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Applying Problem Solving and Graphing Calculator Strategies to Improve Student Achievement with a

Focus on TAKS Objectives

University of Houston – Central Campus

EatMath Workshop

February 28, 2009

Graphing Calculator Scavenger Hunt

1. Press 2nd + ENTER What is the ID# of your calculator? ________________________________________________________

2. For help, what website can you visit? __________________________3. What happens to the screen when you push 2nd ▲ over and over? 2nd ▼ over and over? ________________________________________________________4. is called the "carot" button, and is used to raise a number to a power. Find 65 = ______. To square a number use x2 What is 562? _________To cube a number, press MATH and select option 3. What is 363? _______ 5. Press 2nd Y= to access the STAT PLOTS menu, how many stat plots are there? _____ Which option turns the stat plots off? ________________ 6. Press STAT which option will sort data in ascending order? What do you think will happen if option 3 is selected? _________________________________________________________7. What letter of the alphabet is located above ? _________________8. To get the calculator to solve the following problem: 2{3 + 10/2 + 62 – (4 + 2)}, what do you do to get the { and } ? _________________The answer to the problem is __________.9. To solve a problem involving the area and/or circumference of a circle, which calculator key(s) would you most likely use? __________________________________ (Hint: What color is the sun?)10. Use your calculator to answer the following:

a.) 2 x 41.587 ________ b.) 2578/4 _________ c.) 369 + 578 _________

Now press 2nd ENTER two times. What pops up on your screen? ___________ Arrow left and change the 4 to a 2. What answer do you get? __________ How will this feature be helpful? _________________________________________________________11. What happens when the 10x and 6 keys are pressed? _____________

12. The STO button stores numbers to variables. To evaluate the expression , press 9 STO ALPHA MATH ENTER to store the number 9 to A. Repeat this same process if B = 2 and C = 1, then evaluate the expression by typing in the expression and

pressing ENTER. Is it faster just to substitute the values into the expression and solve the old- fashioned way with paper and pencil? _____________________________

When might this feature come in handy? _________________________________________________________

13. Press 2nd 0 to access the calculator's catalogue. Scroll up, to access symbols. What is the first symbol? _____________ What is the last symbol? _______________

14. Press MATH, what do you think the first entry will do? _____________________________________________________Now press CLEAR , then press 0 . 5 6 MATH and select option 1. What answer do you get? ___________

15. Press 5 9 ENTER. Press 2 to go to the error. The cursor should be blinking on the second /, press DEL ENTER. What answer did you get? To convert this number to a fraction, press MATH ENTER

Tested Curriculum – Mathematics Grade 9

Student Expectations


8.1B A.1A8.3B A.1B8.6A A.1C8.6B A.1D8.7A A.1E8.7B A.2A8.7C A.2B

8.7D A.2C8.8A A.2D8.8B A.3A8.8C A.3B8.9A A.4A8.9B A.4B

8.10A A.4C8.10B A.5A8.11A A.5C8.11B A.6A8.12A A.6B8.12C A.6C8.13B A.6D8.14A A.6E8.14B A.6F8.14C A.6G8.15A A.7A8.16A A.7B8.16B A.7C

A.8AA.9CA.11A




8.3B A.1A8.6A A.1B8.6B A.1C8.7A A.1D8.7B A.1E8.7C A.2A8.7D A.2B

8.8A A.2C8.8B A.2D8.8C A.3A8.9A A.3B8.9B A.4A

8.10A A.4B8.10B A.4C8.11A A.5A8.11B A.5C8.12A A.6A8.12C A.6B8.13B A.6C8.14A A.6D8.14B A.6E8.14C A.6F8.15A A.6G8.16A A.7A8.16B A.7B

A.7CA.8AA.8BA.8CA.9BA.9CA.9DA.10AA.10BA.11A

Tested Curriculum – Mathematics Exit Level




8.3B A.1A G.4A8.11A A.1B G.5A8.11B A.1C G.5B8.12A A.1D G.5C8.12C A.1E G.5D8.13B A.2A G.6B8.14A A.2B G.6C

8.14B A.2C G.7A8.14C A.2D G.7B8.15A A.3A G.7C8.16A A.3B G.8A8.16B A.4A G.8B

A.4B G.8CA.4C G.8DA.5A G.9DA.5C G.10AA.6A G.11AA.6B G.11BA.6C G.11CA.6D G.11DA.6EA.6FA.6GA.7AA.7BA.7CA.8AA.8BA.8CA.9BA.9CA.9DA.10AA.10BA.11A


A 1A describe independent and dependent quantities in functional relationships.

