Math

Students draw on their knowledge of fractions and fraction equivalence to develop understanding of ratios and rates. They use this understanding to build fluency with finding equivalent ratios and rates, as well as finding unit rates. They also apply their understanding of ratios and rates to solve real-word problems.

Students draw on their knowledge of fractions, decimals, ratios, and rates to build fluency with finding percents of a quantity. They apply their fluency with percents to solve real-world problems.

Students draw on their knowledge of basic computation to develop understanding of computation with multi-digit numbers and fractions. They use this understanding to build fluency with the four basic operations involving whole numbers and decimals, as well as division of fractions and mixed numbers. They also apply their understanding of fractions to write and solve real-world story contexts

Students draw on their knowledge of whole numbers and number lines to develop understanding of integers, rational numbers, and the coordinate plane. They use this understanding to build fluency with representations of integers and absolute value, comparing and ordering rational numbers, and graphing points and finding distance on the coordinate plane. They also apply their understanding of integers, rational numbers, and the coordinate plane to solve real-world problems.

Students draw on their knowledge of the four basic operations to develop understanding of numerical and algebraic expressions. They use this understanding to build fluency with using powers and exponents, order of operations, and mathematical properties, as well as evaluating multi-step algebraic expressions and generating and simplifying equivalent algebraic expressions. They also apply their understanding of numerical and algebraic expressions to solve real-world problems.

Students draw on their knowledge of expressions, inequality symbols, and inverse operations to develop understanding of equations and inequalities. They use their understanding of models, properties of equality, and substitution to build fluency with writing and solving one-step addition, subtraction, multiplication, and division equations. Fluency is also built through writing, solving, and graphing inequalities. They apply their understanding of equations and inequalities to solve multi-step, real-world problems.

Students draw on their knowledge of tables, equations, and the coordinate plane to develop understanding of relationships between two variables. They build fluency with using a table to find variable values, writing equations, and graphing the relationship. They also apply their understanding of relationships between two variables to solve real-world problems.

Students draw on their knowledge of polygons, basic computation, and the coordinate plane to develop understanding of area. They use this understanding to build fluency with finding the area of parallelograms, triangles, trapezoids, and regular polygons. They also build fluency with finding area by using coordinates of polygons on the coordinate plane. They apply their understanding of area to solve multi-step, real-world problems.

Students draw on their knowledge of polygons and area to develop understanding of volume and surface area. They use this understanding to build fluency with finding the volume of rectangular prisms and making and using nets to find the surface area of rectangular prisms, triangular prisms, and pyramids. They also apply their understanding of volume and surface area to solve multi-step, real-world problems

Students draw on their knowledge of representing and interpreting data to develop understanding of statistical measures. They use this understanding to build fluency with finding measures of center and variation as well as identifying outliers. They also build fluency with constructing and interpreting dot plots, histograms, and box plots. They apply their understanding of statistical measures to solve real-world problems.

Students draw on their knowledge of ratios and rates to develop understanding of proportional relationships. They use this understanding to build fluency with proportional relationships by representing them with tables, graphs, and equations and finding the constant of proportionality

Students draw on their understanding of proportional relationships to build fluency with using ratio reasoning and properties of operations to solve algebraic equations involving percents. They apply their fluency to solve multi-step ratio and percent problems.

Students draw on their knowledge of rational numbers to develop understanding of operations with integers. They use this understanding to build fluency with integer operations and the order of operations. They will apply their fluency to solve multi-step problems involving integer operations.

Students draw on their knowledge of rational numbers and their knowledge of integers to develop and understanding of performing mathematical operations with rational numbers. They will use that understanding to build fluency in using mathematical operations with rational numbers.

Students draw on their knowledge of operations with algebraic expressions, greatest common factors, and the distributive property to gain an understanding of simplifying algebraic expressions which includes distributing integers across algebraic expressions, adding and subtracting algebraic expressions, combining like terms, and factoring algebraic expressions.

Students will draw on their knowledge of solving one-step equations to develop an understanding of solving two-step equations with rational numbers. They will use this understanding to gain fluency in writing and solving two-step equations. They will apply their understanding to solve real-world problems.

