Here is your NEW Activity! YOU MUST work with a partner! The Candy Store Lesson and Activities T B P Here is your NEW Activity! YOU MUST work with a partner! YOU MUST collaborate as you problem solve! YOU MUST show work neatly in your spirals!

T B P The Candy Store Lesson and Activities Our 4th Unit in math will take us DEEEEEEEper into expressions and equations with variables. So hang on….here comes some “food” for thought! (Pretty funny, aren’t I?) Think of each of the candy bars at the top as a variable. When you combine the candy bars, you are only allowed to combine the candy bars that are ALIKE – this means you cannot combine a Baby Ruth with a Pay Day into one candy bar! You can only ADD them together, putting the “+” sign in between. For example, If I had three Baby Ruth bars, I could say “3B”. If I add two Twix bars, I have “3B + 2T”. If I then add a payday bar, I have “3B + 2T +P”. Easy, right?

Let’s use the Candy in an expression B P Let’s organize the candy store into columns of candy and our “cash drawer” to simplify this expression: 3T – B + 3P + 6 – 2T + 4B -1 Twix Baby Ruth Payday Cash $ +3T -2T -B +4B +3P +6 -1 Final Expression: 1T 3B 3P 5 + + +

Organizing an expression or equation by combining the terms that are alike is absolutely necessary to simplify the expression or equation. It helps us to solve with accuracy. Using the “column” method is one strategy. Try the column method on the next slides…

T B P 1) T + 2B – 3T – 2P + 10 + 4C -3P -20B + 4P -5 + 12T + 2 –T The Candy Store T B P Copy these problems. Use the column method to organize. Write your final expression. 1) T + 2B – 3T – 2P + 10 + 4C -3P -20B + 4P -5 + 12T + 2 –T 45P – (-8) + 2P + 3(B + P) 12 + 4(2B + 6P) – 3P +2(3T –B) 14B -5(P + T) -6P – 10(2B + 6)

T B P Answers can be found from Mrs. Foster if Mrs. R gets them to her! If not, go on with the next slide….. Make sure you AND your partner have the same answers and agree. She will check you both!

NOW…. For Part Two…..

X² X X³ The Candy Store What if we changed the variables? These are all still different terms. So, what is a “TERM”? You have probably guessed by now. In Algebra a term is either: * a single number, or * a variable, or * numbers and variables multiplied together. *different variables are different terms *If an X is a single X, that is a different term than an X² which is also different than an X³

Do you like how I color-coded the terms? The Candy Store X² X X³ Now, see how the following expression is simplified. See if you agree…. 3x² + 2 – 10 – 2x³ - 5x² + 5x³ + 8x -x Twix 3x² -5x² Baby Ruth 8x -1x PayDay -2x³ 5x³ Cash 2 -10 Final Expression: -2x² 7x 3x³ -8 + + + Do you like how I color-coded the terms?

“Like Terms” – terms that go together Essential Vocabulary you need to know…… Parts of an Equation So people can talk about equations, there are names for different parts (better than saying "that thingy there"!) Here we have an equation that says 4x − 7 equals 5, and all its parts Variable Coefficient Operator or Operation Constant Term “Like Terms” – terms that go together A Variable is a symbol for a number we don't know yet. It is usually a letter like x or y. A number on its own is called a Constant. A Coefficient is a number used to multiply a variable (4x means 4 times x, so 4 is a coefficient)

Now…. Get ready for some more complex problems….. You can solve this by using columns or you can circle the terms that are alike and combine them. Just DON’T forget to circle the operational sign in front! Ready?

“SIMPLIFYING COMPLEX EXPRESSIONS” Simplify each expression. Neatly copy the problems in your spiral notebooks. Show ALL your work. Title this work page “SIMPLIFYING COMPLEX EXPRESSIONS” 7K² - P + 4K³ - 5K² -8 + 3(3P + 2) -2 + 9P 6(4X + 2X – 5X²) + 10 ¼(12w² + 3w – 6) + 2(5w - w²) 10m + 3 – (-3m²) + m² (-10x + 5y – 15)(¾) (2³+ 6) (m) ÷ 3(m⁴ + m) -9p – (-k) + p (-33v – 49v) ÷ 3(v⁴ +2m) 2(3m + 5) – (-m – 1) (2x – 8) + (10x + 4) - 36x⁻² (5x)⁻⁴ (15x) + 65 Get your answers checked! Be sure you are collaborating with a partner and agreeing on your outcomes.

How did you do? If you missed any, see WHY you missed them…. Write your reflections on a note card and turn that in. You should answer this question in several complete sentences: Why is it important to be organized with terms in simplifying expressions?

Congratulations. You have passed the first level of simplifying expressions….Get a Lollipop! Now, Work on Logic Links for a while or challenge 24 for a break. You have a new packet in your green folder to work on next.