IDAHO ACHIEVEMENT STANDARDS



IDAHO CONTENT STANDARDS

GRADE 8 MATHEMATICS

|Cognitive level codes: |Calculator codes: |

|B: Memorize |CN: “calculator neutral.” Having or not having a calculator on this item will not affect students’ ability to |

|C: Perform procedures |demonstrate proficiency on this objective. |

|D: Demonstrate understanding |YES: calculator MUST be available in order for the student to demonstrate proficiency on this objective. |

|E: Conjecture, generalize, prove |NO: student MUST NOT have a calculator while completing this item in order to assess this objective. |

|F: Solve non-routine problems, make connections |CR: “calculator recommended.” For all items not assessing computation or estimation, calculator availability is |

| |recommended. |

Shaded objectives should be assessed in the classroom, but not included on the ISAT assessment.

Standard 1: Number and Operation

|Goals: |Objective 1 |Objective 2 |Objective 3 |Objective 4 |Objective 5 |Objective 6 |Objective 7 |

|Goal 2.1: Understand|8.M.2.1.1 Select and use |8.M.2.1.2 Apply estimation |8.M.2.1.3 Compare the |8.M.2.1.4 Given the |8.M.2.1.5 Convert units of |8.M.2.1.6 Solve problems |8.M.2.1.7 Use appropriate |

|and use U.S. |appropriate units and tools |of measurement to real-world|differences and |formulas, find the |measurement within each |involving area of circles |vocabulary and notations. |

|customary and metric|to make formal measurements |and content problems using |relationships among measures|circumference, perimeter, or|system in problem solving |and the perimeter and area |(339.01.f) |

|measurements. |in both systems. (339.01.a) |standard measuring devices. |of perimeter, area, and |area of triangles, circles, |situations. (339.01.e) |of rectangles and triangles.| |

| | |(339.01.b) |volume (capacity) within |and quadrilaterals, and the | |(339.01.d) |CL: |

| |CL: C | |both systems. (339.01.c) |volume and surface area of |CL: C | |Calc: |

| |Calc: YES |CL: | |rectangular prisms. |Calc: YES |CL: C |Content Limit: Assessed in |

| |Content Limit: Select |Calc: |CL: |(341.01.e) |Content Limit: All |Calc: YES |the classroom, not on the |

| |appropriate units and tools |Content Limit: Assessed in |Calc: | |conversions must be within |Content Limit: Graphics |ISAT. |

| |only. Units for length are |the classroom, not on the |Content Limit: Assessed in |CL: C |the same system of |should be used in most of | |

| |inches, feet, yards, miles, |ISAT. |the classroom, not on the |Calc: YES |measurement. Customary units|these items, as appropriate.| |

| |millimeters, centimeters, | |ISAT. |Content Limit: Items assess |may include inches, feet, |Items should be set in a | |

| |and meters. Units for time | | |finding linear measure, |yards, miles, ounces, |real-world context. | |

| |are seconds, minutes, hours,| | |capacity, perimeter, |pounds, tons, fluid ounces, |Measurements may be in | |

| |days, and years. Units for | | |circumference, area, surface|cups, pints, quarts, and |either metric or customary | |

| |weight are ounces, pounds, | | |area, and/or volume. Items |gallons. Metric prefixes may|units. Problems may include | |

| |tons, grams, and kilograms. | | |may include composite |include milli-, centi-, and |shapes that are formed by a | |

| |Units for volume (capacity) | | |figures. Graphics are used |kilo- with base units of |combination of two shapes. | |

| |are cups, quarts, gallons, | | |in most of these items. |grams, liters, and meters. | | |

| |milliliters, and liters. | | |Items requiring |Time units may include | | |

| |‘use … tools to make formal | | |three-dimensional graphics |years, months, weeks, days, | | |

| |measurements’ to be assessed| | |must be realistic and |hours, minutes, and seconds.| | |

| |in the classroom, not on the| | |include verbal descriptions.|Items should be set in a | | |

