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Students know the properties of rational and irrational numbers expressed in a variety of forms. They understand and use exponents, powers, and roots. 8.1.1 Read, write, compare, and solve problems using decimals in scientific notation.
8.1.2 Know that every rational number is either a terminating or repeating decimal and that every irrational number is a non-repeating decimal.
8.1.3 Understand that computations with an irrational number and a rational number (other than zero) produce an irrational number.
8.1.4 Understand and evaluate negative integer exponents.
8.1.5 Use the laws of exponents for integer exponents.
8.1.7 Calculate and find approximations of square roots. Quiz, Flash Cards, Worksheet, Game & Study Guide Real numbers
Students compute with rational numbers expressed in a variety of forms. They solve problems involving ratios, proportions, and percentages. 8.2.1 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) in multi-step problems.
8.2.2 Solve problems by computing simple and compound interest.
8.2.4 Use mental arithmetic to compute with common fractions, decimals, powers, and percents.
IN.8.3.Algebra and Functions
Students solve simple linear equations and inequalities. They interpret and evaluate expressions involving integer powers. They graph and interpret functions. They understand the concepts of slope and rate. 8.3.1 Write and solve linear equations and inequalities in one variable, interpret the solution or solutions in their context, and verify the reasonableness of the results.
8.3.2 Solve systems of two linear equations using the substitution method and identify approximate solutions graphically.
8.3.3 Interpret positive integer powers as repeated multiplication and negative integer powers as repeated division or multiplication by the multiplicative inverse.
8.3.4 Use the correct order of operations to find the values of algebraic expressions involving powers.
8.3.5 Identify and graph linear functions, and identify lines with positive and negative slope.
8.3.7 Demonstrate an understanding of rate as a measure of one quantity with respect to another quantity.
8.3.9 Represent simple quadratic functions using verbal descriptions, tables, graphs, and formulas, and translate among these representations. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
Students deepen their understanding of plane and solid geometric shapes and properties by constructing shapes that meet given conditions, by identifying attributes of shapes, and by applying geometric concepts to solve problems. 8.4.1 Identify and describe basic properties of geometric shapes: altitudes, diagonals, angle bisectors, perpendicular bisectors, central angles, radii, diameters, and chords of circles.
8.4.3 Identify properties of three-dimensional geometric objects (e.g., diagonals of rectangular solids) and describe how two or more figures intersect in a plane or in space.
8.4.4 Draw the translation (slide), rotation (turn), reflection (flip), and dilation (stretches and shrinks) of shapes.
8.4.5 Use the Pythagorean Theorem and its converse to solve problems in two and three dimensions.
Students convert between units of measure and use rates and scale factors to solve problems. They compute the perimeter, area, and volume of geometric objects. They investigate how perimeter, area, and volume are affected by changes of scale. 8.5.2 Solve simple problems involving rates and derived measurements for such attributes as velocity and density.
8.5.3 Solve problems involving scale factors, area, and volume using ratio and proportion.
8.5.4 Use formulas for finding the perimeter and area of basic two-dimensional shapes and the surface area and volume of basic three-dimensional shapes, including rectangles, parallelograms, trapezoids, triangles, circles, prisms, cylinders, spheres, cones, and pyramids.
IN.8.6.Data Analysis and Probability
Data Analysis and Probability
Students collect, organize, represent, and interpret relationships in data sets that have one or more variables. They determine probabilities and use them to make predictions about events. 8.6.2 Identify different methods of selecting samples, analyzing the strengths and weaknesses of each method, and the possible bias in a sample or display.
8.6.3 Understand the meaning of, and be able to identify or compute the minimum value, the lower quartile, the median, the upper quartile, the interquartile range, and the maximum value of a data set.
8.6.4 Analyze, interpret, and display single- and two-variable data in appropriate bar, line and circle graphs, stem-and-leaf plots and box-and-whisker plots, and explain which types of display are appropriate for various data sets.
8.6.5 Represent two-variable data with a scatterplot on the coordinate plane and describe how the data points are distributed. If the pattern appears to be linear, draw a line that appears to best fit the data, and write the equation of that line.
8.6.6 Understand and recognize equally likely events.
8.6.7 Find the number of possible arrangements of several objects by using the Basic Counting Principle.
Students determine when a solution is complete and reasonable, and move beyond a particular problem by generalizing to other situations. 8.7.11 Decide whether a solution is reasonable in the context of the original situation.
8.7.12 Note the method of finding the solution and show a conceptual understanding of the method by solving similar problems.
Students use strategies, skills, and concepts in finding and communicating solutions to problems. 8.7.10 Make precise calculations and check the validity of the results in the context of the problem.
8.7.4 Apply strategies and results from simpler problems to solve more complex problems.
8.7.5 Make and test conjectures by using inductive reasoning.
8.7.6 Express solutions clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work.
8.7.7 Recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
Students make decisions about how to approach problems and communicate their ideas. 8.7.1 Analyze problems by identifying relationships, telling relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
8.7.2 Make and justify mathematical conjectures based on a general description of a mathematical question or problem.
8.7.3 Decide when and how to divide a problem into simpler parts.