Number Sense Unit 2

Virginia SOL Standards 7.16 apply the following properties of operations with real numbers: The commutative and associative properties for addition and multiplication; The distributive property; The additive and multiplicative inverse properties; and The multiplicative property of zero. 7.1 Investigate and describe the concept negative exponents for powers of ten; Determine scientific notation for numbers greater than zero;* Compare and order fractions, decimals, percents and numbers written in scientific notation;* Determine square roots;* and Identify and describe absolute value for rational numbers. *SOL test items measuring Objective 7.1b-d will be completed without the use of a calculator. 2016 7.2 solve practical problems involving operations with rational numbers expressed as integers, fractions, mixed numbers, and percents.

Bell Ringer September 25, 2017 Get a colorful piece of paper on the side table! Write these vocabulary words in your Glossary Associative Property of Addition: Regrouping the addends does not change the sum. Example: 5 + (4 + 3) = (5 + 4) + 3 Associative Property of Multiplication: Regrouping the factors does not change the product. Example: 5 (4 x 3) = (5 x 4) 3 Commutative Property of Addition: Changing the order of the addends does not change the sum! Example: 5 + 4 = 5 + 4 Commutative Property of Multiplication: Changing the order of the factors does not change the product. Example: 5 x 4 = 4 x 5

Properties are statements that are true for all numbers.

Associative Property of Addition The root word is associate, meaning to join or unite in a relationship. At school, it is easy to identify associates in the hallway. Who are your associates?

Associative Property of Addition Associative property for addition could put three friends together... Notice their order is the same from one side of the equal sign to the other. ONLY the groups change! Preston Emma Owen Preston Emma Owen

Associative Property of Addition The associative property for addition is easy to follow. Example: Notice that changing the order does not change the answer! Reminder: When you see the equal sign say "same as" and ask yourself if the number sentence is true or false.

The Associative Property of Multiplication The associative property is the same for multiplication! Order remains the same on both sides, and only the grouping changes. 2 (x • y) = (2 • x) y  Guided Practice: Let x and y be any two different numbers. Substitute the values and evaluate each side of the equation. What value did you get?

Independent Practice Your turn... Working in a pair, create several other examples that illustrate the associative property for addition and multiplication. Make one example a real-life application. Make on example that is algebraic (like the problem on the last slide). You may use your dry erase boards. Be ready to share your examples. 

Commutative Property The root word is commute which means to travel from one place to another as in going to and from work, or to and from school. Do you have a typical morning route that you take to school? Is it the same route going home? 

Let’s Commute to and from School. Going to school, you pass Giant (G) and then McDonald's (M), but on the way home, you pass McDonald's (M) and then Giant (G). TO FROM G + M = Switching Occurs!

Communicative Property of Multiplication Yet again, communicative property of multiplication is no different than communicative property of addition.

Commutative Property of Multiplication For example: 2 (3 + 5) = (3 + 5) 2 Notice that the only changes from one side of the equal sign to the other. The 2 and the (3 + 5) switched places. Look carefully If there is any switching in the order of values from one side of the equation to the other, the commutative property is being used.

Independent Practice Working with a partner, create several other examples that illustrate the commutative property for addition and multiplication. Create one example using a real-life application. Create the other example using an algebraic equation. You may use your white boards. Be prepared to share.

Homework September 25, 2017 Which property of real numbers justifies the statement BC = CB? Which property of real numbers justifies the statement? a + 3 = 3 + a Look at the expression being simplified. 6 + (5 + 4) + x Step 1: 6 + (4 + 5) + x Step 2: (6 + 4) + 5 + x Step 3: 10 + 5 + x Step 4: 15 + x In which step is the commutative property of addition applied?