| |ISAT. | | |Items should be set in a |real-world context. | | |

| | | | |real-world context. Answer | | | |

| | | | |options may be left in terms| | | |

| | | | |of π. | | | |

|Goal 2.3: Apply |8.M.2.3.1 Illustrate the | | | | | | |

|dimensional |interrelationship of | | | | | | |

|analysis. |measurement units through | | | | | | |

| |dimensional analysis | | | | | | |

| |conversions. (339.04.a) | | | | | | |

| | | | | | | | |

| |CL: C, D | | | | | | |

| |Calc: YES | | | | | | |

| |Content Limit: Customary | | | | | | |

| |units may include inches, | | | | | | |

| |feet, yards, miles, ounces, | | | | | | |

| |pounds, tons, fluid ounces, | | | | | | |

| |cups, pints, quarts, and | | | | | | |

| |gallons. Metric prefixes may| | | | | | |

| |include milli-, centi-, and | | | | | | |

| |kilo- with base units of | | | | | | |

| |grams, liters, and meters. | | | | | | |

| |Time units may include | | | | | | |

| |years, months, weeks, days, | | | | | | |

| |hours, minutes, and seconds.| | | | | | |

| |No more than two conversion | | | | | | |

| |ratios should be used in any| | | | | | |

| |item. | | | | | | |

Standard 3: Concepts and Language of Algebra and Functions

|Goals: |Objective 1 |Objective 2 |Objective 3 |

|Goal 3.1: Use |8.M.3.1.1 Use variables in expressions, equations, and |8.M.3.1.2 Translate simple word statements and story problems into |8.M.3.1.3 Use symbols “,”“=,” “(,” “(,” and “(” to express |

|algebraic symbolism |inequalities. (340.01.a) |algebraic expressions and equations. (340.01.b) |relationships. (340.01.c) |

|as a tool to | | | |

|represent |CL: D |CL: D |CL: D |

|mathematical |Calc: CN |Calc: CN |Calc: CN |

|relationships. |Content Limit: Evaluate an expression by substituting a number for |Content Limit: Items should be set in a real-world context. |Content Limit: Items should be set in a real-world context. Item |

| |every variable in the expression. Items are limited to at most |Expressions and equations may contain at most three operations and |may include integers between −50 and 50, up to three operations, at|

| |three variables at a time. Items may also check solutions to |may require at most two grouping symbols. May contain one or two |most two grouping symbol, and exponents limited to 2, 3, and 4. May|

| |equations or inequalities by substituting values for the |variables. |include one variable. |

| |variable(s) in an equation or inequality. | | |

|Goal 3.2: Evaluate |8.M.3.2.1 Use and apply the following properties in evaluating |8.M.3.2.2 Use the order of operations in evaluating simple |8.M.3.2.3 Simplify algebraic expressions. (340.02.c) |

|algebraic |algebraic expressions: commutative, associative, identity, zero, |algebraic expressions. (340.02.b) | |

|expressions. |inverse, distributive, and substitution. (340.02.a) | |CL: C |

| | |CL: C |Calc: CN |

| |CL: C |Calc: CN |Content Limit: Items can use positive fractions with no more than |

| |Calc: CN |Content Limit: Expressions may include parentheses, exponents, |two-digit numerators and denominators or decimals less than |

| |Content Limit: Items can use positive fractions with no more than |multiplication, division, addition, and/or subtraction. Items can |ten-thousandths. Expressions may include integers between −50 and |

| |two-digit numerators and denominators or decimals less than |use positive fractions with no more than two-digit numerators and |50, up to three operations, at most two grouping symbol, and |

| |ten-thousandths. Expressions may include integers between −50 and |denominators or decimals less than ten-thousandths. Roots are |exponents limited to 2, 3, and 4. May include one or two variables.|

| |50, up to three operations, at most two grouping symbol, and |limited to square roots and cube roots. Items require students to | |

| |exponents limited to 2, 3, and 4. May include one variable. |compute only the cube root of 8, 27, 64, 125, or 1,000. May include| |

| | |one or two variables. | |

|Goal 3.3: Solve |8.M.3.3.1 Solve one- and two-step equations and inequalities. |8.M.3.3.2 Match graphical representations with simple linear | |

