6 th grade taks released tests by objective objective 1numbers, operations, and quantitative...

6th Grade TAKSReleased Tests

by ObjectiveObjective

1 Numbers, operations, and quantitative reasoning

2 Patterns, relationships, and algebraic reasoning

3 Geometry and spatial reasoning

4 Measurement

5 Probability and statistics

6 Mathematical processes and tools

Objective 1:The student will demonstrate an

understanding of numbers, operations, and

quantitative reasoning.

(6.1) Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of equivalent forms. The student is expected to

(A) compare and order non-negative rational numbers;

Sam recorded the lengths of his model cars in inches. Which list shows the lengths in order from greatest to least?

A 6.8 in., 6.78 in., 6.45 in., 6.5 in., 6.34 in.

B 6.34 in., 6.45 in., 6.5 in., 6.78 in., 6.8 in.

C 6.8 in., 6.78 in., 6.45 in., 6.34 in., 6.5 in.

D 6.8 in., 6.78 in., 6.5 in., 6.45 in., 6.34 in.

Spring 2003 #7Correct Answer - D

Amy, Jasmine, Katrina, and Myra each walked from their houses to the mall. Amy walked ½ mile, Jasmine walked ¼ mile, Katrina walked ¾ mile, and Myra walked ⅝ mile. Which list shows these distances in order from greatest to least?

Spring 2003 #16Correct Answer - G

Which statement about the mixed number 1⅓ is true?

April 2004 #31Correct Answer - C

The table below shows thetime it took 4 runners tofinish a 100-meter dash.Which list shows therunners in order fromfastest to slowest?

F Bernice, Elaine, Dawn, Carlene

G Dawn, Carlene, Elaine, Bernice

H Carlene, Bernice, Elaine, Dawn

J Bernice, Carlene, Dawn, Elaine

April 2006 #32Correct Answer - F


(B) generate equivalent forms of rational numbers including whole numbers, fractions, and decimals;

Stephanie bought a basketball on sale for $15, which was 1/5 off the original price. What decimal represents the discount she received?

F 0.05

G 0.15

H 0.20

J 0.50

Spring 2003 #20Correct Answer - H

The formula F = C + 32 can be used to convert a temperature from degrees Celsius to degrees Fahrenheit. Which of the following best represents ?

F 9.5

G 1.8

H 0.55

J 0.18

April 2004 #28Correct Answer - G

Fabian has organized 3/5 of his baseball card collection. Which decimal represents the fraction of Fabian’s collection he has organized?

F 0.4

G 0.6

H 0.35

J 0.12



(C) use integers to represent real-life situations;

The low temperature on Saturday was 10 degrees below zero Celsius. On Sunday the low temperature was 30 degrees above zero Celsius. What integer represents the low temperature on Saturday in degrees Celsius?

F 20

G 10

H -10

J -20


Acorn woodpeckers live in families. The family members collect acorns and store them in the trunks of trees. The table below shows information about the number of acorns collected and eaten by a family ofwoodpeckers on 3 days.Which expression bestdescribes the information inthe table if the family hadstored 428 acorns beforeMonday?

F 428 – 23 + 8 – 29 + 10 – 42 + 9

G 428 + 23 – 8 + 29 – 10 + 42 – 9

H 23 – 8 + 29 – 10 + 42 – 9 – 428

J 23 + 8 – 29 + 10 – 42 + 9 + 428



(D) write prime factorizations using exponents;

Find the prime factorization of 60.

Spring 2003 #14Correct Answer - J

F 32 ∙ 10

G 2 ∙ 3 ∙ 10

H 2 ∙ 2 ∙ 15

J 22 ∙ 3 ∙ 5

Which is the prime factorization of 315?

A 33 ∙ 5

B 33 ∙ 7

C 32 ∙ 5 ∙ 7

D 3 ∙ 52 ∙ 7


What is the prime factorization of 220?

A 2 ∙ 5 ∙ 11

B 22 ∙ 5 ∙ 5

C 22 ∙ 5 ∙ 11

D 2 ∙ 55



(E) identify factors and multiples including common factors and common multiples.

At a spring band concert, a prize was awarded to the person sitting in the chair numbered with the least common multiple of 12, 15, and 30. Find the number of the prizewinning chair.

F 60

G 45

H 30

J 15

Spring 2003 #38Correct Answer - F

Find the greatest common factor of 12, 24, and 36.

A 6

B 12

C 18

D 24

April 2004 #17Correct Answer - B

Which of the following is the least common multiple that Valerie can use to add three fractions with denominators of 6, 8, and 9?

A 48

B 54

C 72

D 144


Mrs. Sandoval has 60 folders, 45 pairs of scissors, and 30 rulers. What is the greatest common factor Mrs. Sandoval can use to divide the school supplies into equal groups?

A 3

B 5

C 10

D 15

April 2006 #15Correct Answer - D

(6.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve problems and justify solutions. The student is expected to

(A) model addition and subtraction situations involving fractions with [objects,] pictures, words, and numbers;

Mara plans to buy fabric for two sewing projects. One project requires ⅛ yard of fabric, and the other requires ¾ yard of fabric. Each strip below represents 1 yard of fabric. Which strip is shaded to show the total amount of fabric that Mara needs for her projects?


Frank and Joe each bought a small pizza and ate only part of their pizza. The pictures below show how much of the pizzas were left. What portion of the pizza did Frank and Joe eat altogether?


To get ready for a race, Louise ran 1⅔ miles on Monday, 2¼ miles on Tuesday, and 2 5/6 miles on Wednesday. Which procedure can Louise use to find the total number of miles she ran on these 3 days?

A Find the product of the sum of the whole numbers andthe sum of the fractions

B Subtract the sum of the fractions from the sum of thewhole numbers

C Find the quotient of the sum of the whole numbers andthe sum of the fractions

D Add the sum of the whole numbers to the sum of the fractions



(B) use addition and subtraction to solve problems involving fractions and decimals;

Harold made a drawing of his rectangular kitchen for art class. The length of the drawing was 8.6 inches, and the width of the drawing was 2.5 inches less than the length. Find the width of the drawing.

F 6.1 in.

G 8.6 in.

H 11.1 in.

J 21.5 in.


The Springer family took a trip for the holidays. When they left home, the odometer in their car read 5,364.6 miles. When they returned from their trip, the odometer read 7,347.0 miles. How many miles did the Springers travel?

Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.

April 2004 #21Correct Answer – 1982.4

John is going to make three kinds of cookies. He will need 2⅓ cups flour for the first kind, 2¼ cups flour for the second kind, and 3⅓ cups flour for the third kind. How much flour does John need for all three kinds of cookies?


Sandra added $0.60 to the $25.00 she had saved. She then bought a CD that cost $13.79, including tax. Exactly how much money in dollars and cents should Sandra have left after paying for the CD?


April 2006 #21Correct Answer – 11.81


(C) use multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates;

Linda bought 2 blouses for a total of $52 and 3 equally priced dresses. She spent a total of $148, not including tax. Find the price of each dress.

F $26

G $32

H $52

J $55


During basketball season Wanda made 2 out of every 3 free throws she attempted. In the last basketball game, Wanda attempted 12 free throws. How many free throws would she have been expected to make?

A 2

B 8

C 24

D 36


At a community center there are a total of 11 tables in the dining room. Six of the tables seat 4 people each. Five of the tables seat 8 people each. What is the maximum number of people who can sit at the tables in the dining room?

F 40

G 12

H 22

J 64

April 2006 #4Correct Answer - J

The ratio of women to men in a local book club is 7 to 3. Which combination of women and men could the club have?

A 21 women and 9 men

B 35 women and 50 men

C 14 women and 9 men

D 21 women and 15 men

April 2006 #11Correct Answer - A


(D) estimate and round to approximate reasonable results and to solve problems where exact answers are not required.

For a science project Ruth is keeping track of the calories her father eats at breakfast. The table shows the number of calories he ate at breakfast on Monday. Which is closest to the number of calories Ruth’s father ate at breakfast on Monday?

F 200 cal

G 300 cal

H 400 cal

J 500 cal


Several middle school bands boarded buses after a marching competition. If there were 21 buses and about 47 band members on each bus, about how many band members were on the buses in all?

A 70

B 900

C 1,000

D 1,250


Mr. Cartwright bought 18 computer books for his bookstore. If he paid $24.95 for each book, about how much did Mr. Cartwright pay for the books?

A $40

B $600

C $500

D $300


Objective 2:The student will demonstrate an

understanding of patterns, relationships, and

algebraic reasoning.

(6.3) Patterns, relationships, and algebraic thinking. The student solves problems involving proportional relationships. The student is expected to

(A) use ratios to describe proportional situations;

There were 14 boats and 42 people registered for a boat race. Which ratio accurately compares the number of people to the number of boats?

F 2:6

G 3:1

H 7:21

J 14:42


If the ratio of boys to girls in the sixth-grade chorus is 2 to 3, which of these shows possible numbers of the boys and girls in the chorus?

A 20 boys, 35 girls

B 24 boys, 36 girls

C 35 boys, 20 girls

D 36 boys, 24 girls

Spring 2003 #35Correct Answer - B

An animal shelter currently has 20 cats and 25 dogs. What is the ratio of cats to dogs?

F 5 to 4

G 4 to 9

H 4 to 5

J 1 to 5

April 2004 #26Correct Answer - H

A recipe for pancakes requires 3 eggs and makes 12 pancakes. What is the ratio of eggs to pancakes?

A 12:3

B 1:4

C 3:1

D 1:3


(6.3) Patterns, relationships, and algebraic thinking. The student solves problems involvingproportional relationships. The student is expected to

(B) represent ratios and percents with [concrete] models, fractions, and decimals;

By 2:30 P.M. on Monday, 25% of the classes at Valley Middle School had finished taking yearbook pictures. What fractional part of the classes had NOT yet taken yearbook pictures?


Each square below is divided into sections of equal size. Which square has 62.5% of its total area shaded?


Franklin’s Vending Service received a shipment of soda for its machines. The manager determined that 15% of the cans were damaged. What fraction of the cans were damaged?


Use the ruler on the Mathematics Chart to measure the lengths of the line segments below to the nearest centimeter. Which best represents the ratio of UV to XY?

F 7:15

G 3:7

H 3:8

J 1:2April 2006 #16Correct Answer - G

0 1 2 3 4 5 6 7 8

Paul made 11 of the 20 shots he took at hockey practice yesterday. What percent of his shots did he make?

F 20%

G 11%

H 45%

J 55%


(6.3) Patterns, relationships, and algebraic thinking. The student solves problems involvingproportional relationships. The student is expected to

(C) use ratios to make predictions in proportional situations.

The ratio of red rosebushes to yellow rosebushes in the school garden is about 3 to 4. If there were 36 yellow rosebushes, about how many red rosebushes would there be?

F 36

G 32

H 27

J 12


Corinne’s group was responsible for painting windows on the set of a school play. The group painted 18 windows in 90 minutes. If they continued painting at this rate, how many windows would they paint in 3 hours?

A 24

B 36

C 54

D 72


Josie’s horse eats about 2 bales of hay every 5 days. About how many bales of hay does Josie’s horse eat in 31 days?

A 8

B 12

C 16

D 78


Manuel’s heart beats 9 times per 10 seconds while Manuel is resting. About how many times would Manuel’s heart beat during 3 minutes of rest?

A 27

B 162

C 270

D 200


Palmer participated in sports for 8 hours and drama for 5 hours during a period of 2 weeks. If Palmer continues participating in these activities at this rate, how many hours will he spend participating in them during 52 weeks?

F 13 hours

G 338 hours

H 8 hours

J 208 hours


(6.4) Patterns, relationships, and algebraic thinking. The student uses letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes. The student is expected to

(A) use tables and symbols to represent and describe proportional and other relationships involving conversions, sequences, perimeter, area, etc.;

The table shows Andre’s age and Maria’s age over 4 consecutive years. Which expression best represents Maria’s age in terms of Andre’s age?

F x + 4

G 2x

H y + 4

J 2y


At Sandra’s school there is 1 teacher for every 15 students. There are 630 students at the school. Which proportion can be used to find x, the number of teachers?


Rafael pays $550 in rent each month. Which table best represents the relationship between m, the number of months, and r, the amount he pays in rent for that length of time?


Which equation best represents the relationship between x and y in the table below?

A y = 7x

B y = 3x + 4

C y = 2x + 5

D y = x + 6


(6.4) Patterns, relationships, and algebraic thinking. The student uses letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes. The student is expected to

(B) generate formulas to represent relationships involving perimeter, area, volume of a rectangular prism, etc., from a table of data.

A certain regular polygon is made of congruent equilateral triangles. The table shows the relationship between the area of the triangle and the area of the polygon it is part of. Which expression can be used to find the area of a similar polygon made of triangles with an area of n square units each?

A 1n

B 6n

C n + 6

D n + 36


The table shows the areas of a triangle where the height of the triangle stays the same but the base changes. Which expression can be used to find the area of a triangle that has a height of 6 units and a base of n units?


What is the rule to find the value of a term in the sequence below?

F n + 3

G 3n – 2

H 3n

J n – 2


Alex found the perimeter of a square to be 12 inches. Which of the following could be used to find l, the length of one edge of the square?

A l = 4 ∙ 12

B l = 12 ÷ 4

C l = 4 + 12

D l = 12 – 4


(6.5) Patterns, relationships, and algebraic thinking. The student uses letters to represent an unknown in an equation. The student is expected to

(A) formulate an equation from a problem situation.

David bought 2 shirts that were originally priced at $26.50 each. Each shirt was on sale for $3.98 off the original price when David bought them. Which equation can be used to find t, the total sale price of the 2 shirts?A t = 26.50 – 3.98

B t = 2(26.50) – 3.98

C t = 2(3.98) – 2(26.50)

D t = 2(26.50) – 2(3.98)


Mr. Chávez distributed 78 sheets of drawing paper to the art students in his class. Each student received 3 sheets of drawing paper. Which equation can be used to find s, the number of students in the class?

A s = 78 ÷ 3

B s = 75 – 3

C s = 78 × 3

D s = 78 + 3

Spring 2003 #45Correct Answer - A

If the cost of renting a canoe is a basic fee of $5 plus an additional $2.50 for each hour that the canoe is rented, which equation can be used to find c, the cost in dollars of the rental for h hours?

A c = 2.5h + 5

B c = 5h + 2.5

C c = 2.5(h + 5)

D c = 5(h + 2.5)


Mr. Duran handed out 32 sheets of graph paper equally among 8 groups of students. Which equation can be used to find s, the number of sheets of paper each group received?

F s = 32 ÷ 8

G s = 32 – 8

H s = 32 ∙ 8

J s = 32 + 8


Zack attended a basketball camp for two weeks. His parents paid $50.00, which was ⅔ the cost of attending the camp. Zack had saved money to pay the rest of the cost. Which equation can be used to find c, the entire cost of attending the camp?


Objective 3:The student will demonstrate an understanding of geometry and

spatial reasoning.

(6.6) Geometry and spatial reasoning. The student uses geometric vocabulary to describe angles, polygons, and circles. The student is expected to

(A) use angle measurements to classify angles as acute, obtuse, or right;

What kind of angle is N?

F Acute

G Right

H Obtuse

J Straight


In which of the pictures does P appear to be an obtuse angle?


The angle at each vertex of a regular octagon is 135°. What type of angle is at each vertex of a regular octagon?

F Obtuse

G Right

H Straight

J Acute


The table below shows different types of volcanoes and the angles formed by their slopes. Based on the data in the table, which of the following statements is true about these volcanoes?

A All the volcanoes have obtuse angles of slope.

B All the volcanoes have acute angles of slope.

C The cinder cone has an obtuse angle of slope, and the composite cone and shield have acute angles of slope.

D The cinder cone has an acute angle of slope, and the composite cone and shield have obtuse angles of slope.


Look at the figure shown below. Which of the following angles in the figure is obtuse?

F angle NMR

G angle MRQ

H angle PQR

J angle MNP



(B) identify relationships involving angles in triangles and quadrilaterals;

The drawing below shows the shape of a plot of land. Find the measure of Z.

F 40°

G 50°

H 99°

J 180°


Triangle XYZ is an isosceles triangle. If the measure of Z is 32°, what is the measure of Y?

F 32°

G 74°

H 148°

J 164°


A triangle has angles measuring 45° and 55°. What is the measure of the triangle’s third angle?

F 80°

G 100°

H 125°

J 135°


Mr. Sosa has a ranch in the shape of a trapezoid. The sides of the ranch form angles measuring 60°, 80°, and 120°. What is the measure of the fourth angle?

F 80°

G 100°

H 240°

J 260°


∆RST shown below is an isosceles triangle. If the measure of R is 40°, what is the measure of S?

A 320°

B 140°

C 70°

D 40°


Look at the parallelogram shown below. Which of the following could be the measures of the angles of the parallelogram?

F 120°, 60°, 120°, 120°

G 80°, 100°, 80°, 100°

H 90°, 90°, 120°, 60°

J 100°, 90°, 80°, 90°



(C) describe the relationship between radius, diameter, and circumference of a circle.

The drawing shows 2 circles that share a common center point. Which expression can be used to find the approximate circumference of the outer circle in centimeters?

A π(3 + 8)

B ½(3 + 8)

C 2π(3 + 8)

D 2(3 + 8)

Spring 2003 #27Correct Answer - C

A circle with center at point O is shown below. Which line segment is 2 times the length of radius OK?

F Segment LN

G Segment LM

H Segment LK

J Segment ON


Trevor knows the circumference of his bicycle tire, but he needs to find the diameter. Which method can Trevor use to find the diameter?

A Multiply the circumference by 2 and divide the result by π

B Divide the circumference by 2 and multiply the result by π

C Multiply the circumference by π D Divide the circumference by π


Rosa sliced an orange into circular pieces to put into a bowl of punch. The piece shown below had a radius of 4 centimeters. Which expression can be used to find the approximate circumference of this piece of orange?

A 2(4)

B π(4)

C 2(π)(8)

D 2(π)(4)


(6.7) Geometry and spatial reasoning. The student uses coordinate geometry to identify location in two dimensions. The student is expected to

(A) locate and name points on a coordinate plane using ordered pairs of non-negative rational numbers;

Which point best represents the location of the ordered pair (1¾, 2)?

A Point P

B Point Q

C Point R

D Point S


Valerie listed the coordinates of 5 of the vertices of the hexagon below.

(1, 2), (1, 4), (2, 1), (4, 1), (5, 5)Which of these shows the coordinates of the vertex that Valerie did not list?

A (1, 3)

B (3, 1)

C (3, 6)

D (6, 3)


Which ordered pair represents a point located inside both the triangle and the circle?

