SME
Grade 8 Math
Expressions & Equations
Integer exponent rules
Main lesson
Dividing powers
Use this for “Write 7⁶ ÷ 7² with a single exponent” or “What is 10³ ÷ 10³?”
A power of a power
Use this for “Write (10⁷)² with a single exponent.”
Zero and negative exponents
Use this for “What is 5⁻¹?” or “Write 10⁻² as a fraction.”
True or false?
Use this for “Is 3⁴ × 3⁵ = 3⁹ true?” or “Which equations are true?”
Scientific notation
Main lesson
Which is bigger, and how many times
Use this for “Which is greater, 2.4 × 10⁷ or 6.5 × 10⁴, and about how many times?”
Multiply in scientific notation
Use this for “(3.1 × 10⁴) × (2 × 10⁶)”.
Add and subtract in scientific notation
Use this for “3.6 × 10⁵ + 2.9 × 10⁵” or “How much larger is 4.2 × 10⁸ than 7.5 × 10⁷?”
Powers of ten by name
Use this for “Match 1,000,000 to one million and to a power of ten.”
Slope and rate of change
Main lesson
Slope as a unit rate
Use this for “Ana bikes 3 miles in 0.25 hours at a constant speed. What is her speed, and how far in 2 hours?”
Compare two rates
Use this for “One company charges $140 for 5 cubic yards, the other $93 for 3. Which is cheaper per cubic yard?”
The signs of the slope and intercept
Use this for “Which line rises to the right and crosses the y-axis below 0?”
Linear equations with variables on both sides
Main lesson
Negatives on a balance
Use this for “4x − 7 = −2x + 11” or “2x − 3 = −x + 6”.
Brackets first
Use this for “3(2x + 1) = 4x + 15”.
Clear the fraction
Use this for “3/4 x + 2 = −7”.
One, none or infinitely many?
Use this for “Does 5x + 2 = 5x − 9 have one solution, none, or infinitely many?”
Steps to solve 3x + 4 = x + 10
Use this for “What do you do first to solve 3x + 4 = x + 10?”
Systems of two linear equations
Main lesson
When do two plans cost the same?
Use this for “Gym A: $150 to join and $20 a month. Gym B: $60 and $35. When do they cost the same?”
How many of each
Use this for “8 tickets cost $41. Adult tickets are $7 and child tickets $4. How many of each?”
Lines written ax + by = c
Use this for “Which point is on both 2x + y = 9 and x − y = 3?”
How many solutions does the system have?
Use this for “Do y = 3x − 2 and y = 3x + 5 have a solution?”