Ratios, Rates and Proportional Relationships

End of Year Standards Review

• The review includes ratios and proportional relationships, rates and percentages, expressions and equations, rational numbers, data sets and distributions, and area and surface area.
• The review is designed to help refresh knowledge from the year.
• Videos are linked within speaker notes to give problem-solving assistance.

Ratios and Proportional Relationships

• To make a snack mix, combine 2 cups of raisins with 4 cups of pretzels and 6 cups of almonds.
• A particular shade of orange paint has 2 cups of yellow paint for every 3 cups of red paint.
• A recipe for tropical fruit punch says, “Combine 4 cups of pineapple juice with 5 cups of orange juice.”
• Tulip bulbs are on sale at store A, at 5 for 11.00,theregularpriceatstoreBis6for11.00, the regular price at store B is 6 for 11.00,theregularpriceatstoreBis6for13.
• At the kennel, the ratio of cats to dogs is 4:5, there are 27 animals in total.
• Peyton rode her scooter 3 miles in 6 minutes, riding at a constant speed.

Unit Rates and Percentages

• Noah buys 15 baseball cards for $9.00, with each card costing the same.
• Mai traveled 15 meters in 6 seconds, Priya traveled 22 meters in 10 seconds on scooters.
• Skateboarder A travels at a steady rate of 15 feet per second, skateboarder B travels at a steady rate of 22 feet per second.
• A kangaroo hops 2 kilometers in 3 minutes.
• Mai attempted 40 free throws and was successful 25% of the time.
• Priya successfully made 12 free throws yesterday, and today she made 150% as many.
• A bathtub can hold 80 gallons of water, the faucet flows at a rate of 4 gallons per minute.
• At a hardware store, a tool set normally costs 80,butduringathisweek,thetoolsetcosts80, but during a this week, the tool set costs 80,butduringathisweek,thetoolsetcosts12 less than usual.
• Values to order from greatest to least: 55% of 180, 300% of 26, and 12% of 700.
• In a school band of 70 students, 40% are sixth graders and 20% are seventh graders, while the rest are eighth graders.
• Find which is the better deal: 5 tickets for 12.50or8ticketsfor12.50 or 8 tickets for 12.50or8ticketsfor20.16

Expressions and Equations

• Write an equation to represent each hanger, that include variables such as x, w, y and z.
• Match equations to diagrams, and solve for m in: 12 - m = 4, 12 = 4m, m - 4 = 12, and m/4 = 12.
• Solve each equation, including 2x = 5, y + 1.8 = 14.7, 6 = (1/2)z, 3 1/4 = (1/2) + w, and 2.5t = 10.
• Solve each equation, including 4x = 32, 4 = 32x, 10x = 26, and 26 = 100x.
• Determine the equations that equal 3.15/0.45 from the following: (3.15)•(0.45), (3.15) ÷ (0.45), (3.15) • 1/0.45, (3.15) ÷ 45/100, (3.15) • 100/45 and 0.45/3.15
• Instructions for a craft project say that the length of a red ribbon should be 7 inches less than the length of a blue ribbon.
• Determine which equation represents the large, outer rectangle as: 5(2 + 4), 5 • 2 + 4, 5 • 2 + 5 • 4, 5 • 2 • 4, 5 + 2 + 4 or 5 • 6.
• Complete each calculation using the distributive property, for questions 98 • 24, 21 • 15 and 0.51 • 40.
• Determine the expressions equivalent to 4b as: b + b + b + b, b + 4, 2b + 2b, b • b • b • b, and b ÷ 1/4.
• Choose expressions that do not represent the total area of the rectangle as: 5t + 4t, t + 5 + 4, 9t, 4 • 5 • t, or t(5 + 4)
• Indicate equations that equal 3^4, with options 7, 4^3, 12, 81, 64 and 9^2.
• Find two different ways to rewrite 3xy + 6yz using the distributive property.
• Determine the expressions that represent the area of a shaded rectangle.
• Show all expressions that are equal to 3 • 3 • 3 • 3 • 3, as options 3 • 5, 3^5, 3^4 • 3, 5 • 3, and 5^3.
• Evaluate each expression: 7 + 2^3, 9 • 3^1, 20 - 2^4, 42 • 6^2 and 8 • (1/2)^2
• Evaluate each expression for the given value of x: 2 + x^3, x is 3, x^2, x is 1/2, 3x^2, x is 5, 100 - x^2, x is 6.

Rational Numbers

• Plot the numbers -1.5, 3/2, -3/2, and -4/3 on a number line, labeling each point with its numeric value.
• Compare each pair of expressions using >, <, or =, in the following equations: -32 _ 15, |-32| _ |15|, 5 _ -5, |5| _ |-5|, 2 _ -17, 2 _ |-17|, |-27| _ |-45|, and |-27| _ -45.
• Write the coordinates of each point on a graph.
• Graph these points in a coordinate plane: (-2, 3), (2, 3), (-2, -3), (2, -3).
• A sign reads "Speed limit, 60 miles per hour".
• List all the factors of 42.
• A green light blinks at a rate of every 4 seconds, and a yellow light blinks every 5 seconds.
• Diego has 48 chocolate chip cookies, 64 vanilla cookies, and 100 resin cookies for a bake sale.

Data-sets and Distributions

• Mai played 10 basketball games and recorded the number of points she scored in a dot plot.
• Sixth Grade times, in minutes, it took 40 sixth-grade students to run 1 mile.
• Noah scores 20 points, Mai scores 30, the mean score for Noah, Mai, and Clare was 40.
• Han recorded the number of pages that he read each day for five days in a dot plot.
• The five-number summary to draw a box plot: Minimum: 40, First Quartile (Q1): 45, Median: 48, Third Quartile (Q3): 50 and Maximum: 60.

Area and Surface Area

• Select all parallelograms that have a correct height labeled for the given base.
• Determine which pairs of base and height produces the greatest area, with all measurements in centimeters: A.b=4, h=3.5, B.b=0.8, h=20, C.b=6, h=2.25 and D.b=10, h=1.4
• Determine the triangle that has the greatest area and show your reasoning.
• Find the area of a trapezoid, and explain your strategy.
• What is the surface area of a rectangular prism?
• What three-dimensional figure can be assembled from the net?
• What is the volume of a cube?
• Find the surface area of this triangular prism, with all measurements in meters.