8.EE. Grade 8 - Expressions and Equations

8.EE.A. Work with radicals and integer exponents.

8.EE.A.1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, $3^2\times3^{-5} = 3^{-3} = 1/3^3 = 1/27$.

• Ants versus humans
• Extending the Definitions of Exponents, Variation 1
• Raising to the zero and negative powers

8.EE.A.2. Use square root and cube root symbols to represent solutions to equations of the form $x^2 = p$ and $x^3 = p$, where $p$ is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that $\sqrt{2}$ is irrational.

• No tasks yet illustrate this standard.

8.EE.A.3. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as $3 \times 10^8$ and the population of the world as $7 \times 10^9$, and determine that the world population is more than $20$ times larger.

• Ant and Elephant
• Orders of Magnitude
• Pennies to heaven

8.EE.A.4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

• Ants versus humans
• Choosing appropriate units
• Giantburgers
• Pennies to heaven

8.EE.B. Understand the connections between proportional relationships, lines, and linear equations.

• Different Areas?
• DVD Profits, Variation 1
• Equations of Lines
• Find the Change
• Folding a Square into Thirds
• Proportional relationships, lines, and linear equations
• Stuffing Envelopes

8.EE.B.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

• Coffee by the Pound
• Comparing Speeds in Graphs and Equations
• Peaches and Plums
• Sore Throats, Variation 2
• Stuffing Envelopes
• Who Has the Best Job?

8.EE.B.6. Use similar triangles to explain why the slope $m$ is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation $y = mx$ for a line through the origin and the equation $y = mx + b$ for a line intercepting the vertical axis at $b$.

• Slopes Between Points on a Line

8.EE.C. Analyze and solve linear equations and pairs of simultaneous linear equations.

• Two Lines

8.EE.C.7. Solve linear equations in one variable.

• Coupon versus discount
• Sammy's Chipmunk and Squirrel Observations
• Solving Equations
• The Sign of Solutions

8.EE.C.7.a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form $x = a$, $a = a$, or $a = b$ results (where $a$ and $b$ are different numbers).

• No tasks yet illustrate this standard.

8.EE.C.7.b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

• No tasks yet illustrate this standard.

8.EE.C.8. Analyze and solve pairs of simultaneous linear equations.

• Cell Phone Plans
• Fixing the Furnace
• Folding a Square into Thirds
• How Many Solutions?
• Kimi and Jordan

8.EE.C.8.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.

• The Intersection of Two Lines

8.EE.C.8.b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. 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 $6$.

• No tasks yet illustrate this standard.

8.EE.C.8.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.

• Quinoa Pasta 1
• Summer Swimming