Idaho Content Standards Grade 6 Mathematics

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Idaho Content Standards Grade 6 Mathematics



    Cognitive level codes: Calculator codes:

    o B: Memorize ? CN: “calculator neutral.” Having or not having a calculator on this item will not o C: Perform procedures affect students‟ ability to demonstrate proficiency on this objective. o D: Demonstrate understanding ? YES: calculator MUST be available in order for the student to demonstrate

    o E: Conjecture, generalize, prove proficiency on this objective.

    o F: Solve non-routine problems, make connections ? NO: student MUST NOT have a calculator while completing this item in order to

     assess this objective.

    ? 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 Objective 8

    6.M.1.1.1 Compare 6.M.1.1.2 Explain the 6.M.1.1.3 Locate the 6.M.1.1.4 Convert 6.M.1.1.5 Apply 6.M.1.1.6 Solve 6.M.1.1.7 Describe 6.M.1.1.8 Use Goal 1.1: magnitudes and interrelationship of position of integers between decimals number theory problems using the 4-the use of integers in appropriate Understand and relative magnitudes fractions, decimals, on a number line. and fractions. concepts (prime, step process of real-world situations. vocabulary. use numbers. of positive rational and percents. (317.01.b) composite, prime problem solving (317.01.f)

    numbers, including (317.01.b) CL: B factorization) and (explore, plan, solve, CL:

    whole numbers Calc: CN CL: B, C identify common and examine). CL: Calc:

    through billions, CL: Content Limit: Limit Calc: NO factors and common (318.01.b) Calc: Content Limit:

    fractions, and Calc: numbers between Content Limit: multiples. (317.01.e) Content Limit: Assessed in the

    decimals. (317.01.a, Content Limit: ?50 and 50. Fraction CL: Assessed in the classroom, not on the

    317.01.d) Assessed in the denominators limited CL: B, C Calc: classroom, not on the ISAT.

     classroom, not on the to 2, 3, 4, 5, 6, 8, 10, Calc: CR Content Limit: ISAT.

    CL: B, C ISAT. 12, 20, and 25. Can Content Limit: Assessed in the

    Calc: CN use mixed numbers. Whole numbers less classroom, not on the

    Content Limit: Decimals to than or equal to 300. ISAT.

    Fraction thousandths place. Prime factors less

    denominators limited than 13. Answer

    to 2, 3, 4, 5, 6, 8, 10, options may be

    12, and 25. Can use written using

    mixed numbers. exponents.

    Decimals limited to

    tenths, hundredths,

    and thousandths.

    Numbers may be

    ordered least to

    greatest or greatest to


    February, 2007 1

6.M.1.2.1 Recall 6.M.1.2.2 Add, 6.M.1.2.3 Evaluate 6.M.1.2.4 Select and 6.M.1.2.5 Use a 6.M.1.2.6 Use Goal 1.2: basic multiplication subtract, multiply, numerical use an appropriate variety of strategies appropriate Perform and division facts and divide whole expressions with method of to solve real-life vocabulary and computations from 12 x 12 Times numbers, decimals, whole numbers using computation from problems. (318.01.a) notations. (317.02.i) accurately.

    Table. (317.02.d) and simple fractions the order of mental math, paper

     (including unlike operations (excluding and pencil, calculator CL: C, D CL: CL: denominators). exponents). or a combination of Calc: YES Calc: Calc: (317.02.a, 317.02.b, (317.02.e) the three. (317.02.h) Content Limit: Content Limit: Content Limit: 317.02.c, 317.02.g) Multiplication items Assessed in the Assessed in the CL: B CL: may include two-classroom, not on the classroom, not on the CL: B, C Calc: NO Calc: digit factors. Division ISAT. ISAT. Calc: NO Content Limit: Content Limit: items may involve a

     Content Limit: Operations may Assessed in the one-digit divisor and

    Multiplication items include addition, classroom, not on the a three-digit

    have at most a three-subtraction, ISAT. dividend. Fraction

    digit number multiplication, and denominators limited

    multiplied by a two-division. Grouping to 2, 3, 4, 5, 6, 8, 10,

    digit number. May symbols may be used 12, and 25. Decimals

    include and nested two levels limited to

    multiplication of at most. thousandths place.

    fractions or fraction Multiplication items Expression should

    and whole number. may include at most not be stated. The

    Division items have two-digit factors. problems could be

    at most a three-digit such that a variety of

    number divided by a strategies could be

    two-digit whole used, but ability to

    number. Items do not „Use a variety of

    include negative strategies‟ to be

    numbers. Fraction assessed in the

    denominators limited classroom, not on the

    to 2, 3, 4, 5, 6, 8, 10, ISAT.

    and 12. Subtraction

    cannot be a mixed

    number minus a

    mixed number

    requiring regrouping.

    Fraction division

    must have a whole

    number divisor.

    Expression must be

    clearly stated.

    February, 2007 2

6.M.1.3.1 Estimate to 6.M.1.3.2 Explain 6.M.1.3.3 Identify 6.M.1.3.4 Use a four-6.M.1.3.5 Formulate 6.M.1.3.6 Use Goal 1.3: predict computation when estimation is whether a given function calculator to conjectures and appropriate Estimate and results. (317.03.a) appropriate. estimate is an solve complex grade-discuss why they vocabulary. judge (317.03.b) overestimate or level problems. must be or seem to be (317.03.d) reasonableness

    CL: underestimate. true. (318.02.c) of results. Calc: CL: (317.03.c) CL: CL: Content Limit: Calc: Calc: CL: Calc: Assessed in the Content Limit: CL: E Content Limit: Calc: Content Limit: classroom, not on the Assessed in the Calc: NO Assessed in the Content Limit: Assessed in the ISAT. classroom, not on the Content Limit: classroom, not on the Assessed in the classroom, not on the

    ISAT. Estimates will ISAT. classroom, not on the ISAT.

    involve addition or ISAT.

    subtraction only.

    Standard 2: Concepts and Principles of Measurement

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

    6.M.2.1.1 Select and use 6.M.2.1.2 Apply 6.M.2.1.3 Apply 6.M.2.1.4 Given the 6.M.2.1.5 Convert units 6.M.2.1.6 Solve 6.M.2.1.7 Use Goal 2.1: appropriate units and estimation of understanding of formulas, find the of measurement within problems involving appropriate vocabulary Understand and

    tools to make formal measurement to real-relationships to solve perimeter or each system in one-step perimeter and area of and notations. (319.01.g) use U.S. measurements in both world and content real-world problems circumference and area problems (e.g., quarts to rectangles. (321.01.d) customary and systems. (319.01.a) problems using standard related to elapsed time. of triangles, circles and gallons and gallons to CL: B, D metric measuring devices. (319.01.f) parallelograms (all quarts). (319.01.e) CL: B, C Calc: CN measurements. CL: B, C (319.01.b) kinds). (319.01.c, Calc: YES Content Limit: Assessed

    Calc: CN CL: F 321.01.e) CL: B, C Content Limit: Formulas in the classroom, not on

    Content Limit: Select CL: B, C Calc: CN Calc: CN are not provided. the ISAT.

    appropriate units and Calc: CN Content Limit: Time is CL: B, C Content Limit: tools only. Units for Content Limit: Assessed limited to ?, ?, and ? Calc: YES Conversion within length are inches, feet, in the classroom, not on hours and listed in Content Limit: Items systems only (not yards, miles, the ISAT. fraction form. may involve between). Customary millimeters, centimeters, measurement, using a length units are inches, and meters. Units for grid, or using a formula. feet, and yards; weight time are seconds, Formulas are given units are ounces and minutes, hours, days, within the item. When pounds; and capacity and years. Units for using a grid, lengths of units are cups, pints, weight are ounces, sides of a figure are quarts, and gallons. pounds, tons, grams, and limited to whole Customary conversions kilograms. Units for numbers. The pi symbol must be given within volume (capacity) are (π) will be used. Answer item. Time units are cups, quarts, gallons, choices will be seconds, minutes, hours, milliliters, and liters. numerical only (e.g., days, and weeks. Metric Use … tools to make answer 43.96, not 14π). prefixes include milli-, formal measurements‟ to Items will not provide centi-, and kilo- using be assessed in the area or circumference base units of meter, classroom, not on the and then require gram and liter. Items ISAT. determining radius or should be set in real-

    diameter. world context.

    February, 2007 3

6.M.2.2.1 Identify and Goal 2.2: Apply write ratios and scales the concepts of (on a map). (319.03.a) rates, ratios, and

    CL: B, C, proportions. Calc: YES

    Content Limit: „On a

    map‟ does not limit this

    to a map only. Use real-

    world situations. Scales

    in increments of 1, 2, 5,

    or 10, or consistent with

    real-world applications

    such as inches to feet as

    in a room (1 inch

    represents 5 feet),

    centimeters to meters as

    for a house (1 centimeter

    represents 2 meters) or

    inches to miles on earth

    (1 inch represents 60


    No objectives at this Goal 2.3: Apply grade level. dimensional


    Standard 3: Concepts and Language of Algebra and Functions

    Goals: Objective 1 Objective 2 Objective 3 Objective 4

    6.M.3.1.1 Discuss the meaning and use of 6.M.3.1.2 Translate simple word statements 6.M.3.1.3 Read and use symbols of “<,” “>,” Goal 3.1: Use variables in simple expressions and into algebraic equations. (320.01.b) and “=” to express relationships. (320.01.c) algebraic equations. (320.01.a) symbolism as a CL: C CL: C tool to represent CL: Calc: CN Calc: CN mathematical Calc: Content Limit: Whole numbers less than 50. Content Limit: Use whole numbers less than relationships.

    Content Limit: Assessed in the classroom, Equations include one operation. May 50 and expressions with no more than one

    not on the ISAT. include one or two variables. operation on each side of the relation symbol.

    May include one variable.

    6.M.3.2.1 Use the following properties in 6.M.3.2.2 Evaluate simple algebraic Goal 3.2: evaluating numerical expressions: expressions using substitution. Evaluate commutative, associative, identity, zero, algebraic inverse, and distributive. (320.02.a) CL: C expressions. Calc: CN CL: B, C Content Limit: Limit numbers to whole Calc: CN numbers less than 100. Content Limit: Whole numbers less than 100.

    February, 2007 4

    6.M.3.3.1 Solve one-step equations with Goal 3.3: Solve whole numbers. (320.03.a) algebraic equations and CL: C inequalities.

    Calc: YES

    Content Limit: Limit to whole number

    solutions less than 100. Addition,

    subtraction, multiplication, and division are


    6.M.3.4.1 Extend simple patterns and state a 6.M.3.4.2 Describe and extend patterns by 6.M.3.4.3 Use mathematical models to show 6.M.3.4.4 Use appropriate vocabulary. Goal 3.4: rule (function) that generates the pattern using manipulatives and pictorial change in a real-world context. (323.01.c) (323.01.d) Understand the

    using whole numbers, decimals, and representations. (323.01.b) concept of fractions as inputs. (323.01.a) CL: D CL: functions. CL: D Calc: YES Calc:

    CL: E Calc: CN Content Limit: Content Limit: Assessed in the classroom,

    Calc: YES Content Limit: Models appropriate for this grade level not on the ISAT.

    Content Limit: Patterns involve adding or Pictorial only. Patterns must be growth would include graphing linear relationships

    subtracting whole numbers, decimals, or patterns not repeating patterns. Shapes used in the first quadrant on a coordinate plane.

    fractions. Fraction denominators limited to 2, may include squares and/or triangles.

    3, 4, and 5. Decimals to hundredths place.

    Items may ask the student to extend the

    pattern, state the rule for the pattern, or both.

    No objectives at this grade level. Goal 3.5:



    inequalities and

    functions in a

    variety of


    6.M.3.6.1 Use patterns to represent and solve Goal 3.6: Apply simple problems. functions to a

     variety of CL: C, D problems. Calc: YES

    Content Limit: Given an illustration of a

    pattern or a situation in words that describes

    a pattern, students extend the pattern to solve

    a problem. Patterns may involve addition,

    subtraction, or multiplication and whole

    numbers less than 100.

February, 2007 5

    Standard 4: Concepts and Principles of Geometry

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

    6.M.4.1.1 Describe 6.M.4.1.2 Draw and 6.M.4.1.3 Apply 6.M.4.1.4 Describe 6.M.4.1.5 Identify 6.M.4.1.6 Discuss the 6.M.4.1.7 Use Goal 4.1: Apply

    relationships among measure various angles fundamental concepts, reflections, translations, congruence, similarities, spatial relationship appropriate vocabulary concepts of size, types of one- and two- and shapes using properties, and and rotations on various and line symmetry of between two- and three-and symbols. (323.01.h) shape, and dimensional geometric appropriate tools. relationships among shapes. (321.01.g) shapes. (321.01.d) dimensional objects. spatial figures, using their (321.01.b) points, lines, rays, and (321.01.f) CL: relationships. defining properties. angles. (321.01.c) CL: C CL: D Calc: (321.01.a) CL: Calc: CN Calc: CN CL: Content Limit: Assessed

     Calc: CL: C Content Limit: Content Limit: Shapes Calc: in the classroom, not on CL: Content Limit: Assessed Calc: CN Describe allows for limited to two-Content Limit: Assessed the ISAT. Calc: in the classroom, not on Content Limit: Include selection of description. dimensional figures. in the classroom, not on Content Limit: Assessed the ISAT. parallel, intersecting and Rotations may be the ISAT. in the classroom, not on perpendicular lines. clockwise or

    the ISAT. Angles include acute, counterclockwise.

    right, obtuse, and Rotations are in

    straight. Symbols that increments of 90

    may be used include: degrees. Responses will

    capital letter for points, not require naming of x-

    two-headed arrow above axis or y-axis. Only one

    two capital letters for transformation per item

    lines, line segment above is allowed. Items may

    two capital letters for include a given

    line segments, one-description and a graphic

    headed arrow above two shown for each answer

    capital letters for rays, option.

    angle symbol with one

    capital letter or angle

    symbol with three

    capital letters for angles,

    and symbols for parallel,

    perpendicular, and right


    No objectives at this Goal 4.2: Apply grade level. the geometry of

    right triangles.

    February, 2007 6

6.M.4.3.1 Identify and Goal 4.3: Apply plot points in the first graphing in two quadrant on a coordinate dimensions. plane. (321.02.a)


    Calc: CN

    Content Limit:

    Coordinates are whole

    numbers. Point may be

    on positive x- or y-axis.

    Standard 5: Data Analysis, Probability, and Statistics

    Goals: Objective 1 Objective 2 Objective 3

    6.M.5.1.1 Read and interpret tables, charts, and graphs, 6.M.5.1.2 Explain and justify stated conclusions drawn from 6.M.5.1.3 Use appropriate vocabulary and notations. Goal 5.1: including broken line graphs, bar graphs, frequency tables, tables, charts, and graphs. (322.01.b) (322.01.c) Understand line plots, and circle graphs. (322.01.a) data analysis. CL: CL:

    CL: C, D Calc: Calc:

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

    Content Limit: Graphics may have at most ten data

    categories. Scales are in increments of 1, 2, 5, or 10, or must

    be consistent with real-world application. Bar graphs can be

    horizontal or vertical. Circle graphs may have at most six

    sectors. Data may be categorical or numerical.

    6.M.5.2.1 Collect, organize, and display the data with Goal 5.2: appropriate notation in tables, charts, and graphs, including Collect, broken line graphs, bar graphs, frequency tables and line organize, and plots. (322.02.a) display data.


    Calc: CR

    Content Limit: Given data, choose a display. Displays

    limited to broken line graph, bar graph, frequency table, and

    line plots. „Collect‟ data should be assessed in the classroom,

    not on the ISAT.

    February, 2007 7

6.M.5.3.1 Find measures of central tendency mean, 6.M.5.3.2 Calculate the range of a set of data. (322.03.b) Goal 5.3: Apply median, and mode with simple sets of data. (322.03.a) simple statistical measurements. CL: C CL: C

    Calc: YES Calc: CR Content Limit: At most five numbers are used to calculate Content Limit: Data set contains no more than 10 numbers.

    mean. At most nine numbers are used to calculate median Data set may include decimals to tenths. (must be an odd number of items in data set given in numeric

    order). Mode can use up to 10 numbers. When determining

    the mode, the data set must contain a unique mode. Numbers

    are less than 300.

    6.M.5.4.1 Predict, perform, and record results of simple 6.M.5.4.2 Use the language of probability. (322.04.b) Goal 5.4: probability experiments. (322.04.a) Understand CL: basic concepts of CL: C Calc: probability.

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

    Content Limit: Items using multiple trials must be done with

    replacement. Items may ask for the probability of a

    combination of outcomes (e.g., the probability of drawing a

    red marble or a green marble). Items may require the

    representation of all possible outcomes.

    6.M.5.5.1 Make predictions based on data. (318.01.c) Goal 5.5: Make predictions or CL: E decisions based Calc: YES on data. Content Limit: Data given in bar graph, circle graph, or table.

    February, 2007 8

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