Unit 1 – Expressions

WARM UP – in your notebook MAKE 24 Using the numbers 5 5 4 3 22 20 13 9 8/11/17 - OB JECTIVE : Given a verbal situation We will WRITE and EVALUATE An ALGEBRAIC EXPRESSION

VOCABULARY EXPRESSION – MAY CONTAIN NUMBERS, VARIABLES, AND EXPONENTS THAT ARE CONNECTED BY OPERATORS ( + , -, • , ÷ ) EQUATION- MUST CONTAIN TWO OR MORE EXPRESSIONS CONNECTED BY AN EQUAL SIGN INEQUALITY – MUST CONTAIN TWO OR MORE EXPRESSION CONNECTED BY AND INEQUALITY SYMBOL ( < , ≤ , > , ≥ )

How to READ THE SCENARIO CHOOSE VARIABLE THAT MAKE SENSE TO YOU DEFINE THE VARIABLE BY SAYING “ LET d = ………..” WRITE THE EXPRESSION USING THE VARIABLE EVALUATE BY SUBSTITUTING IN A GIVEN VALUE

LET’S PRACTICE TOGETHER

MORE PRACTICE -

Practice

Sully and Genesis purchase two matinee movie tickets. Monday August 14, 2017 Warm up – keep in your notebook SUPPLIES- notebook and paper- pencil and colored pencils Sully and Genesis purchase two matinee movie tickets. A matinee ticket costs $6.50 , a drink costs $5.50, And a bag of popcorn costs $6.00. Define each variable. Write an algebraic expression to describe how They spend based on the number of drinks and bags of popcorn they buy.

Objective – students will classify and describe polynomials by degree and number of terms Standard 912.A-SSE.1.1 Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression such a term, like terms, factors and coefficients. IN YOUR OWN WORDS……

Understanding polynomials Polynomials- expression made up of at least 1 monomial and usually many- each is called a term. Classify polynomials by degree or by the number of terms Classify by degree Classify by number of terms

terms- constant variable or multiplicative combination of the two terms- constant variable or multiplicative combination of the two. they are separated by addition and subtraction. How many terms? Underline each term. How many terms? Underline each term

Coefficient- if a term has a variable , the number in front of the variable is called the coefficient. −3𝑥𝑦 2 constant – if the term has no variable it is a constant

Like terms – same variable same power Combine like terms by adding or subtracting the coefficient EXAMPLE: x + 6 - 3x + 5 how many terms? Rearrange it to put like terms together x -3x + 6 + 5 -2x +11 CLT by adding/subtracting coefficients

Degree of a monomial – add up the exponents 8𝑥 2 𝑦 3 What is the degree? 8𝑥 2 𝑦 3 2 + 3 = 5 5th degree monomial −3𝑎𝑏 2 What is the degree? −3𝑎 1 𝑏 2

Degree of a polynomial = if only 1 variable it is the exponent of the leading term Leading term – the term with the highest degree Leading coefficient- number in front of the leading term standard form – Alphabetical and descending (getting smaller) order of exponents Write the polynomial in standard form - state the degree – name it By terms- what is the leading coefficient? 9𝑥 7 + 3 4 𝑥 4 - 5𝑥 3

Wrap up- Turn this in 3𝑥 4 − 5𝑥 7 + 11𝑥 2 Write it in standard form 3𝑥 4 − 5𝑥 7 + 11𝑥 2 Write it in standard form How many terms? What is the degree of the polynomial? What is the leading term? What is the leading coefficient?

Tuesday Aug 15 supplies: notebook- paper –warm up and notes from yesterday do this warm up on the same page as yesterday 

Examples from yesterday ------ Is the expression a polynomial?

Find degree ---

Write in standard form….

