Math TAKS

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					Math TAKS

  Grade 6th, 7th, and 8th
Test Format
    The 6th. 7th, and 8th grade tests include a test booklet
     and a separate machine-scorable answer document.
    Enough room is left around each item in the booklet
     for students to work each problem.
    However, student responses must be recorded on the
     separate answer document.
    Any item may include application context and
     extraneous information.
    Most items will be in a multiple-choice format with four
     answer choices.
    Not here or a variation of this phrase may be used as
     the fourth answer choice when appropriate.


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Test Format
      There will be a limited number of
       open-ended griddable items. For
       these items a seven-column grid
       (with one column designated as a
       fixed decimal point) will be provided
       on the answer document for
       students to record and bubble in
       their answers. Digits must be in the
       correct column(s) with respect to
       the fixed decimal point. This
       griddable format is intended to
       allow students to work a problem
       and determine the correct answer
       without being influenced by answer
       choices.


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Mathematics Chart

   The Mathematics Chart includes measurement
    conversions on the front and formulas on the
    back.
   A metric ruler and a customary ruler will be
    provided on the front of the separate
    Mathematics Chart.
   Items that require students to measure with a
    ruler from the Mathematics Chart may be
    found in any objective as appropriate.

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6th, 7th, and 8th Grade Objectives

    Objective 1: The student will demonstrate an
     understanding of numbers, operations, and
     quantitative reasoning.
    Objective 2: The student will demonstrate an
     understanding of patterns, relationships, and
     algebraic reasoning.
    Objective 3: The student will demonstrate an
     understanding of geometry and spatial
     reasoning.

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6th, 7th, and 8th Grade Objectives

    Objective 4: The student will demonstrate an
     understanding of the concepts and uses of
     measurement.
    Objective 5: The student will demonstrate an
     understanding of probability and statistics.
    Objective 6: The student will demonstrate an
     understanding of the mathematical processes
     and tools used in problem solving.



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Objective 6 Problem Solving Plan
      Understand the problem
       Organize the information you are given and identify exactly what you must find.
       You may need information that is not given in the problem, such as a formula. You
       may be given information that is not needed in order to solve the problem.

      Make a plan
       After you have organized the information, decide how to use this information to
       find an answer. Think about the math concepts that apply to the situation. Identify
       the order in which you will find new information and the formulas or equations you
       will use to find it.

      Carry out the plan
       After you have chosen a problem-solving strategy, use the strategy to work
       toward a solution to the problem. Go step-by-step through your plan, writing down
       important information at each step.

      Check to see whether your answer is reasonable
       Check to see whether your answer makes sense. Does it answer the question
       asked? Is it stated in the correct units? Is it reasonable? You can estimate the
       solution and then compare the estimate to your answer. They should be
       approximately equal.


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6th, 7th, and 8th Grade Objective 1
Numbers, Operations, and Quantitive Reasoning

    10 test items in all grades
    At 6th, 7th, and 8th grade, students should be
     able to:
            sequence numbers or the words associated with
             numbers;
            work with problems that include information
             expressed as numbers or ranges of numbers; and
            round numbers before performing any
             computations when estimating. The use of
             compatible numbers (numbers that are easy to
             compute mentally) may be helpful.


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6th Grade Objective 1 Example
        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?
         A 3                  B 1 3
           8                      4

         C 7                  D 1 5
           8                      8
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7th Grade Objective 1 Example

      Identify the group that does NOT contain
       equivalent fractions, decimals, and
       percents.

       A 1, 0.05, 5%                            B 7, 0.7, 70%
        20                                       10

       C 1, 0.125, 12.5%                        D 3 , 0.3, 3%
         8                                       100

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8th Grade Objective 1 Example
      A math club is selling 3 different sizes of book covers
       as a fund-raiser. Large covers sell for $4.50 each,
       medium covers sell for $4.00 each, and small covers
       sell for $3.50 each. Shanna bought 3 large, 1 medium,
       and 2 small book covers. Which equation can be used
       to find c, the total cost of Shanna’s book covers?

