Standards
Students evaluate algebraic expressions, write algebraic expressions to represent quantities in context, and create equivalent algebraic expressions.
Generate resourceDefine and use multiple variables when writing expressions to represent real-world and other mathematical problems, and evaluate them for given values.
Generate resourceDemonstrate which values from a specified set, if any, make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
Generate resourceSolve equations of the form <em>x + p = q, x - p = q, px = q</em> , and <em>x/p = q</em> fluently for cases in which <em>p, q</em> and <em>x</em> are all nonnegative rational numbers. Represent real-world problems using equations of these forms and solve such problems.
Generate resourceWrite an inequality of the form <em>x > c, x ≥ c, x < c,</em> or <em>x ≤ c</em> , where <em>c</em> is a rational number, to represent a constraint or condition in a real-world or other mathematical problem. Explain that inequalities have infinitely many solutions and how to represent solutions on a number line diagram.
Generate resourceSolve real-world and other mathematical problems by graphing points with rational number coordinates on a coordinate plane. Include the use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
Generate resourceSelect, create, and interpret graphical representations of numerical data, including line plots, histograms, and box plots.
Generate resourceFormulate statistical questions; collect and organize the data (e.g., using technology), and display and interpret the data with graphical representations (e.g., using technology).
Generate resourceSummarize numerical data sets in relation to their context in multiple ways, such as:
Generate resourceDescribe the nature of the attribute under investigation, including how it was measured and its units of measurement;
Generate resourceDetermine quantitative measures of center (mean and/or median) and spread (range and interquartile range);
Generate resourceDescribe any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered; and
Generate resourceRelate the choice of measures of center and spread to the shape of the data distribution and the context in which the data were gathered.
Generate resourceConvert between measurement systems (Customary to metric and metric to Customary) given the conversion factors, and use these conversions in solving real-world problems.
Generate resourceApply the sums of interior angles of triangles and quadrilaterals to solve real-world and mathematical problems.
Generate resourceFind the area of complex shapes composed of polygons by composing or decomposing into simple shapes; apply this technique to solve real-world and other mathematical problems.
Generate resourceFind the volume of a right rectangular prism with fractional edge lengths using unit cubes of the appropriate unit fraction edge lengths (e.g., using technology or concrete materials) and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas <em>V = lwh</em> and <em>V = Bh</em> to find volumes of right rectangular prisms with fractional edge lengths to solve real-world and other mathematical problems.
Generate resourceStudents begin to apply negative integers within real-world contexts and use number lines to model opposite signed numbers as located on opposite sides of zero.
Generate resourceUse positive and negative numbers to represent and compare quantities in real-world contexts, explaining the meaning of 0 in each situation.
Generate resourceExplain how opposite signs of numbers indicate locations on opposite sides of 0 on the number line; identify the opposite of the opposite of a number.
Generate resourceCompare and order rational numbers and plot them on a number line. Write, interpret, and explain statements of order for rational numbers in real-world contexts.
Generate resourceSolve real-world problems with positive fractions and decimals by using one or two operations.
Generate resourceApply the order of operations and properties of operations (i.e., identity, inverse, commutative properties of addition and multiplication, associative properties of addition and multiplication, and distributive property) to evaluate numerical expressions with nonnegative rational numbers, including those using grouping symbols, such as parentheses, and involving whole number exponents.
Generate resourceFind the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers from 1 to 100, with a common factor as a multiple of a sum of two whole numbers with no common factor.
Generate resourceApply the properties of operations (i.e., identity, inverse, commutative, associative, distributive properties) to create equivalent linear expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless of which value is substituted into them.
Generate resourceStudents use ratios and reasoning to compare two quantities and understand unit rate. Students use ratios and unit rates to model and solve real-world problems.
Generate resourceConvert between any two representations (fractions, decimals, percents) of positive rational numbers without the use of a calculator.
Generate resourceUnderstand the concept of a unit rate and use terms related to rate in the context of a ratio relationship.
Generate resourceMake tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane.
Generate resourceSolve real-world and other mathematical problems involving rates and ratios using models and strategies such as reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
Generate resourceUse variables to represent two quantities in a proportional relationship in a real-world problem; write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
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