Unit C: Expressions Lesson 03: Mathematical Properties with Variables 6th Grade Math Unit C: Expressions Lesson 03: Mathematical Properties with Variables

Lesson 02 – Mathematical Properties with Variables. Unit C– Expressions Lesson 02 – Mathematical Properties with Variables. GLE 0606.3.2 Interpret and represent algebraic relationships with the variables in expressions, simple equations and inequalities

Note taking Guide Click on link below to download note taking guide.

Vocabulary Associative Property of Addition and Multiplication Commutative Property of Addition and Multiplication Distributive Property

You may remember… A + B = B + A A * B = B * A Using these properties at earlier grade levels… The only difference now is that we are using variables with the properties.. A + B = B + A 6 + 3 = 3 + 6 Bring in the you may remember… and the visuals Bring in the first statement Then bring in the second after about 5 seconds A * B = B * A

A mathematical property is a statement that will always be true. The mathematical properties that we will be discussing in today’s lesson are: Associative Commutative Distributive Bring in the picture then bring in the first bullet After about 5-6 seconds bring in the second bullet to the word are: Then bring in the 3 properties one at a time… Associative Commutative Distributive

Mathematical Properties There are 3 basic properties that we will be learning about in this lesson. Every math system you've ever worked with will obey these properties! You will need to keep these properties straight. Many people get them confused. We are going to go through them one at a time. Bring in title Then bring in each bullet waiting about 10 seconds between each one.

You will see a set of parentheses or brackets in these problems. Associative Property The word "associative" comes from "associate" or "group." The Associative Property is the rule that refers to grouping. This will deal with 3 or more numbers or variables. You will see a set of parentheses or brackets in these problems. Bring in title and picture. Then bring in the text. Wait about 15 sec. or so to before they advance.

Associative examples: with addition numbers variables 3 + (2 + 1) = 6 We can also say: 2 + (1 + 3) = 6 Since we can re-group and they are still equal this shows the “associative property” 3 + (2 + 1) = 2 + (1 + 3) a + (b + c) = 10 We can also say: b + (c + a) = 10 Since we can re-group and they are still equal this shows the “associative property” a + (b + c) = b + (c + a) Bring in title. Then bring in the blue side of the slide. Bring in the first three lines one at a time. Then bring in the “since paragraph at once.. Then show the last math statement Do the same with the green box as the blue.

Guided Practice: Let’s try it…. Example # 1 Lets say a = 6 b = 12 Plug in the correct numbers for each problem and then solve Example # 1 Lets say a = 6 b = 12 c = 3 a + (b + c) = or b + ( c + a)= Let’s try it….this time with 4 numbers Plug in the correct numbers for each problem and then solve Example # 2 Lets say a = 6 ; b =12 c = 3 ; d = 5 a + (b + c) + d = or b + ( d + a) + c= (c+ d) + b + a= Bring in title: Left text first. List the example 1 and the values for a, b, and c Then bring in the first problem.. I need some annimation here. I need the numbers to appear their corresponding letter then show the answer.. Then do the same for the second equation. Emphasize they are both equal to each other. On the right hand side… do the exact same thing for all three equations.. One at a time… Once again emphasize that they are all equal… Then to the right in a different font and text.. Flash up the following statement: See.. It doesn’t matter what order or even if you move the parenthese.. The answer remains the same.

Associative examples: with multiplication numbers variables 3 * (2 * 4) = 24 We can also say: 2 * (3 * 4) = 24 Since we can re-group and they are still equal this shows the “associative property” 3 + (2 + 1) = 2 + (1 + 3) a * (b * c) = 10 We can also say: b * (c * a) = 10 Since we can re-group and they are still equal this shows the “associative property” a * (b * c) = b * (c * a) Do the same as slide 8

Guided Practice: Let’s try it…. Example # 1 Lets say a = 2 b = 3 c = 4 or b * ( c * a) Let’s try it….this time with 4 numbers Example # 2 Lets say a = 2 ; b = 3 c = 4 ; d = 5 a * (b * c) * d = or b * ( d * a) * c (c* d) * b * a Do the same as slide 9

Remember that was Associative Property Works for groups of 3 or more numbers or variables and the must be “grouped” differently Flash in the title and pic… then bring in the green text

Commutative Property The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. Bring in title and picture. Then bring in the text. Wait about 15 sec. or so to before they advance.

Commutative examples: with addition numbers variables 3 + 2 + 1 = 6 We can also say: 2 + 1 + 3 = 6 Since we are just moving the numbers around and they are still equal this shows the “commutative property” 3 + 2 + 1 = 2 + 1 + 3 a + b + c = 10 We can also say: b + c + a = 10 Since we are just moving the letters around and they are still equal this shows the “commutative property” a + b + c = b + c + a Bring in title. Then bring in the pink side of the slide. Bring in the first three lines one at a time. Then bring in the “since paragraph at once.. Then show the last math statement Do the same with the purple box as the blue.

