2017 TEXAS STAAR TEST GRADE 6 MATH

Transcription

1 2017 TEXAS STAAR TEST GRADE 6 MATH Total Possible Score: 38 Needed Correct to Pass: 23 Needed Correct to Master: 31 Time Limit: 4 Hours This file contains the State of Texas Assessments of Academic Readiness (STAAR) administered in Spring, 2017, along with the answer key, learning objectives, and, for writing tests, the scoring guide. This document is available to the public under Texas state law. This file was created from information released by the Texas Education Agency, which is the state agency that develops and administers the tests. All of this information appears on the Texas Education Agency web site, but has been compiled here into one package for each grade and subject, rather than having to download pieces from various web pages. The number of correct answers required to "pass" this test is shown above. Because of where the "passing" score is set, it may be possible to pass the test without learning some important areas of study. Because of this, I believe that making the passing grade should not be considered "good enough." A student's goal should be to master each of the objectives covered by the test. The "Needed Correct to Master" score is a good goal for mastery of all the objectives. The test in this file may differ somewhat in appearance from the printed version, due to formatting limitations. Since STAAR questions are changed each year, some proposed questions for future tests are included in each year's exams in order to evaluate the questions. Questions being evaluated for future tests do not count toward a student's score. Those questions are also not included in the version of the test made available to the public until after they used as part of the official test. The test materials in this file are copyright 2017, Texas Education Agency. All rights reserved. Reproduction of all or portions of this work is prohibited without express written permission from the Texas Education Agency. Residents of the state of Texas may reproduce and use copies of the materials and related materials for individual personal use only without obtaining written permission of the Texas Education Agency. For full copyright information, see: Questions and comments about the tests should be directed to: Texas Education Agency Student Assessment Division 1701 N. Congress Ave, Room 3-122A Austin, Texas phone: Student.Assessment@tea.state.tx.us Hard copies of the released tests may be ordered online through ETS at: When printing questions for math, make sure the print menu is set to print the pages at 100% to ensure that the art reflects the intended measurements. For comments and questions about this file or the web site, you can me at scott@scotthochberg.com. Please direct any questions about the content of the test to the Texas Education Agency at the address above. Provided as a public service by Former State Representative Scott Hochberg. No tax dollars were used for this web site.

2 STAAR State of Texas Assessments of Academic Readiness GRADE 6 Mathematics Administered May 2017 RELEASED Copyright 2017, Texas Education Agency. All rights reserved. Reproduction of all or portions of this work is prohibited without express written permission from the Texas Education Agency.

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4 STAAR GRADE 6 MATHEMATICS REFERENCE MATERIALS AREA Triangle STAAR State of Texas Assessments of Academic Readiness A = 1 bh 2 Rectangle or parallelogram A = bh Trapezoid VOLUME A = 1 (b + b ) h Rectangular prism V = Bh Inches

5 Centimeters STAAR GRADE 6 MATHEMATICS REFERENCE MATERIALS LENGTH Customary Customary Metric 1 gallon (gal) = 4 quarts (qt) 1 liter (L) = 1,000 milliliters (ml) 1 quart (qt) = 2 pints (pt) 1 pint (pt) = 2 cups (c) 1 cup (c) = 8 fluid ounces (fl oz) Metric 1 mile (mi) = 1,760 yards (yd) 1 kilometer (km) = 1,000 meters (m) 1 yard (yd) = 3 feet (ft) 1 meter (m) = 100 centimeters (cm) 1 foot (ft) = 12 inches (in.) 1 centimeter (cm) = 10 millimeters (mm) VOLUME AND CAPACITY WEIGHT AND MASS Customary Metric 1 ton (T) = 2,000 pounds (lb) 1 kilogram (kg) = 1,000 grams (g) 1 pound (lb) = 16 ounces (oz) 1 gram (g) = 1,000 milligrams (mg)

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8 Mathematics Page 7 MATHEMATICS

9 DIRECTIONS Read each question carefully. For a multiple-choice question, determine the best answer to the question from the four answer choices provided. For a griddable question, determine the best answer to the question. Then fill in the answer on your answer document. 1 Which list shows the temperatures in order from coldest to warmest in degrees Fahrenheit? A 10 F 8 F 5 F 0 F B 5 F 10 F 0 F 8 F C 10 F 5 F 0 F 8 F D 0 F 5 F 8 F 10 F Mathematics Page 8

