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Number and Operations 1. Demonstrate computational fluency with addition, subtraction, and multiplication of integers. Developing algorithms for performing operations on integers Using inverse properties of addition and of multiplication Practice site—computational fluency (choose operation) 2. Use order of operations to evaluate numerical expressions. Computing absolute values Finding square roots of perfect squares through 225 Evaluating powers Applying properties of operations to compute with integers, fractions, and decimals Order of Operations Four (game) 3. Solve problems requiring the use of operations on rational numbers. Describing the method used Determining the reasonableness of results Using percents to solve problems, including problems involving discounts, taxes, commissions, and simple interest Algebra 4. Express a pattern shown in a table, graph, or chart as an algebraic equation. Recognizing the relationships between numerical patterns in tables and their respective graphs in the coordinate plane Determining if a constant rate of change exists in a pattern 5. Translate verbal phrases into algebraic expressions and algebraic expressions into verbal phrases. Exhibiting understanding of a variable as an unknown quantity 6. Solve one- and two-step equations. Solving inequalities in one variable Graphing solution sets of inequalities on a number line Recognizing properties of equality Geometry 7. Determine the transformation(s), including translations, reflections, or rotations, used to alter the position of a polygon on the coordinate plane. Determining the type of symmetry (rotational or line) found in a reflection or rotation Graphing transformations of quadrilaterals on the Cartesian plane by plotting the vertices Graphing figures which are similar to other figures using dilations 8. Recognize geometric relationships among two-dimensional and three-dimensional objects. Drawing geometric figures when given specified components, including base and height Investigating properties and relationships among congruent figures Identifying geometric ideas in settings outside the mathematics classroom Examples: recognizing Escher drawings as examples of tessellations, the geodesic dome as an example of triangulation, and architecture as an example of constructing three-dimensional shapes; identifying landscape design as an example of area Using networks to represent and solve problems Measurement 9. Solve problems involving circumference and area of circles. Estimating circumference, diameter, and area Determining appropriate units of measure to describe circumference, diameter, and area Measuring circumference and diameter using customary and metric units Using circumference and diameter to approximate the value of π Identifying π as an irrational number Developing formulas for determining circumference and area 10. Find the perimeter of polygons and the area of triangles and trapezoids. Developing formulas for determining perimeter and area of triangles and trapezoids 11. Solve problems involving ratios or rates, using proportional reasoning. Determining the unit rate Converting rates from one unit to another Example: determining the number of minutes in three days Converting units of length, weight, or capacity from metric to customary and from customary to metric Data Analysis and Probability 12. Determine measures of central tendency (mean, median, and mode) and the range using a given set of data or graphs, including histograms, frequency tables, and stem-and-leaf plots. Creating histograms 13. Determine the probability of a compound event. Example: finding the probability of selecting at random a hamburger and lemonade when choosing a sandwich and drink from two sandwich choices and three drink choices Representing outcomes as a list, chart, picture, or tree diagram Determining the number of possible outcomes by using the fundamental counting principle or other techniques Modeling the probability of events through simulations with random numbers |