Wednesday aug 16 Activity polynomial not polynomial

Thursday/Friday AUg 17 and Aug 18 Supplies – notebook- paper to turn in Warm – up – do this problem on the warm up paper from Tuesday

Properties distributive – commutative – associative Distributive a(b+ c) = a∙b + a∙c -6(x- 2) #1 -3(a+1) Double distribute DRAW ARROWS (a+3)(a + 2) #2 (2m + 3) (m-1)

Distribute as many times a needed

Commutative property a+b = b+ a The order of the numbers can be without affecting the or . 5 + 2 2 + 5 or 9(3) 3(9) Does the commutative property hold true for subtraction? Does the commutative property hold true for division? #1 p + (u + t ) (t + u) + p

Associative Property (a + b) + c = a + (b + c) put parenthesis around adjacent numbers 2 + 4 + 6 2 + 4 + 6 3 ∙ 6 ∙ 4 3 ∙ 6 ∙ 4 The Of the numbers does not change The grouping of the numbers can change and does not affect the or .

Monday Aug 21, 2018 Suppplies- notebook(notes from last week) -paper- pencil/pens Warm-up – Complete the paper below (from last week If you turned it in pick it up from the folder.

Objective: use the properties of exponents to write equivalent expressions Standard:MAFS.912.N-RN.1.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

REVIEW ----

17x – 25 x -8x −15𝑎 3 bc + 6𝑎 3 bc −9𝑎 3 bc DO all Check your answers for the odd - 5. 2ab + 9ac 7. 1mn 9. −50𝑥𝑦 2 11. 7y – 6 z 13. 17𝑦 2 - 22y 15. 11𝑦 2 17. - 24a

We will do these together

You do the remaining problems check your answers to 𝑎 10 30𝑥 6 −30𝑦 6 80𝑐 5 𝑑 6 8𝑥𝑦 5

Tuesday Aug 22 Check seating chart Need notebook and all notes Warm up – keep in your notebook Commutative – associative – distributive

Together Coefficients Distribute exponents on the outside MULTIPLY EXPONENTS Multiply exponents- “distributive” property Together 𝑥 10 𝑥 9 𝑦 9 ∙ 𝑥𝑦 2 𝑥 10 𝑦 11 Distribute to the -2 and the a and b also the 3 and the a and the b −4𝑚 3 𝑛 12 4𝑎 2 𝑏 4 ∙ 9𝑎 4 𝑏 2 Don’t multiply exponents here ADD them 36𝑎 6 𝑏 6 −81𝑥 6 Combine like terms Stays 𝑎 6 8𝑎 6 + 3𝑎 6 4𝑎 8 𝑏 12

Wednesday Aug 23 –Pictures last 15 min – Bring your text book tomorrow or Friday we are turning them back in. SUPPlies today - NoteBook – green exponent rules notes pencil/pen Warm up – write down the expression and then decide if it is a polynomial or not polynomial – write p(polynomial) or n (not) next to the expression 1. 5 6. 5 𝑥 2. y + 4 7. 3 2𝑥 3. 𝑥 7 8. 2x + 6 4. 𝑥𝑦 −2 9. 1 2 𝑥 4 2 5. 2𝑎 2 + πa + 6 10. 𝑎𝑥 2 + bx + c

Coefficients SUBTRACT EXPONENTS Exponents by subtracting 12𝑥 9 𝑦 4 16𝑥 2 𝑦 2 9𝑥 10 27𝑥 3 𝑥 7 3 𝑥 2 3𝑥 7 𝑦 2 4 1 3x 144𝑥 10 225𝑥 2 16𝑥 8 25 −9𝑏 2 1 2 𝑛 4 or 𝑛 4 2

August 28 need – paper notebookpen/pencil Warm- up

Combine like terms when adding or subtracting make sure terms are alike- same variable same exponent- DON’t touch the variables or exponents just add/subtract the coefficient TRY-

Review – multiply same base – Add exponents

Tuesday August 29 Supplies - Green paper 6 rules for exponents notebook for notes -worksheet Dividing exponents -worksheet negative exponents -worksheet mixed practice from Mon Aug 28 Warm up (-4 𝑦 4 ) 2 mixed practice 10 ( 𝑎 2 𝑏 𝑐 3 ) 3 ∙( 𝑏 2 𝑐 ) 3 - mixed practice 11

base −6 3 exponent coefficient 2𝑥 4 exponent base Negative exponents move and become positive but only the base and the exponent not the coefficient. 𝑥 −2 is 1 𝑥 2 but also 1 𝑥 −3 is 𝑥 3

2nd period and 5th period Do the last column (3-6-9-12-15-18-21-23-25) on negative exponents Complete the back of the worksheet from yesterday Wrap – up(do on the back of the negative exponents ) – please answer (show all work) these Essential Questions and turn your papers into the folder

4th period Negative exponents Do 1- 4 -7 -13 -16 and 19 on your own Complete the back of the worksheet from yesterday

Friday Sept 1 - MONDAY is no school today we will …. 1. warm up. 2 Friday Sept 1 - MONDAY is no school today we will ….. 1. warm up 2. fraction exponents 3. complete negative exponents paper 4 complete practice paper 5. complete triples Warm up 1-2-3

Rational exponents Objective: write fraction exponents as radicals and write radicals with fraction exponents Essential Question: How can we use fraction exponents to write radical expressions 𝑥 2 3 rewrite “think” 𝑝𝑜𝑤𝑒𝑟 (𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡) 𝑟𝑜𝑜𝑡 ( 2 3 ) 3 𝑥 2 2 1 𝑝𝑜𝑤𝑒𝑟 2 𝑟𝑜𝑜𝑡 2 2 1 or 2 3 𝑥 7 rewrite 𝑥 7 3 𝑥+2 𝑥+2 1 2

Write these in your notebook think 𝑝𝑜𝑤𝑒𝑟 𝑟𝑜𝑜𝑡

Tuesday Sept 5 Supplies – notebook- paper- pencil/pen Warm up – re-write 1. 5 0 4. 15 𝑥 3 4 2. 5 −2 5. (15x ) 3 4 3. 5 1 2 6. 3 125𝑑 2

Standard : MAFS.912.n-rn.1.2 simplify radicals Objective: - simplify radical expression to prime factors Essential question: Which of the following expressions are equivalent to 3 2

Wrap – up Essential question: Which of the following expressions are equivalent to 3 2

Wednesday Sept 6 Supplies – notebook – paper/pen Warm up 1. Simplify 2. Which of the following are equivalent to 𝑥 9 5

Standard : MAFS.912.n-rn 1.1 rewrite expressions involving radicals Objective: use radicals or rational exponents and properties of exponents to add and multiply with radicals Essential Question: What is the perimeter of a rectangle having side lengths of 4 8 and 5 12 + 6 20

Adding and subtracting radicals 1. must have same index 2. always check to see if you can simplify 3. if you have the same index and radicand then you can add or subtract 4. add or subtract the coefficient like normal

Thursday Sept 7 Supplies – notebook- notes – add/mult radical paper - pen/pencil – colored pencils Warm- up – use properties of exponents to find the value of k that makes the statement true. 7 9 𝑘 27 7 15 −𝑘 45 = 7 3 2 ∙ 7 3 2

standard : MAFS.912.n-rn 1.1 rewrite expressions involving radicals Objective: use radicals or rational exponents and properties of exponents to add and multiply with radicals Essential Question:

Monday Sept 18 Supplies –notebook- paper- pencil all papers Warm up-check the seating chart

REVIEW simplify radicals (we do 1st column) 2nd column #5,14,20 Simplify non (4th 2-11-14-20) Review Add Radicals (we do #2 and #12) # 4 and # 6

Multiplying radicals 1. Must have same index 2. Multiply coefficients like normal 3. Multiply radicands 4. Simplify WE DO #13 #17 YOU DO #14-16-18

Sept 19 supplies – paper-pencil notebook remember- backpack and cellphones go against the wall right or left Warm- up Simplify 3 12 2 27 𝑚 4 𝑛 11 7 − 4 7 2 54 +3 96

Sept 20- substitute Make 24 7,8,4,2

September 22 Supplies – notebook –paper – pencil – colored pencils – computer Warm up – 1. 3 ( 5 + 3 ) 3. ( 3 + 6 ) ( 3 - 6 ) 2. 2 10 ( 5 - 4 10 )

Real Number system

Monday Sept 25 Supplies – paper- notebook- pencil warm up

September 26 Supplies – notebook- pencil- pen warm- up 3 problems Quiz

Learning Goal – predict outcomes to operations with rational and irrational numbers. Notebook quiz – Work with a partner to complete the sorting activity