10 2 A coordinate grid is shown below. y x Which ordered pair describes a point that is located 4 units to the left of the origin and 2 units below the x-axis? F (4, 2) G ( 4, 2) H ( 4, 2) J (4, 2) 3 A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint in order to make a green paint. Which ratio of gallons of blue paint to gallons of yellow paint will make the same shade of green paint? A 30 : 54 B 6: 10 C 10 : 45 D 27 : 15 Mathematics Page 9

11 4 The students in a class were each asked to name their favorite meal of the day. The results are shown in this percentage bar graph. Favorite Meal 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% KEY Supper Lunch Breakfast Which table could be represented by the percentage bar graph? Student Results Student Results F Meal Number of Students Breakfast 3 H Meal Number of Students Breakfast 9 Lunch 4 Lunch 3 Supper 10 Supper 18 Student Results Student Results G Meal Number of Students Breakfast 4 J Meal Number of Students Breakfast 0 Lunch 4 Lunch 3 Supper 12 Supper 4 Mathematics Page 10

12 5 What value of x makes this equation true? 90 = x A 10 B 10 C 190 D A team of workers took hours to complete a task. A smaller team of workers will complete the same task, but it will take them 1.25 times as long as it took the first team. Based on this information, which statement is true? F The task will take the smaller team of workers hours to complete, because = G The task will take the smaller team of workers hours to complete, because = H The task will take the smaller team of workers hours to complete, because = J The task will take the smaller team of workers hours to complete, because = Mathematics Page 11

13 7 The playground at a park is shaped like a trapezoid. The dimensions of the playground are shown in the diagram. 68 ft 30 ft 34 ft 36 ft What is the area of the playground in square feet? A 3,120 ft 2 B 1,560 ft 2 C 1,768 ft 2 D 3,536 ft 2 8 Liang has a goal of walking at least 18 miles. She walks at a rate of 4 miles per hour. Which inequality can Liang use to find h, the number of hours she should walk in order to meet or exceed her goal? F 4h 18 G 4h 18 H h J h Mathematics Page 12

14 9 Leon wrote an expression that is equivalent to (30 + 6) 12. Which expression could be the one Leon wrote? A B (3 3 4) 4 3 C D (3 2 ( ) 2) 10 In triangle XYZ the measure of angle YXZ is 50, and the measure of angle XYZ is 75. What is the measure of angle XZY in degrees? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. 11 Customers at an ice-cream shop took a survey. The results showed that 144 customers rated the shop as being very satisfactory. This number represented 45% of the total number of customers who took the survey. What was the total number of customers who took the survey? A 189 B 65 C 99 D 320 Mathematics Page 13

15 12 Mr. Lloyd wants to buy a new television, but he does not have enough money in his bank account to pay for one. Which of these is NOT an option for Mr. Lloyd? F He can use his credit card to buy the television now. G He can save money and pay cash for the television at a later date. H He can use his debit card to buy the television now. J He can save money and use his debit card to buy the television at a later date. 13 The graph shows the number of points, y, a player earns in a balloon game based on the number of balloons the player pops, x. Balloon Game y Number of Points x Number of Balloons Popped Which equation best represents the relationship between x and y? A y = x + 25 B x = y + 25 C x = 25y D y = 25x Mathematics Page 14

16 14 The box plots summarize the attendance for the spring musical and the fall musical. Each musical was performed for six evenings. Spring musical: Fall musical: Attendance Which statement best describes the data represented in the box plots? F The range in attendance for the fall musical is 85. G The interquartile range for the spring musical is 45. H For half the evenings at the fall musical, the attendance was less than 160 people. J For half the evenings at the spring musical, the attendance was between 155 and 200 people. x 15 Jamal wrote the inequality 6. Which situation is best represented by this inequality? 16 A B C Jamal divided x pieces of paper among 16 students, and each student received fewer than 6 pieces of paper. Jamal placed x cards in 16 stacks, and there were no more than 6 cards in each stack. Jamal separated x shirts into 6 stacks, and each stack had at least 16 shirts. D Jamal shared 16 markers with x classmates, and each classmate had fewer than 6 markers. Mathematics Page 15

17 16 Which expression is equivalent to y 48? F (y 40) + 8 G (y 4 ) 8 H (y 40) + (y 8) J (y 4) Megan and Desmond each added the same amount of water to their aquariums. Megan mixed 5 ml of a chemical solution with every gallon of water for her aquarium. Desmond mixed 8 ml of the chemical solution with every 2 gallons of water for his aquarium. Which of these statements is true? A B C Megan used more solution per gallon of water than Desmond, because 5: 1 is greater than 8:2. Megan used more solution per gallon of water than Desmond, because 5 ml is greater than 2 ml. Desmond used more solution per gallon of water than Megan, because 8 ml is greater than 5 ml. D Desmond used more solution per gallon of water than Megan, because 8: 2 is greater than 5:1. Mathematics Page 16

18 18 Dana placed the following points on a number line. Point P at Point Q at Point R at Point S at Which point is NOT correctly placed on this number line? F Point P G Point Q H Point R J Point S Mathematics Page 17

19 2 19 Which statement about 3 multiplied by must be true? 3 A The product is between 3 and 4. B C 2 The product is less than. 3 2 The product is between and 3. 3 D The product is greater than Elida will use six different wires for a science project. The fractions represent the diameters of these wires in inches ,,,,, Which list shows the diameters of the wires in order from least to greatest? F G H J ,,,,, ,,,,, ,,,,, ,,,,, Mathematics Page 18

20 21 Mr. Gonzales showed students part of the prime factorization of 90. One factor is missing What number completes this prime factorization? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. 22 A rectangular computer screen has an area of A square inches. The width of the computer screen is 7 inches. Which equation represents x, the length of the computer screen in inches? F 7 x = A G x = A + 27 H x = A 2(7) A J x = 7 Mathematics Page 19

21 23 Yvonne is researching the effect of education on annual income. A summary of her research is shown in the table. Effect of Education on Annual Income Level of Education Annual Income (dollars) High school diploma 33,904 Associate s degree 40,820 Bachelor s degree 55,432 Based on the data in the table, how much more does a person with an associate s degree earn than a person with only a high school diploma over 10 years? A $6,916 B $74,724 C $747,240 D $69, The list shows the number of viewers of an online music video each day for 5 consecutive days ,715 12,005 By what factor did the number of viewers change each day from the first day to the fifth day? F 7 G 12,000 H 2,401 J 30 Mathematics Page 20

22 25 Which expression has a value of 22? A 8 ( 3) + 33 ( 3) B C 3 + ( 2) ( 8) ( 15) D The rectangle shown represents the base of a rectangular prism. Use the ruler provided to measure the length and width of the rectangle to the nearest 1 4 inch. The height of the prism is 2 inches. Which measurement is closest to the volume of the prism in cubic inches? F 27 in. 3 G 22 in. 3 H 11 in. 3 J 12 in. 3 Mathematics Page 21

23 27 Mr. Martínez asked his students to write a situation that could describe the relationship between all the values of x and y in the table. x y Which situation best describes the relationship between all the values of x and y in the table? A B C Rachel had six dollars and then started to save one dollar each week. Beatriz ran one mile the first week and one mile each week after that. James read zero books in six months and then started to read one book each week. D Marion has six times the number of toy trains that Tony has. 28 The total number of items sold by each student who participated in a fund-raiser is shown in the stem and leaf plot. Stem Items Sold Leaf means 12 items. Which statement is best supported by the data in the stem and leaf plot? F The number of students who sold between 10 and 20 items is greater than the number of students who sold more than 40 items. G The number of students who sold more than 30 items is greater than the number of students who sold fewer than 30 items. H The most common number of items sold is 30. J The most common number of items sold is 15. Mathematics Page 22

24 29 In Austin, Texas, 8 bats ate 40 grams of insects in one night. At this rate, how many grams of insects could 64 bats eat in one night? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. 30 Which expression is equivalent to 30 (3 + x)? F (3 + x) 30 G 30 (x + 3) H (3 30) + x J x 31 Saritha will construct a rectangle that has a height of 4 units and an area of up to 48 square units. Which inequality represents all the possible lengths in units of the bases, b, that Saritha can use to construct this rectangle? A b 44 B b 52 C b 12 D b 192 Mathematics Page 23

25 32 There are 90 girls and 60 boys in the sixth grade at a middle school. Of these students, 9 girls and 3 boys write left-handed. What percentage of the sixth graders at this middle school write left-handed? F 10% G 8% H 5% J 15% 33 The list shows the area in square feet of each apartment available for rent in a building. 565, 961, 867, 517, 627, 714, 517, 728 What is the range of these areas in square feet? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. 34 Amy has 5 yd of border to put around a garden. She uses all the border to make four sections that are the same length. Which expression does NOT equal the length of one of these sections in yards? F 4 5 G 4) 5 H 5 4 J 5 4 Mathematics Page 24

26 35 Which model shows two equal expressions when the value of x is 4? A x x x x = B x x x x = 1 C x 1 1 = D x x = A company spent 32% of its annual budget developing a new machine. What fraction of the company s budget was spent developing the new machine? F G H J Mathematics Page 25

27 37 The dot plot shows the number of touchdowns a football team scored in 10 games last season. Number of Touchdowns Scored Which statement best describes the data shown in the dot plot? A The peak of the data is at 5. B The data are clustered from 0 to 2. C The data distribution has no gaps. D The data distribution is symmetrical. 38 A warehouse floor has a perimeter of 6,615 feet. What is the perimeter of the floor in yards? F 2,205 yd G 19,845 yd H 78,380 yd J 735 yd Mathematics Page 26 BE SURE YOU HAVE RECORDED ALL OF YOUR ANSWERS ON THE ANSWER DOCUMENT. STOP

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29 STAAR GRADE 6 Mathematics May 2017

30 STAAR Grade 6 Mathematics Answer Key Paper 2017 Release Item Number Reporting Category Readiness or Supporting Content Student Expectation 1 1 Readiness 6.2(D) C 2 3 Readiness 6.11(A) G 3 1 Supporting 6.4(C) A 4 4 Readiness 6.12(D) H 5 2 Readiness 6.10(A) B 6 2 Readiness 6.3(E) J 7 3 Readiness 6.8(D) B 8 2 Supporting 6.9(A) F 9 1 Readiness 6.7(A) D 10 3 Supporting 6.8(A) Readiness 6.5(B) D 12 4 Supporting 6.14(B) H 13 2 Readiness 6.6(C) D 14 4 Readiness 6.13(A) F 15 2 Supporting 6.9(C) B 16 1 Readiness 6.7(D) H 17 2 Readiness 6.4(B) A 18 1 Supporting 6.2(C) G 19 2 Supporting 6.3(B) C 20 1 Readiness 6.2(D) J 21 1 Readiness 6.7(A) Supporting 6.8(C) J 23 4 Supporting 6.14(H) D 24 2 Supporting 6.5(A) F 25 2 Readiness 6.3(D) D 26 3 Readiness 6.8(D) G 27 2 Readiness 6.6(C) A 28 4 Readiness 6.13(A) J 29 2 Readiness 6.4(B) Readiness 6.7(D) G 31 2 Readiness 6.10(A) C 32 2 Readiness 6.5(B) G 33 4 Readiness 6.12(C) Supporting 6.2(E) F 35 2 Supporting 6.10(B) D 36 1 Readiness 6.4(G) H 37 4 Supporting 6.12(B) B 38 3 Readiness 6.4(H) F Correct Answer Copyright 2017, Texas Education Agency (TEA). All rights reserved.