A (8, 4)

B (8, 10)

C (14, 8)

D (15, 9)


What point on the grid below corresponds tothe coordinate pair (5½, 8)?

A Point W

B Point X

C Point Y

D Point Z


The coordinate grid shows point L, the position of the rover Spirit when it landed on Mars, and the path it followed to point M. Point M shows the position of the rover after it traveled 100 meters. Which of the following best shows the position of the rover when it was halfway between point L and point M?

A (2, 4)

B (4, 8)

C (4, 2)

D (8, 4)


A window is shown on the grid below. Which ordered pairs best represent the 4 vertices of the window?

A (4, 2), (2, 2), (5, 2), (4, 5)

B (2, 2), (2, 4), (5, 2), (5, 4)

C (2, 2), (4, 2), (4, 5), (2, 5)

D (4, 2), (5, 4), (5, 2), (2, 2)


Objective 4:

The student will demonstrate an understanding of the concepts and uses

of measurement.

(6.8) Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, capacity, weight, and angles. The student is expected to

(A) estimate measurements and evaluate reasonableness of results;

On Tuesday night Lucas spent 18 minutes on social studies homework, 29 minutes on language arts homework, and 59 minutes on mathematics homework. About how much time in all did Lucas spend on his homework?

F 1 hour 50 minutes

G 1 hour 10 minutes

H 1.5 hours

J 1.10 hours


Gerald got out of bed at 7:05 A.M. and returned home from school at 2:50 P.M. About how many hours elapsed between the time he got out of bed and the time he returned home from school?

F 4 h

G 5 h

H 7 h

J 8 h


The temperature was 47°F at 10 A.M. and 68°F at 3 P.M. The temperature decreased by about 4°F per hour after 3 P.M. About how much warmer was the temperature at 5 P.M. than it was at 10 A.M.?

F 0°F

G 10°F

H 20°F

J 30°F


The total length of all the songs on a CD Mohammed bought is about 80 minutes. Each song is between 4 and 6 minutes long. Which is a reasonable number of songs that could be on the CD?

A 10

B 40

C 74

D 16



(B) select and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter and circumference), area, time, temperature, capacity, and weight;

Lauren cut a triangle out of construction paper for a geometry project. Find the perimeter of the triangle in centimeters.


Spring 2003 #21Correct Answer - 91

Francesca used a square piece of poster board to show the main points of her history presentation. The length of each side of the poster board was 24 inches. Find the area of the poster board.

A 48 in.2

B 96 in.2

C 400 in.2

D 576 in.2


A family put a rectangular patio in their backyard and planted grass in the rest of the yard. The rectangular backyard is 100 feet by 80 feet, and the patio is 13 feet by 8 feet. What is the area of the backyard that is planted with grass?

F 402 sq ft

G 7,896 sq ft

H 8,000 sq ft

J 8,104 sq ft


Mrs. Gold designed a piece of art by outlining equilateral triangles with wire. How much wire did Mrs. Gold use to complete her piece of art?

F 9 m

G 33 m

H 90 m

J 57 m


Nicole was on the decorating committee for a school dance. She made 5 different circular designs for the decorations. The committee agreed to use a design with a diameter of 19 inches. Which is closest to the circumference in inches of the design the committee chose?

F 13 in.

G 60 in.

H 95 in.

J 300 in.



(C) measure angles;

A parallelogram is shown. Find the measurement of ∠S to the nearest degree.

A 136°

B 124°

C 64°

D 56°


Lynn’s garden is shaped like an isosceles trapezoid. Find the measure of ∠T to the nearest degree.

A 65°

B 75°

C 115°

D 125°


Triangle VUW is shown below. What is the measure of ∠ VUW to the nearest degree?

F 57°

G 63°

H 123°

J 137°



(D) convert measures within the same measurement system (customary and metric) based on relationships between units.

Anna’s brother is 117 centimeters tall. How is 117 centimeters expressed in meters?

A 0.117 m

B 1.17 m

C 11.7 m

D 117 m


Pedro bought a 2-liter bottle of soda. What is the volume of the bottle in milliliters?

F 20,000 mL

G 2,000 mL

H 200 mL

J 20 mL


Ted collected 22 pounds of aluminum cans. How many ounces of aluminum cans did he collect?

A 6 oz

B 38 oz

C 352 oz

D 220 oz


Objective 5:

The student will demonstrate an understanding of probability and

statistics.

(6.9) Probability and statistics. The student uses experimental and theoretical probability to make predictions. The student is expected to

(A) construct sample spaces using lists, tree diagrams, and combinations;

Charlie had 1 red marble, 1 blue marble, 1 yellow marble, and 1 green marble in a bag. He picked 2 marbles at random from the bag. Which diagram shows all the possible color combinations of the 2 marbles that Charlie picked?


Bob’s Lunch Café offers 3 kinds of sandwich fillings and 3 kinds of bread. Which table shows all the possiblesandwichcombinations atBob’s Lunch Café?


A customer at Steven’s Sub Stop can choose from white, wheat, and rye bread. The customer can also choose from American and Swiss cheese. Which diagram shows all the possible combinations of 1 type of bread and 1 type of cheese?

April 2006 #6

CorrectAnswer

H

(6.9) Probability and statistics. The student uses experimental and theoretical probability to make predictions. The student is expected to

(B) find the probabilities of a simple event and its complement and describe the relationship between the two.

Scott has 5 green marbles, 8 red marbles, 2 purple marbles, and 6 blue marbles in a container. If he draws a marble at random from the container, what is the probability that he will NOT draw a blue marble?


Nate has a bag containing 3 red, 2 blue, 4 yellow, and 3 green marbles. If he randomly chooses one marble from the bag, what is the probability that the marble will be blue?


Jocelyn made a spinner with equal sections, as shown below. If Jocelyn spins only one time, what is the probability that the arrow will NOT land on a red section of the spinner?


(6.10) Probability and statistics. The student uses statistical representations to analyze data. The student is expected to

(A) [draw and] compare different graphical representations of the same data;

Cynthia surveyed the students at her school about their favorite month during the school year. The table shows the results of the survey. Which graph correctly displays the data in the table?


Of the 100 people An Li surveyed about their favorite sport, 45 said football, 30 said wrestling, 20 said baseball, and 5 said basketball. Which circle graph best displays the data?


The table shows the gross income of 5 of the highest-grossing U.S. movies from 1982 to 1996. Which graph most accurately displays the information in the table?



(B) use median, mode, and range to describe data;

Mr. Franks recorded these mathematics test scores of his sixth-grade students.

67, 69, 71, 73, 74, 75, 79, 81, 81, 82, 83, 87, 88, 88, 88, 88, 90, 91, 93, 95, 99, 100

What is the median of these test scores?

F 83

G 85

H 87

J 88


The Q&R Band performed concerts from 1992 to 2001. The table shows the number of concerts the band performed each year. What is the median of the number of concerts?

A 162

B 170

C 180

D 172


There are 6 children in Todd’s family, including Todd. Their ages in years are listed below.

1, 2, 2, 8, 9, 14What is the median of the children’s ages?

F 6

G 5

H 2

J 13



(C) sketch circle graphs to display data;

At Central City Music Store, 15% of the music sold is classical,20% is blues,25% is rock, and40% is country.Which graph bestrepresentsthese data?


Angela receives a $20.00 allowance each week. She spends $4.00 on art supplies, $6.00 on movies, and $7.50 on school lunches, and she puts $2.50 into savings. Which graph best represents Angela’s allowance?

April 2006 #1

Correct Answer

C


(D) solve problems by collecting, organizing, displaying, and interpreting data.

The line plot shows the homework grades of the students in Mrs. Smith’s class. Which information is supported by the information in the line plot?

F The same number of students received a B as received a D.

G Eighteen students received a C or higher.

H The same number of students received a D or an F as received an A or a B.

J Sixteen students received a C or lower.


F More than 25% of the students were born in either January or March.G The second half of the year had fewer births than the first half.H May was the birth month for 30 students.J The same number of births per month occurred in February, October, and November.


Apollo Middle School collected the following data from students. Which statement is supported by the graph?

Dee and Ella kept track of the miles they hiked over 4 days, as shown in the graph below. Which statement is best supported by the information inthe graph?

F Dee walked more miles each day than Ella did.

G Ella walked more miles in all than Dee did on these 4 days.

H Dee and Ella walked more than 15 miles each on these 4 days.

J Ella walked 0.5 mile farther than Dee each day.


Objective 6:

The student will demonstrate an understanding of the mathematical

processes and tools used in problem solving.

(6.11) Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to

(A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;

Cindy and 2 friends ordered a large pizza for $9.00, 3 large drinks for $0.99 each, and a salad for $1.50. If they split these costs evenly, which equation can be used to find c, the amount in dollars and cents each person should pay, not including tax?A c = 9.00 + 0.99 + 1.50 ÷ 3

B c = 9.00 + 3 × 0.99 + (1.50 ÷ 3)

C c = (9.00 + 0.99 + 1.50) ÷ 2

D c = (9.00 + 3 × 0.99 + 1.50) ÷ 3


The weight limit for an elevator is 2,000 pounds. Which statement is best supported by this information?

A The elevator can carry more than 20 adults.

B The elevator can carry more than 20 crates that weigh 100 pounds each.

C The elevator can carry up to 8 people who each weigh as much as 250 pounds.

D The elevator can carry twice as many children as adults.


Mr. and Mrs. Gunther tiled their rectangular porch using square tiles. Each box of tile contained 30 square tiles. The rectangular porch measured 38 feet by 22 feet. What missing piece of information is needed in order to find the number of boxes of tile the Gunthers needed?

F Area of each square tile

G Perimeter of the box

H Perimeter of the porch

J Area of the porch


Irma has $10.00 to buy apples. Apples at the market are $2.50 per bag. Which additional information is needed to find the number of apples Irma can buy?

F The cost of apples per pound.

G The size of each bag of apples.

H The weight of each apple.

J The number of apples in each bag.


Ms. Meléndez needs to replace the batteries in 20 calculators. Each calculator uses 4 batteries. The batteries are sold in packages of 16. How many packages of batteries does Ms. Meléndez need to buy?

A 64

B 4

C 80

D 5



(B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness;

Stan must buy paper plates and plastic forks for a picnic. Plates are sold in packages of 8 and forks in packages of 12. What is the least number of packages of plates and packages of forks that Stan can buy to have an equal number of plates and forks?

A 2 packages of plates and 3 packages of forks

B 3 packages of plates and 2 packages of forks

C 4 packages of plates and 6 packages of forks

D 6 packages of plates and 4 packages of forks


Antonio saved $30 to go to a carnival. He needs a certain amount of money for bus fare and admission. Antonio wants to find the amount of money he will have left for rides and food.

Look at the problem-solving steps shown below. Arrange the steps in the correct order for Antonio to find the amount of money he will have left for rides and food.

Step P: Identify the cost of bus fare and then the cost of admission.

Step Q: Find the difference between $30 and the sum of the costs of bus fare and admission.

Step R: Find the sum of the costs of bus fare and admission.

Which list shows the steps in the correct order?A P, Q, R

B Q, P, R

C P, R, Q

D Q, R, P Spring 2003 #41Correct Answer - C

Mrs. Miller is baking cookies for 16 children. She has baked 2 dozen cookies. If she wants each child to receive exactly 2 cookies and have no cookies left over, how many more cookies should she bake?

F 1.5

G 8

H 24

J 32


Tickets for a circus performance cost $9.50 for an adult and $6.75 for a child. Mr. Snyder and some of his friends, a group of 4 adults and 5 children, went to the circus performance. Mr. Snyder paid for all the tickets.Read the problem-solving steps shown below. Arrange the steps in the correct order for Mr. Snyder to find the total cost for the tickets.Step K: Add the two products togetherStep L: Write down the number of adults and the number of children

going to the circus performanceStep M: Multiply the cost of an adult ticket by the number of adultsStep N: Multiply the cost of a child’s ticket by the number of childrenWhich list shows the steps in the correct order?

A L, K, M, N

B L, M, N, K

C N, M, L, K

D M, N, L, K


Jeremy received $70 as a gift. He wanted to use the money to go to the movies and to buy a book. He wanted to save the money he had left. Which is the correct order of steps to find the amount of money Jeremy would have left to save?

Step K: Find the sum of the costs of the movie and the book.Step L: Find the difference between $70 and the sum of the

costs of the movie and the book.Step M: Identify the cost of the movie and the cost of the

book.A L, K, M

B M, K, L

C L, M, K

D K, L, MApril 2006 #5Correct Answer - B


(C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.

When Marco’s dog got loose, it ran ⅓ mile on Pine Street, 1½ miles on Oak Street, and 2 5/6 miles on Hickory Street. Which procedure can Marco use to find the total distance in miles that his dog ran?

F Multiply the sum of the whole numbers by the sum of the fractions, using a common denominator when necessary

G Find the difference between the sum of the whole numbers and the sum of the fractions, using a common denominator when necessary

H Add the sum of the whole numbers and the sum of the fractions, using a common denominator when necessary

J Divide the sum of the whole numbers by the sum of the fractions, using a common denominator when necessary


Miss Caruso’s car travels an average of 22 miles per gallon of gasoline. The gas tank holds 12 gallons. How would you find the number of miles Miss Caruso can drive on 1 full tank of gasoline?

F Add the car’s average mileage in miles per gallon to the number of gallons the tank can hold

G Subtract the number of gallons the tank can hold from the car’s average mileage in miles per gallon

H Multiply the car’s average mileage in miles per gallon by the number of gallons the tank can hold

J Divide the car’s average mileage in miles per gallon by the number of gallons the tank can hold


Jade is 3 years older than Steven, and Steven is 5 years younger than Andrew, who is 15 years old. Which table could be used to find Jade’s age?


Felicia went shopping for clothes. She bought a pair of jeans priced at $28.00, a sweater priced at $32.50, and a belt priced at $18.75. If there was an 8.75% tax on clothing items, which procedure could be used to find the amount of tax Felicia paid?

F Multiply the tax rate by the sum of the prices of the clothing items

G Add the prices of the clothing items to the tax rateH Add the prices of the clothing itemsJ Multiply the tax rate by the price of the most expensive clothing item


The table below shows the number of minutes it takes to wash different vehicles at Jay Dee’s Car Wash. When the car-wash machine has been in use for a total of 2 hours, Jay must add one bottle of liquid soap to the machine. What is the number of trucks the machine can wash with each bottle of liquid soap?

F 5

G 12

H 20

J 32


A parent group is planning an awards dinner for students, teachers, and parents. The parent group plans to seat the guests around a circular table that has seating for 30. The guests will be seated in the order of student, teacher, parent, in a repeating pattern. Will the 20th guest be a student, a teacher, or a parent?

A Student

B Teacher

C Parent

D Cannot be determined


(6.12) Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models. The student is expected to

(A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models.

Mr. Ortega gave his social studies students a map of Texas. According to the map scale, 1 inch on the map represents 100 actual miles. Which strategy can Mr. Ortega’s students use to find the actual distance in miles between points on the map?

A Measure the number of inches between points and then divide by 100

B Measure the number of inches between points and then multiply by 100

C Measure the number of inches between points and then subtract 100

D Measure the number of inches between points and then add 100


Each number in the sequence below has the same relationship to the number immediately before it.

24, 12, 6, 3, 1½, …

How can the next number in the sequence be found?

A By subtracting 12 from the previous number

B By adding 1½ to the previous number

C By multiplying the previous number by 2

D By dividing the previous number by 2


Mrs. Valcome has $25.00 to spend on seeds for her flower garden. Marigold seeds cost $1.50 per package, and zinnia seeds cost $1.25 per package, tax included. If Mrs. Valcome buys 10 packages of marigold seeds, how can she determine how much money she has left to spend on zinnia seeds?

A Add $1.50 and $1.25

B Subtract the product of 10 and $1.50 from $25.00

C Multiply $1.25 and 10

D Divide 10 by $1.25


If Mr. Albright drives at a constant speed of 65 miles per hour, which method can be used to find the number of hours it will take him to drive 260 miles?

F Add 65 and 260

G Subtract 65 from 260

H Multiply 260 by 65

J Divide 260 by 65


Elm’s Carpeting Company sellscarpet by the square yard. Asalesperson at the company uses thetable to calculate the amountof carpet needed to cover floor areasof different sizes. Which statementdescribes the calculation used todetermine the amount of carpetneeded for a given area of floor?

F The area of the floor is divided by 12.

G The area of the floor is divided by 10.

H The area of the floor is divided by 9.

J The area of the floor is divided by 3.April 2006 #22Correct Answer - H

Three friends attended a football game and agreed to share the cost evenly. The total cost of the tickets was $51, the taxi ride to and from the game was $24, and snacks and drinks were $30. Which equation can be used to find c, the amount each friend should have paid?

F c = (51 + 24 + 30) ∙ 3

G c = (51 + 24 + 30) ÷ 3

H c = 51 + 24 + 30 + 3

J c = 51 + 24 + 30 – 3


(6.13) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to

(A) make conjectures from patterns or sets of examples and nonexamples;

The side lengths and perimeters of some regular polygons are shown in the table. Which geometric figure is represented by the information in the table?

A Pentagon

B Square

C Hexagon

D Triangle


Look at the shapes below. Which statement best describes these shapes?

A They all appear to be regular polygons.

B They all have an even number of sides.

C They all have an even number of angles.

D They all contain only right angles.


Look at Set V and Set W shown below.Set V = {1, 3, 5, 7, 9, 11, . . .}

Set W = {3, 6, 9, 12, 15, 18, . . .}Which of the following numbers could belong to both Set V and Set W?

F 35

G 25

H 21

J 31


(6.13) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to

(B) validate his/her conclusions using mathematical properties and relationships.

Laurence was asked to find 2 integers that have a difference of 1 and a sum of 59. He said the integers were 29 and 28. Why was Laurence’s answer incorrect?

F The difference between 29 and 28 is not 1.

G The difference between 29 and 28 is 1.

H The sum of 29 and 28 is 59.

J The sum of 29 and 28 is not 59.


Zane is reading a history book for a project. The graph below shows how many pages he read during a 5-day period. Which statement is best supported by the information in the graph?

F Zane read more pages on Monday and Wednesday than he did on Tuesday and Thursday, because 40 + 80 > 70 + 60.G Zane read fewer pages on Tuesday and Wednesday than he did on Thursday and Friday, because 70 + 80 < 60 + 90.H Zane read more pages on Thursday and Friday than he did on Tuesday and Wednesday, because 60 + 90 > 70 + 80.J Zane read fewer pages on Wednesday and Thursday than he did on Tuesday and Friday, because 80 + 60 < 70 + 90.


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