Intercession: Skill Prep Ask Questions, Focus on the Skill

Which point on the number line below is closest to ? | | | | | | | | | 4 5 A B C D Take a few moments and study the line. Notice how many segments there are between the numbers. Decide what each line represents. C

What value of p makes the equation 2p – 8 = 14 ? Usually students would take the answer choices, plug in each value to see which one works. This is fine, but let’s actually solve it!!! When we solve equations, we use inverse operations. We also save the step that isolates the variable until the last step. 2p – 8 = 14 + 8 + 8 3 7 11 22 2p = 22 ___ ____ 2 2

Why Don’t they Just use numbers? Simplify this expression: 5( n + 4n) - 3 = 5(5n) – 3 = We don’t know the value of “n” but we can take it throughout the expression. The associative property lets me move the parentheses. (5 x 5)n – 3 = 25n - 3 I would like to do more, but I CAN’T. I do not know the value of n.

a Which point on the number line is closest to 4.75? | | | | | | | | | | | | | | | | | | c d a b 2 6 3 4 5 a

Use the distributive property to get these values out of the ( ). 6(x + y) 6x + 6y

I know this is a calculator problem I know this is a calculator problem. Make sure you punch it in correctly.

Make sure the rule you choose works on ALL values as you travel from one number to the next!

+ 4 14 -

We are estimating. Think of the nearest whole numbers! Did you see the word “product?”

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3(4y + 6) (3∙4)y + (3∙6)

The number of customers that Just Pants had in its first five months of business is shown on the graph. If the number of customers continues to increase as shown, which is the BEST prediction of the number of customers Just Pants will have in July and August combined? 1600 1800 3400 4000 1400 1200 1000 800 600 400 200 Number of Customers Jan. Feb. Mar. Apr. May Months

Solving Equations 4n + 25 = 325 4n = 300 ___ ____ 4 4 n = 75 -25 -25 Remember, isolating the variable from its coefficient is the LAST step!! What can we remove without touching the 4n? 4n + 25 = 325 -25 -25 Now we are down to a one-step equation! 4n = 300 ___ ____ 4 4 n = 75

Algebra Models Key Key -x2 x2 x -x -1 1 1. 2. The + is invisible!!! What expression is represented by each model?

Simplify the Expression 3(5p – 6) + 8p 15p – 18 + 8p 7p – 6 16p – 18 17p 23p - 18

KEY We are just combing, or counting, the values…. = 1 = x = -1 = - x -x -x 1 1 1 1 -2x – 4 -2x + 4 -4x – 2 -4x + 2

Survey the first 50 students to arrive at school Debbie is conducting a survey to find out which candidate students want for their sixth-grade student council president. Which method BEST explains how to make sure Debbie’s survey is NOT biased? Survey the first 50 students to arrive at school Survey as many students as possible that will vote the same way she will Write the names of each student in the band on a slip of paper and draw 50 names randomly Write the names of each sixth-grade student and draw 50 names randomly

Where am I? Which point is located at (-6, -4) on the coordinate plane? . M . F M P F R . . R P

Algebra Models Key The + is invisible!!! x 1 Which model is equal to

How Would You Write This???? A loss of $55.00? Climbing 15 steps? Four seconds before blastoff? Falling down those 15 steps? Digging a four-foot hole? Earning 5 bonus points? Depositing $100 in your bank? -55 +15 -4 -15 -4 +5 +100

2 (4 + $3) - 2 8 + $6 - 2 8 + - 2 + $6 6 + $6 2(4p +3) -2p 8p + 6 -2p 6p + 6

What’s Your Point? 1. (-3, 5) 2. ( 0, -6) 3. (7, 3) 4. (3, 7) E Match the point to the coordinates. C B 1. (-3, 5) 2. ( 0, -6) 3. (7, 3) 4. (3, 7) 5. (-5, -2) 6. (6, -1) C X F D A B A E D F

Match each value with its graphed point on the number line. 2.25 b) -1 ¾ c) 4.75 d) -3.5 A C B D

Use the key below to determine the value of each model. - 1 1 x2 x -x x2 + -x + 2 ? + ? + ? ? + ? 2x + -3

How many ¾ ft. pieces of rope could we cut from a piece that is long? What operation will we use? What makes you think this? 1 2 We would have two pieces of rope, with 1/6 of a ft. left over. How many inches are in 1/6 of a foot?

Kathleen wants to find out how students in her school communicate with their friends when they are outside of school. Which best explains how to make sure Kathleen gets a sample that is NOT biased? Kathleen can call every fiftieth name from the phone book and survey them. Kathleen can get the names of all the students in her school and survey every tenth student. Kathleen can get e-mail addresses from students in her school and survey them. Kathleen can call her friends on their cell phones to survey them.

p = (48 – 21) ∙ 3 p= (48 – 21) ÷ 3 p= (48 + 21) ÷ 3 p= 48 – (21÷3) The tigers scored 48 points in their last basketball game. The team’s best player scored 21 points in the game. The rest of the points were scored equally by 3 other players. Which equation could be used to find p, the number of points that each of the 3 players scored? p = (48 – 21) ∙ 3 p= (48 – 21) ÷ 3 p= (48 + 21) ÷ 3 p= 48 – (21÷3)

Alex read 5 pages in 9 minutes Alex read 5 pages in 9 minutes. If he continued to read at the same rate, how many pages could Alex read in 45 minutes? Problems like this can be solved by writing the rate in the form of a fraction……even though it is a rate. This is what we know. Let’s treat it like a fraction and create an equal value…….line up like measures …….. 81 41 25 10

Ronald and Donald are going hiking on Saturday Ronald and Donald are going hiking on Saturday. They plan to hike the Blue Trail and the 4 ¾ mile Red Trail. The Blue Trail is 2.7 miles long. How many miles do they plan to hike? 2.7 + 4.75 7.45

Sarah is picking a T-shirt out of her dresser drawer Sarah is picking a T-shirt out of her dresser drawer. She has 6 white shirts, two black shirts, three blue shirts, two gray shirts, and two red shirts in the drawer. What is the likelihood that she will pick a blue shirt?

Which situation is best represented by the integer 7 ? An elevation of 7 ft. below sea level Loaning someone $7 A loss of 7 yards in football An elevator that is on the 7th floor

72(2b + 4b) - 16 49(2b + 4b) - 16 49(6b) - 16 32b – 16 84b – 16 What is the simplest form of this expression? Remember to think of variables as “something!” 72(2b + 4b) - 16 49(2b + 4b) - 16 49(6b) - 16 32b – 16 84b – 16 102b – 16 294b - 16 294b - 16

At the clothing store, Wendy paid a total of $48. 58 At the clothing store, Wendy paid a total of $48.58. She bought a T-shirt for $12.76 and two sweaters. The sweaters were both the same price. What was the cost of one sweater? $12.76 + sweater + sweater = $48.58 We know both sweaters cost the same thing, so……. $12.76 + 2n = $48.58 Subtract the $12.76 $16.19 $17.91 $24.29 $30.67 2n = $35.82 If two cost this amount, how do we find the price of one?

The table below shows values for x and y The table below shows values for x and y. Which expression can be used to find all the y-values in this table? You are being asked to find the rule that changes x into y. X Y 2 1 4 6 3 8 10 x + 2 2x + 2 3x – 1 3x + 1 The rule has to work for ALL values!

Which point is located at (-3,5) ? D B C A A B C D

X Y 2 1 4 6 3 8 10 a) b) c) Choose the graph that shows these points.

Find the Rule The table shows values for x and y. X 3 4 5 6 7 Y 9 12 15 18 21 Which expression can be used to find the x values using the y values? 3y y – 6 y + 6 y

Each lap in the park is 1 ½ miles. Joel cycled for 3 ½ laps Each lap in the park is 1 ½ miles. Joel cycled for 3 ½ laps. How many miles did Joel cycle?

Properties! 8 x 3 x 1 = 8 x 3 (8 x 3) x 4 = 8 x (3 x 4) Which equation represents the commutative property of multiplication? 8 x 3 x 1 = 8 x 3 (8 x 3) x 4 = 8 x (3 x 4) 8 x 3 = (4 x 3) + (4 x 3) (8 x 3) x 4 = (3 x 8) x 4

How many 8 in. by 10 in. rectangular tiles would be needed to cover a 16 ft by 20 ft floor? A = lw WAIT…..if you are thinking of all the multiplying you have to do . . . . here is another way. 576 You should notice the two dimensions you are given: one measure in feet, the other in inches. Regardless, the problem is about floor area. Normally you would multiply both the 16 and the 20 by 12 to change them to inches…….. Why not use factors and save time? 2 (12) 2 (12) = 2 2 16 (12) ∙ 20 (12) would give the area in inches Why not do it all at once??? 8 (10) Then you would divide by the area created by an 8 x 10 tile.

Properties! 9 + (5 + 4) = (9 + 5) + 4 9 + (5 + 4) = 9 + (4 + 5) Which equation represents the distributive property? 9 + (5 + 4) = (9 + 5) + 4 9 + (5 + 4) = 9 + (4 + 5) 9 x (5 + 4) = (9 x 5) + (9 x 4) 9 x (5 + 4) = (9 x 5) x (9 x 4)

Find the Point Point A Point B Point C Point D Which point on the number line below is closest to 3 1/3 ? A B C D | | | | | | | | | 3 4 There are 8 segments, so ½ would be after the 4th segment on point B. Point A Point B Point C Point D Is 1/3 more or less than ½?

Which point on the number line represents 3.7? A. Point R B. Point S Think money? $3.70 Which point on the number line represents 3.7? A. Point R B. Point S C. Point T D. Point U 3.25 3.50 3.75 This is a little more than half. Which point on the number line represents 2/3? F

Which point on the number line represents 2.35? A. Point K B. Point L C. Point M D. Point N | 2.50 Think money again.

Chrissy wants to paint a circle with a radius of 4 feet on her bedroom wall. If 1 can of paint covers 26 square feet, how many cans of paint will Chrissy need? A. 1 B. 2 C. 3 D. 4 One can will not quite cover the circle, so she will need to get two cans.

In Ms. James’ class, 65% of the students have a pet In Ms. James’ class, 65% of the students have a pet. What FRACTION of the class does not have a pet? Remembering that 65% means 65 hundredths…… …and rereading to find the exact question…….. 65 % of the students do have pets, so 35% do NOT have pets….the percents have to equal 100%. .65 b) c) .35 d)

a) b) c) X Y -1 1 -2 3 -3 4 -4 X Y 1 -1 2 -2 -4 4 X Y 5 4 3 2 1 -2 a) Choose the chart that matches the graph.

A group of students were asked to name their main after-school activity. The results are shown in the graph. If 12 students named soccer as their main after-school activity, how many students were surveyed? We could use a proportion to solve this. 5 60 people a) 20 b) 60 c) 100 d) 80

Translate the description below into an algebraic equation. Six less than the quotient of a number and 5. Which equation is a correct translation? ( n ÷ 5) - 6 6 – ( n ÷ 5 ) ( 5 ÷ n ) - 6 6 – (5 ÷ n)

Which point on the number line below is closest to 4.8 ? 4.50 4.6 4.7 4.8 4.9 5.0 | | | | | | | | | | | 4.5 5 D A C B Take a few moments and study the line. Notice how many segments there are between the numbers. Decide what each line represents. C