÷5= Think how many groups of 5 are in 20? Or 5x?=20 Another important strategy for teaching division is thinking multiplication.

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= 62x21=1302 x 20 1 60 1200 2 40 Traditional Algorithm (Left to Right) 26 X 8 160 + 12 172

15 x 6 = Add 15 six times 30 + 30 + 30 90 Repeated Addition 15 + 15 + 15 + 15 + 15 + 15 = 30 + 30 + 30 90

Place Value (Distributive Property) 15 x 6 (10 x 6) + (5 x 6) 60 + 30 = 90 x 6 10 60 5 30 In this example I am using what I know about 15 which is that 15=10 and 5 and then multiplying those 2 numbers by 6 and adding them together. Looking at multiplication in this way lends itself easily to mental math. Practice

Place Value (Left to Right) 15 x 6 60 +30 90 This is similar to the previous example except that is lined up in a traditional way. Practice

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 3 3 3 3 Algorithm

Division Place Value 4 136 30 -120 + 4 16 34 -16 0 In this example I am using the traditional algorithm in a way that accurately represents the value of the digits. If I was practicing this method with students I would first have them provide me with a word problem which represents the question. I.e. I have 136 candies and I want to share them with 4 friends. How many candies does each friend get? Students can use what they know about multiplication to solve this problem. I can start by giving 30 candies to each friend which is 120 candies. I subtract this from 136 to find out how many candies are left=16. Now I have 16 candies that I need to share with 4 friends. If I give 4 candies to my 4 friends I have shared all my candies and each person gets 34. Practice 80/5 or 84/7

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…..