GRADE: 6

Units and Concepts

 (Approximate Number of Instructional Days)

PA Core Standards

Concepts and Competencies

Objectives

Assessments

(*Common)

Materials

& Resources

Module 1:  Ratios and Unit Rates

7 weeks

Focus Standard(s)

CC.2.1.6.D.1 - Understand ratio concepts and use ratio reasoning to solve problems.

Ratios, Proportions, and Percent

Represent ratio relationships in various forms.

Determine unit rates in context.

Convert measurement units using equivalent ratios

Solve problems using ratio and rate reasoning.

At the end of this module, students will be able to independently use their learning to:

• Use ratio language and notation to describe a ratio relationship between two quantities
• Find the unit rate a/b associated with a ratio a: b (with b ≠ 0) and use rate language in the context of a ratio relationship
• Construct tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and/or plot the pairs of values on the coordinate plane. Use tables to compare ratios
• Solve unit rate problems including those involving unit pricing and constant speed
• Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent

*Common assessments MUST come from GoMath! Assessment Guide Form B.

GO Math! Grade 6 – Chapter 4

GO Math! Grade 6 – Chapter 5

GO Math! Grade 6 – Chapter 6

Module 2:  Arithmetic Operations

5 weeks

Focus Standard(s)

CC.2.1.6.E.1 - Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

CC.2.1.6.E.2 - Identify and choose appropriate processes to compute fluently with multi-digit numbers.

CC.2.1.6.E.3 - Develop and/or apply number theory concepts to find common factors and multiples.

Number Theory Concepts and Operations

Interpret and compute quotients of fraction.

Solve problems and compute fluently with whole numbers and decimals.

Find common multiples and factors including greatest common factor and least common multiple.

Use the distributive property to express a sum of two numbers.

At the end of this module, students will be able to independently use their learning to: 

• Interpret and compute quotients of fractions (including mixed numbers), and solve word problems involving division of fractions by fractions
• Solve problems involving operations (+,–, ×, ÷) with whole numbers, decimals (through thousandths), straight computation, or word problems
• Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12
• Apply the distributive property to express a sum of two while numbers, 1 through 100, with a common factor as a multiple of a sum two whole numbers with no common factor  

*Common assessments MUST come from GoMath! Assessment Guide Form B.

GO Math! Grade 6 – Chapter 1

GO Math! Grade 6 – Chapter 2

GO Math! Grade 6 – Chapter 8

GO Math! Grade 6 – Chapter 10

GO Math! Grade 6 – Chapter 12

Module 3:  Rational Numbers

5 weeks

Focus Standard(s)

CC.2.1.6.E.4 - Apply and extend previous understandings of numbers to the system of rational numbers.

Integers and Other Rational Numbers

Interpret and compute quotients of fraction.

Solve problems and compute fluently with whole numbers and decimals.

Find common multiples and factors including greatest common factor and least common multiple.

At the end of this module, students will be able to independently use their learning to: 

• Represent quantities in real-world contexts using positive and negative numbers, explaining the meaning of 0 in each situation
• Determine the opposite of a number and recognize that the opposite of the opposite of a number is the number itself
• Locate and plot integers and other rational numbers on a horizontal or vertical number line; locate and plot pairs of integers and other rational numbers on a coordinate plane

*Common assessments MUST come from GoMath! Assessment Guide Form B.

GO Math! Grade 6 – Chapter 2

GO Math! Grade 6 – Chapter 3

GO Math! Grade 6 – Chapter 10

Module 4:  Expressions and Equations

9 weeks

Focus Standard(s)

CC.2.2.6.B.1 - Apply and extend previous understandings of arithmetic to algebraic expressions.

CC.2.2.6.B.2 - Understand the process of solving a one-variable equation or inequality and apply to real-world and mathematical problems.

CC.2.2.6.B.3 - Represent and analyze quantitative relationships between dependent and independent variables.

Algebraic Expressions

Algebraic Equations

Write, identify and evaluate numerical expressions involving exponents.

