Math - Sixth Grade

These Open Educational Resources are comprehensive and coherent curricular materials that may be used to teach a course or grade level.

 

• Chapter 0 - Mathematical Foundations (UMSMP)
  This is Chapter 0 of the Utah Middle School Math: Grade 6 textbook. It provides a Mathematical Foundation for Fluency.
• Chapter 0 - Student Workbook (UMSMP)
  This is Chapter 0 of the Utah Middle School Math: Grade 6 student workbook. It covers the following topics: Fluency.
• Chapter 1 - Mathematical Foundations (UMSMP)
  This is Chapter 1 of the Utah Middle School Math: Grade 6 textbook. It provides a Mathematical Foundation for Ratio Relations.
• Chapter 1 - Student Workbook (UMSMP)
  This is Chapter 1 of the Utah Middle School Math: Grade 6 student workbook. It covers the following topics: Ratio Relations.
• Chapter 2 - Mathematical Foundations (UMSMP)
  This is Chapter 2 of the Utah Middle School Math: Grade 6 textbook. It provides a Mathematical Foundation for Percent, Division with Fractions, and Measurement Conversion.
• Chapter 2 - Student Workbook (UMSMP)
  This is Chapter 2 of the Utah Middle School Math: Grade 6 student workbook. It covers the following topics: Percent, Division with Fractions, and Measurement Conversion.
• Chapter 3 - Mathematical Foundations (UMSMP)
  This is Chapter 3 of the Utah Middle School Math: Grade 6 textbook. It provides a Mathematical Extending the Number System.
• Chapter 3 - Student Workbook (UMSMP)
  This is Chapter 3 of the Utah Middle School Math: Grade 6 student workbook. It covers the following topics: Extending the Number System.
• Chapter 4 - Mathematical Foundations (UMSMP)
  This is Chapter 4 of the Utah Middle School Math: Grade 6 textbook. It provides a Mathematical Foundation for Fluency.
• Chapter 4 - Student Workbook (UMSMP)
  This is Chapter 4 of the Utah Middle School Math: Grade 6 student workbook. It covers the following topics: Statistics.
• Chapter 5 - Mathematical Foundations (UMSMP)
  This is Chapter 5 of the Utah Middle School Math: Grade 6 textbook. It provides a Mathematical Foundation for Geometry.
• Chapter 5 - Student Workbook (UMSMP)
  This is Chapter 5 of the Utah Middle School Math: Grade 6 student workbook. It covers the following topics: Geometry.
• Chapter 6 - Mathematical Foundations (UMSMP)
  This is Chapter 6 of the Utah Middle School Math: Grade 6 textbook. It provides a Mathematical Foundation for Expressions and Equations.
• Chapter 6 - Student Workbook (UMSMP)
  This is Chapter 6 of the Utah Middle School Math: Grade 6 student workbook. It covers the following topics: Expressions and Equations.



 

Engage NY
• Grade 6 Math Module 1: Ratios and Unit Rates (EngageNY)
  Students begin their sixth grade year investigating the concepts of ratio and rate. They use multiple forms of ratio language and ratio notation, and formalize understanding of equivalent ratios. Students apply reasoning when solving collections of ratio problems in real world contexts using various tools (e.g., tape diagrams, double number line diagrams, tables, equations and graphs). Students bridge their understanding of ratios to the value of a ratio, and then to rate and unit rate, discovering that a percent of a quantity is a rate per 100. The 35 day module concludes with students expressing a fraction as a percent and finding a percent of a quantity in real world concepts, supporting their reasoning with familiar representations they used previously in the module.
• Grade 6 Math Module 2: Arithmetic Operations Including Division of Fractions (EngageNY)
  In Module 2, students complete their understanding of the four operations as they study division of whole numbers, division by a fraction and operations on multi-digit decimals. This expanded understanding serves to complete their study of the four operations with positive rational numbers, thereby preparing students for understanding, locating, and ordering negative rational numbers (Module 3) and algebraic expressions (Module 4).
• Grade 6 Math Module 3: Rational Numbers (EngageNY)
  Students are familiar with the number line and determining the location of positive fractions, decimals, and whole numbers from previous grades. Students extend the number line (both horizontally and vertically) in Module 3 to include the opposites of whole numbers. The number line serves as a model to relate integers and other rational numbers to statements of order in real-world contexts. In this module's final topic, the number line model is extended to two-dimensions, as students use the coordinate plane to model and solve real-world problems involving rational numbers.
• Grade 6 Math Module 4: Expressions and Equations (EngageNY)
  In Module 4, Expressions and Equations, students extend their arithmetic work to include using letters to represent numbers in order to understand that letters are simply "stand-ins" for numbers and that arithmetic is carried out exactly as it is with numbers. Students explore operations in terms of verbal expressions and determine that arithmetic properties hold true with expressions because nothing has changedthey are still doing arithmetic with numbers. Students determine that letters are used to represent specific but unknown numbers and are used to make statements or identities that are true for all numbers or a range of numbers.
• Grade 6 Math Module 5: Area, Surface Area, and Volume Problems (EngageNY)
  In this module, students utilize their previous experiences in order to understand and develop formulas for area, volume, and surface area. Students use composition and decomposition to determine the area of triangles, quadrilaterals, and other polygons. Extending skills from Module 3 where they used coordinates and absolute value to find distances between points on a coordinate plane, students determine distance, perimeter, and area on the coordinate plane in real-world contexts
• Grade 6 Math Module 6: Statistics (EngageNY)
  In this module, students move from simply representing data into analysis of data. Students begin to think and reason statistically, first by recognizing a statistical question as one that can be answered by collecting data. Students learn that the data collected to answer a statistical question has a distribution that is often summarized in terms of center, variability, and shape.



 

Georgia Standards of Excellence Curriculum Frameworks
• Grade 6 Unit 1: Number System Fluency (Georgia Standards)
  In this unit students 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.
• Grade 6 Unit 2: Rate, Ratio, and Proportional Reasoning Using Equivalent Fractions (Georgia Standard
  In this unit, students will gain a deeper understanding of proportional reasoning through instruction and practice, develop and use multiplicative thinking, develop a sense of proportional reasoning, develop the understanding that ratio is a comparison of two numbers or quantities, find percents using the same processes for solving rates and proportions and solve real-life problems involving measurement units that need to be converted.
• Grade 6 Unit 3: Expressions (Georgia Standards)
  In this unit students will represent repeated multiplication with exponents. Evaluate expressions containing exponents to solve mathematical and real world problems. Translate verbal phrases and situations into algebraic expressions. Identify the parts of a given expression. Use the properties to identify equivalent expressions. Use the properties and mathematical models to generate equivalent expressions.
• Grade 6 Unit 4: One Step Equations and Inequalities (Georgia Standards)
  In this unit students will: Determine if an equation or inequality is appropriate for a given situation. Solve mathematical and real-world problems with equations. Represent real-world situations as inequalities. Interpret the solutions to equations and inequalities. Represent the solutions to inequalities on a number line. Analyze the relationship between dependent and independent variables through the use of tables, equations and graphs.
• Grade 6 Unit 5: Area and Volume (Georgia Standards)
  In 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 prisms. Find the surface area of rectangular and triangular prisms by using manipulatives and by constructing nets.
• Grade 6 Unit 6: Statistics (Georgia Standards)
  In this unit students will: Analyze data from many different sources such as organized lists, box-plots, bar graphs, histograms and dot plots. Understand that responses to statistical questions may vary. Understand that data can be described by a single number. Determine quantitative measures of center (median and/or mean). Determine quantitative measures of variability (interquartile range and range).
• Grade 6 Unit 7: Rational Explorations: Numbers and their Opposites (Georgia Standards)
  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 sides of 0 on the number line. Recognize that the opposite of the opposite of a number is the number itself.



 

 

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