Evaluate Expressions
Evaluate the expression when s=1/2: Use the formula V=s^3 to find the volume of a cube with side length s=1/2
1/8 cubic units
Use the distributive property to rewrite: 3(2+x) as an equivalent expression.
3(2+x)=6+3x
Identify independent and dependent variables: In the formula d=65t for a car going at constant speed, which variable is independent and which is dependent?
Independent: t (time). Dependent: d (distance).
Context: If the temperature is −3°C in the morning and rises 5 degrees, what is the new temperature?
New temp: −3+5=2°C.
Plotting: Plot the point (3,2). Which quadrant is it in?
(3,2) is in Quadrant I.
Evaluate the expression when s=1/2: Use the formula A=6s^2 to find the surface area of the same cube with side length s=1/2
3/2 or 1 1/2
Factor the expression: 24x+18y; write an equivalent expression showing the greatest common factor.
24x+18y=6(4x+3y).
Create an equation: Jenna is paid $8 per hour. Let h be hours worked and p be pay. Write an equation for pay in terms of hours.
p=8h.
Ordering: Which is greater: −2 or −7? Explain using number line reasoning.
−2>−7 because −2 is closer to zero.
Quadrants: Name the quadrant for each point: (−4,5),(2,−3),(−1,−6).
(−4,5) Quadrant II; (2,−3) Quadrant IV; (−1,−6) Quadrant III.
Evaluate: 3(2+x) for x=4
18
Write an equivalent expression for y+y+y using multiplication.
y+y+y=3y.
Table & equation: A skateboarder travels at a constant speed of 10 feet per second. Fill in the table for times t=1,2,3 and write the equation relating distance d and time t.
Table: t:1,2,3 → d:10,20,30. Equation: d=10t
Real-world: A submarine is at −120 meters. It ascends 45 meters. What is its new elevation?
New elevation: −120+45=−75 meters.
Graph & distance: Find the distance between the points (4,2) and (4,−3). Explain how you used coordinates and absolute value.
Distance = ∣2−(−3)∣=∣5∣=5 (since same x-coordinate).
Evaluate using order of operations (no parentheses): 2^3+4×3−5
15
Use properties of operations to show an equivalent expression: Rewrite 5(a+4)+3a as a simplified single expression.
5(a+4)+3a=5a+20+3a=8a+20.
Graph & interpret: Given the equation d=12t, list three ordered pairs (distance, time) with whole-number times, then explain what the slope represents in this real-world context.
Ordered pairs e.g., (0,0) (if starting at 0), (1,12), (2,24). Slope 12 = speed in miles per hour (distance per hour).
Absolute value distance: Find the distance between temperatures −4°C and 3°C using absolute value. Show your work.
Distance = ∣−4−3∣=∣−7∣=7 degrees (or compute ∣−4∣+∣3∣=4+3=7).
Real-world & variables: A cyclist’s position along an east-west number line is given by x (miles). At time tt hours, the cyclist’s position is x=−2+5t. Give the ordered pair for t=1 and state what negative and positive values of x represent.
At t=1 → x=−2+5(1)=3 → ordered pair (1,3) if listing (t,x) or position x=3. Negative x could represent west of origin, positive x east.
Real-world: A bike travels at a constant speed of 12 miles per hour. Evaluate the expression for distance d=12t when t=2.5 hours.
30 miles
True/False with explanation: The expression 2(3x+5) is equivalent to 6x+10. If true, explain which property justifies it; if false, correct it.
True.2(3x+5)=6x+10 by distributive property.
Challenge: A rectangular garden’s area A (in square feet) is related to its side length s by A=s^2. If the side length is measured in meters and converted to feet by f=3s (where s is in meters and f is in feet), write an equation that gives area in square feet in terms of s (meters). Simplify the expression.
If f=3s (feet) and A=f^2, then A=(3s)^2=9s^2 (square feet).
Context & zero meaning: Describe a real-world situation where zero has a meaningful interpretation, include positive and negative values, and show one numerical example using integers.
Example: Bank account with deposits (positive) and withdrawals (negative); zero means no balance. E.g., deposit +50, withdrawal −20 → balance 30.
Challenge graph problem: Draw (or list) the vertices of a rectangle with corners at (−2,1),(3,1),(3,−4),(−2,−4). Use coordinates to find the length and width, then compute the area.
Length = distance between x-coordinates 3−(−2)=5; width = distance between y-coordinates 1−(−4)=5; area = 5×5=25 square units.