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7.1 Number & Operation
- 7.1.1 Read, write, represent and compare positive and negative rational numbers, expressed as integers, fractions and decimals.
- 22.214.171.124 Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. Recognize that pi is not rational, but that it can be approximated by rational numbers such as 22/7 and 3.14.
- 126.96.36.199 Understand that division of two integers will always result in a rational number. Use this information to interpret the decimal result of a division problem when using a calculator.
- 188.8.131.52 Locate positive and negative rational numbers on the number line, understand the concept of opposites, and plot pairs of positive and negative rational numbers on a coordinate grid.
- 184.108.40.206 Compare positive and negative rational numbers expressed in various forms using the symbols <, >, =, “less than or equal to”, “greater than or equal to”.
- 220.127.116.11 Recognize and generate equivalent representations of positive and negative rational numbers, including equivalent fractions.
- 7.1.2 Calculate with positive and negative rational numbers, and rational numbers with whole number exponents, to solve real-world and mathematical problems.
- 18.104.22.168 Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions and terminating decimals; use efficient and generalizable procedures, including standard algorithms; raise positive rational numbers to whole-number exponents.
- 22.214.171.124 Use real-world contexts and the inverse relationship between addition and subtraction to explain why the procedures of arithmetic with negative rational numbers make sense.
- 126.96.36.199 Understand that calculators and other computing technologies often truncate or round numbers.
- 188.8.131.52 Solve problems in various contexts involving calculations with positive and negative rational numbers and positive integer exponents, including computing simple and compound interest.
- 184.108.40.206 Use proportional reasoning to solve problems involving ratios in various contexts.
- 220.127.116.11 Demonstrate an understanding of the relationship between the absolute value of a rational number and distance on a number line. Use the symbol for absolute value.
- 7.2.1 Understand the concept of proportionality in real-world and mathematical situations, and distinguish between proportional and other relationships.
- 18.104.22.168 Understand that a relationship between two variables, x and y, is proportional if it can be expressed in the form y/x = k or y = kx. Distinguish proportional relationships from other relationships, including inversely proportional relationships (xy=k or y= k/x).
- 22.214.171.124 Understand that the graph of a proportional relationship is a line through the origin whose slope is the unit rate (constant of proportionality). Know how to use graphing technology to examine what happens to a line when the unit rate is changed.
- 7.2.2 Recognize proportional relationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols and graphs; solve problems involving proportional relationships and explain results in the original context.
- 126.96.36.199 Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations.
- 188.8.131.52 Solve multi-step problems involving proportional relationships in numerous contexts.
- 184.108.40.206 Use knowledge of proportions to assess the reasonableness of solutions.
- 220.127.116.11 Represent real-world or mathematical situations using equations and inequalities involving variables and positive and negative rational numbers.
- 7.2.3 Apply understanding of order of operations and algebraic properties to generate equivalent numerical and algebraic expressions containing positive and negative rational numbers and grouping symbols; evaluate such expressions.
- 18.104.22.168 Use properties of algebra to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents. Properties of algebra include associative, commutative and distributive laws.
- 22.214.171.124 Evaluate algebraic expressions containing rational numbers and whole number exponents at specified values of their variables.
- 126.96.36.199 Apply understanding of order of operations and grouping symbols when using calculators and other technologies.
- 7.2.4 Represent real-world and mathematical situations using equations with variables. Solve equations symbolically, using the properties of equality. Also solve equations graphically and numerically. Interpret solutions in the original context.
- 188.8.131.52 Represent relationships in various contexts with equations involving variables and positive and negative rational numbers. Use the properties of equality to solve for the value of a variable. Interpret the solution in the original context.
- 184.108.40.206 Solve equations resulting from proportional relationships in various contexts.
7.3 Geometry & Measurement
- 7.3.1 Use reasoning with proportions and ratios to determine measurements, justify formulas and solve real-world and mathematical problems involving circles and related geometric figures.
- 220.127.116.11 Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is pi. Calculate the circumference and area of circles and sectors of circles to solve problems in various contexts.
- 18.104.22.168 Calculate the volume and surface area of cylinders and justify the formulas used.
- 7.3.2 Analyze the effect of change of scale, translations and reflections on the attributes of two-dimensional figures.
- 22.214.171.124 Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors.
- 126.96.36.199 Apply scale factors, length ratios and area ratios to determine side lengths and areas of similar geometric figures.
- 188.8.131.52 Use proportions and ratios to solve problems involving scale drawings and conversions of measurement units.
- 184.108.40.206 Graph and describe translations and reflections of figures on a coordinate grid and determine the coordinates of the vertices of the figure after the transformation.
7.4 Data Analysis & Probability
- 7.4.1 Use mean, median and range to draw conclusions about data and make predictions.
- 220.127.116.11 Design simple experiments and collect data. Determine mean, median and range for quantitative data and from data represented in a display. Use these quantities to draw conclusions about the data, compare different data sets, and make predictions.
- 18.104.22.168 Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Know how to create data displays using a spreadsheet to examine this impact.
- 7.4.2 Display and interpret data in a variety of ways, including circle graphs and histograms.
- 22.214.171.124 Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology.
- 7.4.3 Calculate probabilities and reason about probabilities using proportions to solve real-world and mathematical problems.
- 126.96.36.199 Use random numbers generated by a calculator or a spreadsheet or taken from a table to simulate situations involving randomness, make a histogram to display the results, and compare the results to known probabilities.
- 188.8.131.52 Calculate probability as a fraction of sample space or as a fraction of area. Express probabilities as percents, decimals and fractions.
- 184.108.40.206 Use proportional reasoning to draw conclusions about and predict relative frequencies of outcomes based on probabilities.