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NM.A. Algebra: Students will understand algebraic concepts and applications.
5-8.A.1. Understand patterns, relations, and functions.
6.A.1.1. Solve problems involving proportional relationships.
6.A.1.2. Graph ordered pairs in the coordinate plane.
6.A.1.3. Explain and use symbols to represent unknown quantities and variable relationships.
6.A.1.4. Explain and use the relationships among ratios, proportions, and percents.
5-8.A.2. Represent and analyze mathematical situations and structures using algebraic symbols.
6.A.2.1. Solve problems involving proportional relationships.
6.A.2.2. Use letters to represent an unknown in an equation.
6.A.2.3. Solve one-step linear equations and inequalities in one variable with positive whole-number solutions.
6.A.2.4. Demonstrate that a variable can represent a single quantity that changes.
5-8.A.3. Use mathematical models to represent and understand quantitative relationships.
6.A.3.1. Develop and use mathematical models to represent and justify mathematical relationships found in a variety of situations.
6.A.3.2. Create, explain, and use mathematical models such as:
6.A.3.2.b. Equations and inequalities to model numerical relationships
5-8.A.4. Analyze changes in various contexts.
6.A.4.1. Represent and explain changes using one-step equations with one variable.
6.A.4.2. Solve problems that involve change using proportional relationships.
6.A.4.3. Use ratios to predict changes in proportional situations.
6.A.4.4. Use tables and symbols to represent and describe proportional and other relationships involving conversions, sequences, and perimeter.
6.A.4.5. Generate formulas to represent relationships involving changes in perimeter.
NM.D. Data Analysis and Probability: Students will understand how to formulate questions, analyze data, and determine probabilities.
5-8.D.1. Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.
6.D.1.1. Use statistical representations to analyze data.
6.D.1.11. Formulate and solve problems by collecting, organizing, displaying, and interpreting data.
6.D.1.3. Use mean, median, mode, and range to describe data.
6.D.1.4. Sketch circle graphs to display data.
6.D.1.5. Solve problems by collecting, organizing, displaying and interpreting data.
6.D.1.8. Determine the median for a rational number data set containing an odd number of data points.
6.D.1.9. Calculate and explain the median for a whole number data set containing an even number of data points.
5-8.D.3. Develop and evaluate inferences and predictions that are based on data.
6.D.3.2. Conduct observations, surveys, experiments and/or simulations, record the results in charts, tables, or graphs, and use the results to draw conclusions and make predictions.
6.D.3.3. Find all possible combinations in a given set (e.g., the number of ways a set of books can be arranged on a shelf).
6.D.3.4. Compare expected results with actual results in a simple experiment.
5-8.D.4. Understand and apply basic concepts of probability.
6.D.4.1. List all possible outcomes for a compound event composed of two independent events and recognize whether an outcome is certain, impossible, likely, or unlikely.
6.D.4.2. Determine and compare experimental (empirical) and mathematical (theoretical) probabilities (e.g., flipping two color counters).
6.D.4.3. Determine theoretical and experimental probabilities and use them to make predictions about events.
6.D.4.4. Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome.
6.D.4.6. Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1- P is the probability of the event not occurring.
6.D.4.7. Describe the difference between independent and dependent events and identify situations involving independent or dependent events.
NM.G. Geometry: Students will understand geometric concepts and applications.
5-8.G.1. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematics arguments about geometric relationships.
6.G.1.1. Identify, describe, and classify the properties of, and the relationships between, plane and solid geometric figures:
6.G.1.1.a. Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor, drawing software)
6.G.1.2. Classify angles as right, obtuse, or straight.
6.G.1.3. Describe the properties of geometric figures that include regular polygons, circles, ellipses, cylinders, cones, spheres, and cubes.
6.G.1.4. Classify polygons as regular or irregular.
6.G.1.6. Identify angle, line, segment, and ray and use the symbols for each.
6.G.1.7. Describe the relationship between radius, diameter, and circumference of a circle.
5-8.G.2. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
6.G.2.1. Use coordinate geometry to describe location on a plane.
NM.M. Measurement: Students will understand measurement systems and applications.
5-8.M.1. Understand measurable attributes of objects and the units, systems, and processes of measurement.
6.M.1.1. Perform multi-step conversions of measurement units to equivalent units within a given system (e.g., 36 inches equals 3 feet or 1 yard).
6.M.1.3. Select and use units of appropriate size and type to measure angles (e.g., degrees, radians), perimeter, area, and capacity in both U.S. customary and metric systems.
6.M.1.4. Use standard units of linear measurement to the nearest sixteenth of an inch; metric measurements to the nearest millimeter.
5-8.M.2. Apply appropriate techniques, tools, and formulas to determine measurements.
6.M.2.1. Apply various measurement techniques and tools, units of measure, and degrees of accuracy to find accurate rational number representations for length, liquid, weight, perimeter, temperature, and time.
6.M.2.2. Select and use formulas for perimeters of squares and rectangles.
6.M.2.4. Select and justify the selection of measurement tools, units of measure, and degrees of accuracy appropriate to the given situation.
NM.N. Numbers and Operations: Students will understand numerical concepts and mathematical operations.
5-8.N.1. Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
6.N.1.1. Compare and order rational numbers.
6.N.1.2. Use equivalent representations for rational numbers (e.g., integers, decimals, fractions, percents, ratios, numbers with whole-number exponents).
6.N.1.4. Identify greatest common factor and least common multiples for a set of whole numbers.
5-8.N.2. Understand the meaning of operations and how they relate to one another.
6.N.2.2. Factor a whole number into a product of its primes.
6.N.2.3. Demonstrate the relationship and equivalency among ratios and percents.
6.N.2.4. Use proportions to solve problems.
6.N.2.5. Explain and perform:
6.N.2.5.a. Whole number division and express remainders as decimals or appropriately in the context of the problem
6.N.2.5.b. Addition, subtraction, multiplication, and division with decimals
6.N.2.5.c. Addition and subtraction with integers
6.N.2.5.d. Addition, subtraction, and multiplication with fractions and mixed numerals
6.N.2.6. Determine the least common multiple and the greatest common divisor of whole numbers and use them to solve problems with fractions.
5-8.N.3. Compute fluently and make reasonable estimates.
6.N.3.1. Estimate quantities involving rational numbers using various estimations.
6.N.3.2. Use estimates to check reasonableness of results and make predictions in situations involving rational numbers.
6.N.3.4. Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.
6.N.3.5. Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.
6.N.3.6. Interpret and use ratios in different contexts.
6.N.3.7. Compute and perform multiplication and division of fractions and decimals and apply these procedures to solving problems.
NewPath Learning resources are fully aligned to US Education Standards. Select a standard below to view correlations to your selected resource: