Download Consensus Map Grade Level

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:
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
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: