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Course Details:
Course Details:
Grades: 7-8
Length: two semesters
Prerequisite: Math 6
Course Description:
Course Description:
Math 7 is for students to extend and apply many of the concepts they have learned in the previous year, to discover new types of relationships, new and efficient ways to solve problems, and new ways to analyze and look at data and associations. Students will investigate proportional relationships and use this understanding to solve real-world problems involving discounts, interest, taxes, and scale drawings. Building off their understanding of integers, students will apply the properties of operations to all rational numbers in order to efficiently and thoughtfully work with the number system, including how it applies to expressions and equations.
Mathematical Topics
Mathematical Topics
(Recommended Order)
Semester 1
Semester 1
Rational numbers arithmetic, including percent problems
Order of operations with rational numbers, including exponents
Unit rates, proportions, and constant of proportionality (k), including graphing k
Solving two-step equations, including distributive property equations
Semester 2
Semester 2
Scale factors (proportions)
Supplemental and complementary angles and triangle measures
Perimeter, area, surface area, and volume of two- and three-dimensional figures (formulas forward and backward)
Statistical displays and measure of central tendencies
Course/ Grade Competencies
Course/ Grade Competencies
Semester 1
Semester 1
M1.7-8.1: 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.
M2.7-8.1: The learner will expand their understanding of number systems thinking flexibly and attending to precision and reasonableness when solving problems using rational and irrational numbers.
M3.7-8.2: The learner will use reasoning and metacognitive skills through making conjectures, justifying, and effectively communicating mathematical solutions and arguments.
M5.7-8.1: The learner will make use of structure to describe and compare situations that involve proportionality, change, or patterns, and use the information to make conjectures and justify conclusions/ solutions.
Semester 2
Semester 2
M3.7-8.1: The learner will expand the use of computational strategies, algorithms, and proportional reasoning to rational and irrational numbers.
M4.7-8.1: The learner will strategically use tools and apply proportional reasoning and precision to solve measurement problems in pure/ theoretical and authentic applied contexts.
M6.7-8.1: The learner will solve problems involving reasoning using properties of two- and three- dimensional shapes to analyze, represent, and model geometric relationships in pure/ theoretical and authentic applied contexts.
M7.7-8.1: The learner will design investigations and conduct probability experiments involving populations.
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:
M2.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Add and subtract integers.
Add and subtract rational numbers (fractions and decimals).
Standards:
Standards:
AKSS
7.NS.1
Mathematical Practices
Rational Numbers
Arithmetic
Course/ Grade Competencies:
Course/ Grade Competencies:
M2.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Multiply and divide integers.
Multiple and divide rational numbers (fractions and decimals).
Standards:
Standards:
AKSS
7.NS.2
Mathematical Practices
Rational Numbers
Arithmetic
Course/ Grade Competencies:
Course/ Grade Competencies:
M2.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Understand the order of operations with integers.
Understand the order of operations with rational numbers (fractions and decimals).
Standards:
Standards:
AKSS
7.NS.3
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 units 2 – 3
Ratios, Rates, & Proportions -
Ratios, Rates, & Proportions -
Constant of Proportionality (K), Including Graphing K
Constant of Proportionality (K), Including Graphing K
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.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.7-8.1
M5.7-8.1
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
7.PR.1
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.7-8.1
M5.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Determine if fractions, tables, and graphs are proportional and justify their answer.
Calculate and write an equation for the constant of proportionality from tables, graphs, equations and real-world problems.
Standards:
Standards:
AKSS
7.PR.2
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.7-8.1
M5.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Graph the constant of proportionality from tables, equations, and real-world problems.
Standards:
Standards:
AKSS
7.PR.2
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 unit 1
Percent Problems
Percent Problems
Graduate-Level Competency:
Graduate-Level Competency:
M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.
Course/ Grade Competencies:
Course/ Grade Competencies:
M5.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Calculate percent of a number.
Determine a number when given the percent.
Calculate percent increase or decrease.
Standards:
Standards:
AKSS
7.PR.3
Course/ Grade Competencies:
Course/ Grade Competencies:
M5.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Solve real-world problems involving percent off, and items with and without a sales tax.
Can be Covered:
The learner will:
Calculate simple interest.
Standards:
Standards:
AKSS
7.PR.3
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
Calculate sale prices with percent off and include sales tax.
Compare simple interest versus compound interest on final cost of cars, mortgages, etc.
Khan Academy
iReady lessons 20 – 21
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.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Add, subtract, factor, expand, and simplify expressions and linear equations.
Can be Covered:
The learner will:
Simplify expressions and equations with fractions and decimals by multiplying each term by the greatest common factor.
Standards:
Standards:
AKSS
7.EE.1, 7.EE.2
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Solve multi-step problems with rational numbers.
