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STAAR Training Day 1

Station 1: Distribution/Collect Like Terms of Expressions SE# A.4.A Station 2: Multiply Polynomials/Collect Like Terms SE# A.4.A Station 3: Distribution/Collect Like Terms of Equations …. Solve SE# A.2.D A.4.A Station 4: Properties of Linear Equations (slope, y-‐intercept, etc.) SE# A.1.E A.6.B A.6.C A.6.F Station 5: Solving equations for “y”/Function Notation SE# A.2.D A.7.B Station 6: Solving inequalities for “y” SE# A.7.B Station 7: Writing/Solving Systems of Equations SE# A.5.C A.8.B Station 8: Quadratic Functions SE# A.4.A A.9.D


Station 1:

Distribution/Collect Like Terms of Expressions (SE# A.4.A)

Some Tips: Group like terms vertically: 12𝒎𝟐 + 2𝒎+ 4

+(8𝒎𝟐 − 3𝒎 + 5) or Group like terms horizontally with symbols or highlighters:

12𝑚! + 2𝒎+ 4 + (8𝑚! − 3𝒎 + 5) Then add the coefficients (the numbers in front of the matching variables) *Note, if there is a “minus” sign in front of a parenthesis, remember to write in a “one”, and distribute the “negative one” to everything in parenthesis BEFORE adding like terms!!!

1. Simplify 𝟒𝒙𝟐 + 𝟔𝒙 + 𝟕 + (𝟐𝒙𝟐 − 𝟗𝒙 + 𝟏) 2. Simplify 𝒗𝟑 + 𝟔𝒗𝟐 − 𝒗 − (𝟗𝒗𝟑 − 𝟕𝒗𝟐 + 𝟑𝒗)


Station 2:

Multiply Polynomials/Collect Like Terms (SE# A.4.A)

Some Tips: There are 3 methods you can use depending on the situation

• Distribution • Box Method • FOIL

Keep in mind that not every problem should be tackled with the same method… you must choose the best method for you AND for the problem. Always simplify (collect like terms) after you multiply, if possible. …. Remember, multiplication … then addition

Simplify each product:

1. 𝟒𝒃 𝟓𝒃𝟐 + 𝒃 + 𝟔 2. 𝟒𝒙𝟐 + 𝒙 − 𝟔 (𝟐𝒙 − 𝟑)


Station 3: Distribution/Collect Like Terms of Equations …. Solve

(SE# A.2.D A.4.A)

1. Make a scatterplot for the following data. (don’t forget to label your axis!!!)

Gasoline Purchases

Dollars Spent

10 11 9 10 13 5 8 4

Gallons Bought

6.3 6.1 5.6 5.5 8.3 2.9 5.2 2.7

2. What is the trend of your plot? Positive correlation, Negative correlation, No correlation 3. State what kind of correlation you would expect from each of the two data sets described in each situation below. a. the amount of free time you have & the number of classes you take

b. the sales of sunscreen & the average daily temperature

c. the length of a baby at birth & the month in which the baby is born


Station 4:

Properties of Linear Equations (slope, y-‐intercept, etc.) (SE# A.1.E A.6.B A.6.C A.6.F)

Some Tips: Direct Variation is any function in form y = kx (where k≠0). The constant for variation, k, is the coefficient of x. The variables y and x are said to vary directly with each other. A function rule is written using the independent variable (x), and the dependent variable (y), with an equal sign as shown in the direct variation equation above. OR, It may also be written in function notation: f(x) = kx

As you watch a movie, 24 individual pictures, or frames, flash on the screen each second. 1. Model this relationship in three ways: a. a table b. a graph c. a function rule

2. If 120 seconds pass, how many frames have flashed on the screen?


Station 5: Solving equations for “y”/Function Notation

(SE# A.2.D A.7.B) Some Tips:

• Follow the rules of PEMDAS to simplify • Do any distribution BEFORE collecting like terms • Collect like terms on the same side of the equal sign BEFORE moving terms

across the equal sign • Follow the song: (First you box your variable… cancel what’s beside it…. ) • Remember to “undo” the operations addition/subtraction BEFORE

multiplication/division

1. Solve −𝟐 𝒃 − 𝟒 = 𝟏𝟐 2. 𝟏𝟓 = −𝟑 𝒙 − 𝟏 + 𝟗 3. 𝟐𝒙

𝟑+ 𝒙

𝟐= 𝟕


Station 6:

Solving inequalities for “y” (SE# A.7.B)

Some Tips: Remember this chart to help you with inequalities: Solve inequality equations just like you solve regular equations, with only ONE change: If you divide/multiply by a negative number, you MUST switch the direction of the inequality!

Solve & Graph each inequality. 1. 𝟐𝒙 − 𝟑 < 𝟏

2. 𝟕 + 𝟔𝒂 ≥ 𝟏𝟗


Station 7:

Writing/Solving Systems of Equations (SE# A.5.C A.8.B)

Some Tips: A system of equations uses the same variables in BOTH equations. The solution to a system of equations is where the two functions cross (ie. …where both functions have the same x and y values.)

Conserving Water The equation 𝑤 = 6𝑚 models the gallons of water 𝑤 used by a standard shower head for a shower that takes 𝑚 minutes. The function 𝑤 = 3𝑚 models the water-‐saving shower head. 1. Make a table of values for both functions 2. Graph both functions on the same graph. 3. Suppose you take a 6 minute shower using a water-‐saving shower head. How much water do you save compared to an average shower with a standard shower head?


Station 8: Quadratic Functions (SE# A.4.A A.9.D)

1. Write and graph the parent function of the linear equation AND the quadratic equation on the same graph.

2. Identify the vertex, axis of symmetry, and y-‐intercept of 𝒚 = 𝒙𝟐 − 𝟒

3. If the equation 𝒚 = 𝒙𝟐 − 𝟒 is shifted up by 3 units, what is the new equation?

4. What are the solutions to the equation 𝒚 = 𝒙𝟐 − 𝟒, when f(x) = -‐3


Training Day Assessment

Day 1

Expression

𝟒𝒚− 𝟓𝒙 ∗ 𝟕+ 𝟑

𝒙+ 𝟐𝒙+ 𝟑𝒙+ 𝟒𝒙

𝟑 ∗ 𝟒− 𝟔𝒚+ 𝟐𝒚+ 𝒙+ 𝟐𝒙

Operation

Subtraction Multiplication addition

Variables

x

Terms

Like Terms

3 & 4 -‐6y & 2y x & 2x

Coefficients

4 -‐5

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