TCAP MATH PLAYBOOK 7th Grade

Notes about TCAP TCAP is the state mandated test. It will cover all subjects and will be multiple choice. It will be given April 28-May 2. TCAP will count 25% of your second semester average. The grades will be shown on your final report card.

Helpful Tips Get a good night sleep and eat a healthy breakfast. Your brain works better when it is well rested. Take your time and completely read each question. Make sure you know exactly what the question is asking *don’t just assume! Highlight/ underline important parts in the question. Work out the problems. You can write in the book- so do it! DO YOUR BEST AND ROCK THE TEST!

Day 1: Bell Work 1) A jar contains 7 green, 19 black, and 13 pink marbles. A marble is drawn at random.P(not pink). 2) You flip a coin and toss a 1-6 number cube.P(heads and 2)

Day 2: Bell Work The heights, in inches, of the five starting players on a basketball team are listed below. 73, 79, 76, 74, 73 What is the mean of this data set? F 73 inchesG 74 inches H 75 inchesJ 76 inches

Day 3: Bell Work Hector’s art teacher is giving prizes to the 10 students who worked on a mural for the school. The teacher will write the name of one prize on each of 10 slips of paper, as shown below. - She will write “set of markers” on 4 slips of paper - She will write “set of colored pencils” on 3 slips of paper - She will write “drawing paper” on 2 slips of paper - She will write “set of watercolor paints” on 1 slip of paper The teacher will then randomly select one of the slips of paper, and Hector will win the prize that is written on the slip of paper. What is the probability that Hector will win a set of markers or a set of colored pencils? A 1/5B 3/7 C 1/2 D 7/10

Day 4: Bell Work A small rectangular prism is 4 inches long. A large rectangular prism is 24 inches long. These two prisms are similar. Which statement is true? a. The volume of the large rectangular prism is 6 times the volume of the small one. b. The volume of the large rectangular prism is 20 times the volume of the small one. c. The volume of the large rectangular prism is 36 times the volume of the small one. d. The volume of the large rectangular prism is 216 times the volume of the small one.

Day 5: Bell Work Jamie has two cartons. The dimensions of the smaller carton are one-third the size of the larger carton. If the volume of the smaller carton is 120 cm3, find the volume of the larger carton. a. 40 cm3 b. 3,240 cm3 c. 1,080 cm3 d. 360 cm3

Day 1: Data Analysis, Statistics and Probability Part 1: Calculate and interpret mean, median, mode, upper-quartile, lower- quartile, and interquartile range of a data set

Vocabulary Mean- average of the numbers (divide the sum by the amount of numbers added) Median- number in the middle *****list least to greatest! Mode- number used most often ****there can be more than one or none at all Range- difference of the whole data set (largest # - smallest #= range) Upper-Quartile- median of the upper set of numbers Lower-Quartile- median of the lower set of numbers Interquartile range- difference of the quartiles (upper- quartile – lower-quartile = interquartile range)

1) The test scores of several students are listed below. 2, 27, 6, 29, 22, 6, 11, 8, 30, 6, 25, 19 Which box-and-whisker plot accurately represents this data? **What steps do we need to follow to make the plot! ** List the 5 parts –Lower extreme –Lower quartile –Median –Upper quartile –Upper Extreme

2) What is the upper quartile of the numbers listed below? 6, 47, 54, 15, 42, 41, 7, 39, 36, 41, 43 F 28G 41H 43J 48 3) What is the mean of the numbers listed below? 18, 2, 29, 33, 67, 89, 5, 13, 56, 44 F 31G 35.6H 38.2J 42 4) What is the inter-quartile range of the numbers listed below? 21, 10, 96, 74, 32, 8, 47, 59, 83, 65, 16 F 96G 88H 58J 47 5) What is the median of the numbers listed below? 1, 24, 7, 12, 38, 58, 19, 75 F 22.5G 19H 24J ) What is the lower quartile of the numbers listed below? 3, 88, 17, 11, 39, 62, 43, 22, 76 F 17G 14H 15J 11

Part 2: Use theoretical probability to make predictions Theoretical Probability: It is the likeliness of an event happening based on all the possible outcomes. C A L I F O R N I A One card is randomly selected from the bag. 1 ) What is the probability that the selected card shows the letter A? A 1/10B 2/5C 3/10 D 1/5

TCAP Practice Book Questions: # 11, 16, 24, 42, 45, 50

Day 2 and 3: Geometry and Measurement Part 1: Solve contextual problems involving similar triangles. Similar triangles: same shape but sizes are different (each side forms a ratio) *You can create a proportion to see if two triangles are similar. If you know that 2 triangles are similar then you can, create a proportion to solve for a missing side length.

1) The two similar triangles shown are patterns used to create a design on a jacket. What is the value of x, the height of the smaller triangle, in inches? A) 5 ½ in B) 2 1/5 in C) 5 in D) 2 in 11 in 5 in X 2 ½ in

2) The diagram below represents a triangular section of a park. Triangle WST is similar to Triangle WXY. If the length of WS is 234 feet, what is the length of XY ? A 39 feetB 58.5 feet C 117 feetD feet W X Y ST 117 ft

*Use this same methods when given a shadow. *indirect measurement

3) A triangle has side lengths of 28 inches, 32 inches, and 36 inches. Which list shows the side lengths of a similar triangle? F 6 inches, 8 inches, 9 inches G 14 inches, 16 inches, 18 inches H 21 inches, 26 inches, 27 inches J 54 inches, 64 inches, 72 inches 4) A triangle has side lengths of 3 inches, 5 inches, and 10 inches. Which list shows the side lengths of a similar triangle? F 9 inches, 12 inches, 30 inches G 12 inches, 20 inches, 45 inches H 16 inches, 30 inches, 60 inches J 24 inches, 40 inches, 80 inches

TCAP Practice Book Questions: # 4, 19, 54

Part 2: Apply scale factor to solve problems involving area and volume. Notes about Scale Factor Area uses an exponent of 2. You will always square the scale factor. Volume uses an exponent of 3. You will always cube the scale factor. There are 3 ways you will be asked these types of problems. #1 Given the area/volume of 1 figure and the scale factor- find the area/volume of the similar figure. #2 Given the area/volume find the side length ratio **Remember to “undo an area” you will square root it (√) and to “undo a volume” you will cube root it (exponent 1/3) #3 Given the 2 side lengths- find the difference in the figures (how many times larger/smaller one is)

#1 A rectangular painting has an area of 720 square inches. Jasmine reduced the length and width of this painting by a scale factor of 1/6to create a miniature copy. What is the area of the miniature copy? A 12 square inchesB 20 square inches C 60 square inches D 120 square inches Change 16 to 1/6 (fraction) on your packet

#2 Two squares are similar. The area of the smaller square is 256 square inches. The are of the larger square is 324 square inches. What is the ratio of the side length of the smaller square to the side length of the larger square? A 256/324B 64/81 C 1/4D 8/9

#3 Keziah built a scale model of the Gateway Arch in St. Louis, Missouri. A picture of the arch is shown below. The base at each end of the actual arch is shaped like an equilateral triangle with side lengths of 54 feet. Keziah built her model using equilateral triangles for each base that were foot long on each side. Which statement about the areas of these triangles is true? A) The area of the triangle at the base of the actual arch is 27 times the area of the triangle Keziah used for the base of her model. B) The area of the triangle at the base of the actual arch is 108 times the area of the triangle Keziah used for the base of her model. C) The area of the triangle at the base of the actual arch is 729 times the area of the triangle Keziah used for the base of her model. D) The area of the triangle at the base of the actual arch is 11,664 times the area of the triangle Keziah used for the base of her model.

TCAP Practice Book Questions: # 7, 25, 32

Day 4 and 5: Mathematical Processes Part 1: Use proportional reasoning to solve mixture/concentration problems.

1) A recipe for making 8 cups of soup requires 4 cups of water. At this rate, how many cups of water are required to make 16 cups of soup? A 8 cups B 12 cups C 16 cups D 32 cups 2) To make a certain concentration of a chemical, a scientist mixes 81 milliliters of the chemical with 180 milliliters of distilled water. To make more of this chemical concentration, exactly how many milliliters of the chemical should the scientist mix with 260 milliliters of distilled water? A36 millilitersB65 milliliters C117 millilitersD161 milliliters

Part 2: Generalize a variety of patterns to a symbolic rule from tables, graphs, or words.

1) The graph shows five points of a relation. Which equation best represents this relation? F y = x + 2G y = 2x + 3 H J

2) The table shows values of x and y. Which equation represents the pattern shown by the data in the table? X Y

Part Recognize whether information given in a table, graph, or formula suggests a directly proportional, linear, inversely proportional, or other nonlinear relationship.

Which table represents a relationship between x and y that is inversely proportional? A B C D

2) The table shows values of x and y. Which equation represents the pattern shown by the data in the table? A) inversely proportional B) directly proportional C) linear D) Exponential X Y

Part 4: Use scales to read maps.

The map below shows three towns on the same highway. The scale shown on the map relates centimeters (cm) to kilometers (km). - The distance between Oaktown and Crestview is 2 cm on the map. - The distance between Crestview and Maple Grove is 5 cm on the map. According to the scale, what is the actual distance between Oaktown and Maple Grove along the highway? F 98 kmG 70 km H 49 kmJ 28 km

According to the scale drawing, which city is approximately 400 miles from Washington, D.C.? A Richmond B Charleston C Columbia D Raleigh

TCAP Practice Book Questions: # 2, 10, 14, 21, 26, 29, 36, 44, 48, 51

Simplify numerical expressions involving rational numbers. TCAP Practice Book Questions: 12, 28, 46

1) What is the value of the expression shown below? A B C D A B C D

Compare rational numbers using appropriate inequality symbols. TCAP Practice Book Questions: 5, 31, 53

1) Which value of m does not make this inequality true? 0.5 ≤ m ≤ 0.8 F 5/8G 7/10H 8/10J 7/8

2) Which value of m does not make this inequality true? 0.25 < m ≤ 0.75 F 1/4G 3/7H 2/3J 3/5

Which inequality is true? F G HJ

4/17 Bell Work: work on worksheet (due Friday) Reminder: CRA due Thursday (show work) On desk have your *homework, *TCAP book, *TCAP playbook! Make sure that we have completed the following questions from yesterday: 1, 8, 17, 30, 34, 38, 40, 47, 55 We will be reviewing!

Solve contextual problems that involve operations with integers. TCAP Practice Book Questions: 8, 34, 47

1) At 6:00 A.M. on Friday, the outside temperature was 5 degrees below freezing. At 5:00 P.M. on Friday, the outside temperature was 15 degrees above freezing. Which integer best represents the change in temperature from 6:00 A.M. to 5:00 P.M. on Friday? A -20B -10C 20D 10

2) The Titans started their drive at their own 30 yard line and lost 5 yards on the play. Which integer best represents the change in yardage for the Titans? A -5B -35C 5D 35

3) An east-west highway has mile markers that show greater numbers to the east. Part of this highway is represented below. - Mr. Simon got on the highway at mile marker He drove east on the highway for 5 miles and stopped to pick up a friend. - He then drove west on the highway for 12 miles to his office. Which integer best represents the number on the mile marker that is closest to Mr. Simon’s office? A48B38 C24D14

Express the ratio between two quantities as a percent, and a percent as a ratio or fraction. TCAP Practice Book Questions: 1, 38, 55

Mrs. Bryant asked her students if they would prefer to have a pizza party or an ice cream party at the end of the year. She found that 50% of the students prefer a pizza party, 40% prefer an ice cream party, and the rest have no preference. Use this information to answer questions ) What is the ratio of students who have no preference to the students who prefer to have a pizza party? F 1:5G 1:4H 4:1J 5:1 2) What is the ratio of students who have no preference to the students who prefer to have an ice cream party? F 1:5G 1:4H 4:1J 5:1