Can be Covered:
The learner will:
Solve two-step equations with the integer on both sides.
Standards:
Standards:
AKSS
6.EE.3
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Solve two-step equations with integers.
Can be Covered:
The learner will:
Solve two-step equations with fractions and decimals.
Standards:
Standards:
AKSS
7.EE.4a
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Solve two-step equations with distributive property.
Can be Covered:
The learner will:
Solve two-step equations with the integer on both sides.
Standards:
Standards:
AKSS
7.EE.4a
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.7-8.1
M3.7-8.2
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Solve and graph two-step inequalities and check for reasonableness.
Standards:
Standards:
AKSS
7.EE.4b
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
Plan a holiday party for the class that includes the total cost of pizza, snacks, and drinks.
Students expand or reduce the holiday party by adding another classroom to the plan, or break the party into two or three smaller groups.
Plan potluck with the necessary utensils included in the final cost.
Khan Academy
iReady unit 4
Scale Drawings
Scale Drawings
Graduate-Level Competency:
Graduate-Level Competency:
M4 - Measurement: The learner will explain reasoning when applying and modeling geometric principles.
Course/ Grade Competencies:
Course/ Grade Competencies:
M4.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Solve problems involving scale drawings.
Adjust to the appropriate unit as needed.
Standards:
Standards:
AKSS
7.G.1
Course/ Grade Competencies:
Course/ Grade Competencies:
M4.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Bisect a line segment using a compass.
Draw various polygons (triangle, square, hexagon, and octagon) with given conditions using a compass and ruler.
Standards:
Standards:
AKSS
7.G.2
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
Recreate a picture that is a different scale.
Draw and calculate ratios to determine various side lengths of polygons based on the initial circle.
Khan Academy
iReady lesson 1
Angles & Circles
Angles & Circles
Graduate-Level Competency:
Graduate-Level Competency:
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:
M3.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Calculate area and circumference of circles with given conditions.
Calculate volume and surface area of cylinders.
Can be Covered:
The learner will:
Calculate volume and surface area of cones.
Standards:
Standards:
AKSS
7.G.4
Course/ Grade Competencies:
Course/ Grade Competencies:
M3.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Calculate supplemental and complementary angles with given conditions.
Calculate angles of triangles with given conditions.
Can be Covered:
The learner will:
Alternate and same-side angles with transversals.
Calculate remote interior angles.
Standards:
Standards:
AKSS
7.G.5
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
Lab using milliliters of water to fill a cylinder and then calculate the volume of the same cylinder in cubic centimeters for comparison.
Determine the area of a cross-section of boys’ and girls’ basketball.
Create a scale drawing of a parking lot with angled and perpendicular parking spaces, and justify which is the better use of space within a given area.
Khan Academy
iReady lessons 6, 28, and 29
Perimeter, Area, Surface Area, &
Perimeter, Area, Surface Area, &
Volume of Prisms & Pyramids
Volume of Prisms & Pyramids
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:
M6.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Calculate the volume and surface area of rectangular and triangular prisms.
Can be Covered:
The learner will:
Calculate the volume and surface area of other regular prisms.
Standards:
Standards:
AKSS
7.G.6
Course/ Grade Competencies:
Course/ Grade Competencies:
M6.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Determine the different types of cross-sections of three-dimensional figures.
Standards:
Standards:
AKSS
7.G.3
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
Calculate the volume of fuel and water tanks used at students’ homes.
Determine the best practice per capacity for new water and fuel tanks.
Create a regular polyhedron.
Khan Academy
Shodor’s interactive cross section flyer: http://www.shodor.org/interactivate/activities/CrossSectionFlyer
Polyhedron: http://www.polytope.net/hedrondude/regular3.htm
iReady lessons 25 – 27
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:
M7.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Understand valid and invalid samples, and why they are valid or invalid.
Can be Covered:
The learner will:
Create valid and invalid samples of a population.
Write valid and invalid sample questions.
Standards:
Standards:
AKSS
7.SP.1, 7.SP.2
Course/ Grade Competencies:
Course/ Grade Competencies:
M7.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Calculate interquartile range
Calculate standard deviation
Can be Covered:
The learner will:
Calculate mean absolute deviation
Standards:
Standards:
AKSS
7.SP.3, 7.SP.4
Course/ Grade Competencies:
Course/ Grade Competencies:
M7.7-8.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Calculate simple and compound probability.
Create a theoretical simple and compound probability model.
Complete an experimental simple and compound probability model.
Can be Covered:
The learner will:
Calculate the probability of flipping specific suits, numbers, or specific cards in a deck followed by a different suit, number, or specific card.
Standards:
Standards:
AKSS
7.SP.5, 7.SP.6,
7.SP.7, 7.SP.8
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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