A 1B [gather and record data and] use data sets to determine functional relationships between quantities.

A 1C describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations.

A 1D represent relationships among quantities using [concrete] models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities.

A 1E interpret and make decisions, predictions, and critical judgments from functional relationships.

A 2A identify [and sketch] the general forms of linear (y = x) and quadratic (y = x2) parent functions.

A 2B identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete.

A 2C interpret situations in terms of given graphs [or creates situations that fit given graphs].

A 2D [collect and] organize data, [make and] interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations.

A 3A use symbols to represent unknowns and variables.

A 3B look for patterns and represent generalizations algebraically.

A 4A find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations.

A 4B use the commutative, associative, and distributive properties to simplify algebraic expressions.

A 4C connect equation notation with function notation, such as y = x + 1 and f(x) = x + 1.

A 5A determine whether or not given situations can be represented by linear functions.

A 5C use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions.

A 6A develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations.

A 6B interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs.

A 6C investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b.

A 6D graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y intercept.

A 6E determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations.

A 6F interpret and predict the effects of changing slope and y-intercept in applied situations.

A 6G relate direct variation to linear functions and solve problems involving proportional change.

A 7A analyze situations involving linear functions and formulate linear equations or inequalities to solve problems.

A 7B investigate methods for solving linear equations and inequalities using [concrete] models, graphs, and the properties of equality, select a method, and solve the equations and inequalities.

A 7C interpret and determine the reasonableness of solutions to linear equations and inequalities.

A 8A analyze situations and formulate systems of linear equations in two unknowns to solve problems.

A 9C investigate, describe, and predict the effects of changes in c on the graph of y = ax2 + c.

A 11A use [patterns to generate] the laws of exponents and apply them in problem-solving situations.

8.1B select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships.

8.3B estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates.

8.6A generate similar figures using dilations including enlargements and reductions.

8.6B graph dilations, reflections, and translations on a coordinate plane.

8.7A draw three-dimensional figures from different perspectives.

8.7B use geometric concepts and properties to solve problems in fields such as art and architecture..

8.7C use pictures or models to demonstrate the Pythagorean Theorem.

8.7D locate and name points on a coordinate plane using ordered pairs of rational numbers.

8.8A find lateral and total surface area of prisms, pyramids, and cylinders using [concrete] models and nets (two-dimensional models).

8.8B connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects.

8.8C estimate measurements and use formulas to solve application problems involving lateral and total surface area and volume.

8.9A use the Pythagorean Theorem to solve real-life problems.

8.9B use proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements.

8.10A describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally.

8.10B describe the resulting effect on volume when dimensions of a solid are changed proportionally.

8.11A find the probabilities of dependent and independent events.

8.11B use theoretical probabilities and experimental results to make predictions and decisions.

8.12A select the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situation.

8.12C select and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, [stem and leaf plots,] circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams, [with and] without the use of technology.

8.13B recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis.

8.14A identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics.

8.14B use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.

8.14C 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.

8.15A communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models.

8.16A make conjectures from patterns or sets of examples and nonexamples.

8.16B validate his/her conclusions using mathematical properties and relationships.


























A 7B investigate methods for solving linear equations and inequalities using [concrete] models, graphs, and the properties of equality, select a method, and solve the equations and

inequalities.A 7C interpret and determine the reasonableness of solutions to linear equations and inequalities.


A 8B solve systems of linear equations using [concrete] models, graphs, tables, and algebraic methods.

A 8C interpret and determine the reasonableness of solutions to systems of linear equations.

A 9B investigate, describe, and predict the effects of changes in a on the graph of y = ax2 + c.


A 9D analyze graphs of quadratic functions and draw conclusions.

A 10A solve quadratic equations using [concrete] models, tables, graphs, and algebraic methods.

A 10B make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function.



8.6A generate similar figures using dilations including enlargements and reductions.

8.6B graph dilations, reflections, and translations on a coordinate plane.

8.7A draw three-dimensional figures from different perspectives.

8.7B use geometric concepts and properties to solve problems in fields such as art and architecture..

8.7C use pictures or models to demonstrate the Pythagorean Theorem.

8.7D locate and name points on a coordinate plane using ordered pairs of rational numbers.

8.8A find lateral and total surface area of prisms, pyramids, and cylinders using [concrete] models and nets (two-dimensional models).

8.8B connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects.

8.8C estimate measurements and use formulas to solve application problems involving lateral and total surface area and volume.

8.9A use the Pythagorean Theorem to solve real-life problems.

8.9B use proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements.

8.10A describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally.

8.10B describe the resulting effect on volume when dimensions of a solid are changed proportionally.












Tested Curriculum – Mathematics Exit Level

G 4A select an appropriate representation ([concrete,] pictorial, graphical, verbal, or symbolic) in order to solve problems.

G 5A use numeric and geometric patterns to develop algebraic expressions representing geometric properties.

G 5B (FORMERLY PART OF G.5A) use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles.

G 5C (FORMERLY G.5B) use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations.

G 5D (FORMERLY G.5C) identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.

G 6B use nets to represent [and construct] three-dimensional geometric figures.

G 6C use orthographic and isometric views of three-dimensional geometric figures to represent [and construct] three-dimensional geometric figures and solve problems.

G 7A use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures.

G 7B use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and [special segments of] triangles and other polygons.

G 7C derive and use formulas involving length, slope, and midpoint.

G 8A find areas of regular polygons, circles, and composite figures.

G 8B find areas of sectors and arc lengths of circles using proportional reasoning.

G 8C [derive,] extend, and use the Pythagorean Theorem.

G 8D find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations.

G 9D analyze the characteristics of polyhedra and other three-dimensional figures and their component parts based on explorations and [concrete] models.

G 10A use congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane.

G 11A use and extend similarity properties and transformations to explore and justify conjectures about geometric figures.

G 11B use ratios to solve problems involving similar figures.

G 11C [develop,] apply, and justify triangle similarity relationships, such as right triangle ratios, [trigonometric ratios,] and Pythagorean triples using a variety of methods.

G 11D describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems.















A 7B investigate methods for solving linear equations and inequalities using [concrete] models, graphs, and the properties of equality, select a method, and solve the equations and inequalities.

A 7C interpret and determine the reasonableness of solutions to linear equations and inequalities.


A 8B solve systems of linear equations using [concrete] models, graphs, tables, and algebraic methods.

A 8C interpret and determine the reasonableness of solutions to systems of linear equations.

A 9B investigate, describe, and predict the effects of changes in a on the graph of y = ax2 + c.


A 9D analyze graphs of quadratic functions and draw conclusions.

A 10A solve quadratic equations using [concrete] models, tables, graphs, and algebraic methods.

A 10B make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function.














TAKS VERBSVERBSWeek 1 – March 2-6

MathVerb Dictionary definition(s) of Verb in Student Expectationact to perform in or as if in a play; represented dramatically: act out a story add find the sum of analyze to examine methodically by separating into parts and studying their interrelations make a

mathematical, chemical, or grammatical analysis of; break down into components of essential featuresto examine carefully and in detail so as to identify causes, key factors, possible results, etc.

answer to speak or write in response to; reply toapply to make use of as relevant, suitable, or pertinent

to use for or assign to a specific purposeto put into effect: They applied the rules to new members only.

approximate to come near to; approach closely to: to approximate an idealto estimate

carry to put into operation; executeto effect or accomplish; complete

choose to select from a number of possibilities; pick by referenceclassify to arrange or organize according to class or category collect to bring together in a group or mass; gathercommunicate to impart knowledge of; make knowncompare to examine (two or more objects, ideas, etc.) in order to note similarities and

differencesto consider or describe as similar, equal, or analogous; liken

ScienceVerb Dictionary definition(s) of Verb in Student Expectationactivate to make active; cause to function or actanalyze to examine methodically by separating into parts and studying their interrelations make a

mathematical, chemical, or grammatical analysis of; break down into components of essential featuresto examine carefully and in detail so as to identify causes, key factors, possible results, etc.