Students will draw on their knowledge of inequalities and equations to build an understanding of writing, solving, and graphing one- and two-step inequalities.  They will use this understanding to build fluency in solving and graphing one- and two-step inequalities. They will apply their fluency to write, solve, and graph one- and two-step inequalities that represent real-world situations.

Students will draw on their knowledge of lines and angles, equivalent ratios, and three-dimensional figures to gain understanding of angles, triangles, and scale drawings. They will use this understanding to develop fluency with vertical, adjacent, complementary and supplementary angles, classifying and drawing triangles, scale drawings, and three-dimensional figures. They will apply their fluency to solve real-world problems.

Students will develop an understanding of radius and diameter, and how they relate to finding the circumference and area of circles. They will also draw on their knowledge of finding the area of triangles and quadrilaterals to gain fluency in finding the area of composite figures, volume, and surface area. They will use this knowledge to gain fluency in finding the volume and surface area of composite three-dimensional figures. They will also apply their fluency to solve real-world problems.

Students will develop an understanding of probability of simple and compound events. They will use this understanding to develop fluency in finding likelihoods, relative frequencies, and determining the sample space for compound events. They will also compare probabilities, design simulation, and apply their understanding of probability to solve real-world problems.

Students will draw upon their knowledge of measures of center, measures of variation, and ratios to develop understanding about statistical sampling and making inferences and predictions. Students come to understand that taking multiple samples can help them gauge the variation in their predictions. Students build fluency in using ratio reasoning to make predictions about a population and in using the measures of center and variation to compare two sample distributions. They apply their understanding of the mean and mean absolute deviation to informally assess the degree of visual overlap between two distributions to infer how close the population means might be.

Students draw on their knowledge of exponents to develop understanding of the properties of exponents and scientific notation. They use this understanding to build fluency with simplifying algebraic expression involving powers and computing with scientific notation. They apply their fluency to solve multi-step real-world problems

Students draw on their knowledge of the set of rational numbers to develop understanding of the set of real numbers. They use this understanding to build fluency with determining if numbers are rational or irrational, finding roots of perfect squares and cubes, and estimating roots of numbers. They apply their fluency to solve multi-step real-world problems

Students draw on their knowledge of solving one- and two-step equations to build fluency with solving equations with variables on each side. They apply their fluency to solve real-world problems by writing and solving multi-step equations. Using their knowledge of solving multi-step equations, they determine if an equation has one, no, or infinitely many solutions.

Students draw on their knowledge of proportional relationships to develop understanding of the concept of slope. They use this understanding to build fluency with finding the slope of a line, as well as writing and graphing linear equations. They apply their fluency to solve multi-step real-world problems.

Students draw on their knowledge of linear relationships to develop understanding of functions. They come to understand how to identify functions and the graphs of functions. Students use this understanding to build fluency with constructing linear functions and identifying nonlinear functions. They apply their understanding by comparing linear functions and analyzing functions quantitatively.

Students draw on their knowledge of linear equations to develop understanding of how to solve and determine the number of solutions to a system of two linear equations. They use this understanding to build fluency with solving a system of equations graphically and algebraically. They apply their fluency to solve real-world problems.

Students draw on their knowledge of angles and triangles to develop understanding of the Pythagorean Theorem. They use this understanding to build fluency with finding side lengths of right triangles. They apply their fluency to solve multi-step, real-world problems.

Students draw on their knowledge of graphing in the coordinate plane to develop understanding of transformations. They use their understanding to build fluency with graphing and describing translations, reflections, rotations, and dilations using coordinates.

Students draw on their knowledge of transformations to develop understanding that two figures are congruent or similar if the second figure can be obtained from the first by a series of transformations. They sue their understanding to build fluency with naming corresponding parts of congruent and similar figures.  They apply their fluency to solve real-world indirect measurement problems.

Students will draw on their knowledge of finding volume of prisms to develop understanding of how to find the volume of cylinders, cones, and spheres. They use this understanding to build fluency with finding missing dimensions and finding volume of composite figures.  They apply their fluency to solve real-world volume problems.

Students draw on their knowledge of linear functions and relative frequency to develop understanding of scatter plots and two-way tables. They use their understanding to build fluency with constructing and interpreting scatter plots and two-way tables. They apply their understanding to solve real-world problems that involve lines of fit and associations in two-way tables.