       A c = (3 + 1 + 2)(4.50 + 4.00 + 3.50)
       B c = 3(4.50) + 2(4.00) + 2(3.50)
       C c = 3(4.50) + 4.00 + 2(3.50)
       D c = (3 + 1 + 2)(4.50 + 4.00 + 3.50)
                                  3

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6th Grade Objective 2
Patterns, Relationships, and Algebraic Reasoning

    9 test items
    At sixth grade, students should be able to:
            match a description of a proportional situation with
             a ratio, which may or may not be expressed in
             lowest terms;
            identify the method for finding any term of a
             numerical or geometric sequence;
            match a relationship represented by an equation or
             written description with the same relationship
             shown in pairs of numbers; and
            match an equation with a given context.


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7th Grade Objective 2
Patterns, Relationships, and Algebraic Thinking

    10 test items
    At seventh grade, students should be able to:
            write an expression to find the nth term where n
             represents the position of the term in the sequence;
            identify the expression when given terms in a
             sequence, and vice versa; and
            match a relationship represented by an equation or
             written description with the same relationship
             shown in pairs of numbers.



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8th Grade Objective 2
Patterns, Relationships, and Algebraic Reasoning

    10 test items
    At eighth grade, students should be able to:
            identify proportional and non-proportional
             relationships;
            write an expression to find the nth term where n
             represents the position of the term in the sequence;
             and
            identify the expression when given terms in a
             sequence, and vice versa.



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6th Grade Objective 2 Example

      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?

       A x = 1                                  B 15 = x
        15 630                                     1 630
       C 1 = x                                  D x = 15
         15 630                                   1 615

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7th Grade Objective 2 Example




      Which description shows the relationship between a
       term and n, its position in the sequence?
       A Add 3 to n
       B Multiply n by 2 and then subtract 3
       C Multiply n by 2 and then add 3
       D Multiply n by 3 and then subtract 2

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8th Grade Objective 2 Example




      The table shows land-speed records. Whose land-
       speed record did Green exceed by exactly 368.84
       miles per hour?
       A Elyston              B Cobb
       C Breedlove            D Noble

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6th Grade Objective 3
Geometry and Spatial Reasoning

    7 test items
    At sixth grade, students should be able to:
            use geometric models shown individually or as part
             of a more complex figure (for example, an obtuse
             angle may be shown as part of a trapezoid);
            identify a method for finding the radius, diameter, or
             circumference of a circle. The method can be
             written in words or as a mathematical equation or
             expression; and
            graph points, including fractions and decimals, on
             coordinate grids limited to the first quadrant.


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7th Grade Objective 3
Geometry and Spatial Reasoning


    7 test items
    At seventh grade, students should be
     able to:
          use geometric models shown individually or
           as part of a more-complex figure (for
           example, supplementary angles may be
           shown as part of a parallelogram); and
          graph points on coordinate grids using all
           four quadrants.

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8th Grade Objective 3
Geometry and Spatial Reasoning

      7 test items
      At eighth grade, students should be able to:
            find and apply scale factors in problem-solving
             situations;
            match a two-dimensional representation of a solid
             with a three-dimension representation of the same
             solid, using the top, front, and/or side views of the
             solid;
            graph points on coordinate grids using all four
             quadrants; and
            recognize a picture or model of the Pythagorean
             Theorem.


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6th Grade Objective 3 Example
      A circle with center at point O is shown. Which
       line segment is 2 times the length of radius
       OK?

       F Segment LN
       G Segment LM
       H Segment LK
       J Segment ON



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7th Grade Objective 3 Example
      Use the protractor in the diagram to read the measure of each
       angle. One pair of complementary angles is —

       A ∠DXE and ∠BXC
       B ∠AXC and ∠CXE
       C ∠DXE and ∠AXB
       D ∠CXD and ∠AXB




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8th Grade Objective 3 Example
      Jackie built a fence
       around her garden to
       keep animals out. The
       dimensions of the area
       enclosed by the fence
       are shown in the
       diagram. What is the
       total area, in square
       feet, enclosed by the
       fence? Record your
       answer and fill in the
       bubbles on your answer
       document. Be sure to
       use the correct place
       value.

