8Th Grade Math Review Bank 2014-15

8th Grade Math Review Bank 2014-15

This collection of items came from a variety of sources, including from released assessments in and outside of the state of Texas. Only items that could be correlated to the new 8th grade TEKS were included.

The items are purposefully scrambled and not grouped by strand. Part of review should involve students identifying the mathematics needed to solve the problem. During the year their practice and assessments are typically categorized, which gives them hints as to the type of mathematics they’ll need to use (a quiz over proportions, or a test over perimeter and area…). Giving students a mix of items allows the teacher to see if students can identify the mathematics needed to solve the problem, in addition to actually solving the problem.

This bank should not be used as a “packet” to be distributed to students to complete in isolation. Some items may be completed individually while others can be completed in pairs or with small groups. What is important is that the students’ work is accompanied by discussion about strategies, and that their work is used as formative assessment data for the teacher to respond to with further instruction as needed. Some suggestions for use are listed on the following page.

Suggested Structures and Strategies

(to increase engagement)

Math Mystery

Organize students into four groups using a 4-Corners activity: Corner 1 – like Coca Cola best, Corner 2 – like Sprite best, Corner 3 – Dr. Pepper, Corner 4 – Sports Drinks, (or use vacation destinations, snacks, sports)

Students practice one assessment item, targeted toward an SE that students find difficult according to the data. Four copies of the same assessment item are used (hang one in each corner).

Corner groups are assigned one answer choice and must either …

Defend the answer to the class as “innocent of a crime” because it is the correct response.

Prosecute the answer in front of the class as “guilty of a crime” explaining why the answer is the incorrect response.

Corner 1 focus on answer choice A, Corner 2 on answer choice B, Corner 3 on answer choice C, and Corner 4 answer choice D.

Teacher decides to include this option: Your group MAY choose to try and trick the class by purposefully defending an incorrect answer to make the other students identify a flaw in their reasoning.

Sage-N-SCRIBE

Teacher provides at least 2 problems for students to work in pairs.

Within each pair, decide who will take on which role for the first problem (“partner with the longer hair will be the Sage for the first problem”).

The Sage talks through the problem and instructs the Scribe what to write on the paper.

The Scribe does not talk. He/she writes exactly what the Sage instructs, while thinking about accuracy of the Sage’s procedures (but doesn’t give feedback yet).

Once the Sage is finished, the Scribe gives feedback on how the problem was solved.

Pairs switch roles for the next problem.

One STRAY

Put students in groups of 4 and give each student a number (1, 2, 3, or 4).

Groups work together to solve the first problem.

Everyone must record the group’s work on his/her own paper & everyone in the group should be able to explain how the problem was solved.

Once all groups are finished the teacher calls out a number (1 through 4) and says “Stray!”

The selected number must go find another group and share how their original group solved the problem. Their new group listens then gives feedback and/or shares any different strategies they used. Repeat with the next problem (select a different person to “stray”).

SHOWDOWN

Teacher provides each group of 3-4 students with a set of problems, each one on a separate “card” (set is face down in middle of table).

Each student has a dry erase board.

Showdown captain turns up first problem, reads it aloud, then everyone works alone to solve. Establish a signal for when finished.

When showdown captain sees all are finished, he says “1, 2, 3, SHOWDOWN!” and everyone reveals their work. Captain facilitates discussion and leads everyone in checking their answers. Once everyone agrees on a correct solution and understands the process to solve the problem, the role of Showdown Captain rotates to the next person.

Tour of Knowledge

1. Students are organized into groups (no more than 3 per group).

2. Each group is given a different colored marker.

3. Groups will rotate through stations observing a given assessment stimuli – no question and no answers

(i.e. graph, table, equation, verbal description, problem scenario, etc.).

4. Groups will be given three minutes at each station to record anything they know or notice about the given stimuli on the provided chart paper. Groups may not repeat previously provided information from the other groups. This is the “I Notice” or “I See” round of rotations.

5. Teacher may elect to reward the group that provided the most observant information, or unique information, from each of the four posters.

6. Repeat steps #1-5; however, groups will now record a question that could be asked of the provided stimulus. This is the “I Wonder” round of rotations.

7. Students work a problem associated to the given stimulus, identifying what information was needed to answer the question.

Optional: If using stimuli from released items, show students the original questions to see how they compare to the student-written questions.

Item # / Key / TEKS / Teacher Notes / Student Data
1 / A / 8.7D
2 / D / 8.7B – readiness
3 / C / 8.11B
4 / A / 8.10C– readiness
5 / C / 8.5F
6 / A / 8.10B
7 / D / 8.7D
8 / A / 8.10C– readiness
9 / B / 8.5D– readiness
10 / B / 8.10A
11 / A / 8.4C– readiness
12 / B; # of years when the populations are equal / 8.9
13 / C / 8.5I– readiness
14 / B / 8.5D– readiness
15 / 301.44 / 8.7A– readiness
16 / D / 8.5G– readiness
17 / A / 8.5G– readiness
18 / A / 8.3C– readiness
19 / B / 8.8C– readiness
20 / A / 8.5I– readiness
21 / D / 8.5A
22 / B / 8.5C
23 / a) yes b) Andy’s
c) Bargain Hardware / 8.4B & 8.5A
24 / B / 8.5A
25 / B / 8.5I– readiness
26 / A / 8.3A
27 / i, ii, vi / 8.5F
28 / B / 8.10C– readiness
29 / B / 8.5F
30 / B / 8.8D
31 / A / 8.10C
32 / D / 8.7C– readiness
33 / A / 8.6A
34 / C / 8.8D
35 / A / 8.3C– readiness
36 / D / 8.5G– readiness
37 / A / 8.8C– readiness
38 / C / 8.5G– readiness
39 / C / 8.7A– readiness
40 / D / 8.8C– readiness
41 / C / 8.7C– readiness
42 / C / 8.4C– readiness
43 / A / 8.7A– readiness
44 / A / 8.4B– readiness
45 / B / 8.4C– readiness
46 / A / 8.5G– readiness
47 / C / 8.2D– readiness
48 / B / 8.5G– readiness
49 / A / 8.7B– readiness
50 / C / 8.7C– readiness
51 / B / 8.4B – readiness
52 / B / 8.3C – readiness
53 / D / 8.8D
54 / C / 8.12D – readiness
55 / B / 8.8D
56 / B / 8.11B

8th Grade Review Items

In the coordinate plane, what is the distance between (3, 5) and (3, 8)?

A 3 units B 6 units

C 8 units D 13 units

What is the surface area of the figure below?

A 54 ft2 B 84 ft2

C 72 ft2 D 90 ft2

Below are the grades for three students on five assignments. Each student has an average of 83.

Student 1: 77, 80, 100, 75, 83

Student 2: 82, 90, 80, 81, 82

Student 3: 83, 83, 84, 82, 83

Which statement is true about how their mean absolute deviations (MAD) compare?

A TheMAD of Student 3 is the greatest.

B The MAD of Student 2 is the greatest.

C The MAD of Student 1 is the greatest.

D The MAD of all three students is the same.

Point Qis shown on the coordinate grid below.

Which statement correctly describes the relationship between the point (3, 2) and point Q?

AIt is a reflection across the x-axis.

BIt is a reflection across the y-axis.

CIt is the result of a translation described by (x + 5, y – 1).

DIt is the result of a translation described by (x + 4, y).

Jocelyn was shopping at a farmers’ market. She observed the prices of cucumbers at several stands. Which sign shows a proportional relationship in the pricing of the cucumbers?

A sequence of transformations was applied to an equilateral triangle in a coordinate plane. The transformations used were rotations, reflections, and translations. Which statement about the resulting figure is true?

A It must be an equilateral triangle with the same side lengths as the original triangle.

B It must be an equilateral triangle, but the side lengths may differ from the original triangle.

C It may be a scalene triangle, and all the side lengths may differ from the original triangle.

D It may be an obtuse triangle with at least one side the same length as the original triangle.

The coordinates of the vertices of a rectangle are (–2, 3), (4, 3), (4, –4), and (–2, –4).

What are the dimensions of the rectangle?

A1 unit by 2 unitsB1 unit by 6 units

C7 units by 2 unitsD7 units by 6 units

Figure Q was the result of a sequence of transformations on figure P, both shown below.

Which sequence of transformations could take figure P to figure Q?

Areflection over the x-axis and translation 7 units right

Breflection over the y-axis and translation 3 units down

Ctranslation 1 unit right and 180° rotation about the origin

Dtranslation 4 units right and 180° rotation about the origin

The trend line below approximates the relationship shown in scatterplot.

Based on the trend line, what y-value corresponds to an x-value of 6?

A4B6.4

C5.5D7.5

Rectangle R undergoes a dilation with scale factor 0.5 and then a reflection over the y- axis. The resulting image is Rectangle S. Which statement about Rectangles R and S is true?

AThey are congruent and similar.

BThey are similar but not congruent.

CThey are congruent but not similar.

DThey are neither congruent nor similar.

The table below shows the cost of different numbers of goldfish at a pet store.

The cost is a linear function of the number of goldfish. Which statement describes the

rate of change of this function?

AThe cost increases $0.30 each time 1 goldfish is added.

BThe cost increases $1.50 each time 1 goldfish is added.

CThe cost increases $3.00 each time 5 goldfish are added.

DThe cost increases $6.00 each time 5 goldfish are added.

The population growth of two towns over a period of five years is represented by the system of equations below, both algebraically and graphically.

Which ordered pair is the solution to the system of equations?

A (2, 6)B (4, 10)

C (6, 2)D(10, 4)

What does this solution represent about this situation?

Which equation represents the relationship shown in the table below?

Ay = x – 4By = 2x + 9

Cy = 3x – 2 Dy = 3x – 5

A researcher studied the eyesight of people at different ages. She calculated a vision score for each person in the study and plotted the data on the graph below.

The researcher used the line y = -0.1x + 110 to model the data. When she substituted

the value x =65 into this equation, what did the result tell her?

Athe exact value for the vision score of a 65-year-old

Bthe predicted value for the vision score of a 65-year-old

Cthe minimum possible value for the vision score of a 65-year-old

Dthe maximum possible value for the vision score of a 65-year-old

A box contains 9 identical glass spheres that are used to make snow globes. The spheres are tightly packed, as shown below. What is the total volume, in cubic inches, of all 9 spheres? Bubble your answer in the grid provided. Use 3.14 for pi and round your answer to the nearest tenth of a cubic inch.

The table below represents a relationship.

Which statement is true about the relationship shown in the table?

AIt is a proportional relationship.

BThe y-intercept is 5.

CThe slope is 4.

DIt is a linear function.

Which graph represents a function?

The circle shown below is centered at (0,0) and passes through point P located at (2,0).

The circle is dilated with the center of dilation at the origin and a scale factor of 0.5.

What will be the coordinates of the image of point P afterthis transformation?

A(1, 0)B(4, 0)

C(1, 0.5)D (1.5, 1)

The equation 5w + 3 = 4w + 9 is modeled below.

What value of w makes this equation true?

A1B6

C5D 12

Which equation represents the line shown on the coordinate grid below?

Which equation has a constant of proportionality equal to 4?

A4y = 4xBy = x + 4

Cy = ¼ xD3y = 12x

The scatter plot below shows the sizes and annual rents of some office spaces in the downtown area of a city.

Which best describes the association between office space and rent shown in the scatterplot?

ANo associationBPositive linear association

CNon-linear associationDNegative association

The table shown below was posted on the wall at Andy’s Hardware to show the price of varying lengths of chain-link fencing.

a.)Does this represent a proportional relationship? Explain.

b.)The price of the same fencing at Bargain Hardware can be determined by the equation y = 2.5x where y is the price, in dollars, for x feet of fencing. Who has the cheaper unit price per foot, Bargain Hardware or Andy’s Hardware?

c.)If both store’s pricing were graphed on the same coordinate grid, which store’s graph would be steeper? Explain.

Chad built a scale model of a statue. He built the model 7 inches tall to represent the actual height of 15 feet. Which equation below represents the relationship between the actual height (a), in feet, and the height of the model (m), in inches?

Consider the values in the table below.

Which equation represents the data in the table?

Ay = 1.25xBy = x

Cy = 0.625x + 1.25Dy = 1.6x – 1.95

Two similar quadrilaterals are shown below. The ratio of the lengths of the corresponding sides MN and ST is 2:3, respectively.

What is the measure of RS?

A 18 centimetersB 15 centimeters

C 14 centimetersD 8 centimeters

Which options represent proportional relationships between x and y? Select all that apply.

i. / ii. / iii.
iv. / v. / vi.

Triangle PQR is shown on the coordinate plane.

Triangle PQR is rotated 90° counterclockwise about the origin to form the image triangle PQR (not shown). What are the signs of the coordinates (x,y) of point Q?

ABoth x and y are positive.

B x is negative and y is positive.

