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Course Details:
Course Details:
Grade: 6
Length: two semester
Prerequisite: Math 5
Course Description:
Course Description:
In Math 6, instructional time should focus on four critical areas:
Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems;
Completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers;
Writing, interpreting, and using expressions and equations; and
Developing understanding of statistical thinking.
Mathematical Topics
Mathematical Topics
(Recommended Order)
Semester 1
Semester 1
Number Systems
Expressions and Equations
Semester 2
Semester 2
Writing Ratios, Finding Unit Rates, and Solving Proportions
Perimeter, Area, Surface Area, Volume of Polygons and Rectangular Prisms
Statistics and Probability
Course/ Grade Competencies
Course/ Grade Competencies
Semester 1
Semester 1
M1.5-6.1: The learner will reason abstractly and manipulate symbolic expressions to represent relationships and interpret expressions and equations in terms of a given context for determining an unknown value.
M2.5-6.1: The learner will expand their understanding of number systems, thinking flexibly and attending to precision and reasonableness when solving problems using rational numbers.
M3.5-6.2: The learner will use reasoning and metacognitive skills through making conjectures, justifying, and communicating mathematical solutions and arguments.
M5.5-6.1: The learner will make use of structure to describe and compare situations that involve change or patterns and use the information to make conjectures and justify conclusions/solutions.
Semester 2
Semester 2
M3.5-6.1: The learner will expand the use of computational strategies, algorithms, and proportional reasoning to rational numbers.
M4.5-6.1: The learner will use tools and apply precision and reasoning to solve measurement problems in authentic applied contexts.
M6.5-6.1: The learner will solve problems involving reasoning using properties of two- and three-dimensional shapes to analyze, represent, and model geometric relationships in authentic applied contexts.
M7.5-6.1: The learner will design investigations and gather data involving populations (data sets).
Number Systems
Number Systems
Graduate-Level Competency:
Graduate-Level Competency:
M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.
Course/ Grade Competencies:
Course/ Grade Competencies:
M2.5-6.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Add and subtract rational numbers (fractions and decimals).
Find and use the greatest common factor for adding fractions.
Find and use least common multiple for reducing fractions.
Standards:
Standards:
AKSS
6.NS.1-4
Mathematical Practices
Rational Numbers
Arithmetic
Course/ Grade Competencies:
Course/ Grade Competencies:
M2.5-6.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Multiply and divide rational numbers (fractions and decimals).
Find and use least common multiple for reducing fractions.
Standards:
Standards:
AKSS
6.NS.1-4
Mathematical Practices
Rational Numbers
Arithmetic
Course/ Grade Competencies:
Course/ Grade Competencies:
M2.5-6.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Understand and order of rational numbers on a number line.
Understand absolute value.
Graph points on a coordinate plane.
Can be Covered:
The learner will:
Add and subtract integers.
Standards:
Standards:
AKSS
6.NS.5-8
Mathematical Practices
Rational Numbers
Arithmetic
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
Number tiles for positive and negative integers.
“Good Guys (+) and Bad Guys (-)” and they battle it out for addition and subtraction.
Khan Academy
iReady unit 2, lesson 6
iReady unit 6
Expressions & Equations
Expressions & Equations
Graduate-Level Competency:
Graduate-Level Competency:
M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.
M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.5-6.1
M3.5-6.2
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Write and solve exponential problems, including expanded form.
Standards:
Standards:
AKSS
6.EE.1
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.5-6.1
M3.5-6.2
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Write, read and solve expressions with variables.
Use distributive property and factoring to simplify expressions.
Write mathematical expressions and equations from real-world problems.
Can be Covered:
The learner will:
Write two-step equations for real-world problems.
Standards:
Standards:
AKSS
6.EE.2-3, 6
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.5-6.1
M3.5-6.2
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Solve one-step equations with integers and rational numbers.
Show the relationship between the dependent and independent variables in an equation.
Can be Covered:
The learner will:
Solve two-step equations with integers.
Standards:
Standards:
AKSS
7.EE.5, 7-9
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
Khan Academy
iReady lesson 5 and unit 5
Writing Ratios, Finding Unit Rates, & Solving Proportions
Writing Ratios, Finding Unit Rates, & Solving Proportions
Graduate-Level Competency:
Graduate-Level Competency:
M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.
M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.
M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.5-6.1
M3.5-6.1
M5.5-6.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Simplify proportions and know how to write them three different ways.
Standards:
Standards:
AKSS
6.RP.1
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.5-6.1
M3.5-6.1
M5.5-6.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Calculate unit rates using the same units with rational numbers (decimals and fractions).
Can be Covered:
The learner will:
Calculate unit rates using the different units with rational numbers (decimals and fractions).
Standards:
Standards:
AKSS
6.RP.2
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.5-6.1
M3.5-6.1
M5.5-6.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Write and solve proportions including real-world problems.
Standards:
Standards:
AKSS
6.RP.3
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
Compare unit rates for groceries (unit prices), cars (MPG), and wood prices (dollars per cord).
Khan Academy
iReady units 3-4
Perimeter, Area, Surface Area, Volume of Polygons, & Rectangular Prisms
Perimeter, Area, Surface Area, Volume of Polygons, & Rectangular Prisms
Graduate-Level Competency:
Graduate-Level Competency:
M6 - Geometry: The learner will solve problems involving spatial reasoning and model geometric concepts in applied contexts.
Course/ Grade Competencies:
Course/ Grade Competencies:
M6.5-6.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Calculate the area of regular polygons (including on coordinate planes).
Identify the different parts of a circle.
Can be Covered:
The learner will:
Calculate the circumference and area of circles.
Standards:
Standards:
AKSS
6.G.1, 3, 5
Course/ Grade Competencies:
Course/ Grade Competencies:
M6.5-6.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Represent three-dimensional figures as nets.
Calculate the volume and surface area of rectangular prisms.
Can be Covered:
The learner will:
Calculate the volume and surface area of triangular prisms.
Standards:
Standards:
AKSS
6.G.2, 4
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
Calculate the volume of fuel and water tanks used at students’ homes.
Calculate the surface area and volume of their bedroom at home.
Khan Academy
iReady unit 1
Statistics & Probability
Statistics & Probability
Graduate-Level Competency:
Graduate-Level Competency:
M7 – Data, Analysis, Probability, and Statistics: The learner will apply statistical methods to summarize, represent, analyze, and interpret data.
Course/ Grade Competencies:
Course/ Grade Competencies:
M7.5-6.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Write valid and invalid statistical questions, and be able to explain identify why they are valid or invalid.
Identify the distribution of a data set.
Standards:
Standards:
AKSS
6.SP.1-2
Course/ Grade Competencies:
Course/ Grade Competencies:
M7.5-6.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Calculate measures of center, including range and finding outliers.
Identify when to use the different measures of center.
Explain the effect of adding or removing an outlier to the measures of center.
Standards:
Standards:
AKSS
6.SP.3, 5
Course/ Grade Competencies:
Course/ Grade Competencies:
M7.5-6.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Calculate interquartile range and create box plots.
Read and create dot plots, histograms, and pie charts.
Can be Covered:
The learner will:
Calculate the standard deviations.
Standards:
Standards:
AKSS
6.SP.4-5
Course/ Grade Competencies:
Course/ Grade Competencies:
M7.5-6.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Calculate simple and compound theoretical probability.
Determine whether a game is fair or unfair based on probability.
Can be Covered:
The learner will:
Calculate the experimental probability.
Standards:
Standards:
AKSS
6.SP.6-7
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
Create a game that involves probability.
Khan Academy
iReady unit 7
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