31 2017 STAAR Grade 6 Math Rationales Item # Response A/F Response B/G Response C/H Response D/J 1 A is incorrect because 8 F is warmer than 0 F. B is incorrect because -5 F is warmer than -10 F. 2 F is incorrect because the ordered pair (4, 2) describes a point that is 4 units to the right of the origin and 2 units above the x-axis. 3 A is correct because 30 : 54 is equivalent to 5 : 9. 4 F is incorrect because the values for Breakfast; 3/17 30%, Lunch; 4/17 10%, and Supper; 10/17 60%, do not match the percentage bar graph shown. 5 A is incorrect because is -110, not F is incorrect because should be multiplied by 1.25, not added. G is correct because the ordered pair (-4, -2) describes a point that is 4 units to the left of the origin and 2 units below the x-axis. B is incorrect because 6 : 10 is not equivalent to 5 : 9. G is incorrect because the values for Breakfast; 4/20 30%, Lunch; 4/20 10%, and Supper; 12/20 60%, do not match the percentage bar graph shown. B is correct because = -90. G is incorrect because should be multiplied by 1.25, not added. 7 A is incorrect because the formula for the area of a B is correct because the formula for the area of a trapezoid is A = (1/2)(b 1 + b 2 )h, trapezoid is A = (1/2)(b 1 + so A = (1/2)( )(30) = 1,560, not 3,120. b 2 )h, so A = (1/2)( )(30) = 1, F is correct because the rate G is incorrect because the rate Liang walks, 4 miles/hour, Liang walks, 4 miles/hour, multiplied by the time she multiplied by the time she walks, h hours, is at least 18 walks, h hours, is at least 18 miles which is represented by miles which is represented by 9 A is incorrect because = 48, not = F; 55 is correct because ( ) = A is incorrect because 144 should be divided by 0.45, not added to 45. B is incorrect because (3 3 4) 4 3 = 27, not = 3. G; Students may have added together to get 125. B is incorrect because 144 should be divided by 0.45, not multiplied by C is correct because the temperatures are listed in order from coldest to warmest. H is incorrect because the ordered pair (-4, 2) describes a point that is 4 units to the left of the origin and 2 units above the x-axis. C is incorrect because 10 : 45 is not equivalent to 5 : 9. H is correct because the values for Breakfast; 9/30 = 30%, Lunch; 3/30 = 10%, and Supper; 18/30 = 60% match the percentage bar graph shown. C is incorrect because = -290, not -90. H is incorrect because should be multiplied by 1.25, which equals , not C is incorrect because the formula for the area of a trapezoid is A = (1/2)(b 1 + b 2 )h, so A = (1/2)( )(30) = 1,560, not 1,768. H is incorrect because the rate Liang walks, 4 miles/hour, multiplied by the time she walks, h hours, is at least 18 miles which is represented by B is incorrect because = 38, not = 3. C is incorrect because 144 should be divided by 0.45, not subtracted by 45. D is incorrect because -10 F is colder than 0 F. J is incorrect because the ordered pair (4, -2) describes a point that is 4 units to the right of the origin and 2 units below the x-axis. D is incorrect because 27 : 15 is not equivalent to 5 : 9. J incorrect because the values for Breakfast; 0/7 30%, Lunch; 3/7 10%, and Supper; 4/7 60%, do not match the percentage bar graph shown. D is incorrect because = 90, not -90. J is correct because should be multiplied by 1.25, which equals D is incorrect because the formula for the area of a trapezoid is A = (1/2)(b 1 + b 2 )h, so A = (1/2)( )(30) = 1,560, not 3,536. J is incorrect because the rate Liang walks, 4 miles/hour, multiplied by the time she walks, h hours, is at least 18 miles which is represented by D is correct because ( ) (3 2 2) = 3 which is equivalent to = 3. D is correct because = 320. Texas Education Agency Student Assessment Division September 2017

32 2017 STAAR Grade 6 Math Rationales Item # Response A/F Response B/G Response C/H Response D/J 12 F is incorrect because he can use his credit card to buy the television now. G is incorrect because he can save money and pay cash for the television later. 13 A is incorrect because the graph shows that a player receives 25 points for each balloon popped, which is represented by y = 25x, not y = x F is correct because = 85. B is incorrect because the graph shows that a player receives 25 points for each balloon popped, which is represented by y = 25x, not x = y G is incorrect because = 60, not A is incorrect because x B is correct because x cards pieces of paper divided by 16 divided by 16 stacks is no students is fewer than 6 more than 6 cards in each pieces for each student can be stack can be represented by represented by x/16 < 6, not 16 F is incorrect because (y 40) + 8 = 40 y + 8, not y 48. G is incorrect because (y 4) 8 = y 32, not y 48. H is correct because he CANNOT use his debit card to buy the television now because he does not have enough money in his bank account now. C is incorrect because the graph shows that a player receives 25 points for each balloon popped, which is represented by y = 25x, not x = 25y. H is incorrect because the median attendance at the fall musical was 165. J is incorrect because he can save money and use his debit card to buy the television at a later date. D is correct because the graph shows that a player receives 25 points for each balloon popped, which is represented by y = 25x. J is incorrect because the lower and upper quartiles for the attendance at the spring musical are 135 and 195. C is incorrect because x shirts D is incorrect because 16 divided by 16 stacks is at least markers divided by x 6 shirts for each stack can be classmates is fewer than 6 markers for each classmate can be represented by 16/x < H is correct because (y 40) + (y 8) = y 48. J is incorrect because (y 4) + 8 = 4 y + 8, not y A is correct because Megan used more solution per gallon than Desmond because 5 : 1 is greater than 8 : 2, which is equivalent to 4 : F is incorrect because point P is correctly placed at -24/3 on the number line. 19 A is incorrect because 3 multiplied by 2/3 is equal to 1, and 1 is not between 3 and 4. B is incorrect because Megan used more solution per gallon than Desmond because 5 : 1 is greater than 8 : 2, which is equivalent to 4 : 1, not because 5 ml is greater than 2 ml. C is incorrect because Megan used more solution per gallon than Desmond because 5 : 1 is greater than 8 : 2, which is equivalent to 4 : 1. G is correct because point Q is H is incorrect because point R NOT correctly placed at -9/2 = -is correctly placed at 7/2 on 4.5 on the number line. The the number line. number line shows point Q at B is incorrect because 3 multiplied by 2/3 is equal to 1, and 1 is not less than 2/3. C is correct because 3 multiplied by 2/3 is equal to 1, and 1 is between 2/3 and 3. D is incorrect because Megan used more solution per gallon than Desmond because 5 : 1 is greater than 8 : 2, which is equivalent to 4 : 1. J is incorrect because point S is correctly placed at 15/3 on the number line. D is incorrect because 3 multiplied by 2/3 is equal to 1, and 1 is not greater than F is incorrect because the list is not in order from least to greatest; 1/2 is greater than 3/8. 21 A; 5 is correct because 90 = G is incorrect because the list is not in order from least to greatest; 15/32 is greater than 5/16. B; Students may have solved = 18. H is incorrect because the list is not in order from least to greatest; 1/2 is greater than 3/8. J is correct because the list is in order from least to greatest. Texas Education Agency Student Assessment Division September 2017

33 2017 STAAR Grade 6 Math Rationales Item # Response A/F Response B/G Response C/H Response D/J 22 F is incorrect because the G is incorrect because the H is incorrect because the J is correct because the length length of the screen, x, can be length of the screen, x, can be length of the screen, x, can be of the screen, x, can be found found by dividing the area, A, by 7, as represented by x = A/7, not x = 7/A. found by dividing the area, A, by 7, as represented by x = A/7, not x = A found by dividing the area, A, by 7, as represented by x = A/7, not x = A - 2(7). by dividing the area, A, by 7, as represented by x = A/7. 23 A is incorrect because 40,820-33,904 = 6,916, multiplied over 10 years is equal to 69,160, not 6, F is correct because each day's number of viewers is multiplied by the factor 7 to get the next day's number of viewers. 25 A is incorrect because 8 - (-3) + 33 (-3) = 0, not F is incorrect because the length is about 4 and the width is about 2 3/4. The formula for volume of a rectangular prism is V = Bh, so V = (4)(2 3/4)(2) which is closest to 22, not A is correct because a dollar saved each week multiplied by the number of weeks, x, and added to six dollars will give the correct y values in the table. 28 F is incorrect because 6 students sold more than 40 items, which is greater than 5 students who sold between 10 and 20 items. 29 A; 320 is correct because if 8 bats ate 40 grams, then each bat ate 8 grams, multiply 8 by 64 bats equals F is incorrect because 30 (3 + x) is not equivalent to (3 + x) 30. B incorrect because 40,820-33,904 = 6,916, multiplied over 10 years is equal to 69,160, not 74,724. G is incorrect because each day's number of viewers is multiplied by the factor 7 to get the next day's number of viewers, not 12,000. B is incorrect because -3 + (- 2) - (-8) - 1 = 2, not -22. C is incorrect because 40,820 - D is correct because 40,820-33,904 = 6,916, multiplied 33,904 = 6,916, multiplied over 10 years is equal to over 10 years is equal to 69,160, not 747, ,160. H is incorrect because each day's number of viewers is multiplied by the factor 7 to get the next day's number of viewers, not 2,401. C is incorrect because (-15) = 3, not -22. G is correct because the H is incorrect because the length is about 4 and the width length is about 4 and the width is about 2 3/4. The formula for is about 2 3/4. The formula for volume of a rectangular prism volume of a rectangular prism is V = Bh, so V = (4)(2 3/4)(2) is V = Bh, so V = (4)(2 3/4)(2) which is closest to 22. which is closest to 22, not 11. B is incorrect because one mile each week multiplied by the number of weeks, x, and added to one mile will not give the correct y values in the table. G is incorrect because 11 students sold less than 30 items, which is greater than 10 students who sold more than 30 items. B; Students may have multiplied 40(64) = 2,560 and not divided 2,560 by 8. G is correct because 30 (3 + x) = 30 (x + 3). C is incorrect because one book read each week multiplied by the number of weeks, x, and added to zero books will not give the correct y values in the table. H is incorrect because the most common number of items sold is 15, not 30. H is incorrect because 30 (3 + x) is not equivalent to (3 30) + x. J is incorrect because each day's number of viewers is multiplied by the factor 7 to get the next day's number of viewers, not 30. D is correct because = -22. J is incorrect because the length is about 4 and the width is about 2 3/4. The formula for volume of a rectangular prism is V = Bh, so V = (4)(2 3/4)(2) which is closest to 22, not 12. D is incorrect because six multiplied by the number of toy trains, x, will not give the correct y values in the table. J is correct because the most common number of items sold is 15. J is incorrect because 30 (3 + x) is not equivalent to x. 31 A is incorrect because the B is incorrect because the C is correct because the D is incorrect because the formula for the area of a formula for the area of a formula for the area of a formula for the area of a 48, divide both sides by 4 to 48, divide both sides by 4 to 48, divide both sides by 4 to 48, divide both sides by 4 to Texas Education Agency Student Assessment Division September 2017

