GLE-Math7
COLORADO MODEL CONTENT
STANDARDS FOR MATHEMATICS
7th Grade Level Expectations
Standard 1:
Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems.
1.1 Demonstrating meanings for integers, rational numbers, percents, exponents, square roots, and pi (•) using physical materials and technology in problem-solving situations.
Seventh grade students will:
1.1.1 locate integers and positive rational numbers on the number line (for example, -6, 3/4,
1.81)
1.1.2 identify subsets of rational numbers, including counting and whole numbers and
integers
1.1.3 demonstrate the equivalence of positive fractions, decimals, and percents
1.1.4 demonstrate the relationship of the circumference to the diameter of a circle as
approximating •
1.1.5 demonstrate the meaning of square roots of perfect square numbers
1.2 Reading, writing, and ordering integers, rational numbers, and common irrational
numbers such as •2 and •5 and •.
Seventh grade students will:
1.2.1 read, write, and order integers and positive rational numbers
1.2.2 compare integers and positive rational numbers using the symbols =, •, <, >
1.3 Applying number theory concepts (for example, primes, factors, multiples) to represent numbers in various ways.
Seventh grade students will:
1.3.1 express 100 as 1
1.3.2 write rational numbers in expanded form without negative powers of ten (for example,
579.42 = 5 x 100 + 7 x 10 + 9 x 1 + 4 x 1/10 + 2 x 1/100)
1.3.3 demonstrate the divisibility rules for 2, 3, 4, 5, 6, 9, and 10
1.3.4 determine the greatest common factor and least common multiple of whole numbers
using prime factorization
1.3.5 demonstrate the meaning of an, where ‘a’ is a positive rational number and ‘n’ is a
counting number
1.4 Using the relationships among fractions, decimals, and percents, including the concepts of ratio and proportion, in problem-solving situations.
Seventh grade students will:
1.4.1 demonstrate the equivalent relationships among fractions, decimals, and percents
1.5 Developing, testing, and explaining conjectures about properties of integers and rational numbers.
Seventh grade students will:
1.5.1 demonstrate properties for integers
1.5.2 demonstrate the distributive property of multiplication over addition for whole numbers
1.6 Using number sense to estimate and justify the reasonableness of solutions to problems involving integers, rational numbers, and common irrational numbers such as •2, •5, and •.
Seventh grade students will:
1.6.1 estimate, using appropriate techniques, determine, and, then, justify the reasonableness
of solutions to problems involving positive rational numbers
Standard 2:
Students use algebraic methods to explore, model and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in solving these problems.
2.1 Representing, describing, and analyzing patterns and relationships using tables graphs, verbal rules, and standard algebraic notation.
Seventh grade students will:
2.1.1 represent, describe, and analyze patterns with positive rational numbers and integers
2.1.2 identify the algebraic terms ‘expression’, ‘equation’, ‘term’, ‘variable’,’ coefficient’,
and ‘constant’
2.3 Analyzing functional relationships to explain how a change in one quantity results in a change in another (for example, how the area of a circle changes as the radius increases, or how a person’s height changes over time).
Seventh grade students will:
2.3.1 in any functional relationship involving positive rational numbers and integers, describe how a change in one quantity affects the other
2.4 Distinguishing between linear and nonlinear functions through informal investigations.
Seventh grade students will:
2.4.1 graph discrete linear and nonlinear functions
2.4.2 graph a continuous nonlinear function for a given situation
2.5 Solving simple linear equations in problem-solving situations using a variety of methods (informal, formal and graphical) and a variety of tools (physical materials, calculators and computers).
Seventh grade students will:
2.5.1 translate written expressions or equations to algebraic expressions or equations, and
vice versa
2.5.2 using formal methods, solve one-step linear equations involving integers
2.5.3 solve linear equations with variables and constants on both sides of the equation by
informal methods using manipulatives, tables, graphs, or technology
Standard 3:
Students use data collection and analysis, statistics, and probability in
problem-solving situations and communicate the reasoning and processes used in solving these problems.
Seventh grade students will:
3.1.1 organize and display data using appropriate graphs, such as line, bar, circle, dot plots,
frequency tables, stem-and-leaf, histograms, scatter plots, and box-and-whiskers
3.1.2 read, interpret, and draw conclusions from various displays of data
3.2 Displaying and using measures of central tendency, such as mean, median, and mode, and measures of variability, such as range and quartiles.
Seventh grade students will:
3.2.1 determine the quartiles of a set of data
3.2.2 demonstrate the basic concepts of frequency distribution, percentiles, and dispersion of
data (for example, evenly distributed, one or more outliners)
3.2.3 given various displays of the same set of data (line, bar, circle, stem-and-leaf,
histograms, and box-and-whiskers), determine which measure of central tendency is
most evident
3.2.4 given sets of data, identify the most appropriate measure of central tendency which
typifies each set
3.3 Evaluating arguments that are based on statistical claims.
Seventh grade students will:
3.3.1 determine the improper computation of percent in articles or advertising
3.3.2 evaluate and correct an improperly selected measure of central tendency
3.4 Formulating hypotheses, drawing conclusions, and making convincing arguments based on data analysis.
Seventh grade students will:
3.4.1 critically evaluate survey questions and possible errors in experimental designs
3.4.2 use appropriate simulations to collect and analyze data
3.5 Determining probabilities through experiments or simulations.
Seventh grade students will:
3.5.1 demonstrate the equivalence of probabilities as either a common fraction, decimal, or
percent
3.5.2 perform experiments of independent compound events with two different chance
devices to estimate probability
3.5.3 perform experiments of sampling with replacement to estimate probability
3.6 Making predictions and comparing results using both experimental and theoretical
probability drawn from real-world problems.
Seventh grade students will:
3.6.1 predict the probability of independent compound events with two different chance
devices and conduct an experiment or simulation to determine the probability
3.6.2 demonstrate that the probability of independent compound events is the same as the
product of the probabilities of the two simple events
3.6.3 demonstrate that the sum of all the probabilities of the events in a sample space is equal
to one
3.6.4 analyze games of chance to determine whether they are fair or unfair; if unfair, decide
which player has a greater probability of winning and find that probability
3.7 Using counting strategies to determine all the possible outcomes from an experiment (for example, the number of ways students can line up to have their picture taken).
Seventh grade students will:
3.7.1 determine the number of outcomes of independent compound events involving two
different chance devices by making a list or tree diagram
Standard 4:
Students use geometric concepts, properties, and relationships in problemsolving situations and communicate the reasoning used in solving these problems.
4.1 Constructing two- and three-dimensional models using a variety of materials and tools.
Seventh grade students will:
3.4.1 using a straight edge and a compass, paper folding, or computer software application,
demonstrate the geometric construction of a perpendicular bisector of a segment
3.4.2 build models of cones, cylinders, pyramids and their nets
3.4.3 given a three-dimensional model built with cubes, use isometric dot paper to draw the
isometric drawing (that is, a drawing that shows the corner view and the top or bottom
view) and, conversely, given the isometric drawing, build the model
3.4.5 given nets, determine which would form a cube
4.2 Describing, analyzing, and reasoning informally about the properties (for example,
parallelism, perpendicularity, congruence) of two- and three-dimensional figures; and
4.3 Applying the concepts of ratio, proportion, and similarity in problem-solving situations.
Seventh grade students will:
4.3.1 describe the properties of circles (including radius and diameter)
4.3.2 recognize properties and use correct geometric symbols of overlapping geometric
figures
4.3.3 identify and reason informally about angle relationships formed by intersecting lines
(for example, adjacent and vertical angles)
4.3.4 reason informally about the properties (including lines of symmetry) of isosceles
trapezoids and pyramids
4.3.5 reason informally about the sides and angles of congruent and similar polygons
4.4 Solving problems using coordinate geometry.
Seventh grade students will:
4.4.1 set up a coordinate graph (include axes, origin, and scale) and use it to mark and read
coordinate pairs in all four quadrants
4.4.2 write a scenario from a given graph
4.4.3 enlarge figures on a coordinate plane by positive integral scale factors
4.4.4 reduce figures on a coordinate plane by the scale factor one-half
4.4.5 describe the relationship between two different points on the coordinate plane
4.4.6 given a distance, find pairs of points on the coordinate plane separated by that distance
4.5 Solving problems involving perimeter and area in two dimensions, and involving surface area and volume in three dimensions.
Seventh grade students will:
4.5.1 solve problems involving circumference and area of circles
4.5.2 solve problems involving volume of cylinders
4.5.3 solve problems involving surface area of triangular prisms
4.6 Transforming geometric figures using reflections, translations, and rotations to explore congruence.
Seventh grade students will:
4.6.1 state and justify the types of polygons which will tile a plane
4.6.2 state the coordinates to describe the translation of a figure on a coordinate plane
Standard 5:
Students use a variety of tools and techniques to measure, apply the results in problem-solving situations, and communicate the reasoning used in solving these problems.
5.1 Estimating, using, and describing measures of distance, perimeter, area, volume, capacity, weight, mass, and angle comparison.