ask to put a question to; to seek an answer to calculate to determine or ascertain by mathematical methods; compute

to determine by reasoning, common sense, or practical experience; estimate; evaluate; gauge

classify to arrange or organize according to class or category collect to bring together in a group or mass; gather


MathVerb Dictionary definition(s) of Verb in Student Expectationconnect make a logical or casual connection

to join, link or fasten together; unite or bindconstruct draw with suitable instruments and under specified conditions; "construct an

equilateral triangle” contrast to compare in order to show unlikeness or differences; note the opposite natures,

purposes, etc., ofconvert to obtain an equivalent value for in an exchange or calculation, as money or units of

measurement: to convert bank notes into gold; to convert yards into metersdefine to state the precise meaning of (a word or sense of a word, for example)

to describe the nature or basic qualities of; explaindemonstrate prove, establish the validity of something

to describe, explain, or illustrate by examples, experiments, or the likederive to arrive at by reasoning; deduce or inferdescribe to give an account of in words; to tell in words what something or someone is likedetermine to conclude or ascertain, as after reasoning, observation, etc.develop to elaborate or expand in detaildisplay show or bring to the attention of another or others

to spread something out so that it may be most completely and favorably seendivide to separate into equal parts by the process of mathematical division, apply the

mathematical process of division to eight divided by four is two.

ScienceVerb Dictionary definition(s) of Verb in Student Expectationcommunicate to impart knowledge of; make knowncompare to examine (two or more objects, ideas, etc.) in order to note similarities and

differencesto consider or describe as similar, equal, or analogous; liken

construct draw with suitable instruments and under specified conditions: construct an equilateral triangle

demonstrate prove, establish the validity of somethingto describe, explain, or illustrate by examples, experiments, or the like

describe to give an account of in words, to tell in words what something or someone is likedetermine to conclude or ascertain, as after reasoning, observation, etc.


MathVerb Dictionary definition(s) of Verb in Student Expectationdraw to sketch (someone or something) in lines or words; delineate; depict

to frame or formulate: to draw a distinctionestimate to calculate approximately ( the amount, extent, magnitude, position, or value of

something)evaluate to ascertain or fix the value or worth of

to examine and judge carefully; appraiseto calculate the numerical value of; express numerically

explore to look into closely; scrutinize; examineexpress to represent by a sign or a symbol; symbolizeextend to expand the influence of

to make more comprehensive or inclusivefactor to express (a mathematical quantity) as a product of two or more quantities of like

kind as 30=2 • 3 • 5, or x2 – y2 = (x + y) (x - y)find to locate, attain, or obtain by search or effort

to discover or ascertain through observation, experience, or studyformulate to state as or reduce to a formula

to express in systematic terms or conceptsgenerate to bring into existence, cause to be; produce

to act as base for all the elements of a given set: the number 2 generates the set 2, 4, 8, 16graph to draw (a curve) as representing a given function

to represent by means of a graphguess to arrive at or commit oneself to an opinion about (something) without having

sufficient evidence to support the opinion fullyto estimate or conjecture correctly

ScienceVerb Dictionary definition(s) of Verb in Student Expectationdifferentiate to constitute the distinction betweendistinguish to divide into classes; classify

to recognize as distinct or different; recognize the salient or individual features or characteristics of

draw to sketch (someone or something) in lines or words; delineate; depictto frame or formulate: to draw a distinction

evaluate to ascertain or fix the value or worth ofto examine and judge carefully; appraiseto calculate the numerical value of; express numerically

examine to inspect or scrutinize carefullyexplain to make plain or clear, render understandable or intelligible

to make known in detail

TAKS VERBSVERBSWeek 4 – March 30-April 3

MathVerb Dictionary definition(s) of Verb in Student Expectationidentify recognize as being

to establish the identity of interpret to give or provide the meaning of; explain; explicate; elucidate

to conceive the significance of; construeinvestigate to observe or inquire into in detail; examine systematicallyjustify to recognize or establish as being a particular person or thing; verify the identity oflist a series of names or other items written or printed together in a meaningful grouping

or sequence so as to constitute a recordlocate to determine or specify the position or limits of

to find by searching, examining, or experimentinglook to seek; search formake to produce; cause to exist or happen, bring about

to draw a conclusion as to the significance or nature of to judge or interpret, as to the truth, nature, meaning, etc.

