## Overview of units FOR THE YEAR

## FIRST SEMESTER
Unit 1: Number System FluencyIn this unit, student will; find the greatest common factor of two whole numbers less than or equal to 100, find 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 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. Interpret and compute quotients of fractions. Solve word problems involving division of fractions by fractions using visual fraction models and equations to represent the problem. Fluently divide multi-digit numbers using the standard algorithm Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Unit 2: ExpressionsIn this unit, students understand the use of variables in mathematical expressions. They become more fluent at viewing expressions as objects in their own right versus calculations. Students write expressions that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. Students will understand that expressions in different forms can be equivalent, and they will use the properties of operations to generate and rewrite expressions in equivalent forms. The Mathematical Practices should be evident throughout instruction of symbolic expressions and connected to the content. Students should engage in mathematical tasks that provide an opportunity to connect content and practices. Unit 3: One-Step Equations and Inequalities In this unit, understand Solving and Equation or Inequality is based on understanding the important role equivalence plays in the number and operation strand of mathematics. Based on the equivalence understanding, students learn a process for solving equations (6.EE.5), and begin to see the usefulness of variables (6.EE.8). Students learn to use equations and inequalities to describe relationships in data or in patterns of numbers or shapes, and then make statements about these relationships based on the structure of mathematics. This includes processes such as: using substitution to make an equation true, and using variables to represent numbers and inequalities. Students practice using critical thinking to solve word problems using number lines and equations to model thinking. Unit 4a: Rate, Ratio, and Proportional Reasoning Using Equivalent Fractions Students learn that a ratio expresses the comparison between two quantities. Special types of ratios are rates, unit rates, measurement conversions, and percentages are concepts that are applied to a variety of real world and mathematical situations. Students gain a deeper understanding of proportional reasoning through instruction and practice. They develop and use multiplicative thinking to develop a sense of proportional reasoning as they describe ratio relationships between two quantities. |
## SECOND SEMESTER
Unit 4b: Analyzing Quantitative Relationships In this unit, Student will analyze the relationship between dependent and independent variables through the use of tables, equations and graphs. Ratios and rates can be used in ratio tables and graphs to solve problems. Previously, students have used additive reasoning in tables to solve problems. Graph data that occurs as a result of relationships between varying quantities in the coordinate plane. Analyze graphs and tables to determine the relationship between varying quantities. Describe how change in one variable affects the other. Use written descriptions, tables, graphs and equations to represent relationships between varying quantities. Unit 5: Area and VolumeIn this unit students will: Find areas of right, equilateral, isosceles, and scalene triangles, and special quadrilaterals, Find areas of composite figures and polygons by composing into rectangles and decomposing into triangles and other shapes, Solve real-world and mathematical problems involving area Decipher and draw views of rectangular and triangular prisms from a variety of perspectives, Recognize and construct nets for rectangular and triangular prism, Find the surface area of rectangular and triangular prisms by using manipulatives and by constructing nets, Determine the surface area of rectangular and triangular prisms by substituting given values for their dimensions into the correct formulas; Solve real-world that require determining the surface area of rectangular and triangular prisms Unit 6: Rational Explorations: Numbers and Their Opposites In this unit students will: understand that positive and negative numbers are used together to describe quantities having opposite directions or values, understand a rational number as a point on the number line, Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates, recognize opposite signs of numbers as indicating locations on opposite recognize that the opposite of the opposite of a number is the number itself, understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane, recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes, find and position integers and other rational numbers on a horizontal or vertical number line diagram, find and position pairs of integers and other rational numbers on a coordinate plane, understand ordering and absolute value of rational numbers, interpret statements of inequality as statements about the relative write, interpret, and explain statements of order for rational numbers in real-world contexts, understand the absolute value of a rational number as its distance from 0 on the number line, interpret absolute value as magnitude for a positive or negative quantity in a real-world situation, distinguish comparisons of absolute value from statements about order, solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Unit 7: Statistics Students develop a sense of statistical variability, summarizing and describing distributions. Students gain experience doing investigations, especially statistical investigations, by starting with a question. The data gathered to answer the question is interpreted in light of the variability of the data relative to the situation where the data resides, the question being asked and how the data is distributed over the data set. Whether larger numbers such as those involving populations of states or small, such as the changes in plant height over a week, the variability of the data matters. Student learn to make histogram and box plot data displays, and further their expertise with dot plots (line plots) when working with measurements or quantities that are counted. The shape of displayed data, especially symmetry, is considered in analysis of data distributions, including the identification of clusters, peaks and gaps. Measures of central tendency and spread, including median, quartiles, the interquartile range, are used. |