MA8.5 Standards
From Brush Schools Wiki
Go back to main Math page.
Colorado Model Content Standards: Algebra 1/2
1. Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems.
1.1a Compare and order sets of rational numbers and common irrational numbers (v2, v5, and p.).
1.1b Recognize and use equivalent representations of rational numbers and common irrational numbers (v2, v5, and p.), including scientific notation.
1.2 Develop, test, and conjectures* about the properties of number systems and sets of numbers.
1.2a Verify and apply the properties of the operation “to the power of” (for example, 23 = 8, 22 = 4, 21= 2, 20 = ___, 2-1 = ___2-2 = ___ ).
1.3 Use number sense to estimate and justify the reasonableness of solutions to problems involving real numbers.
1.3a Use number sense to estimate and justify the reasonableness of solutions to problems involving rational numbers and common irrational numbers (for example, circumference, area of a circle, and Pythagorean Theorem).
1.6b Product of prime numbers. ES
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 Model real world phenomena (for example, distance-versus-time relationships, compound interest, amortization tables, mortality rates) using functions*, equations, inequalities, and matrices*.
2.1a Model* real world phenomena involving linear and non-linear relationships using multiple repre-sentations of rules that can take the form of recursive processes, functions, equations, or inequalities.
2.2 Represent functional relationships using written explanations, tables, equations, and graphs and describe the connections among these representations.
2.2a Represent functional relationships using written explanations, tables, equations, and graphs, and describe the connections among these representations.
2.2b Convert from one functional representation to another.
2.2c Interpret a graphical representation of a real-world situation.
2.3 Solve problems involving functional relationships using graphing calculators and/or computers as well as appropriate paper-and-pencil techniques.
2.3a Solve problems involving functions and relations using calculators, graphs, tables, and algebraic methods*.
2.3b Solve simple systems of equations using algebraic, graphical or numeric methods.
2.3c Solve equations with more than one variable* for a given variable (for example, solve for p in 1= prt or for r in C=2pr).
2.4 Analyze and explain the behaviors, transformations*, and general properties of types of equations and functions (for example, linear*, quadratic*, exponential*).
2.4a Identify and interpret x and y intercepts in the context of a problem.
2.4b Using a graph, identify the maximum and minimum value within a given domain.
2.4c Analyze the effects of change in the leading coefficient and/or the vertical translation (for example, given y = kx² + c, how do changes in k and/or c affect the graphs?
2.5 Interpret algebraic equations and inequalities geometrically and describe geometric relationships algebraically.
2.5a Graph solutions to equations and inequalities in one-and two-dimensions and determine solutions. ES
2.5b Express the perimeter, area and volume* relationships of geometric figures algebraically.
2.7c Solve simple multistep equations. ES
3 Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning used in solving these problems.
3.1 Design and conduct a statistical experiment to study a problem, and interpret and communicate the results using the appropriate technology (for example, graphing calculators, computer software).
3.1a Identify factors which may have affected the outcome of a survey (for example, biased questions or collection methods).
3.1b Using large populations, formulate hypothesis, draw conclusions, and make convincing arguments based on data analysis.
3.1c Select and use an appropriate display to represent and describe a set of data (for example, scatter plot, line graph and histogram).
3.2 Analyze statistical claims for erroneous conclusions or distortions.
3.2a Analyze a graph, table, or summary for misleading characteristics.
3.2b Recognize the misuse of statistical data in written arguments.
3.3 Fit curves to scatter plots using informal methods or appropriate technology to determine the strength of the relationship between two data sets and to make predictions.
3.3a Fit curves to scatter plots using informal methods or appropriate technology to make predictions about the data.
3.3b Fit curves to scatter plots using informal methods or appropriate technology to determine the type (positive, negative, or non-existent) of relationship between two data sets.
3.4 Draw conclusions about distributions of data based on analysis of statistical summaries (for example, the combination of mean and standard deviation, and differences between the mean and median).
3.4b Use averages (including averages per trial, expected value) to draw conclusions about distributions of data (for example, if there are 10 people with one five dollar bill and one dollar bill in their wallets and they each randomly place one of the bills in a donation box, what will be the average amount of money donated per person?).
3.5 Use experimental and theoretical probability* to represent and solve problems involving uncertainty (for example, the chance of playing professional sports if a student is a successful high school athlete).
3.5a Determine the probability of an identified event using the sample space.
3.5b Make predictions using theoretical probability in real-world problems.
3.5c Use a model (list, tree diagram, area model) to determine theoretical probabilities to solve problems involving uncertainty.
3.6 Solve real-world problems* with informal use of combinations* and permutations* for example, determining the number of possible meals at a restaurant featuring a given number of side dishes).
3.6a Solve real-world problems with informal use of combinations and permutations (for example, determining the number of possible meals at a restaurant featuring a given number of side dishes).
4&5 4. Students use geometric concepts, properties, and relationships in problem-solving situations and communicate the reasoning used in solving these problems.
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.
4.1 Find and analyze relationships among geometric figures using transformations (for example, reflections*, translations*, rotations*, dilations*) in coordinate systems*.
4.1a Find and analyze relationships among geometric figures using transformation (for example, reflections, translation, rotations, dilation) in coordinate systems.
4.2 Derive and use methods to measure perimeter, area, and volume of regular and irregular geometric figures.
4.2a Solve problems involving perimeter, area, and volume of regular and irregular geometric figures. ES
4.2b Use the Pythagorean theorem to solve real-world problems.
4.3 Make and test conjectures about geometric shapes and their properties, incorporating technology where appropriate.
4.3a Make and test conjectures about geometric shapes and their properties (for example, parallelism, perpendicularity, similarity, congruence, symmetry).
4.3b Use coordinate geometry to solve problems involving shapes and their properties.
5.1 Measure quantities indirectly using techniques of algebra*, geometry, or trigonometry.
5.1a Use appropriate measurements to solve problems indirectly (for example, find the height of a flagpole using similar triangles.
5.1b Use measurement to solve real-world problems involving rate of change (for example, distance traveled using rate and time).
5.1c Describe how changing one attribute of a shape affects its angle measure, perimeter, circumference, area, surface area and volume.
5.2 Select and use appropriate tools and techniques to measure quantities in order to achieve specified degrees of precision, accuracy and error (or tolerance) of measurements.
5.2a Select and use appropriate tools and techniques to measure quantities in order to achieve specified degrees of precision, accuracy, and error (or tolerance) of measurements.
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 Use ratios, proportions, and percents in problem solving situations. ES
6.1a Use ratios, proportions, and percents in problem solving situations that involve rational numbers.
6.1b Convert from one set of units to another using proportions (for example, feet/minute to miles/hour). ES
6.1c Apply direct variation to problem solving situations.
6.2 Select and use appropriate methods for computing with real numbers in problem-solving situations from among mental arithmetic*, estimation, paper-and-pencil, calculator, and computer methods, and determine whether the results are reasonable.
6.2a Apply appropriate computational methods to solve multi-step problems involving rational numbers. ES