Students draw on their knowledge of ratios and rates to develop understanding of proportional relationships. They use this understanding to build fluency with proportional relationships by representing them with tables, graphs, and equations, and finding the constant of proportionality

Students draw on their understanding of proportional relationships to build fluency with using ratio reasoning and properties of operations to solve algebraic equations involving percents. They apply their fluency to solve multi-step ratio and percent problems.

Students draw on their knowledge of rational numbers to develop understanding of operations with integers and rational numbers. They use this understanding to build fluency with rational number operations and the order of operations. They will apply their fluency to solve multi-step problems involving integers and rational numbers.

Students draw on their knowledge of operations with algebraic expressions, greatest common factors, and the distributive property to gain an understanding of simplifying algebraic expressions which include distributing integers across algebraic expressions, adding and subtracting algebraic expressions, combining like terms, and factoring algebraic expressions.

Students will draw on their knowledge of solving one-step equations to develop an understanding of solving equations and inequalities. They will use this understanding to gain fluency in writing and solving equations and inequalities. They will apply their understanding to solve real-world problems.

Students will draw on their knowledge of lines and angles, equivalent ratios, and three-dimensional figures to gain understanding of angles, parallel lines, triangles, and scale drawings. They will use this understanding to develop fluency with vertical, adjacent, complementary and supplementary angles, angle relationships and triangles, classifying and drawing triangles, scale drawings and three-dimensional figures. They will apply their fluency to solve real-world problems.

Students will develop an understanding of radius and diameter and finding the circumference and area of circles. They will also gain fluency in finding the area of composite figures, volume, and surface area.  They will use this knowledge to gain fluency in finding the volume and surface area of composite three-dimensional solids. They will also apply their fluency to solve real-world problems.

Students will develop an understanding of probability of simple and compound events. They will use this understanding to develop fluency in finding likelihoods, relative frequencies, and determining the sample space for compound events. They will also compare probabilities, design simulations, and apply their understanding of probability to solve real-world problems

Students will draw upon their knowledge of measures of center, measures of variation, and ratios to develop understanding about statistical sampling and making inferences and predictions.  Students come to understand that taking multiple samples can help them gauge the variation in their predictions. Students build fluency in suing ratio reasoning to make predictions about a population and in using the measures of center and variation to compare two sampling distributions. They apply their understanding of the mean and mean absolute deviation to informally assess the degree of visual overlap between two distributions to infer how close the population means might be.

Students draw on their knowledge of exponents to develop understanding of the properties of exponents and scientific notation. They sue this understanding to build fluency with simplifying algebraic expressions involving powers and computing with scientific notation. They apply their fluency to solve multi-step real-word problems.

Students draw on their knowledge of the set of rational numbers to develop understanding of the set of real numbers.  They use this understanding to build fluency with determining if numbers are rational or irrational, finding roots of perfect squares and cubes, and estimating roots of numbers. They apply their fluency to solve multi-step real-world problems.

Students draw on their knowledge of graphing in the coordinate plane to develop understanding of transformations. They use their understanding to build fluency with graphing and describing translations, reflections, rotations, and dilations using coordinates. They develop understanding that two figures are congruent or similar if the second figure can be obtained from the first by a series of transformations. They apply their understanding to solve real-world indirect measurement problems.

Students draw on their knowledge of proportional relationships to develop understanding of the concept of slope. They use this understanding to build fluency with finding the slope of a line, as well as writing and graphing linear equations. They apply their fluency to solve multi-step real-world problems.

Students will use the properties of real numbers to classify numbers as being rational or irrational, compare real numbers, evaluate numerical expressions, and simplify square roots.

Students will write and solve linear equations and use them to solve real-world problems.

Students will write, solve, and graph solution sets to linear inequalities and use them to solve real-world problems.

Students will represent, interpret, describe, and analyze relations and functions in various forms.

Students will represent real-world situations by writing and/or graphing linear equations or inequalities.

Students will write, solve, and graph systems of linear equations and inequalities and use them to solve real-world problems.

Students will use various operations to simplify polynomial expressions.

Students will use different methods to factor polynomial expressions.

Students will use statistical techniques to find probability, represent data, and solve real-world problems.