TX Obj 2: Patterns, relationships, and algebraic thinking Grade 8

TX Obj 2: Patterns, relationships, and algebraic thinking (8.3) Patterns, relationships, and algebraic thinking. The student identifies proportional or non-proportional linear relationships in problem situations and solves problems. The student is expected to (A) compare and contrast proportional and non-proportional linear relationships; and (B) estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates.

TX Obj 2: Patterns, relationships, and algebraic thinking (8.4) Patterns, relationships, and algebraic thinking. The student makes connections among various representations of a numerical relationship. The student is expected to (A) generate a different representation of data given another representation of data (such as a table, graph, equation, or verbal description).

TX Obj 2: Patterns, relationships, and algebraic thinking (8.5) Patterns, relationships, and algebraic thinking. The student uses graphs, tables, and algebraic representations to make predictions and solve problems. The student is expected to (A) predict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations; and (B) find and evaluate an algebraic expression to determine any term in an arithmetic sequence (with a constant rate of change).

Patterns, relationships, and algebraic thinking (1) A sequence of numbers was generated using the rule 2j + 1, where j represents a number’s position in the sequence. Which sequence fits this rule? 3, 5, 7, 9, 11,.... 5, 8, 5, 8, .... 7, 77, 777, 7777, ...... 4, 8, 12, 16, 20, ... A

Patterns, relationships, and algebraic thinking (2) Look at the sequence in the table below. Which expression can be used to find the value of the term in the nth position? n/2 2n 5 + 2n 3n/4 Position Value of term 1 7 2 9 3 11 4 13 n C

Patterns, relationships, and algebraic thinking (3) A Rose plant grew 3 inches during the last 5 months. If Rubber plant grew at a proportional rate to Rose plant, how long did it take to grow 1 inch? 5/3 months 5/2 months 5/4 months 4/3 months A

Patterns, relationships, and algebraic thinking (4) The number missing in the series is 1, 3, 7, 15, x, 63, .... 33 32 31 30 C

Patterns, relationships, and algebraic thinking (5) The ratio of men to women in the Public Auditorium is 6 to 7. If the number of women present is 240, which proportion can be used to find the number of men, b? 6/b = b/240 6/7 = 240/b 6/7 = b/240 6/7 = b/24 C

Patterns, relationships, and algebraic thinking (6) Square ABCD was dilated to form square PQRS. Which number best represents the scale factor used to change square ABCD to square PQRS? 1/4 1/5 1/7 1/8 A B P Q S 5 in R B D 25 in C

Patterns, relationships, and algebraic thinking (7) What rule can be used to find the n th term in the sequence? 4, 7, 10, 13, ---- 3n + 1 3n 3n – 5 3n + 2 A

Patterns, relationships, and algebraic thinking (8) Let n represent the term’s position in a sequence. Which algebraic expression can be used to find the nth term of the sequence below. 1, 3, 5, 2n – 1 2n + 1 2n 2n - 6 A

Patterns, relationships, and algebraic thinking (9) Sam can type 280 words in 8 minutes. If Sam continues to type at the same rate, which equation can be used to find n, the number of words he can type in half an hour? 280/8 = n/2 280/8 = n/30 280/8 = 30/n Not here B

Patterns, relationships, and algebraic thinking (10) Briana delivers newspapers. She can deliver 60 papers in 45 minutes. Which of these represents an equivalent rate of delivering newspapers? 30 papers in ½ hour 75 papers in 1 hour 120 papers in 1 ½ hours 100 papers in 1 hour C

Patterns, relationships, and algebraic thinking (11) At Austin Shoe Factory 5 pairs of shoes, on average, can be placed in shoe boxes every 3 minutes. At this rate, how many pairs of shoes can be placed in shoe boxes during 8 hours of work? 48 2,880 13.3 800 D

Patterns, relationships, and algebraic thinking (12) At Cantor Middle School 78% of the students ride the bus to school. If 975 students ride the bus, how many students attend the school? 760 975 1,250 1,053 C

Patterns, relationships, and algebraic thinking (13) The Williamson Lumber Company charges a fee of $25 for a lumber delivery plus an additional fee based on the number of pieces of lumber being delivered. Which equation can be used to find the total cost in dollars, c, to deliver n pieces of lumber? c = 0.48n + 25 c = 0.24n + 25 c = 2.5n + 4.80 c = 0.24n • 25 B

Patterns, relationships, and algebraic thinking (14) Camp Wharton serves milk to its campers at every meal. The graph shows the number of gallons of milk that was served each day during one week. Which table best represents the information in the graph? A

Patterns, relationships, and algebraic thinking (15) Linden Bank pays its customers interest on money kept in savings accounts. The table shows how much interest will be earned on $1,500 for different numbers of years the money is kept in the account. Use the information in the table to determine how much interest in dollars and cents will be earned at Linden Bank in 11 years. $1,072.50 $1,987.50 $1,695.00 $1,792.50 A

Patterns, relationships, and algebraic thinking (16) A swim club charges its members a $25 annual membership fee plus $2 every time a member visits the pool. If Joanne spent a total of $365 last year in swim club charges, how many times did she visit the pool? 183 170 195 158 B

Patterns, relationships, and algebraic thinking (17) Let n represent a term’s position in a sequence. Which algebraic expression can be used to find the nth term of the sequence below? 2, 5, 8, 11, 14, . . . 3n − 1 2n 3n + 2 2n + 1 A

Patterns, relationships, and algebraic thinking (18) A sequence of numbers was formed using the rule , where n represents the number’s position in a sequence. Which sequence fits this rule? D

Patterns, relationships, and algebraic thinking (19) Team A gave 32 correct answers of the 40 questions asked in the Science Quiz. Which proportion can be used to find k, the percent of the questions answered wrong. 8/40 = k/100 8k = 400 8/100 =40/k 8k x 400 A

Patterns, relationships, and algebraic thinking (20) Mr. Smith owns an apple tree farm. Every year he plants 180 seedlings. During the summer for every 9 seedlings he plants, 1 tree dies. How many seedlings survive after the summer? 160 120 145 174 A