measure to ascertain the extent, dimensions, quantity, capacity, etc., of, especially by comparison with a standardto mark, layout, or establish dimensions for by measuring

model to plan, construct, or fashion according to a modelto make conform to a chosen standard

multiply to find the product of by multiplicationname to identify, specify, or mention by name

ScienceVerb Dictionary definition(s) of Verb in Student Expectationformulate to state as or reduce to a formula

to express in systematic terms or conceptsgive to impart or communicateidentify to recognize or establish as being a particular person or thing, verify the identity of illustrate to make clear or intelligible, as by examples or analogies; exemplifyimplement to put into practical effect; carry outinterpret to give or provide the meaning of; explain; explicate; elucidate

to conceive the significance of; construeinvestigate to observe or inquire into in detail; examine systematicallymake to produce; cause to exist or happen, bring about

to draw a conclusion as to the significance or nature of to judge or interpret, as to the truth, nature, meaning, etc.

TAKS VERBSVERBSWeek 5 – April 6-10

MathVerb Dictionary definition(s) of Verb in Student Expectationorder to arrange (the elements of a set) so that if one element precedes another, it cannot be

preceded by the other or by elements that the other precedesorganize to arrange in a coherent form; systematize

to arrange in a desired pattern or structureperform to execute or do somethingpredict to state, tell about, or make known in advance, especially on the basis of special

knowledgeread interpret something that is written or printed

to look at carefully so as to understand the meaning of (something written, printed, etc.)recall to bring back from memory; recollect; rememberrecognize to identify from knowledge of appearance or characteristicsrecord to set down in writing or the like, as for the purpose of preserving evidencerelate to tell; give an account of, or describe in some detailrepresent to express or designate by some term, character, symbol, or the likeround to reduce successively the number of digits to the right of the decimal point of a mixed

number by dropping the final digit and adding 1 to the next preceding digit if the dropped digit was 5 or greater, or leaving the preceding digit unchanged if the dropped digit was 4 or less

select to choose in preference to another or others, pick out

ScienceVerb Dictionary definition(s) of Verb in Student Expectationmeasure to ascertain the extent, dimensions, quantity, capacity, etc., of, especially by

comparison with a standardmodel to plan, construct, or fashion according to a model

to make conform to a chosen standardobserve to regard with attention, esp. so as to see or learn somethingorganize to arrange in a coherent form; systematize

to arrange in a desired pattern or structureplan to formulate a scheme or program for the accomplishment, enactment, or attainment ofpredict to state, tell about or make known in advance, especially on the basis of special

knowledgerecognize to identify as something previously seen, known, etc.

to identify from knowledge of appearance or characteristics

TAKS VERBSVERBSWeek 6 – April 13-17

MathVerb Dictionary definition(s) of Verb in Student Expectationsimplify to make less complex or complicated; make plainer or easiersketch to make a sketch ofsolve to work out the answer or solution to (a mathematical problem)subtract to take (one number or quantity) from anothertell to reckon, calculate, consider, counttransform to change the form of (a figure, expression, etc.) without in general changing the valuetranslate to perform a translation on (a set, function, etc.)understand to perceive the meaning of; grasp the idea of; comprehend to have understanding,

knowledge, or comprehensionuse to employ for some purpose; put into service; make use ofvalidate to make valid; substantiate; confirmverify to ascertain the truth or correctness of, as by examination, research, or comparisonwork to bring about (any result) by or as by work or effortwrite to express or communicate in writing; give a written account of

to execute or produce by setting down words, figures, etc.

ScienceVerb Dictionary definition(s) of Verb in Student Expectationrecord to set down in writing or the like, as for the purpose of preserving evidencerelate to tell; give an account of, or describe in some detailrepresent to express or designate by some term, character, symbol, or the likereview to look over, study or examine againselect to choose in preference to another or others; pick outsummarize to make a summary of; state or express in a concise formtest to administer or conduct a testunderstand to perceive the meaning of; grasp the idea of; comprehend

to have understanding knowledge, or comprehensionuse to employ for some purpose; put into service; make use ofverify to ascertain the truth or correctness of, as by examination, research or comparison

TAKS Objective 1

1. A function is described by the equation f(x) = x2 + 5. The replacement set for the independent variable is {1, 5, 7, 12}. Which of the following is contained in the corresponding set for the dependent variable?