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6th Grade Objective 4
Measurement

      5 test items
      At sixth grade, students should be able to:
            utilize the conversions and formulas on the
             Mathematics Chart to solve problems;
            measure with the ruler on the Mathematics Chart
             only if the item specifically instructs students to use
             the ruler;
            use the given dimensions of a figure to solve
             problems;
            recognize abbreviations of measurement units; and
            use a pictorial representation of a protractor to
             measure angles.


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7th Grade Objective 4
Measurement

    5 test items
    At seventh grade, students should be able to:
            utilize the conversions and formulas on the
             Mathematics Chart to solve problems;
            measure with the ruler on the Mathematics Chart
             only if the item specifically instructs students to use
             the ruler;
            use the given dimensions of a figure to solve
             problems; and
            recognize abbreviations of measurement units.

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8th Grade Objective 4
Measurement

      5 test items
      At eighth grade, students should be able to:
            utilize the conversions and formulas on the Mathematics
             Chart to solve problems;
            measure with the ruler on the Mathematics Chart only if the
             item specifically instructs students to use the ruler;
            use the given dimensions of a figure to solve problems;
            recognize abbreviations of measurement units; and
            describe, in the form of a verbal or algebraic expression or a
             mathematical solution, the effect on perimeter, area, or
             volume when the dimensions of a figure are changed (for
             example, if the sides of a rectangle are doubled in length, then
             the perimeter is doubled, and the area is four times the
             original area; if the edges of a cube are doubled in length,
             then the volume is eight times the original volume).


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6th Grade Objective 4 Example
      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



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7th Grade Objective 4 Example
      Mrs. Jones wants to paint a wall but not the door on
       the wall. How many square feet of wall does Mrs.
       Jones need to paint?

       F 36 ft2
       G 171 ft2
       H 129 ft2
       J 150 ft2




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8th Grade Objective 4 Example
      Mrs. Juárez has a cylindrical pincushion with the net
       shown below. Use the ruler on the Mathematics Chart
       to measure the dimensions of the net in centimeters.
       Which is closest to the lateral surface area of the
       cylindrical pincushion?

       A 3.0 cm2
       B 6.3 cm2
       C 9.4 cm2
       D 12.6 cm2


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6th Grade Objective 5
Probability and Statistics

      6 test items
      At sixth grade, students should be able to:
            match a situation with a sample space that lists all
             possible combinations or select the missing portion
             of a given sample space;
            match the median, mode, and/or range with a given
             data set, which may be listed in the text of the item
             or presented in a graphical representation;
            identify the missing piece of data that will produce a
             target median, mode, and/or range for a data set;
             and
            match a circle graph with a data set listed in table,
             chart, graph, or sentence form.

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7th Grade Objective 5
Probability and Statistics

       7 test items
       At seventh grade, students should be able to:
             match a situation with a sample space that lists all possible
              combinations or select the missing portion of a given sample
              space;
             determine whether the graphical representation of the given
              data is appropriate and/or accurate;
             distinguish among mean, median, mode, and range to
              determine which is most appropriate for a particular purpose;
             match the mean, median, mode, and/or range with a given
              data set, which may be listed in the text of the item or
              presented in a graphical representation; and
             identify the missing piece of data that will produce a target
              mean, median, mode, and/or range for a data set.

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8th Grade Objective 5
Probability and Statistics

       8 test items
       At eighth grade, students should be able to:
             distinguish between theoretical probability and
              experimental results;
             distinguish among mean, median, mode, and range
              to determine which is most appropriate for a
              particular purpose;
             identify the missing piece of data that will produce a
              target mean, median, mode, and/or range for a
              data set; and
             determine whether the graphical representation of
              the given data is appropriate and/or accurate.


