Students extend their computational work to include fractions and decimals, adding and ...
Students extend their computational work to include fractions and decimals, adding and subtracting numbers in those forms in this unit before moving to multiplication and division in subsequent units.
Students develop an understanding of areas as how much two-dimensional space a ...
Students develop an understanding of areas as how much two-dimensional space a figure takes up, and relate it to their work with multiplication from Units 2 and 3.
Students combine their knowledge of linear functions with knowledge of data representations ...
Students combine their knowledge of linear functions with knowledge of data representations and analysis to make the jump from univariate data in one variable to bivariate data in two variables.
Students expand their knowledge of circles to establish relationships between angle measures ...
Students expand their knowledge of circles to establish relationships between angle measures in and around circles, line segments and lines in and around circles, and portions of circles as related to area and circumference.
Students identify, perform, and algebraically describe rigid motions to establish congruence of ...
Students identify, perform, and algebraically describe rigid motions to establish congruence of two dimensional polygons, including triangles, and develop congruence criteria for triangles.
Students use the properties of circles to construct and understand different geometric ...
Students use the properties of circles to construct and understand different geometric figures, and lay the groundwork for constructing mathematical arguments through proof.
Students expand their conception of what a “number” is as they are ...
Students expand their conception of what a “number” is as they are introduced to an entirely new category of number, decimals, which they learn to convert, compare, and add in simple cases.
Students analyze contextual situations, focusing on single variable data and bivariate data, ...
Students analyze contextual situations, focusing on single variable data and bivariate data, and are introduced to the concept of using data to make predictions and judgments about a situation.
Students use constructions to explore dilations in order to define and establish ...
Students use constructions to explore dilations in order to define and establish similarity, and they prove and use similarity criterion and theorems in the solution of problems.
Students solve equations and inequalities with rational numbers, and encounter real-world situations ...
Students solve equations and inequalities with rational numbers, and encounter real-world situations that can be modeled and solved using equations and inequalities.
Students discover how to use equations and inequalities to model relationships between ...
Students discover how to use equations and inequalities to model relationships between quantities, and investigate the meaning of having a solution to an equation or an inequality.
Students revisit exponential functions, including geometric sequences and series, and learn to ...
Students revisit exponential functions, including geometric sequences and series, and learn to manipulate logarithmic expressions and equations to solve problems involving exponential modeling.
Students extend their understanding of properties of exponents to include rational exponents ...
Students extend their understanding of properties of exponents to include rational exponents and radicals, and investigate rates of change in linear and exponential sequences and functions.
Students learn to simplify complex-looking exponential expressions, and they learn efficient ways ...
Students learn to simplify complex-looking exponential expressions, and they learn efficient ways to describe, communicate, and operate with very large and very small numbers.
Students are exposed to general methods and strategies to recognize and generate ...
Students are exposed to general methods and strategies to recognize and generate equivalent fractions, and learn to compare fractions with different numerators and different denominators.
Students deepen their understanding of halves, thirds, and fourths to understand fractions ...
Students deepen their understanding of halves, thirds, and fourths to understand fractions as equal partitions of a whole, and are exposed to additional fractional units such as fifths, sixths, eighths, ninths, and tenths.
Students learn how to represent, interpret, and analyze functions in various forms, ...
Students learn how to represent, interpret, and analyze functions in various forms, leading to understanding features such as rates of change, initial values, and intervals of increase and decrease.
Students are introduced to the main features of functions that they will ...
Students are introduced to the main features of functions that they will learn throughout the year, providing students with a conceptual understanding of how functions are used to model various situations.
Students take a deeper look at piecewise functions and absolute value functions, ...
Students take a deeper look at piecewise functions and absolute value functions, and study how transformations of functions can be identified graphically and represented algebraically.
Students explore measurements of geometric figures in two-and three-dimensions, finding area, surface ...
Students explore measurements of geometric figures in two-and three-dimensions, finding area, surface area, and volume in mathematical and real-world problems.
Students apply algebraic and proportional reasoning skills to investigate angle relationships, circle ...
Students apply algebraic and proportional reasoning skills to investigate angle relationships, circle measurements, uniqueness of triangles, and solid figure application problems.
Students manipulate, graph, and model with two-variable linear equations and inequalities, are ...
Students manipulate, graph, and model with two-variable linear equations and inequalities, are introduced to inverse functions, and continue studying linear systems of equations and inequalities.
Students become proficient at manipulating and solving single-variable linear equations and inequalities, ...
Students become proficient at manipulating and solving single-variable linear equations and inequalities, and using them to model and interpret contextual situations.
Students review and extend the Algebra 1 skills of graphing, manipulating, and ...
Students review and extend the Algebra 1 skills of graphing, manipulating, and describing solutions in order to deepen their understanding of modeling situations using linear functions.
Students compare proportional relationships, define and identify slope from various representations, graph ...
Students compare proportional relationships, define and identify slope from various representations, graph linear equations in the coordinate plane, and write equations for linear relationships.
Students explore multi-digit division and its applications, which include interpreting a remainder ...
Students explore multi-digit division and its applications, which include interpreting a remainder in division word problems and using division to interpret a repeating pattern.
Students deepen their understanding of multiplication by exploring factors and multiples, multiplicative ...
Students deepen their understanding of multiplication by exploring factors and multiples, multiplicative comparison, as well as multi-digit multiplication.
Students extend their understanding of multiplication and division to divide fractions by ...
Students extend their understanding of multiplication and division to divide fractions by fractions, and develop fluency with whole number and decimal operations.
Students begin to explore the concepts of multiplication and division, beginning in ...
Students begin to explore the concepts of multiplication and division, beginning in the context of equal group and array problems, moving to skip-counting and repeated addition, and ending with more complex and/or abstract problems.
Students deepen their understanding of multiplication and division, including their properties and ...
Students deepen their understanding of multiplication and division, including their properties and extending their study of factors to include all units from 0 to 10, as well as multiples of 10 within 100.
Students use their knowledge of multiplication and division with whole numbers and ...
Students use their knowledge of multiplication and division with whole numbers and with fractions to multiply and divide with decimals, and apply this understanding to the context of measurement conversion.
Students deepen their understanding of fraction multiplication and begin to explore to ...
Students deepen their understanding of fraction multiplication and begin to explore to fraction division (and fractions as division), as well as apply this new understanding to the context of line plots.
Students continue their work with multi-digit multiplication and division and the base-ten ...
Students continue their work with multi-digit multiplication and division and the base-ten system in order to finalize fluency with multi-digit multiplication and extend division to two-digit divisors.
Students venture into the Expressions and Equations domain, using variables to represent ...
Students venture into the Expressions and Equations domain, using variables to represent unknown or changing quantities, and using properties of operations to investigate equivalent expressions.
Students manipulate expressions into different equivalent forms as they expand, factor, add, ...
Students manipulate expressions into different equivalent forms as they expand, factor, add, and subtract numerical and algebraic expressions and face authentic real-world, multi-step problems.
Students extend the operations of addition, subtraction, multiplication, and division to include ...
Students extend the operations of addition, subtraction, multiplication, and division to include positive and negative rational numbers, and build fluency with evaluating numerical expressions.
Students are introduced to the coordinate plane and use it to represent ...
Students are introduced to the coordinate plane and use it to represent the location of objects in space, as well as to represent patterns and real-world situations.
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