Seventh grade students will:
5.1.1 estimate the radius and diameter of circles
5.1.2 estimate the circumference and area of circles
5.1.3 compare the perimeter and area of transformed geometric figures
5.1.4 estimate the volume of cylinders
5.1.5 estimate the surface area of triangular prisms
5.1.6 continue to estimate and use the capacity, weight, and mass measurements from
previous grades
5.1.7 estimate measures of angles
5.2 Estimating, making, and using direct and indirect measurements to describe and make comparisons.
Seventh grade students will:
5.2.1 compare the estimates and direct measurements obtained in benchmarks 5.1, 5.4, and
5.6
5.3 Reading and interpreting various scales including those based on number lines, graphs, and maps.
Seventh grade students will:
5.3.1 read and interpret scales on number lines, graphs, and maps
5.3.2 select the appropriate scale for a given problem
5.3.3 construct scale drawings
5.4 Developing and using formulas and procedures to solve problems involving measurement.
Seventh grade students will:
5.4.1 demonstrate the relationship of circumference to diameter of a circle to approximate
units
5.4.2 develop and use the formula for circumference and area of circles using appropriate
units
5.4.3 develop a procedure to find the area and perimeter of irregularly-shaped polygons
5.4.4 develop and use the formula for volume of cylinders using appropriate units
5.5 Describing how a change in an object’s linear dimensions affects its perimeter, area, and volume.
Seventh grade students will:
5.5.1 describe how changes in the base of a parallelogram and rhombus affect its area when
its height is constant
5.5.2 describe how scale factor changes in the dimensions of a rectangular prism affect its
volume
5.5.3 describe how changes in the distance between the bases of a triangular prism affect its
volume
5.6 Selecting and using appropriate units and tools to measure to the degree of accuracy required in a particular problem-solving situation.
Seventh grade students will:
5.6.1 select and use the appropriate units and tools to measure to the degree of accuracy
required in a particular problem
5.6.2 measure the radius and diameter of circles to the nearest sixteenth inch and nearest
millimeter
5.6.3 using a protractor, measure angles of adjacent and vertical angles of intersecting lines
Standard 6:
Students link concepts and procedures as they develop and use computational techniques, including estimation, mental arithmetic, paper-and-pencil, calculators, and computers, in problem-solving situations and communicate the reasoning used in solving these problems.
6.1 Using models to explain how ratios, proportions, and percents can be used to solve realworld problems.
Seventh grade students will:
6.1.1 demonstrate equivalence of fractions, decimals, and percents using proportions
6.1.2 solve real-world problems using appropriate and convenient forms of fractions,
decimals, and percents
6.2 Constructing, using, and explaining procedures to compute and estimate with whole numbers, fractions, decimals, and integers.
Seventh grade students will:
6.2.1 demonstrate order of operations with positive rational numbers and integers
6.2.2 choose the appropriate representation of the remainder in a division problem
6.2.3 using paper-and-pencil, demonstrate with proficiency computation of fractions
6.2.4 using paper-and-pencil, demonstrate with proficiency the four basic operations of
decimals
6.2.5 demonstrate the inverse relationship of multiplication and division of decimals
6.2.6 demonstrate the meaning of the four basic operations of integers
6.2.7 using paper-and-pencil, demonstrate proficiency in computation of integers
6.2.8 demonstrate the inverse relationship of addition and subtraction of integers
6.2.9 demonstrate the inverse relationship of multiplication and division of integers
6.2.10 demonstrate multiplication of integers as repeated addition
6.2.11 using paper-and-pencil, solve real-world problems involving percents
6.3 Developing, applying and explaining a variety of different estimation strategies in problemsolving situations, and explaining why an estimate may be acceptable in place of an exact answer.
Seventh grade students will:
6.3.1 determine from real-world problems whether an estimated or exact answer is acceptable
6.3.2 use estimation techniques before performing operations
6.4 Selecting and using appropriate methods for computing with commonly-used fractions and decimals, percents, and integers in problem-solving situations from among mental arithmetic, estimation, paper-and-pencil, calculator, and computer methods, and determining whether the results are reasonable.
Seventh grade students will:
6.4.1 determine whether information given in a problem-solving situation is sufficient,
insufficient, or extraneous
6.4.2 given a real-world problem-solving situation, use the correct operation and appropriate
method (mental arithmetic, estimation, paper-and-pencil, calculator, or computer) to
solve the problem
6.4.3 given a math sentence using the four operations with positive rational numbers and
integers, create and illustrate a real-world problem
6.4.4 in a problem-solving situation, determine whether the results are reasonable and justify
those results with correct computations