Review of Standards from September--November
Standards to Address (linear functions and systems of equations):
6.RP.3a—Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by
reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
Make tables of equivalent ratios relating quantities with whole-number measurements, find missing
vales in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
6.EE.9—Use variables to represent two quantities in a real-world problem that change in relationship to
one another; write an equation to express one quantity, thought of as the dependent variable, in terms
of the other quantity, thought of as the independent variable. Analyze the relationship between the
dependent and independent variables using graphs and tables, and relate these to the equation.
Statement of Purpose:
Students will . . .
Know how to:
1. Make a table of equivalent ratios using whole numbers.
2. Find the missing values in a table of equivalent ratios.
3. Plot pairs of values that represent equivalent ratios on the coordinate plane.
4. Define independent and dependent variables.
5. Use variables to represent two quantities in a real-world problem that change in relationship to
one another.
Be able to:
1. Use tables to compare proportional quantities.
2. Solve real-world and mathematical problems involving ratio and rate, e.g., by reasoning about
tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
3. Write an equation to express one quantity (dependent) in terms of the other quantity
(independent).
4. Analyze the relationship between the dependent variable and independent variable using tables
and graphs.
Develop the habits of:
1. Making sense of problems and persevering to solve them.
2. Reasoning abstractly and quantitatively.
3. Modeling with mathematics.
4. Attending to precision.
7.RP.2—Recognize and represent proportional relationships between quantities.
a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent
ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight
line through the origin.
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Review of Standards from September--November
b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and
verbal descriptions of proportional relationships.
c. Represent proportional relationships by equations. For example, if total cost t is proportional to
the number n of items purchased at a constant price p, the relationship between the total cost
and the number of items can be expressed as t = pn.
d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the
situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
Statement of Purpose:
Students will . . .
Know how to:
1. Identify the constant of proportionality as a unit rate.
2. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the
context of the problem.
Be able to:
1. Analyze two ratios to determine if they are proportional to one another with a variety of
strategies. (e.g. using tables, graphs, pictures, etc.)
2. Analyze tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships
to identify the constant of proportionality.
3. Represent proportional relationships by writing equations.
4. Explain what the points on a graph of a proportional relationship means in terms of a specific
situation.
Develop the habits of:
1. Making sense of problems and persevering to solve them.
2. Reasoning abstractly and quantitatively.
3. Modeling with mathematics.
4. Attending to precision.
5. Looking for and expressing regularity in repeated reasoning
8.EE.8 Analyze and solve pairs of simultaneous linear equations.
a. Understand that solutions to a system of two linear equations in two variables correspond to points of
intersection of their graphs, because points of intersection satisfy both equations simultaneously.
b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the
equation. Solve simple cases by inspection. For example, 3x+2y=5 and 3x+2y=6 have no solution because 3x=2y
cannot simultaneously be 5 and 6.
c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example,
given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the
line through the second pair.
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Review of Standards from September--November
8.EE.8a Knowledge


Identify the solution(s) to a system of two linear equations in two variables as the point(s) of intersection
of their graphs
Describe the point(s) of intersection between two lines as points that satisfy both equations
simultaneously
8.EE.8b Reasoning

Estimate the point(s) of intersection for a system of two equations in two unknowns by graphing the
equations
Standards to Address (Pythagorean Theorem):
8.G.6 Explain a proof of the Pythagorean Theorem and it’s converse.
8.G.7 Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world
and mathematical problems in two and three dimensions.
Statement of Purpose:
Students will . . .
Know how to:
1. Define key vocabulary:
square root
Pythagorean Theorem
converse
right triangle
base
legs a & b, sides
height
hypotenuse
proof
right angle
2. Be able to identify the legs and hypotenuse of a right triangle.
3. Explain a proof of the Pythagorean Theorem.
4. Explain a proof of the converse of the Pythagorean Theorem.
Be able to:
1. Solve basic mathematical Pythagorean theorem problems and its converse to find missing
lengths of sides of triangles in two and three-dimensions.
2. Apply Pythagorean theorem in solving real-world problems dealing with two and threedimensional shapes.
Develop the habits of:
1. Making sense of problems and persevering to solve them
2. Modeling with mathematics
3. Look for and make use of structure
4. Use tools appropriately
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Review of Standards from September--November
8.EE.8 Analyze and solve pairs of simultaneous linear equations.
a. Understand that solutions to a system of two linear equations in two variables correspond to points of
intersection of their graphs, because points of intersection satisfy both equations simultaneously.
b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the
equation. Solve simple cases by inspection. For example, 3x+2y=5 and 3x+2y=6 have no solution because 3x=2y
cannot simultaneously be 5 and 6.
c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example,
given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the
line through the second pair.
8.EE.8a Knowledge


Identify the solution(s) to a system of two linear equations in two variables as the point(s) of intersection
of their graphs
Describe the point(s) of intersection between two lines as points that satisfy both equations
simultaneously
8.EE.8b Reasoning

Estimate the point(s) of intersection for a system of two equations in two unknowns by graphing the
equations
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