CBoth x and y are negative.

D x is positive and y is negative.

The numbers of parts produced by three different machines are shown in the table. Only one of the machines produces parts at a constant rate.

Which equation represents y, the number of parts produced in x minutes, for the one machine that produces parts at a constant rate?

Ay = 3xBy = 8x

Cy = 6xDy = 9x

The figure shows line RS parallel to line UV. The lines are intersected by 2 transversals. All lines are in the same plane.

Based on this information, which pair of angles must be congruent?

A TUV  RTSB TUV RST

C TUV  TRSD TUV  TVU

Consider the three figures shown below.

Which statement about these figures is true?

ATriangle ABC is the transformation of triangle ABC after a reflection in the y-axis followed by a translation 2 units to the right.

BTriangle ABC is the transformation of triangle ABC after a reflection across the y-axis.

CTriangle ABC is the transformation of triangle ABC after a reflection across the

line y = x.

DTriangle ABC is the transformation of triangle ABC after a dilation by a scale factor of 2, with the origin as the center of dilation.

A side view of a desk telephone is shown below.

Which of the following is closest to the value of x?

A1.5 cmB3.75 cm

C14.5 cmD5.5 cm

The cylindrical toothbrush holder modeled below has a diameter of 6.5 centimeters and aheight of 9 centimeters. The shaded part represents the base of the cylinder.

Which equation can be used to find B, the area of this cylinder’s base in square centimeters?

The base of triangle ABC and the base of triangle DEF both lie on line m. The measure of 4 is less than the measure of 8.

Based on this information, which statement is true?

Am3  m7Bm3  m7

Cm3 m7Dm3 +m7 = m8

Triangle EFG is shown on the grid below.

Triangle EFG is dilated with the origin as the center of dilation, using the rule (x,y)  (2.5x, 2.5y) to form triangle EFG. Which ordered pair represents the coordinates of E ?

A(−10, 10)B(−2.5,2.5)

C(−6.5, 6.5)D(−8,8)

The four tables below show relationships in which the x values represent inputs and the y values represent the corresponding outputs.

Which table represents a relationship that is not a function?

ATable QBTable R

CTable SDTable T

Triangle ABC and Triangle DEF are similar.

What is the value of x?

A3B35

C11D1

Which graph below does not represent y as a function of x?

A water tank is in the shape of a right circular cylinder with a height of 20 feet and avolume of 320π cubic feet. What is the diameter, in feet, of the water tank?

A16B10

C8D4

Marette solved the equation 0.2(d – 6) = 0.3d + 5 – 3 + 0.1d. Her work is shown below.

Did Marette make a mistake, and if so, where did her mistake occur?

AShe made a mistake in Step 1.BShe made a mistake in Step 3.

CShe made a mistake in Step 4DShe did not make any mistakes.

Inthedrawingbelow,thedashedlinesegment represents the distanceacrossapond.

Whatistheactualdistance,inyards, across the pond?

A14 yardsB10 yards

C20 yardsD28 yards

Students organized a 12-hour “dance-a-thon” as a fundraiser for their summer camp.The graph below represents the amount of money they raised during the first 8 hours.

What is the slope and what does it represent in this situation?

AThe slope is . The students raised an additional $2 for every additional hour of dancing.

BThe slope is 60. The students raised an additional $60 for every additional hour of dancing.

CThe slope is 30. The students raised an additional $30 for every additional hour of dancing.

DThe slope is . The students raised an additional $30 for every additional hour of dancing.

Yadira made a wooden cone with a radius of 1.9inches and a height of 15 inches. Which ofthe following is the best estimate of the volume of this cone?

A60in.3B30in. 3

C180in. 3D90in. 3

The Perry family joined a babysitting service. The service charges an initial flat fee for their one-time membership charge and an additional $12 per hour for each job. Which graph could represent the relationship between the hours of babysitting and total amount paid for the Perry family?

The graph shows the time it took a worker to package 16 bottles of shampoo.

What is the rate of change represented in this graph, and what does it represent?

A2.5; The worker was able to package 2.5 bottles every minute.

B; The worker was able to package 2 bottles every 5 minutes

C2; The worker was able to package 2 bottles every minute.

D0.4; The worker was able to package a bottle every 0.4 minutes

Which set of ordered pairs represents y as a function of x?

Which set of numbers is listed from least to greatest?

A, 4.5%, , 3.06,