3) Mrs. Nelson drives an ice-cream truck. On Friday, of the ice-cream bars she sold were chocolate. What percent of the ice- cream bars Mrs. Nelson sold on Friday were not chocolate? F25%G35%H40%J60%

Use ratios and proportions to solve problems. TCAP Practice Book Questions: 17, 30, 40

1) The price for 3 rolls of paper towels is $2.19. Which of the following represents the same price per roll? A 5 rolls for $3.65B 7 rolls for $5.25 C 9 rolls for $7.11D 11 rolls for $7.48

2) The price for 15 oz. of soup is $1.65. Which of the following represents the same price per oz.? A 4 oz. for $0.65B 6 oz. for $1.20 C 8 oz. for $0.88D 10 oz. for $1.80

Evaluate algebraic expressions involving rational values for coefficients and/or variables. TCAP Practice Book Questions: 15, 33, 52

2) What is the value of when p = 0.8 and r= 1.5? F10.8 G13.2 H18.6 J22.8

Interpret the slope of a line as a unit rate given the graph of a proportional relationship. TCAP Practice Book Questions: 9, 18, 22, 41

Apple pies are made at a restaurant. The graph below shows the relationship between the number of pies made and the number of cups of apples used. Which statement best represents the meaning of the slope of this graph? AFor every 3 cups of apples used, 2 pies are made. BFor every 2 cups of apples used, 3 pies are made. CFor every 1 pie made, 6 cups of apples are used. DFor every 6 pies made, 1 cups of apples is used.

Represent proportional relationships with equations, tables and graphs. TCAP Practice Book Questions: 39

1)Ben is drawing a series of regular polygons. Each side in every polygon is the same length. The table below shows the relationship between the number of sides in the polygon and the perimeter of the polygon. Ben will draw a regular polygon with 12 sides that are all the same length as the sides in the other polygons. What will the perimeter of the 12-sided polygon be? F63 centimeters G77 centimeters H84 centimeters J98 centimeters

Solve linear equations with rational coefficients symbolically or graphically. TCAP Practice Book Questions: 6, 20, 49

3) What value of x is the solution to the equation ? A9 B16 C27 D48

Translate between verbal and symbolic representations of real-world phenomena involving linear equations. TCAP Practice Book Questions: 3, 27, 37

1) A teacher had a total of t pens. She gave an equal number of pens to each of 10 students and had 8 pens left over. Which equation could be used to find x, the number of pens each student received? A t = 10x B t = 18x C t = 8x + 10 D t = 10x + 8

2) Mrs. Bryant had a total of t pencils. She gave an equal number of pencils to each of her two nephews and had 20 pencils left over. Which equation could be used to find p, the number of pencils each nephew received? A t = 2p + 20 B t = 22p C t = 22p + 2 D t = 2p

3) A drinking fountain dispenses water at a rate of 3.6 fluid ounces per second. Haley partially filled a glass with water by using the drinking fountain for 3 seconds. If the glass has a total capacity of 12 fluid ounces, which equation can be used to find x, the capacity of the glass, in fluid ounces, not filled with water? A B C D

Solve contextual problems involving two-step linear equations. TCAP Practice Book Questions: 13, 43

1) Stacy spent $40.50 to purchase 2 adult tickets and 2 child tickets for a movie. The price of one adult ticket was $ The following equation can be used to find p, the price of each child ticket. 2p + 23 = What was the price of each child ticket? F $6.50 G $7.25 H $8.00 J $8.75

2) Brian spent $48.75 to purchase 1 adult ticket and 6 child tickets for a movie. The price of the adult ticket was $9.75. The following equation can be used to find p, the price of each child ticket. 6p = What was the price of each child ticket? F $4.50 G $6.50 H $8.50 J $9.75

3) Mr. Kendall bought a new car for a total price of $22,500. He received a rebate of $1,500 and will pay the remainder of the price of the car in 60 equal payments. The equation below can be used to find p, the amount of each payment, in dollars. What value of p makes the equation true? A$350B$375C$400D$435

Remember that it all will be good Do your best!