Write, read and evaluate algebraic expressions.

Apply the properties of operations to generate equivalent expressions.

Represent and analyze quantitative relationships between Independent and dependent variables.

Solve and interpret one variable equations or inequalities in real world and mathematical problems.

At the end of this module, students will be able to independently use their learning to: 

• Write and evaluate numerical expressions involving whole-number exponents.
• Write algebraic expressions from verbal descriptions
• Identify parts of an expression using mathematical terms (e.g., sum, term, product, factor, quotient, coefficient, quantity)
• Evaluate expressions at specific values of their variables, including expressions that arise from formulas used in real-world problems
• Apply the properties of operations to generate equivalent expressions
• Use substitution to determine whether a given number is a specified set makes an equation or inequality true
• Write algebraic expressions to represent real-world or mathematical problems
• Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all non-negative rational numbers
• Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem and/or represent solutions of such inequalities on number lines
• Write an equation to express the relationship between the dependent and independent variables
• Analyze the relationship between the dependent and independent variables using graphs and tables, and/or relate these to an equation

*Common assessments MUST come from GoMath! Assessment Guide Form B.

GO Math! Grade 6 – Chapter 7

GO Math! Grade 6 – Chapter 8

GO Math! Grade 6 – Chapter 9

GO Math! Grade 6 – Chapter 10

GO Math! Grade 6 – Chapter 11

Module 5:  Area, Surface Area and Volume

5 weeks

Focus Standard(s)

CC.2.3.6.A.1 - Apply appropriate tools to solve real-world and mathematical problems involving area, surface area, and volume.

CC.2.3.6.A.2 – Graph points in all four quadrants on the coordinate plane to solve real world and mathematical problems.

Area, Surface Area, and Volume

Represent and analyze quantitative relationships between Independent and dependent variables.

Find volumes of right rectangular prisms with fractional edge lengths.

Use nets to find surface area of 3 – dimensional figures.

Determine the area of triangles, quadrilaterals, irregular polygons and compound polygons.

Calculate the area of a polygon on a plane given the coordinates of the vertices.

At the end of this module, students will be able to independently use their learning to: 

• Determine the area of triangles and special quadrilaterals (i.e., square, rectangle, parallelogram, rhombus, and trapezoid) formulas will be provided
• Determine the area of irregular or compound polygons
• Determine the volume of right rectangular prisms with fractional edge lengths. formulas will be provided
• Given coordinates for the vertices of a polygon in the plane, use the coordinates to find side lengths and area of the polygon (limited to triangles and special quadrilaterals). formulas will be provided
• Represent three-dimensional figures using nets made up of rectangles and triangles
• Determine the surface area of triangular and rectangular prisms (including cubes). formulas will be provided

*Common assessments MUST come from GoMath! Assessment Guide Form B.

GO Math! Grade 6 – Chapter 10

GO Math! Grade 6 – Chapter 11

Module 6: Statistics

5 weeks

Focus Standard(s)

CC.2.4.6.B.1 - Demonstrate an understanding of statistical variability by displaying, analyzing, and summarizing distributions

CC.2.4.6.B.2 – Use numerical data and apply statistical properties to summarize and describe a distribution.

Data and Distributions

Display data in dot plots, histograms and box-and-whisker plots.

Determine quantitative measures of center and variability.

Choose the appropriate measure of center and variability for a set of data.

At the end of this module students will be able to use their learning to: 

• Display numerical data in plots on a number line, including dot plots, histograms, and box-and-whisker plots
• Determine quantitative measures of center (e.g., median, mean, and/or mode) and variability (e.g., range, interquartile range, and/or mean absolute deviation)
• Describe any overall pattern and any deviations form the overall pattern with reference to the context in which the data were gathered
• Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered

*Common assessments MUST come from GoMath! Assessment Guide Form B.

GO Math! Grade 6 – Chapter 12

GO Math! Grade 6 – Chapter 13