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Intercession: Skill Prep Ask Questions, Focus on the Skill Slide 2 Which point on the number line below is closest to ? | | | | | | | | | 4 5 Take a few moments and study the line. Notice how many segments there are between the numbers. Decide what each line represents. ABCD C Slide 3 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 lets 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 2p = 22 ___ ____ 2 2 a)3 b)7 c)11 d)22 Slide 4 Simplify this expression: 5( n + 4n) - 3 = We dont know the value of n but we can take it throughout the expression. 5(5n) 3 = The associative property lets me move the parentheses. (5 x 5)n 3 = 25n - 3 I would like to do more, but I CANT. I do not know the value of n. Slide 5 Which point on the number line is closest to 4.75? 2 6 | | | | | | | | | cbad 3 4 5 a Slide 6 Slide 7 Use the distributive property to get these values out of the ( ). 6(x + y) 6x + 6y Slide 8 Slide 9 I know this is a calculator problem. Make sure you punch it in correctly. Slide 10 Slide 11 Slide 12 Slide 13 Make sure the rule you choose works on ALL values as you travel from one number to the next! Slide 14 Slide 15 Slide 16 14 - + 4 Slide 17 Slide 18 We are estimating. Think of the nearest whole numbers! Did you see the word product? Slide 19 Slide 20 Slide 21 -++-++ Slide 22 3(4y + 6) (3 4) y+(3 6 ) Slide 23 Slide 24 Slide 25 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? Jan. Feb. Mar. Apr. May Months Number of Customers 1400 1200 1000 800 600 400 200 0 a)1600 b)1800 c)3400 d)4000 Slide 26 Solving Equations 4n + 25 = 325 Remember, isolating the variable from its coefficient is the LAST step!! What can we remove without touching the 4n? -25 Now we are down to a one-step equation! 4n = 300 ___ ____ 4 n = 75 Slide 27 Algebra Models x2x2 x 1 -x 2 -x x 2 + -x + 2 -3x + 3 Key What expression is represented by each model? 1.2. The + is invisible!!! Slide 28 Simplify the Expression 3(5p 6) + 8p a)7p 6 b)16p 18 c)17p d)23p - 18 15p 18 + 8p Slide 29 KEY = 1 = x = -1 = - x a)-2x 4 b)-2x + 4 c)-4x 2 d)-4x + 2 We are just combing, or counting, the values. -x -x 1 1 1 1 Slide 30 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 Debbies survey is NOT biased? a)Survey the first 50 students to arrive at school b)Survey as many students as possible that will vote the same way she will c)Write the names of each student in the band on a slip of paper and draw 50 names randomly d)Write the names of each sixth-grade student and draw 50 names randomly Slide 31 Where am I? Which point is located at (-6, -4) on the coordinate plane? a)M b)P c)F d)R.... M P F R Slide 32 Algebra Models x 1 Key The + is invisible!!! Which model is equal to 2x + 3 ? Slide 33 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 Slide 34 (4 + $3)2- 2 8 + $6 - 2 8 + - 2 + $6 6 + $6 2(4p +3) -2p 8p + 6 -2p 6p + 6 Slide 35 Match the point to the coordinates. 1. (-3, 5) 2. ( 0, -6) 3. (7, 3) 4. (3, 7) 5. (-5, -2) 6. (6, -1) X y A B C D E F C A B E D F Slide 36 ABCD Match each value with its graphed point on the number line. a)2.25 b) -1 c) 4.75 d) -3.5 Slide 37 Use the key below to determine the value of each model. - 1 1 x 2 x -x ? + ? + ? ? + ? x 2 + -x + 2 2x + -3 Slide 38 How many 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? Slide 39 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? a)Kathleen can call every fiftieth name from the phone book and survey them. b)Kathleen can get the names of all the students in her school and survey every tenth student. c)Kathleen can get e-mail addresses from students in her school and survey them. d)Kathleen can call her friends on their cell phones to survey them. Slide 40 The tigers scored 48 points in their last basketball game. The teams 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? a)p = (48 21) 3 b)p= (48 21) 3 c)p= (48 + 21) 3 d)p= 48 (213) Slide 41 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 fractioneven though it is a rate. This is what we know. Lets treat it like a fraction and create an equal value.line up like measures .. a)81 b)41 c)25 d)10 Slide 42 Ronald and Donald are going hiking on Saturday. They plan to hike the Blue Trail and the 4 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 Slide 43 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? Slide 44 Which situation is best represented by the integer 7 ? a)An elevation of 7 ft. below sea level b)Loaning someone $7 c)A loss of 7 yards in football d)An elevator that is on the 7 th floor Slide 45 What is the simplest form of this expression? Remember to think of variables as something! 7 2 (2b + 4b) - 16 a)32b 16 b)84b 16 c)102b 16 d)294b - 16 49(2b + 4b) - 16 49(6b) - 16 294b - 16 Slide 46 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 2n = $35.82 If two cost this amount, how do we find the price of one? a)$16.19 b)$17.91 c)$24.29 d)$30.67 Slide 47 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. XY 02 14 26 38 410 a) x + 2 b) 2x + 2 c) 3x 1 d) 3x + 1 The rule has to work for ALL values! Slide 48 Which point is located at (-3,5) ? D B C A a)A b)B c)C d)D Slide 49 XY 02 14 26 38 410 Choose the graph that shows these points. a) b) c) Slide 50 Find the Rule X34567 Y912151821 The table shows values for x and y. Which expression can be used to find the x values using the y values? a)3y b)y 6 c)y + 6 d) y Slide 51 Each lap in the park is 1 miles. Joel cycled for 3 laps. How many miles did Joel cycle? Slide 52 Properties! Which equation represents the commutative property of multiplication? a)8 x 3 x 1 = 8 x 3 b)(8 x 3) x 4 = 8 x (3 x 4) c)8 x 3 = (4 x 3) + (4 x 3) d)(8 x 3) x 4 = (3 x 8) x 4 Slide 53 How many 8 in. by 10 in. rectangular tiles would be needed to cover a 16 ft by 20 ft floor? A = lw 576 WAIT..if you are thinking of all the multiplying you have to do.... here is another way. 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? 16 (12) 20 (12) would give the area in inches Then you would divide by the area created by an 8 x 10 tile. Why not do it all at once??? 8 (10) 22 2 (12) 2 (12) = Slide 54 Properties! Which equation represents the distributive property? a)9 + (5 + 4) = (9 + 5) + 4 b)9 + (5 + 4) = 9 + (4 + 5) c)9 x (5 + 4) = (9 x 5) + (9 x 4) d)9 x (5 + 4) = (9 x 5) x (9 x 4) Slide 55 Find the Point Which point on the number line below is closest to 3 1/3 ? | | | | | | | | | 3 4 A B C D a)Point A b)Point B c)Point C d)Point D There are 8 segments, so would be after the 4 th segment on point B. Is 1/3 more or less than ? Slide 56 Which point on the number line represents 2/3? Which point on the number line represents 3.7? A. Point R B. Point S C. Point T D. Point U Think money? $3.70 3.25 3.50 3.75 This is a little more than half. F Slide 57 Which point on the number line represents 2.35? A. Point K B. Point L C. Point M D. Point N Think money again. | 2.50 Slide 58 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. Slide 59 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%. a).65 b) c).35 d) Slide 60 XY 00 1 -2 3-3 4-4 Choose the chart that matches the graph. a) a) b) c) XY 00 1 2-2 2 -44 XY 00 54 32 15 2-2 Slide 61 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 Slide 62 Translate the description below into an algebraic equation. Six less than the quotient of a number and 5. Which equation is a correct translation? a)( n 5) - 6 b)6 ( n 5 ) c)( 5 n ) - 6 d)6 (5 n) Slide 63 Which point on the number line below is closest to 4.8 ? | | | | | | | | | | | 4.5 5 Take a few moments and study the line. Notice how many segments there are between the numbers. Decide what each line represents. ABCD C 4.50 4.6 4.7 4.8 4.9 5.0