  Thursday, February 3, 2005     TAKS Math Prep.                   35
6th Grade Objective 5 Example

      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?

       A 5                        B 1
         6                          3
       C 1                        D 1
         4                          6

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7th Grade Objective 5 Example
      Which of the following relationships is best
       represented by the data in the graph?

       F Conversion of
         feet to inches
       G Conversion of
          miles to feet
       H Conversion of
          feet to yards
       J Conversion of
          inches to yards


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8th Grade Objective 5 Example
    Lily surveyed all the members of the middle school band
     about their favorite class this semester. The results are shown
     in the table below. From these results, Lily concluded that
     band was the favorite class among all the students at her
     school. Which is the best explanation for why her conclusion
     might not be valid?
     F The survey should have
       been done each day for
       a week.
     G The sample was not
        representative of all the
        students at the school.
     H The survey should have
        been done with eighth-grade
        students only.
     J The band meets only 3
        days a week.

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6th, 7th, and 8th Grade Objective 6
Mathematical Processes and Tools

      9 test items in 6th and 7th grade, 10 test items in 8th grade
      At 6th, 7th, and 8th grade, students should be able to:
            select the description of a mathematical situation when provided with
             a written or pictorial prompt;
            identify the information that is needed to solve a problem;
            select or describe the next step or a missing step in a problem-
             solving situation;
            match informal language to mathematical language or symbols;
            identify the question that is being asked or answered;
            draw a conclusion by investigating patterns and/or sets of examples
             and nonexamples. A nonexample, or counterexample, proves a
             general statement to be false;
            understand that nonsensical words may be used to label sets of
             examples and/or nonexamples; and
            choose the correct supporting information for a given conclusion.




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6th Grade Objective 6 Example
      Anita found the measures of the angles of an
       isosceles triangle. One angle measured 50°,
       and the other 2 angles were congruent. Which
       method can be used to find the measure of
       each of the congruent angles?

       A Multiply 50 by 2 and then add 180
       B Subtract 50 from 180 and then divide by 2
       C Add 50 to 180 and then divide by 3
       D Divide 50 by 2 and then subtract from 180

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7th Grade Objective 6 Example
      ∠KSD and ∠DSM are supplementary angles. If the
       measure of ∠KSD is 71°, what is the measure of
       ∠DSM?

       A 19°, because the sum of the measures of
       supplementary angles is 90°
       B 71°, because the measures of supplementary
       angles are equal
       C 109°, because the sum of the measures of
       supplementary angles is 180°
       D 289°, because the sum of the measures of
       supplementary angles is 360°

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8th Grade Objective 6 Example




         A rectangle and a semicircle can be combined to make an
          irregular figure. The figures form a pattern. Each rectangle is ½
          the height of the rectangle immediately to its left. What would be
          the area of the next smaller figure in the pattern?

          A 42 mm2              B 207.72 mm2
          C 307.72 mm2          D 349.72 mm2

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Tips for Student Success
      Remind your child that in order to foster learning, distractions
       should always be left outside the classroom.
      Check your child's agenda books daily.
      Ask to see completed homework.
      Periodically, ask to see class folders, notebooks, textbooks and
       go over these materials with your child.
      Ensure that your child is at school every day.
      Remind your child to leave distractions at home or in the lockers.
      Encourage your child to have a positive attitude toward math.
      Provide opportunities for your child to use math skills in a wide
       variety of everyday activities (at the grocery store, reading ads,
       setting the table, buying gasoline, figuring gas mileage, etc.)
      Have your child practice making change.
      Encourage your child to play with numbers.



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More Tips for Student Success
      Read books that are math related with your child.
      Help your child notice mathematical patterns in everyday occurrences.
      Have your child practice sorting and classifying items by common
       attributes, such as color, size, and number of sides in a shape.
      Have your child notice geometric shapes in his/her surroundings.
      Meet with your child's teachers and ask what type of additional help your
       child needs.
      Share with your child examples of how you use math in your job or life.
      Work the online math test produced by TEA with your child
       (www.tea.state.tx.us).
      Develop a sense of reasonableness for solutions or for mathematical
       thinking.
      Watch HISD's After-School Algebra Show with your child.
      Help your child learn how to use a graphing calculator.
      Encourage your child to use mathematical sites on the Internet.




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Useful Web Sites and Q&A

   TAKS Information Booklets:
    http://www.tea.state.tx.us/student.assess
    ment/taks/booklets/index.html
   Released TAKS Tests:
    http://www.tea.state.tx.us/student.assess
    ment/resources/release/taks/index.html
   TAKS Study Guides:
    http://www.tea.state.tx.us/student.assess
    ment/resources/guides/study/index.html

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Objectives and Sub-objectives

   6th, 7th, and 8th Grade
6th Grade Objective 1
      (6.1) 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;
            (B) generate equivalent forms of rational numbers,
             including whole numbers, fractions, and
            decimals;
            (C) use integers to represent real-life situations;
            (D) write prime factorizations using exponents; and
            (E) identify factors and multiples, including common
             factors and common multiples.


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6th Grade Objective 1 (cont.)
      (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;
            (B) use addition and subtraction to solve problems involving
             fractions and decimals;
            (C) use multiplication and division of whole numbers to solve
             problems, including situations involving equivalent ratios and
             rates; and
            (D) estimate and round to approximate reasonable results and
             to solve problems where exact answers are not required.


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6th Grade Objective 2

      (6.3) The student solves problems
       involving proportional relationships. The
       student is expected to:
          (A) use ratios to describe proportional
           situations;
          (B) represent ratios and percents with
           [concrete] models, fractions, and decimals;
           and
          (C) use ratios to make predictions in
           proportional situations.

 Thursday, February 3, 2005   TAKS Math Prep.            49
6th Grade Objective 2 (cont.)
      (6.4) 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.; and
            (B) generate formulas to represent relationships
             involving perimeter, area, volume of a rectangular
             prism, etc., from a table of data.


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6th Grade Objective 2 (cont.)

      (6.5) The student uses letters to
       represent an unknown in an equation.
       The student is expected to:
            (A) formulate an equation from a problem
             situation.




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6th Grade Objective 3

      (6.6) 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;
          (B) identify relationships involving angles in
           triangles and quadrilaterals; and
          (C) describe the relationship between
           radius, diameter, and circumference of a
           circle.

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6th Grade Objective 3 (cont.)

      (6.7) 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.




 Thursday, February 3, 2005   TAKS Math Prep.             53
6th Grade Objective 4
      (6.8) 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;
            (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;
            (C) measure angles; and
            (D) convert measures within the same measurement
             system (customary and metric) based on relationships
             between units.


 Thursday, February 3, 2005       TAKS Math Prep.                       54
6th Grade Objective 5

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


 Thursday, February 3, 2005   TAKS Math Prep.          55
6th Grade Objective 6

      (6.10) The student uses statistical
       representations to analyze data. The student
       is expected to:
            (A) [draw and] compare different graphical
             representations of the same data;
            (B) use median, mode, and range to describe data;
            (C) sketch circle graphs to display data; and
            (D) solve problems by collecting, organizing,
             displaying, and interpreting data.



 Thursday, February 3, 2005    TAKS Math Prep.                   56
6th Grade Objective 6 (cont.)
      (6.11) 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;
            (B) use a problem-solving model that incorporates
             understanding the problem, making a plan, carrying out the
             plan, and evaluating the solution for reasonableness; and
            (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.


 Thursday, February 3, 2005         TAKS Math Prep.                            57
6th Grade Objective 6 (cont.)

      (6.12) The student communicates about
       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.


 Thursday, February 3, 2005   TAKS Math Prep.                58
6th Grade Objective 6 (cont.)

      (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 non-examples; and
          (B) validate his/her conclusions using
           mathematical properties and relationships.