Guided Practice: Let’s try it…. Example # 1 Lets say a = 6 b = 12 a + b + c = or b + c + a Let’s try it….this time with 4 numbers Example # 2 Lets say a = 6 ; b =12 c = 3 ; d = 5 a + b + c + d = or b + d + a + c c+ d + b + a Bring in title: Left text first. List the example 1 and the values for a, b, and c Then bring in the first problem.. I need some annimation here. I need the numbers to appear their corresponding letter then show the answer.. Then do the same for the second equation. Emphasize they are both equal to each other. On the right hand side… do the exact same thing for all three equations.. One at a time… Once again emphasize that they are all equal… Then to the right in a different font and text.. Flash up the following statement: See.. It doesn’t matter what order or even if you move the stuff around.. The answer remains the same.

Commutative examples: with multiplication numbers variables 3 * 2 * 4 = 24 We can also say: 2 * 3 * 4 = 24 Since we are just moving the numbers around and they are still equal this shows the “commutative property” 3 + 2 + 1 = 2 + 1 + 3 a * b * c = 10 We can also say: b * c * a = 10 Since we are just moving the numbers around and they are still equal this shows the “commutative property” a * b * c = b * c * a Same as 14

Guided Practice: Let’s try it…. Example # 1 Lets say a = 2 b = 3 c = 4 or b * c * a Let’s try it….this time with 4 numbers Example # 2 Lets say a = 2 ; b = 3 c = 4 ; d = 5 a * b * c * d = or b * d * a * c c* d * b * a Same as 15

Remember that was Commutative Property Works for any size group of numbers or variables and you must “move” stuff around Bring in title and picture. Then bring in the text. Wait about 15 sec. or so to before they advance.

Sorting Game:::: See attached word document File name 6c03 Drag and Drop 

Distributive Property Our last property to discuss in this lesson is the distributive property The “Distributive Property” got its name because in essence, you are distributing something as you separate or break it into parts. The distributive property makes numbers easier to work with. In algebra when we use the distributive property, we're expanding it. Bring in the title and the boxed text.. Then bring in the other text and pic. Leave on the screen for at least 15 seconds so they can have time to read it.

Examples: Guided Practice Next 6 ( a + 4)= When you see this problem you will distribute the 6 to everything in the parentheses. ** Remember that when you see a letter or number right next to the parentheses that means to multiply. The problem: 6 (a+4)= 6 (a) = 6a then… 6 (4) = 24 So your answer looks like this: 6a + 24 Remember: ( you can not solve the problem completely because we don’t know what the value of “a” is) Next Bring in “examples” and the problem… then the “when you “ section. Last flash up the text in red. Leave a few seconds so they have time to read it. Flash up the arrow On the right text box.. Put in the problem.. I need some annimation on the “the problem” Show an arrow going from the 6 to the a of the problem when you do that flash up the 6(a) = 6a Then do another arrow from the 6 to the 4. and flash up the 6(4) = 24 Then put up the so your answwer looks like this and the answer Last bring in the remember phrase.

Guided Practice Examples: Next 3 ( a - 7)= The problem: 3 (a - 7)= 3 (a) = 3a then… 3 (7) = 21 So your answer looks like this: 3a - 21 Remember: ( you can not solve the problem completely because we don’t know what the value of “a” is) Examples: 3 ( a - 7)= When you see this problem you will distribute the 3 to everything in the parentheses. ** Remember that when you see a letter or number right next to the parentheses that means to multiply. Next Do the same as slide 21

Distributive Property Use the distributive property to expand the following problems. 1.) 2(a + 6) = 2.) 3(a + 7) = 3.) 8(s – 4) = 4.) 10 ( q+ 3) = 5.) 4 ( 4 – r) = 6.) 5 (8 + g) = 7.) (3 + s) 4 = 8.) ( 12 – g) 2 = Answers go next to the equals on each problem: One by one! A second or two between 2a + 12 3a + 21 8s – 32 10q + 30 16 – 4r 40 + 5g 12 + 4s 24 – 2g

Let’s Review and involves grouping. This means either The associative property involves at least 3 numbers and involves grouping. This means either parentheses or brackets. The commutative property involves any amount of numbers and is just about moving them around (their order being changed) The distributive property involves multiplying the number on the outside of the parentheses by everything on the inside of the parentheses.

Reference to: an external (D2L) Quiz. Title: Quiz Slide EXTERNAL REFERENCE Reference to: an external (D2L) Quiz. Title: Quiz Slide Generic instructions: When you are ready to take the quiz over this material, visit the Quiz section of D2L and choose the quiz for this lesson. Here you would state whether or not they could use notes, had a time limit, or give other instructions.

END OF LEARNING OBJECT This slide is required of each lesson and is used as a marker for the students and our software.