Bellringer Round to nearest whole number 1 9

Bellringer Round to nearest whole number. 1. 9. 099 2. 15. 789 9 16 Estimate each sum or difference using front end estimation. 3. 5. 36 + 6. 023 + 9. 902 is about 21 4. 902. 958 – 190. 39 is about 700

Go Over Homework Pg 6 , 6 -32 evens only

Properties of Addition Lesson 1 -2

Three Properties of Addition 1. Commutative 2. Associative 3. Identity

The Commutative Property • Background – The word commutative comes from the verb “to commute. ” – Definition on dictionary. com • Commuting means changing, replacing, or exchanging – People who travel back and forth to work are called commuters. • Traffic Reports given during rush hours are also called commuter reports.

Here are two families of commuters. Commuter B Commuter A & Commuter B changed lanes. Remember… commute means to change. Commuter B Commuter A

Here is another example…

Think of this hypothetical situation: Every day you ride your bike to school. The distance from home to school is 2 miles. The distance from school to home is also 2 miles. How do we know this? Did you notice that hypothetical and hypothesis look almost the same? Hmmmm. . . Think about what hypothesis means…

Home School The distance from Home to School is the same as the distance from school to home. Home + School = School + Home H+S=S+H A+B=B+A

The Commutative Property A+B=B+A

Commutative Property of Addition Changing the order of the addends does not change the sum A+B=B+A 1+2+3=3+1+2 4+5+6=5+6+4

Three Properties of Addition 1. Commutative 2. Associative 3. Identity

The Associative Property • Background – The word associative comes from the verb “to associate. ” – Definition on dictionary. com • Associate means connected, joined, or related – People who work together are called associates. • They are joined together by business, and they do talk to one another.

Let’s look at another hypothetical situation Three people work together. Associate B needs to call Associates A and C to share some news. Does it matter who he calls first?

Here are three associates. B calls A first He calls C last B A If he called C first, then called A, would it have made a difference? NO! C

(The Role of Parentheses) • In math, we use parentheses to show groups. • In the order of operations, the numbers and operations in parentheses are done first. (PEMDAS) So….

The Associative Property The parentheses identify which two associates talked first. (A + B) + C = A + (B + C) B A B THEN C A C

Associative Property of Addition Changing the grouping of the addends does not change the sum (1 + 2) + 3 = 1 +( 2 + 3) (A + B) + C = A +( B + C) (4 + 5) + 6 = 4 + ( 5 + 6 )

Three Properties of Addition 1. Commutative 2. Associative 3. Identity

The Identity Property of Addition I am me! You cannot change My identity!

Zero is the only number you can add to something and see no change.

Identity Property of Addition +0= A+0=A

Identity Property of Addition The sum of zero and anything is anything 0+ 3 = 3 0+C=C 18 + 0 = 18

Let’s practice ! Look at the problem. Identify which property it represents.

(9 + 8) + 7 = 9 + (8 + 7) The Associative Property of Addition It is the only addition property that has parentheses.

12 + 0 = 12 The Identity Property of Addition It is the only addition property that has two addends and one of them is a zero.

9+7=7+9 The Commutative Property of Addition It is the only addition property that has numbers that change places.

4+6=6+4 The Commutative Property of Addition Numbers change places.

3+0=3 The Identity Property of Addition See the zero?

(4 + 3) + 2 = 4 + (3 + 2) The Associative Property of Addition It has parentheses!

a+0=a The Identity Property of Addition Zero!

a+b=b+a The Commutative Property of Addition Moving numbers!

(a + b) + c = a + (b + c) The Associative Property of Addition Parentheses! B A C

Adding and Subtracting Decimals

Essential Question: How do I add and subtract decimals? Steps: 1. Always line up decimals, add in zeros 2. Add and subtract like you always do 3. Bring decimal straight down in your answers

Adding Decimals Examples: When adding or subtracting you always start from the right and work left. 4. 55 + 11. 3 Put the first number on the top of the second number and line up the decimals. 4. 55 + 11. 30 15. 85 You can add a zero to help keep everything lined up

6. 44 + 16 When there is not a decimal put one behind the number. Line up the decimal 6. 44 + 16. 00 22. 44 Add a zero to line up everything

Subtracting Examples: 5. 34 -2. 08 Put the first number on the top of the second number and line up the decimals. 5. 34 -2. 08 3. 26 Different signs Take difference