 Thursday, February 3, 2005   TAKS Math Prep.           59
7th Grade Objective 1

      (7.1) The student represents and uses
       numbers in a variety of equivalent forms.
       The student is expected to:
          (A) compare and order integers and positive
           rational numbers;
          (B) convert between fractions, decimals,
           whole numbers, and percents mentally, on
           paper, [or with a calculator]; and
          (C) represent squares and square roots
           using geometric models.

 Thursday, February 3, 2005   TAKS Math Prep.            60
7th Grade Objective 1 (cont.)
      (7.2) The student adds, subtracts, multiplies, or divides to solve
       problems and justify solutions. The student is expected to:
            (A) represent multiplication and division situations involving fractions
             and decimals with [concrete] models, pictures, words, and numbers;
            (B) use addition, subtraction, multiplication, and division to solve
             problems involving fractions and decimals;
            (C) use models to add, subtract, multiply, and divide integers and
             connect the actions to algorithms;
            (D) use division to find unit rates and ratios in proportional
             relationships such as speed, density, price, recipes, and student-
             teacher ratio;
            (E) simplify numerical expressions involving order of operations and
             exponents;
            (F) select and use appropriate operations to solve problems and
             justify the selections; and
            (G) determine the reasonableness of a solution to a problem.



 Thursday, February 3, 2005            TAKS Math Prep.                                  61
7th Grade Objective 2

      (7.3) The student solves problems
       involving proportional relationships. The
       student is expected to:
          (A) estimate and find solutions to application
           problems involving percent; and
          (B) estimate and find solutions to application
           problems involving proportional
           relationships such as similarity, scaling, unit
           costs, and related measurement units.

 Thursday, February 3, 2005   TAKS Math Prep.            62
7th Grade Objective 2 (cont.)
    (7.4) The student represents a relationship in
    numerical, geometric, verbal, and symbolic
     form. The student is expected to:
            (A) generate formulas involving conversions,
             perimeter, area, circumference, volume, and
             scaling;
            (B) graph data to demonstrate relationships in
             familiar concepts, such as conversions, perimeter,
             area, circumference, volume, and scaling; and
            (C) describe the relationship between the terms in a
             sequence and their positions in the sequence.


 Thursday, February 3, 2005    TAKS Math Prep.                  63
7th Grade Objective 2 (cont.)

      (7.5) Patterns, relationships, and
       algebraic thinking. The student uses
       equations to solve problems. The
       student is expected to:
          (A) use [concrete] models to solve
           equations and use symbols to record the
           actions; and
          (B) formulate a possible problem situation
           when given a simple equation.

 Thursday, February 3, 2005   TAKS Math Prep.           64
7th Grade Objective 3
      (7.6) The student compares and classifies
       shapes and solids using geometric vocabulary
       and properties. The student is expected to:
            (A) use angle measurements to classify pairs of
             angles as complementary or supplementary;
            (B) use properties to classify shapes, including
             triangles, quadrilaterals, pentagons, and
            circles;
            (C) use properties to classify solids, including
             pyramids, cones, prisms, and cylinders; and
            (D) use critical attributes to define similarity.

 Thursday, February 3, 2005     TAKS Math Prep.                  65
7th Grade Objective 3 (cont.)

      (7.7) The student uses coordinate
       geometry to describe location on a
       plane. The student is expected to:
          (A) locate and name points on a coordinate
           plane using ordered pairs of integers; and
          (B) graph translations on a coordinate
           plane.



 Thursday, February 3, 2005   TAKS Math Prep.           66
7th Grade Objective 3 (cont.)

      (7.8) The student uses geometry to
       model and describe the physical world.
       The student is expected to:
          (A) sketch a solid when given the top, side,
           and front views;
          (B) make a net (two-dimensional model) of
           the surface area of a solid; and
          (C) use geometric concepts and properties
           to solve problems in fields such as art and
           architecture.

 Thursday, February 3, 2005   TAKS Math Prep.             67
7th Grade Objective 4

      (7.9) The student solves application
       problems involving estimation and
       measurement. The student is expected
       to:
            (A) estimate measurements and solve
             application problems involving length
             (including perimeter and circumference),
             area, and volume.