|algebraic equations |(340.03.a) |equations. (340.03.b) | |

|and inequalities. | | | |

| |CL: C |CL: C, D | |

| |Calc: YES |Calc: CN | |

| |Content Limit: Items can use positive fractions with no more than |Content Limit: The x- and y-axes may have different scales. Linear | |

| |one-digit numerators and denominators or decimals less than |equations will be given in slope-intercept (y = mx + b) form. | |

| |ten-thousandths. Equations and inequalities may include integers | | |

| |between −50 and 50. Variable may appear on left or right side of | | |

| |equal or inequality sign. | | |

|Goal 3.4: Understand|8.M.3.4.1 Extend patterns and identify a rule (function) that |8.M.3.4.2 Use relationships to explain how a change in one quantity|8.M.3.4.3 Use appropriate vocabulary and notations. (343.01.c) |

|the concept of |generates the pattern using rational numbers. (343.01.a) |may result in a change in another, and identify the relationship as| |

|functions. | |a positive, negative, or neither. (343.01.b) |CL: |

| |CL: E | |Calc: |

| |Calc: YES |CL: |Content Limit: Assessed in the classroom, not on the ISAT. |

| |Content Limit: Items may require a verbal description of the |Calc: | |

| |pattern. Variables can be used to write the rule (function). Items |Content Limit: Assessed in the classroom, not on the ISAT. | |

| |should not include more that two variables or include more than two| | |

| |operations. Fraction denominators limited to 2, 3, 4, 5, 6, 8, and | | |

| |10. Decimals limited to tenths, hundredths, and thousandths. | | |

| |Functions must be expressible as y = mx + b. Items may ask the | | |

| |student to extend the pattern, state the rule for the pattern, or | | |

| |both. | | |

|Goal 3.5: Represent |8.M.3.5.1 Represent a set of data in a table, as a graph, and as a | | |

|equations, |mathematical relationship. (343.02.a) | | |

|inequalities and | | | |

|functions in a |CL: C, D | | |

|variety of formats. |Calc: CN | | |

| |Content Limit: On the graph, x- and y-axes may have different | | |

| |scales. Items do not require students to graph or generate a table | | |

| |of a non-linear relation; students may read points off of a graph | | |

| |of a non-linear relation. Items may include real-world context. | | |

| |Given a continuous (i.e., individual points not indicated) linear | | |

| |graph, students will generate a table of values. Relationship is | | |

| |presented as a table, graph, or equation. The answer options will | | |

| |include a table, a graph, or an equation. | | |

|Goal 3.6: Apply |8.M.3.6.1 Use patterns and linear functions to represent and solve | | |

|functions to a |problems. (343.03.a) | | |

|variety of problems.| | | |

| |CL: D | | |

| |Calc: YES | | |

| |Content Limit: Patterns may include rational numbers. Linear | | |

| |functions are limited to whole number variable values. | | |

Standard 4: Concepts and Principles of Geometry

|Goals: |Objective 1 |Objective 2 |Objective 3 |Objective 4 |Objective 5 |Objective 6 |Objective 7 |

|Goal 4.1: Apply |8.M.4.1.1 Describe and |8.M.4.1.2 Draw and measure |8.M.4.1.3 Apply the |8.M.4.1.4 Identify and model|8.M.4.1.5 Identify |8.M.4.1.6 Explain the |8.M.4.1.7 Use appropriate |

|concepts of size, |classify relationships among|various angles and shapes |fundamental concepts, |the effects of reflections, |congruence, similarities, |concept of surface area and |vocabulary and symbols. |

|shape, and spatial |types of one-, two-, and |using appropriate tools. |properties, and |translations, rotations, and|and line symmetry of shapes.|volume (capacity). |(341.01.h) |

|relationships. |three- dimensional geometric|(341.01.b) |relationships among points, |scaling on various shapes. |(341.01.d) |(341.01.f) | |

| |figures, using their | |lines, rays, planes, and |(341.01.g) | | |CL: |

| |defining properties. |CL: C |angles. (341.01.c) | |CL: E |CL: |Calc: |

| |(341.01.a) |Calc: YES | |CL: D, E |Calc: CN |Calc: |Content Limit: Assessed in |

| | |Content Limit: Measure only |CL: C |Calc: CN |Content Limit: |Content Limit: Assessed in |the classroom, not on the |

| |CL: C, D |using superimposed |Calc: CN |Content Limit: When using |Shapes limited to |the classroom, not on the |ISAT. |

| |Calc: CN |protractor. ‘Draw’ to be |Content Limit: Items may |three-dimensional shapes: |two-dimensional figures. |ISAT. | |

| |Content Limit: Classify |assessed in the classroom, |include parallel, |Transformations may include | | | |

| |only. Figures may include |not on the ISAT. |intersecting and |reflections, rotation and | | | |

| |triangles and | |perpendicular lines |translations. Items are | | | |

| |quadrilaterals. Triangles | |including two parallel lines|limited to one | | | |

| |may be classified by angles | |cut by a transversal and the|transformation per item. | | | |

| |(acute, equiangular, obtuse,| |congruent and supplementary |Rotations occur in | | | |

| |or right) or by sides | |angles formed. Angles may |increments of 90º. When | | | |

| |(equilateral, isosceles, or | |include acute, right, |using two-dimensional | | | |

| |scalene) or both (e.g., an | |obtuse, and straight. Angle |shapes: Transformations may | | | |

| |obtuse isosceles triangle). | |relationships may include |include reflections, | | | |

| |Quadrilaterals may be | |complementary, |rotation, translations, and | | | |

| |classified according to | |supplementary, and |change of scale. Items are | | | |

| |number and position of | |congruent. Symbols used may |limited to two | | | |

| |parallel sides as well as | |include: capital letter for |transformations per item. | | | |

| |angle measure (square, | |points, two-headed arrow |Rotations occur in | | | |

| |trapezoid, parallelogram, | |above two capital letters |increments of 45º. Algebraic| | | |

| |rectangle, or rhombus). | |for lines, line segment |rules limited to | | | |

| |Three-dimensional figures | |above two capital letters |translations and reflections| | | |

| |can include cubes, | |for line segments, |when the figure is shown on | | | |

| |rectangular prisms, spheres,| |one-headed arrow above two |a coordinate grid. No | | | |

| |pyramids, cones, and | |capital letters for rays, |algebraic rules are required| | | |

| |cylinders. ‘Describe’ to be | |angle symbol with one |for items involving more | | | |

| |assessed in the classroom, | |capital letter or angle |than one transformation. | | | |

| |not on the ISAT. | |symbol with three capital |Rotations must indicate | | | |

| | | |letters for angles, and |clockwise or | | | |

| | | |symbols for parallel, |counterclockwise. | | | |

| | | |perpendicular, and right | | | | |

| | | |angle. | | | | |

|Goal 4.3: Apply |8.M.4.3.1 Identify and plot | | | | | | |

|graphing in two |points on a coordinate | | | | | | |

|dimensions. |plane. (341.03.a) | | | | | | |

| | | | | | | | |

| |CL: C | | | | | | |

| |Calc: CN | | | | | | |

| |Content Limit: Points | | | | | | |

| |limited to integer ordered | | | | | | |

| |pairs. Points may appear in | | | | | | |

| |any of the four quadrants or| | | | | | |

| |on either axis. | | | | | | |

Standard 5: Data Analysis, Probability, and Statistics

|Goals: |Objective 1 |Objective 2 |Objective 3 |Objective 4 |

|Goal 5.1: Understand |8.M.5.1.1 Analyze and interpret tables, charts, |8.M.5.1.2 Explain and justify conclusions drawn |8.M.5.1.3 Use appropriate vocabulary and | |

|data analysis. |and graphs, including frequency tables, scatter |from tables, charts, and graphs. (342.01.b) |notations. (342.01.c) | |

| |plots, broken line graphs, line plots, bar graphs,| | | |

| |histograms, circle graphs, and stem-and-leaf |CL: |CL: | |

| |plots. (342.01.a) |Calc: |Calc: | |

| | |Content Limit: Assessed in the classroom, not on |Content Limit: Assessed in the classroom, not on | |