A 0

B 6

C 7

D 15

2. Which equation best describes the relationship between x and y in this table?

x y−4 −11−1 −22 75 16

A y = x + 1

B y = x − 1

C y = 3x − 1

D y = 3x + 1

TAKS Objective 2

20. The energy output from a chemical reaction is dependent on the amount of chemicals

used. The table shows this relationship.

Amount of Chemicals

(moles)

Energy Output(joules)

5 208 3212 4815 60

What is a reasonable amount of energy output from the reaction of 32 moles of the chemicals?

A 77 joules

B 92 joules

C 110 joules

D 128 joules

4. Simplify the expression 3(x + 1) – 2(3x + 7).

A −3x − 11

B −3x − 10

C −3x − 8

D −3x + 17

TAKS Objective 3

5. Which of the following cannot be described by a linear function?

A The amount spent on n shirts that cost $20 each.

B The number of miles driven for h hours at a constant speed of 60 miles per hour.

C The total amount saved after making an initial deposit of $100 and depositing $30 a month thereafter for n months.

D The area of a rectangular garden that is x feet wide and has a length equal to twice its width.

6. What is the y-intercept of the function f(x) = 3(x – 2)?

A 3

B 1

C −2

D −6

TAKS Objective 4

7. What is the value of y if (3, y) is a solution to the equation 5x – 3y = 18?

A 3

B 1

C −1

D −11

20. The cost of renting a DVD at a certain store is described by the function

f(x) = 4x + 3

in which f(x) is the cost and x is the time in days. If Lupe has $12 to spend, what is the maximum number of days that she can rent a single DVD if tax is not considered?

A 1

B 2

C 3

D 7

TAKS Objective 5

20. When graphed, which function would appear to be shifted 2 units up from the graph of

f(x) = x2 + 1?

A g(x) = x2 − 1

B g(x) = x2 + 3

C g(x) = x2 − 2

D g(x) = x2 + 2

10. What is the effect on the graph of the equation y = x2 + 1 when it is changed to y = x2 + 5?

A The slope of the graph changes.

B The curve translates in the positive x direction.

C The graph is congruent, and the vertex of the graph moves up the y-axis.

D The graph narrows.

x0 1 2 3 4 5 8 9 1076-1-2-3-4-5-6-7-8-9-10

10

9

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TAKS Objective 6

20. Quadrilateral PQRS was dilated to form quadrilateral WXYZ.

Which number best represents the scale factor used to change quadrilateral PQRS into quadrilateral WXYZ?

A

B

C 2

D 4

x

y

W

X

Y

Z

P

Q

SR

12 The pentagon in the graph below is to be dilated by a scale factor of .

Which graph shows this transformation?

A C

B D

y

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y

0 1 2 3 4 5 76-1-2-3-4-5-6-7

7

6

5

4

3

2

1

-7

-6

-5

-4

-3

-2

-1

x

U

T

S

V

W

TAKS Objective 7

13. A bicycle wheel travels about 82 inches in 1 full rotation. What is the diameter of the wheel, to the nearest inch?

A 5 in.

B 10 in.

C 13 in.

D 26 in.

20. What is the area of the largest square in the diagram?

A 5 units2

B 9 units2

C 16 units2

D 25 units2

y

0 1-1

1

-1

x

TAKS Objective 8

20. The net of a cylinder is shown below. Use your ruler to measure the dimensions

of the cylinder to the nearest inch.

Which is closest to the total surface area of this cylinder?

A 4 in.2

B 10 in.2

C 14 in.2

D 25 in.2

20. In a town, there is a small garden shaped like a triangle, as shown below. The side of

the garden that faces Sixth Street is 80 feet in length. The side of the garden that faces Third Avenue is 30 feet in length.

What is the approximate length of the side of the garden that faces Elm Street?

A 35 ft

B 40 ft

C 85 ft

D 110 ft

TAKS Objective 9

17 Mr. Dansiger surveyed the students in his science classes about the type and number of pets they owned. The table shows the results of the survey.

Students’ PetsType of Pet Cat Dog Bird FishNumber of Pets 30 90 30 150

Which circle graph best represents the type and number of pets reported by students in the survey?

