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Grade 6 Mathematics In sixth grade, students will use multiplication and division to solve problems about ratio and rate. Students will build on knowledge of multiplication and division to divide fractions by fractions. Computing with multi-digit numbers fluently will assist in finding common factors and multiples. Students will be extending their knowledge of ordering whole numbers to all rational numbers which will include negative numbers. They will be using pairs of numbers including negative numbers to locate and plot points on a graph. Students will be writing, interpreting, and using expressions and equations that correspond to a given situation, evaluate expressions and use expressions and formulas to solve problems. Properties of operations will be used to rewrite equivalent forms. This would include solving one-variable equations and inequalities and being able to represent and analyze quantitative relationships between dependent and independent variables. Building on and reinforcing their understanding of numbers, students begin to develop their ability to think statistically. Solving real-world and mathematical problems involving area, surface area, and volume will be taught. Sixth Grade Math v. 2016 - 2017 Content: Multi-Digit Numbers Essential Question: 1|Page Duration: Sept 4 weeks What strategies and models can we use to understand computation problems? Solve problems involving all four operations with whole numbers. Skill: Solve problems involving all four operations with decimals. Solve problems involving all four operations with word problems. Given several problems with numbers 1-100 find the greatest common factor of two whole Assessment: numbers. Resources: Standards: Vocabulary: Comments: CC.2.1.6.E.2 Identify and choose appropriate processes to compute fluently with multi‐digit numbers. Sixth Grade Math v. 2016 - 2017 2|Page Content: Common Factors and Multiples Duration: Oct/Nov 3 weeks How can divisibility rules help us to determine the greatest factor two numbers have in Essential common? Question: Skill: 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. Apply the distributive property to express a sum of two whole numbers 1 through 100. Assessment: Given examples of numbers from 1 -200, the common factor will be listed. Resources: Standards: Vocabulary: Comments: CC.2.1.6.E.3 Develop and/or apply number theory concepts to find common factors and multiples. Sixth Grade Math v. 2016 - 2017 3|Page Content: Ratios Duration: Oct/Nov. 4 weeks Essential How are rates used in real life? Question: Skill: Use ratio language and notation to describe a ratio relationship. Find the unit rate a/b associated with a ratio. Construct tables of equivalent ratios -Find the missing values in the tables. Plot the pairs of values on the coordinate plane. Compare ratios. Solve unit rate problems involving unit pricing and constant speed. Find a percent of a quantity as a rate per 100. Solve problems involving finding the whole, given a part and the percentage. Given examples problems will be solved using rates, ratios, and/or percents. Assessment: Write the ratio of pretzels to cereal in three different ways. Resources: Standards: Vocabulary: Comments: CC.2.1.6.D.1 Understand ratio concepts and use ratio reasoning to solve problems. Sixth Grade Math v. 2016 - 2017 Content: Fractions (multiplication and division) Essential Question: 4|Page Duration: Nov/Dec 1-2 weeks How does understanding situations that require multiplying and dividing of fractions help to solve real world problems that involve fractions? Interpret and compute quotients of fractions and mixed numbers. Skill: Solve word problems involving division of fractions by fractions. Assessment: Given examples of multiplication and division problems students will show understanding of the skill. Resources: CC.2.1.6.E.1 Apply and extend previous understandings of multiplication and division to divide fractions by Standards: fractions. Vocabulary: Comments: Sixth Grade Math v. 2016 - 2017 Content: Integers Essential Question: 5|Page Duration: Dec. 1 week Why do we need integers? Represent quantities in real-world contexts using positive and negative numbers. Skill: Determine the opposite of a number and recognize that the opposite of the opposite of number line is itself. Example: -(-3) = 3 Locate and plot integers and other rational numbers on a horizontal and vertical number line. Locate and plot pairs of integers and other rational numbers on a coordinate plane. Given a number line positive numbers and negative numbers will be placed on opposite Assessment: directions. (-3) and 3 are opposites Resources: Standards: Vocabulary: Comments: CC.2.1.6.E.4 Apply and extend previous understandings of numbers to the system of rational numbers. Sixth Grade Math v. 2016 - 2017 Content: Absolute Value and Ordering Essential Question: 6|Page Duration: Dec 1-2 weeks How is computation with rational numbers similar and different to whole numbers? Write, interpret, and explain statement of order for rational numbers in real-world contexts. Interpret the absolute value of a rational number as the distance from 0 on a number line. Skill: Solve real-world and math problems by plotting points in all four quadrants of the coordinate plane. -Include the use of coordinates and absolute value to find distances between points. Assessment: Recommended Activity: Standards: CC.2.1.6.E.4 Apply and extend previous understandings of numbers to the system of rational numbers. M06.A‐N.3.2.1 M06.A‐N.3.2.2 M06.A‐N.3.2.3 Vocabulary: Sixth Grade Math v. 2016 - 2017 Comments: 7|Page Sixth Grade Math v. 2016 - 2017 Content: Numerical and Algebraic Expressions Essential Question: 8|Page Duration: Jan.1 week How can mathematical symbols model verbal expressions? Write and evaluate numerical expressions involving whole-number exponents. Write algebraic expressions from verbal descriptions. Skill: Identify parts of an expression using mathematical terms. Evaluate expressions at specific values of their variables including real-world problems. Apply the properties of operations to generate equivalent expressions. Assessment: Evaluate given examples of algebraic expressions. Resources: Standards: Vocabulary: Comments: CC.2.2.6.B.1 Apply and extend previous understandings of arithmetic to algebraic expressions. sum, term, product, factor, quotient, coefficient, quantity Sixth Grade Math v. 2016 - 2017 Content: Equations or Inequality Essential Question: 9|Page Duration: Jan 3 weeks How can we utilize equations to solve problems? Use a substitution to determine whether a given number makes the equation or inequality true. Write algebraic expressions to represent real-world or mathematical problems. Skill: Solve real-world and mathematical problems by writing and solving equations. Write an inequality to represent a constraint or condition in a real-world or mathematical problem. - Represent solutions of inequalities on number lines Assessment: Solve and interpret one variable equations or inequalities in real-world and mathematical problems. Resources: CC.2.2.6.B.2 Understand the process of solving a one‐variable equation or inequality and apply to Standards: real‐world and mathematical problems. Vocabulary: Sum, term, product, factor, quotient, coefficient, quantity Comments: Sixth Grade Math v. 2016 - 2017 Content: Quantitative Relationships Essential Question: 10 | P a g e Duration: Feb 1 week How do dependent and independent variables affect a graph? Write an equation to express the relationship between dependent and independent variables. Skill: Analyze the relationship between the dependent and independent variables using graphs and tables. Relate to an equation. Given examples of real-world problems that change relationship to one another variables will be Assessment: used to represent the two quantities. Resources: CC.2.2.6.B.3 Represent and analyze quantitative Standards: relationships between dependent and independent variables. Vocabulary: dependent variable, independent variable Comments: Sixth Grade Math v. 2016 - 2017 Content: Area, Surface Area and Volume o Essential Question: 11 | P a g e Duration: Feb/ Mar 4 weeks What types of units are necessary for finding the area of two dimensional figures and surface area and volume of three-dimensional figures? Why are these units appropriate? What is the relationship between area and volume? Determine the area of triangles and special quadrilaterals. Determine the area of irregular or compound polygons. Determine the volume of right rectangular prisms. Skill: Given coordinates for the vertices of a polygon in the plane, -Use the coordinates to find side lengths and area of the polygon. Represent three-dimensional figures using nets made of rectangles and triangles. Determine the surface area of triangular and rectangular prisms. Assessment: Use various strategies to calculate the area of a right triangle. Use various strategies to calculate the surface area and volume of a rectangular prism. Resources: CC.2.3.6.A.1 Apply appropriate tools to solve real‐world and mathematical problems involving area, surface Standards: area, and volume. Vocabulary: Comments: Sixth Grade Math v. 2016 - 2017 Content: Statistical Variability 12 | P a g e Duration: Mar/Apr 4 weeks Essential Question: How can the understanding and use of measures of central tendency be useful for interpreting and drawing conclusions about data? Display numerical data in plots on a number line, line plots, histograms and box-andwhisker plots. Determine quantitative measures of center and variability. Skill: Describe any overall pattern and any deviations from the overall pattern. Relate the choice of measures of center and variability to the shape of the data distribution and the context that the data was gathered. Assessment: Given various examples of numerical data sets relation to their context will be determined through a display, analyzing or summarizing. Resources: CC.2.4.6.B.1 Demonstrate an understanding of Standards: statistical variability by displaying, analyzing, and summarizing distributions. Vocabulary: Comments: Sixth Grade Math v. 2016 - 2017 Content: Rational Numbers (After PSSA) 13 | P a g e Duration: April/May 2 weeks Essential Question: Skill: Apply properties of operations to add and subtract rational numbers, including real world contexts. Apply properties of operations to multiply and divide rational numbers, including real world contexts. Assessment: Resources: CC.2.1.7.E.1 Apply and extend previous understandings of operations with fractions to operations with Standards: rational numbers. Vocabulary: Comments: Sixth Grade Math v. 2016 - 2017 Content: 2-step equations 14 | P a g e Duration: May/June (4 weeks) Essential How do you solve equations with more than one operation? Question: Solve multi-step real-world and mathematical problems posed with positive and negative Skill: rational numbers. Assessment: Given examples of equations multiple steps will be shown to solve the problem. Resources: CC.2.2.7.B.3 Model and solve real-world and mathematical problems by using and connecting numerical, Standards: algebraic, and/or graphical representations. Vocabulary: Comments: Sixth Grade Math v. 2016 - 2017 Content: Essential Question: Skill: Assessment: Resources: Standards: Vocabulary: Comments: 15 | P a g e Duration: