MATH CURRICULUM
Seventh Grade
March 2002

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Standard 1: The student uses numerical and computational concepts and procedures in a variety of situations. 

Benchmark 1: NUMBER SENSE - The student demonstrates number sense for rational numbers, pi, and simple algebraic expressions in one variable in a variety of situations.

Seventh Grade Knowledge Base Indicators
The student:

  1. compares and orders rational numbers and pi, and explains the relative magnitude among them.
    Special Note: Remember, rational numbers include large numbers such as one million and small numbers such as one thousandth.
  2. knows, explains, and uses equivalent representations for rational numbers: integers, decimals, fractions, percents, ratios, numbers with whole number exponents, and scientific notation.
  3. explains and determines the absolute value of rational numbers.
  4. knows, explains, and uses equivalent representations for the same simple algebraic expressions such as 2x + 5x could be written as 7x. 
  5. knows and explains what happens to the product or quotient when a number is multiplied or divided by a number between zero and one or a number greater than one.

Seventh Grade Application Indicators
 The student:

  1. uses appropriate representations of rational numbers, pi, and simple algebraic expressions to formulate and solve real-world problems.
    For the purpose of assessing this indicator on the Kansas Assessment the student should be able to use equivalent representations for rational numbers: integers, decimals, fractions, percents, ratios, numbers with whole number exponents, and scientific notation. 
    Special Note: Remember, rational numbers include large numbers such as one million and small numbers such as one-thousandth.
  2. determines reasonableness of solutions to problems involving rational numbers, pi and simple algebraic expressions.

Benchmark 2: NUMBER SYSTEMS AND THEIR PROPERTIES - The student demonstrates an understanding of the rational number system and pi, recognizes, applies, and explains its properties, and extends these properties to algebraic expressions in one variable.

Seventh Grade Knowledge Base Indicators
The student:

  1. recognizes the need for rational numbers and pi.
  2. classifies rational numbers as members of various number systems.
  3. knows or explains the relationships among natural (counting) numbers, whole numbers, integers, and rational numbers (models include number lines, Venn diagrams).
  4. knows the correct terminology for, explains, and uses: addition and multiplication properties of equality; commutative, associative, distributive, and substitution properties, additive and multiplicative identity properties; additive and multiplicative inverse properties; multiplicative property of zero; transitive, reflexive and symmetric properties; transitive property of inequality; and the addition property of inequality.

Seventh Grade Application Indicators
 The student:

  1. uses properties of the rational number system and pi to explain reasoning, and to formulate and solve real-world problems.
    For the purpose of assessing this indicator on the Kansas Assessment the student should be able to use any of the following properties: addition and multiplication properties of equality; commutative, associative, distributive, and substitution properties, additive and multiplicative identity properties; additive and multiplicative inverse properties; multiplicative property of zero; transitive, reflexive and symmetric properties; transitive property of inequality; and the addition property of inequality.
  2. uses rational number properties to perform various computational procedures and explains how they were used.

Benchmark 3: ESTIMATION - The student uses numerical estimation with 
rational numbers and pi in a variety of situations.

Seventh Grade Knowledge Base Indicators
 The student:

  1. uses a variety of computational methods including mental mathematics, paper and pencil, concrete materials, or technological tools such as calculators and computers to estimate quantities involving rational numbers and pi.
  2. estimates quantities involving rational numbers and pi using various estimation techniques such as rounding, special numbers, clustering, truncation, and compatible numbers.
  3. recognizes and explains the difference between exact and approximate values of rational numbers and pi.
  4. discusses the appropriateness of the estimation strategy used and its impact on the result.

Seventh Grade Application Indicators
 The student:

  1. uses estimation to check reasonableness of results, and makes predictions in situations involving rational numbers, pi and simple algebraic expressions.
    For the purpose of assessing this indicator on the Kansas Assessment the student should be able to estimate quantities involving rational numbers and pi using various estimation techniques such as rounding, special numbers, clustering, truncation, and compatible numbers.
  2. determines if a problem situation calls for an exact or approximate answer and performs the appropriate computation with rational numbers and pi. See benchmark 4 for computation expectations.

Benchmark 4: COMPUTATION - The student explains and performs computations with rational numbers, pi and first degree algebraic expressions in one variable in a variety of situations.

Seventh Grade Knowledge Base Indicators
The student:

  1. uses a variety of computational methods including mental arithmetic (doubles and neighbors), paper and pencil, concrete materials, or technological tools such as calculators and computer.
  2. explains and performs computations with rational numbers, pi, and first degree algebraic expressions in one variable. 
    For the purpose of assessing this indicator on the Kansas Assessment the student should be able to perform the following computations without the aid of calculators, abacuses, or computers: addition, subtraction, multiplication and division of rational numbers with a special emphasis on fractions. simplification of expressions using the correct order of operations, express answers in simplest form, find percentages of numbers, find roots of perfect whole number squares, simplification and evaluation of positive rational numbers raised to positive whole number powers. Although not assessed on the Kansas Assessment, the student also explains and performs the following computations: combine like terms of a first degree algebraic expression in one variable, find roots of perfect whole number cubes intuitively.
  3. recognizes, explains, and uses different ways to express arithmetic operations.
  4. analyzes and explains computational procedures including the use of more than one arithmetic approach to perform a computation such as 49x23 = (40x23)+(9x23) or 49x23 = (49x20) + (49x3) or 49x23 = (50x23) - 23.

Seventh Grade Application Indicators
 The student:

1. uses arithmetic operations and inverse relationships to formulate and solve real-world problems involving rational numbers, pi and first degree algebraic expressions in one variable. 
For the purpose of assessing this indicator on the Kansas Assessment the student should be able to perform the following computations: addition, subtraction, multiplication and division of rational numbers with a special emphasis on fractions, simplification of expressions using the correct order of operations, express answers in simplest form, find percentages of numbers, simplification and evaluation of positive rational numbers raised to positive whole number powers.

Standard 2: The student uses algebraic concepts and procedures in a  variety of situations.

Benchmark 1: PATTERNS - The student recognizes, describes, extends, develops, and explains the general rule of patterns from a variety of situations.

Seventh Grade Knowledge Base Indicators
The student:

  1. identifies and continues patterns presented in a variety of formats: numeric, algebraic, visual, oral, written, kinesthetic, pictorial, tabular, graphical, or listing. 
    For the purpose of assessing this indicator on the Kansas Assessment the student should be able to work with the following types of patterns: rational number patterns, patterns established by using units of measure, patterns based on geometric shapes, simple arithmetic and geometric sequences involving whole numbers, patterns occurring in nature, number patterns involving squares, cubes, and reciprocals, numerical and geometric patterns including perfect squares, multiples, and arithmetic sequences using grade appropriate numbers.
  2. recognizes patterns with two simultaneous changes.
  3. creates a pattern.

Special Note: Working with various types of patterns is an important 
precursor to working with functions and sequences in high school.

Seventh Grade Application Indicators
 The student:

  1. generalizes a pattern by using a written description. 
    For the purpose of assessing this indicator on the Kansas Assessment the student should be able to work with the following types of patterns: rational number patterns, patterns established by using units of measure, patterns based on geometric shapes, simple arithmetic and geometric sequences involving whole numbers, patterns occurring in nature, number patterns involving squares, cubes, and reciprocals, numerical and geometric patterns including perfect squares, multiples, and arithmetic sequences using grade appropriate numbers.

Benchmark 2: VARIABLES, EQUATIONS, AND INEQUALITIES - The student uses variables, symbols, rational numbers, and simple algebraic expressions in one variable to solve linear equations and inequalities in a variety of situations.