34 Grade 6 Mathematics Assessment Eligible Texas Essential Knowledge and Skills Texas Education Agency Student Assessment Division January 2014

35 STAAR Grade 6 Mathematics Assessment Mathematical Process Standards These student expectations will not be listed under a separate reporting category. Instead, they will be incorporated into test questions across reporting categories since the application of mathematical process standards is part of each knowledge statement. (6.1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to (A) (B) (C) (D) (E) (F) (G) apply mathematics to problems arising in everyday life, society, and the workplace; use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution; select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems; communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate; create and use representations to organize, record, and communicate mathematical ideas; analyze mathematical relationships to connect and communicate mathematical ideas; and display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication. STAAR Grade 6 Mathematics Page 2 of 9 Texas Education Agency Student Assessment Division January 2014

36 Reporting Category 1: Numerical Representations and Relationships The student will demonstrate an understanding of how to represent and manipulate numbers and expressions. (6.2) Number and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to (A) (B) (C) (D) (E) classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers; Supporting Standard identify a number, its opposite, and its absolute value; Supporting Standard locate, compare, and order integers and rational numbers using a number line; Supporting Standard order a set of rational numbers arising from mathematical and realworld contexts; and Readiness Standard extend representations for division to include fraction notation such as a/b represents the same number as a b where b 0. Supporting Standard (6.4) Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is expected to (C) (D) (E) give examples of ratios as multiplicative comparisons of two quantities describing the same attribute; Supporting Standard give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients; Supporting Standard represent ratios and percents with concrete models, fractions, and decimals; Supporting Standard (F) represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers; and Supporting Standard (G) generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money. Readiness Standard STAAR Grade 6 Mathematics Page 3 of 9 Texas Education Agency Student Assessment Division January 2014

37 (6.5) Proportionality. The student applies mathematical process standards to solve problems involving proportional relationships. The student is expected to (C) use equivalent fractions, decimals, and percents to show equal parts of the same whole. Supporting Standard (6.7) Expressions, equations, and relationships. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to (A) (B) (C) (D) generate equivalent numerical expressions using order of operations, including whole number exponents, and prime factorization; Readiness Standard distinguish between expressions and equations verbally, numerically, and algebraically; Supporting Standard determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations; and Supporting Standard generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties. Readiness Standard STAAR Grade 6 Mathematics Page 4 of 9 Texas Education Agency Student Assessment Division January 2014

38 Reporting Category 2: Computations and Algebraic Relationships The student will demonstrate an understanding of how to perform operations and represent algebraic relationships. (6.3) Number and operations. The student applies mathematical process standards to represent addition, subtraction, multiplication, and division while solving problems and justifying solutions. The student is expected to (A) (B) (C) (D) (E) recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values; Supporting Standard determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one; Supporting Standard represent integer operations with concrete models and connect the actions with the models to standardized algorithms; Supporting Standard add, subtract, multiply, and divide integers fluently; and Readiness Standard multiply and divide positive rational numbers fluently. Readiness Standard (6.4) Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is expected to (A) (B) compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships; and Supporting Standard apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates. Readiness Standard (6.5) Proportionality. The student applies mathematical process standards to solve problems involving proportional relationships. The student is expected to (A) represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions; and Supporting Standard STAAR Grade 6 Mathematics Page 5 of 9 Texas Education Agency Student Assessment Division January 2014

39 (B) solve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, including the use of concrete and pictorial models. Readiness Standard (6.6) Expressions, equations, and relationships. The student applies mathematical process standards to use multiple representations to describe algebraic relationships. The student is expected to (A) (B) (C) identify independent and dependent quantities from tables and graphs; Supporting Standard write an equation that represents the relationship between independent and dependent quantities from a table; and Supporting Standard represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b. Readiness Standard (6.9) Expressions, equations, and relationships. The student applies mathematical process standards to use equations and inequalities to represent situations. The student is expected to (A) (B) (C) write one-variable, one-step equations and inequalities to represent constraints or conditions within problems; Supporting Standard represent solutions for one-variable, one-step equations and inequalities on number lines; and Supporting Standard write corresponding real-world problems given one-variable, onestep equations or inequalities. Supporting Standard (6.10) Expressions, equations, and relationships. The student applies mathematical process standards to use equations and inequalities to solve problems. The student is expected to (A) (B) model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts; and Readiness Standard determine if the given value(s) make(s) one-variable, one-step equations or inequalities true. Supporting Standard STAAR Grade 6 Mathematics Page 6 of 9 Texas Education Agency Student Assessment Division January 2014

40 Reporting Category 3: Geometry and Measurement The student will demonstrate an understanding of how to represent and apply geometry and measurement concepts. (6.4) Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is expected to (H) convert units within a measurement system, including the use of proportions and unit rates. Readiness Standard (6.8) Expressions, equations, and relationships. The student applies mathematical process standards to use geometry to represent relationships and solve problems. The student is expected to (A) (B) (C) (D) extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle; Supporting Standard model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes; Supporting Standard write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers; and Supporting Standard determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers. Readiness Standard (6.11) Measurement and data. The student applies mathematical process standards to use coordinate geometry to identify locations on a plane. The student is expected to (A) graph points in all four quadrants using ordered pairs of rational numbers. Readiness Standard STAAR Grade 6 Mathematics Page 7 of 9 Texas Education Agency Student Assessment Division January 2014

41 Reporting Category 4: Data Analysis and Personal Financial Literacy The student will demonstrate an understanding of how to represent and analyze data and how to describe and apply personal financial concepts. (6.12) Measurement and data. The student applies mathematical process standards to use numerical or graphical representations to analyze problems. The student is expected to (A) (B) (C) (D) represent numeric data graphically, including dot plots, stem-andleaf plots, histograms, and box plots; Supporting Standard use the graphical representation of numeric data to describe the center, spread, and shape of the data distribution; Supporting Standard summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution; and Readiness Standard summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution. Readiness Standard (6.13) Measurement and data. The student applies mathematical process standards to use numerical or graphical representations to solve problems. The student is expected to (A) (B) interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots; and Readiness Standard distinguish between situations that yield data with and without variability. Supporting Standard (6.14) Personal financial literacy. The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in one s life as a knowledgeable consumer and investor. The student is expected to (A) compare the features and costs of a checking account and a debit card offered by different local financial institutions; Supporting Standard STAAR Grade 6 Mathematics Page 8 of 9 Texas Education Agency Student Assessment Division January 2014

42 (B) (C) (E) (F) (G) (H) distinguish between debit cards and credit cards; Supporting Standard balance a check register that includes deposits, withdrawals, and transfers; Supporting Standard describe the information in a credit report and how long it is retained; Supporting Standard describe the value of credit reports to borrowers and to lenders; Supporting Standard explain various methods to pay for college, including through savings, grants, scholarships, student loans, and work-study; and Supporting Standard compare the annual salary of several occupations requiring various levels of post-secondary education or vocational training and calculate the effects of the different annual salaries on lifetime income. Supporting Standard STAAR Grade 6 Mathematics Page 9 of 9 Texas Education Agency Student Assessment Division January 2014