| |CL: D, E |the ISAT. |the ISAT. | |

| |Calc: CR | | | |

| |Content Limit: Graphics may have at most ten data | | | |

| |categories. Circle graphs may have at most eight | | | |

| |sectors. Scales are in increments appropriate to | | | |

| |the application. Histogram intervals must be | | | |

| |consistent. | | | |

|Goal 5.2: Collect, |8.M.5.2.1 Collect, organize, and display data with| | | |

|organize, and display|appropriate notation in tables, charts, and | | | |

|data. |graphs, including scatter plots, broken line | | | |

| |graphs, line plots, bar graphs, histograms, and | | | |

| |stem-and-leaf plots. (342.02.a) | | | |

| | | | | |

| |CL: C | | | |

| |Calc: CN | | | |

| |Content Limit: Given data, choose a display. | | | |

| |Displays limited to scatter plots, broken line | | | |

| |graphs, line plots, bar graphs, histograms, and | | | |

| |stem-and-leaf plots. ‘Collect’ to be assessed in | | | |

| |classroom, not on the ISAT. | | | |

|Goal 5.3: Apply |8.M.5.3.1 Choose and calculate the appropriate |8.M.5.3.2 Explain the significance of distribution| | |

|simple statistical |measure of central tendency – mean, median, and |of data, including range, frequency, gaps, and | | |

|measurements. |mode. (342.03.a) |clusters. (342.03.b) | | |

| | | | | |

| |CL: C |CL: | | |

| |Calc: YES |Calc: | | |

| |Content Limit: Items should be set in a real-world|Content Limit: Assessed in the classroom, not on | | |

| |context. Items may assess finding the range, mean,|the ISAT. | | |

| |median, or mode of a set of data presented in a | | | |

| |chart, table, graph, or plot (e.g., scatter plot, | | | |

| |line plot, or stem-and-leaf plot). Items that | | | |

| |assess understanding of these concepts may ask | | | |

| |students to draw conclusions from an analysis of | | | |

| |range and/or central tendency measures. Data set | | | |

| |should include no more than 12 data points. Data | | | |

| |set may have an even or an odd number of data | | | |

| |points and does not need to be in numeric order. | | | |

| |No more than three categories of information | | | |

| |should be used in data sets. | | | |

|Goal 5.4: Understand |8.M.5.4.1 Model situations of probability using |8.M.5.4.2 Recognize equally likely outcomes. |8.M.5.4.3 Explain that probability ranges from 0% |8.M.5.4.4 Use the language of probability. |

|basic concepts of |simulations. (342.04.a) |(342.01.c) |to 100% and identify a situation as having high or|(342.04.b) |

|probability. | | |low probability. | |

| |CL: |CL: C, D | |CL: |

| |Calc: |Calc: CN |CL: |Calc: |

| |Content Limit: Assessed in the classroom, not on |Content Limit: Items describe familiar situations |Calc: |Content Limit: Assessed in the classroom, not on |

| |the ISAT. |such as spinning a spinner, rolling one or two |Content Limit: Assessed in the classroom, not on |the ISAT. |

| | |dice (does not include sum of two dice), or |the ISAT. | |

| | |drawing different colored objects from a | | |

| | |container. Equally likely outcomes must pertain to| | |

| | |the same event. | | |

|Goal 5.5: Make |8.M.5.5.1 Make predictions based on experimental |8.M.5.5.2 Conduct statistical experiments and |8.M.5.5.3 Use appropriate vocabulary and | |

|predictions or |and theoretical probabilities. (342.05.a) |interpret results using tables, charts, or graphs.|notations. (342.05.b) | |

|decisions based on | |(342.05.c) | | |

|data. |CL: D, E | |CL: | |

| |Calc: YES |CL: |Calc: | |

| |Content Limit: Items may include combinations of |Calc: |Content Limit: Assessed in the classroom, not on | |

| |events (e.g., rolling a number cube then spinning |Content Limit: Assessed in the classroom, not on |the ISAT. | |

| |a spinner or drawing two cards without |the ISAT. | | |

| |replacement). Items may not include conditional | | | |

| |probability. Items may require comparison between | | | |

| |experimental and theoretical probabilities. | | | |

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