Seventh Grade Knowledge Base Indicators
The student:

  1. knows and explains that a variable can represent a single quantity that changes such as daily temperature.
  2. shows and explains how changes in one variable affects other variables such as changes in diameter affects circumference
  3. explains the difference between an equation and an expression.
  4. explains and uses the following words and symbols to represent relationships such as <, <, >, >, =, ≠, and greater than or equal to.
  5. solves two-step linear equations in one variable with whole number coefficients and constants, and positive rational solutions.
  6. solves two-step linear inequalities in one variable with whole number coefficients and constants, and positive rational solutions intuitively, analytically, and graphically such as 2x + 1 > 9.
  7. solves one-step linear equations in one variable.
  8. evaluates formulas using substitution.
  9. knows and explains the relationship between ratios, proportions and percents including solving for a missing term in a proportion.
  10. represents solution sets of linear equations in two variables on the coordinate plane.

Seventh Grade Application Indicators
 The student:

  1. uses symbols, variables, expressions, inequalities, equations and simple systems of equations to represent problem situations which involve variable or unknown quantities.
  2. formulates and solves problems involving simple linear relationships, finding percents of a given number, variable situations and unknown quantities.
    For the purpose of assessing this indicator on the Kansas Assessment the student should be able to solve two-step linear equations in one variable with whole number coefficients and constants, and positive rational solutions as well as two-step linear inequalities in one variable with whole number coefficients and constants, and positive rational solutions intuitively, analytically, and graphically.

Benchmark 3: FUNCTIONS - The student recognizes, describes, and 
examines constant and linear relationships in a variety situations.

Seventh Grade Knowledge Base Indicators
The student:

  1. uses a variety of methods including mental mathematics, paper and pencil, concrete materials, and graphing utilities or other technological tools to recognize and examine constant and linear relationships.
  2. explains or gives examples of relationships which remain constant.
  3. uses ordered pairs to demonstrate relationships.

Seventh Grade Application Indicators
 The student: 

  1. represents a variety of relationships using tables, graphs, verbal rules and when possible symbolic notation. 
  2. converts between numerical, tabular, graphical and verbal rules used to represent relationships.

Benchmark 4: MODELS - The student develops and uses models to 
represent and justify mathematical relationships found in a variety of 
situations.

Seventh Grade Knowledge Base Indicators
The student:

  1. identifies mathematical models to show the relationship between two or more things.
    For Kansas assessment purposes the student could be asked to work with the following types of models: the number line to model the relationship between rational numbers or rational number operations. Venn Diagrams to show the relationship between characteristics of two or more sets, graphs, tables, and charts to organize, interpret or analyze rational number data, scale drawings, three-dimensional geometric models, the coordinate plane to model ordered pairs and linear equations, diagrams, flowcharts, or pictures to represent problem situations. 
    Although not assessed on the Kansas assessments, additional models for the student to know, explain, and use are: equations and inequalities to model numerical relationships between data sets, tessellations to reinforce patterns, area, and transformations, geometric or numerical models to reinforce probability, concrete materials to model the relationship between decimals, percents and fractions, manipulatives to model computation, factor trees, pictures and diagrams to model division of rational numbers.

Seventh Grade Application Indicators
The student:

  1. recognizes that the same situation can be represented in more than one way such as using a table of values, a graph or an equation to represent the amount of money it would take to buy x number of CD's if CD's were $10 each.
  2. explains why some models are more accurate than others in certain situations.
  3. uses the mathematical modeling process to make inferences about real world situations when the mathematical model used to represent the situation is given.
    Special Note: The mathematical modeling process involves:
    1. selecting key features and relationships within the real world situation and representing these concepts in mathematical terms through some sort of mathematical model; 
    2. performing manipulations and mathematical procedures within the mathematical model; 
    3. interpreting the results of the manipulations within the mathematical model and using these results to make inferences about the original real-world situation. 

Standard 3: The student uses geometric concepts and procedures in a variety of situations.

Benchmark 1: GEOMETRIC FIGURES AND THEIR PROPERTIES - The student 
recognizes, applies, and compares properties of geometric figures in a 
variety of situations.

Seventh Grade Knowledge Base Indicators
 The student:

  1. recognizes and uses properties of all geometric figures listed previously, plus the following figures: trapezoid and parallelogram.
  2. classifies triangles as scalene, isosceles, equilateral, acute, right, obtuse, and equiangular, and polygons as regular, irregular, and/or by the number of sides.
  3. recognizes or applies properties of corresponding parts of similar and congruent triangles and quadrilaterals.
  4. uses symbols for perpendicular, parallel, triangle, and right angle. 
  5. uses appropriate technology, manipulatives, constructions or drawings to recognize or compare geometric figures.

Seventh Grade Application Indicators
 The student:

  1. formulates and solves real-world problems by applying properties of geometric figures.
    For the purpose of assessing this indicator on the Kansas Assessment the student is able to:
  1. apply angle and side properties of squares, rectangles, triangles, trapezoids, and parallelograms such as the opposite sides of a parallelogram are equal and parallel or a right triangle has one angle which is 90 or the sum of the angles of a triangle equals 180. Students do NOT need to be able to use the Pythagorean theorem.
  2. classify triangles as scalene, isosceles, equilateral, acute, right, obtuse, and equiangular, and polygons as regular, irregular, and/or by the number of sides. 
  3. use symbols for perpendicular, parallel, triangle, and right angle.
  4. use drawings to recognize or compare geometric figures.
  5. determine the radius or diameter of a circle.

Benchmark 2: MEASUREMENT AND ESTIMATION - The student estimates, 
measures, and uses measurement formulas in a variety of situations.

Seventh Grade Knowledge Base Indicators
The student:

  1. uses various estimation techniques to determine rational number approximations of length, volume, surface area, area, perimeter, weight, capacity, temperature or time.
  2. recognizes, states and uses measurement formulas for perimeter and area of parallelograms, triangles, squares, rectangles, and circles plus the volume of a cube.
  3. applies measurement formulas which are given to three-dimensional figures including surface area of cubes and volume and surface area of rectangular prisms.
  4. finds area and perimeter of two-dimensional figures composed of squares, rectangles, triangles, and circles.
  5. applies various measurement techniques and uses appropriate tools, units of measure and degree of accuracy to find accurate rational number representations for length, volume, surface area, area, perimeter, weight, temperature and time.
  6. uses appropriate units to describe rate as a unit of measure such as miles per hour.
  7. finds missing angle measurements in triangles and quadrilaterals.
  8. performs conversions within the standard measurement system. 
  9. performs conversions within the metric 
    measurement system.

Seventh Grade Application Indicators
 The student:

  1. formulates and solves real-world problems by applying measurements and measurement formulas. For the purpose of assessing this indicator on the Kansas Assessment the student should be able to:
    1. recognize, state, and use measurement formulas for perimeter and area of parallelograms, triangles, squares, rectangles, and circles plus the volume of a cube.
    2. apply measurement formulas which are given to three-dimensional figures including surface area of cubes and volume and surface area of rectangular prisms.
    3. find area and perimeter of two-dimensional figures composed of squares, rectangles, triangles, and circles.
    4. apply various measurement techniques and uses appropriate tools, units of measure and degree of accuracy to find accurate rational number representations for length, volume, surface area, area, perimeter, weight, temperature and time.
    5. use appropriate units to describe rate as a unit of measure. example: miles per hour
    6. find missing angle measurements in triangles and quadrilaterals.
    7. perform conversions within the standard or metric measurement system.
  2. uses estimation to check reasonableness of measurements and calculations and/or adjusts original measurements based on additional information (estimation from a frame of reference).

Benchmark 3: TRANSFORMATIONAL GEOMETRY - The student recognizes and performs transformations of two-dimensional figures in a variety situations.

Seventh Grade Knowledge Base Indicators
 The student:

  1. recognizes, describes, and performs single and multiple transformations [rotation, reflection, translation, shrink or magnify (dilate)] on two-dimensional figures.
  2. recognizes and draws three-dimensional shapes as they would appear from a variety of visual perspectives (top, bottom, side, and corners).

Seventh Grade Application Indicators
 The student:

  1. uses a scale drawing to determine the actual dimensions/measurements of the figure represented in the drawing. 
  2. explains the impact of transformation on area and perimeter of squares and rectangles.

Benchmark 4: GEOMETRY FROM AN ALGEBRAIC PERSPECTIVE - The student will analyze two-dimensional geometry using a coordinate system in a variety of situations.

Seventh Grade Knowledge Base Indicators
 The student:

  1. uses a variety of methods including mental mathematics, paper and pencil, concrete materials, graphing utilities and other technological tools to analyze two-dimensional geometry on the coordinate system.
  2. uses the coordinate plane to:
    1. identify in which quadrant or on which axis a point lies when given the coordinates of the point.
    2. graph or identify points on the coordinate plane in all four quadrants.
    3. determine if a given point is on the line given the graph of the line.
    4. list up to five coordinate pairs on the graph of a line and then state the pattern that exists.
  3. finds the distance between the points on a number line by computing the absolute value of their difference.

Seventh Grade Application Indicators
 The student:

  1. represents, formulates and solves distance problems using a number line.
  2. represents, formulates and solves area and perimeter problems involving squares, rectangles, and triangles on the coordinate plane.
  3. represents, formulates and solves real world geometry problems by using algebraic notation, equations, or inequalities.

Standard 4: The student uses concepts and procedures of data analysis 
in a variety of situations.


Benchmark 1: PROBABILITY - The student uses probability to generate 
convincing arguments, draw conclusions, and make decisions in a variety of situations.

Seventh Grade Knowledge Base Indicators
 The student:

  1. determines the probability of a compound event composed of two independent events.
  2. explains and gives examples of events having probability of one or zero. 
  3. describes probability of events using fractions, decimals and percents. 
    For the purpose of assessing this indicator on the Kansas Assessment the student should be able to determine the probability of a simple event or a compound event composed of two simple, independent events.

Seventh Grade Application Indicators
 The student:

  1. conducts experiments and/or simulations, records the results in charts, tables or graphs, and uses the results to draw conclusions and make predictions.
  2. compares theoretical (expected) results with empirical (experimental) results. 
  3. makes predictions based on theoretical probabilities of compounded events.

Benchmark 2: STATISTICS - The student generates, organizes, and 
interprets rational number and other data in a variety of situations. 
The student applies measures of central tendency when drawing 
conclusions from the data.

Seventh Grade Knowledge Base Indicators
 The student:

  1. organizes, displays and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized and accurate manner including the use of correct titles, labels, and intervals or categories. Specific formats for the display of rational number data and other types of data include: frequency distributions, box-and-whiskers plots, stem-and-leaf plots, scatterplots, bar, line, and circle graphs, Venn diagrams or other pictorial displays, charts and tables. 
  2. determines the measures of central tendency (mean, median, and mode), and the range for a rational number data set containing an even or odd number of data points.
  3. determines and explains the advantages and disadvantages of using each measure of central tendency and the range to describe a data set.

Seventh Grade Application Indicators
 The student: 

  1. uses data analysis to make accurate inferences, decisions/predictions, and to develop convincing arguments from data displayed in a variety of formats. (see listing of graphical displays) 
    For the purpose of assessing this indicator on the Kansas Assessment the student should be able to:
    1. work with the following data displays, frequency distributions,box-and-whiskers plots, stem-and-leaf plots, scatterplots, bar, line, and circle graphs, Venn diagrams or other pictorial displays, charts and tables. 
    2. use any of the following statistical measures: measures of central tendency (mean, median, and mode), quartiles, and the range for a rational number data set containing an even or odd number of data points.
    3. use various scales and formats to display the same data set.
  2. recognizes or explains the affects of scale and/or interval changes on graphs of data sets.
  3. recognizes and explains misleading representations of data.