A C

B D

Students’ Pets

40%Fish

50%Dogs

5%Cats

5%Bird

s

Students’ Pets

75%Fish

15%Dogs

5%Cats

5%Bird

s

Students’ Pets

50%Fish

30%Bird

s

10%Cats

10%Dogs

Students’ Pets

30%Dogs

50%Fish

10%Cats

10%Bird

s

20. Which histogram best reflects the data shown in the table?

U.S. Household Income

Income Range Frequency

Total 100 Households

Under $10,000$10,000–24,999$25,000–49,999$50,000–74,999$75,000–99,999

A


Income (dollars)

Freq

uenc

y

Under $10,000

$10,000–24,999

$25,000–49,999

$50,000–74,999

$75,000–99,999

05

101520253035

C


Income (dollars)

Freq

uenc

y

Under $10,000

$10,000–24,999

$25,000–49,999

$50,000–74,999

$75,000–99,999

05

101520253035

B


Income (dollars)

Freq

uenc

y

Under $10,000

$10,000–24,999

$25,000–49,999

$50,000–74,999

$75,000–99,999

05

101520253035

D


Income (dollars)

Freq

uenc

y

Under $10,000

$10,000–24,999

$25,000–49,999

$50,000–74,999

$75,000–99,999

05

101520253035

TAKS Objective 10

20. Trina was recording the calorie content of the food she ate. For lunch she had 3 ounces of chicken, 2 slices of cheese, 2 slices of wheat bread, one-half tablespoon of mayonnaise, a 16-ounce glass of lemonade, and an apple for dessert. According to the chart below, which equation best represents the total number of calories she consumed during lunch?

Calorie Content

Food Calories (cal.)

Apple (medium) 70

Wheat bread(1 slice) 55

Cheese(1 slice) 45

Chicken(3 oz) 115

Lemonade(8 oz) 110

Mayonnaise(1 tbsp) 100

A. Cal. = 3(115) + 2(45) + 2(55) + (100) + 16(110) + 70

B. Cal. = 115 + 45 + 55 + 100 + 110 + 70

C. Cal. = 115 + 2(45) + 2(55) + (100) + 2(110) + 70

20. Cal. = 115 + + + 2(100) + + 70

20. Mr. McGregor wanted to cover the floor in his living room with carpet that cost $12

per square yard. The blueprint below shows the area of the living room relative to the area of the house.

What information must be provided in order to find the total cost of the carpet?

A The lengths and widths of the adjoining rooms in the blueprint

B The scale of yards to inches in the blueprint

C The total area of the house in the blueprint

D The thickness of the carpeting in inches

2.8 inches2.0 inches

Living Room

KitchenArea

DiningArea

Bedroom

Bath1.0 inch

0.25 inch Hallway

Underlying Processes and Mathematical Tools

Performance TaskA brick company manufactures decorative bricks in the shape of isosceles trapezoids. The longer base of the smallest trapezoid is 20cm. The legs of this trapezoid are 4cm long each, and the trapezoid has a perimeter of 43cm.The next larger trapezoid has the same base lengths as the first, and has a perimeter of 51cm.The third trapezoid in the series has the same base lengths as the other two, and a perimeter of 67cm.If this pattern continues, find the area of the tenth brick. Justify your answer.

This task is an example of assessing multiple concepts and processes within one problem. In this problem, students use, at the least, the concepts of area of a trapezoid, applications of the Pythagorean Theorem, functional relationships, and properties and attributes of functions. Geometric relationships, including the area of a polygon, and patterns and algebraic relationships are concepts addressed in different strands of the 8th grade and Algebra I TEKS as well as Objectives 1, 2, 6, 8, and 10 of the Grade 9 Texas Assessment of Knowledge and Skills (TAKS).

Matching Activity

TAKS Objective Student Expectation

Verb Tested Answer

Resources Used

“Accelerated Curriculum for Mathematics Exit TAKS”. Region IV Education Service Center (2005).

“TAKS Mathematics Preparation”. Region IV Education Service Center (2004).

www.tea.state.tx.us

http://online.math.uh.edu/EatMath/06_07/GraphingCalculatorScavengerHunt.pdf

http://online.math.uh.edu/EatMath/06_07/GraphingCalculatorScavengerHunt.pdf

http://www.tea.state.tx.us/

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