 Thursday, February 3, 2005   TAKS Math Prep.           68
7th Grade Objective 5

      (7.10) The student recognizes that a
       physical or mathematical model can be
       used to describe the probability of real-
       life events. The student is expected to
            (A) construct sample spaces for compound
             events (dependent and independent).




 Thursday, February 3, 2005   TAKS Math Prep.           69
7th Grade Objective 5 (cont.)

      (7.11) The student understands that the
       way a set of data is displayed influences
       its interpretation. The student is
       expected to
          (A) select and use an appropriate
           representation for presenting collected data
           and justify the selection; and
          (B) make inferences and convincing
           arguments based on an analysis of given or
           collected data.

 Thursday, February 3, 2005   TAKS Math Prep.             70
7th Grade Objective 5 (cont.)

      (7.12) The student uses measures of
       central tendency and range to describe a
       set of data. The student is expected to:
          (A) describe a set of data using mean,
           median, mode, and range; and
          (B) choose among mean, median, mode, or
           range to describe a set of data and justify
           the choice for a particular situation.


 Thursday, February 3, 2005   TAKS Math Prep.            71
7th Grade Objective 6
      (7.13) The student applies Grade 7 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;
            (B) use a problem-solving model that incorporates
             understanding the problem, making a plan, carrying out the
             plan, and evaluating the solution for reasonableness; and
            (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.


 Thursday, February 3, 2005         TAKS Math Prep.                            72
7th Grade Objective 6 (cont.)

      (7.14) The student communicates about
       Grade 7 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.

 Thursday, February 3, 2005   TAKS Math Prep.                73
7th Grade Objective 6 (cont.)

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



 Thursday, February 3, 2005   TAKS Math Prep.           74
8th Grade Objective 1
      (8.1) The student understands that different forms of
       numbers are appropriate for different situations. The
       student is expected to:
            (A) compare and order rational numbers in various forms,
             including integers, percents, and positive and negative
             fractions and decimals;
            (B) select and use appropriate forms of rational numbers to
             solve real-life problems, including those involving proportional
             relationships;
            (C) approximate mentally [and with calculators] the value of
             irrational numbers as they arise from problem situations
             (π,√2); and
            (D) express numbers in scientific notation, including negative
             exponents, in appropriate problem situations [using a
             calculator].


 Thursday, February 3, 2005         TAKS Math Prep.                             75
8th Grade Objective 1 (cont.)
      (8.2) The student selects and uses appropriate
       operations to solve problems and justify
       solutions. The student is expected to:
            (A) select and use appropriate operations to solve
             problems and justify the selections;
            (B) add, subtract, multiply, and divide rational
             numbers in problem situations;
            (C) evaluate a solution for reasonableness; and
            (D) use multiplication by a constant factor (unit rate)
             to represent proportional relationships; for example,
             the arm span of a gibbon is about 1.4 times its
             height, a = 1.4h.


 Thursday, February 3, 2005      TAKS Math Prep.                   76
8th Grade Objective 2

      (8.3) The student identifies proportional
       relationships in problem situations and
       solves problems. The student is
       expected to:
          (A) compare and contrast proportional and
           non-proportional relationships; and
          (B) estimate and find solutions to application
           problems involving percents and
           proportional relationships such as similarity
           and rates.

 Thursday, February 3, 2005   TAKS Math Prep.           77
8th Grade Objective 2 (cont.)

      (8.4) The student makes connections
       among various representations of a
       numerical relationship. The student is
       expected to:
            (A) generate a different representation given
             one representation of data, such as a table,
             graph, equation, or verbal description.



 Thursday, February 3, 2005   TAKS Math Prep.            78
8th Grade Objective 2 (cont.)

      (8.5) The student uses graphs, tables,
       and algebraic representations to make
       predictions and solve problems. The
       student is expected to:
          (A) estimate, find, and justify solutions to
           application problems using appropriate
           tables, graphs, and algebraic equations;
           and
          (B) use an algebraic expression to find any
           term in a sequence.

 Thursday, February 3, 2005   TAKS Math Prep.             79
8th Grade Objective 3

      (8.6) The student uses transformational
       geometry to develop spatial sense. The
       student is expected to:
          (A) generate similar shapes using dilations
           including enlargements and reductions; and
          (B) graph dilations, reflections, and
           translations on a coordinate plane.



 Thursday, February 3, 2005   TAKS Math Prep.            80
8th Grade Objective 3 (cont.)

      (8.7) The student uses geometry to model and
       describe the physical world. The student is
       expected to:
            (A) draw solids from different perspectives;
            (B) use geometric concepts and properties to solve
             problems in fields such as art and architecture;
            (C) use pictures or models to demonstrate the
             Pythagorean Theorem; and
            (D) locate and name points on a coordinate plane
             using ordered pairs of rational numbers.


 Thursday, February 3, 2005    TAKS Math Prep.                    81
8th Grade Objective 4

      (8.8) The student uses procedures to
       determine measures of solids. The
       student is expected to:
          (A) find surface area of prisms and cylinders
           using [concrete] models and nets (two-
           dimensional models); and
          (C) estimate answers and use formulas to
           solve application problems involving surface
           area and volume.

 Thursday, February 3, 2005   TAKS Math Prep.          82
8th Grade Objective 4 (cont.)

      (8.9) The student uses indirect
       measurement to solve problems. The
       student is expected to:
          (A) use the Pythagorean Theorem to solve
           real-life problems; and
          (B) use proportional relationships in similar
           shapes to find missing measurements.



 Thursday, February 3, 2005   TAKS Math Prep.              83
8th Grade Objective 4 (cont.)

      (8.10) The student describes how
       changes in dimensions affect linear,
       area, and volume measures. The student
       is expected to:
          (A) describe the resulting effects on
           perimeter and area when dimensions of a
           shape are changed proportionally; and
          (B) describe the resulting effect on volume
           when dimensions of a solid are changed
           proportionally.

 Thursday, February 3, 2005   TAKS Math Prep.            84
8th Grade Objective 5

      (8.11) The student applies concepts of
       theoretical and experimental probability
       to make predictions. The student is
       expected to:
          (A) find the probabilities of compound
           events (dependent and independent); and
          (B) use theoretical probabilities and
           experimental results to make predictions
           and decisions.

 Thursday, February 3, 2005   TAKS Math Prep.         85
8th Grade Objective 5 (cont.)

      (8.12) The student uses statistical
       procedures to describe data. The student
       is expected to:
          (A) select the appropriate measure of
           central tendency to describe a set of data
           for a particular purpose;
          (B) draw conclusions and make predictions
           by analyzing trends in scatterplots; and
          (C) construct circle graphs, bar graphs, and
           histograms, [with and] without technology.

 Thursday, February 3, 2005   TAKS Math Prep.             86
8th Grade Objective 5 (cont.)

      (8.13) The student evaluates predictions
       and conclusions based on statistical
       data. The student is expected to:
          (A) evaluate methods of sampling to
           determine validity of an inference made
           from a set of data; and
          (B) recognize misuses of graphical or
           numerical information and evaluate
           predictions and conclusions based on data
           analysis.

 Thursday, February 3, 2005   TAKS Math Prep.          87
8th Grade Objective 6
      (8.14) The student applies Grade 8 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;
            (B) use a problem-solving model that incorporates
             understanding the problem, making a plan, carrying out the
             plan, and evaluating the solution for reasonableness; and
            (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.


 Thursday, February 3, 2005         TAKS Math Prep.                            88
8th Grade Objective 6 (cont.)

      (8.15) The student communicates about
       Grade 8 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.

 Thursday, February 3, 2005   TAKS Math Prep.                89
8th Grade Objective 6 (cont.)

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



 Thursday, February 3, 2005   TAKS Math Prep.           90

				
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