Interactive study guide — Reveal Math Unit 3 · Standard 6.AT
Write ratios in three forms, identify part-to-part vs. part-to-whole relationships, and calculate unit rates.
A ratio compares two quantities. It can be written three ways: a : b, a to b, or a/b.
A part-to-part ratio compares one part of a group to another part (e.g., red marbles to blue marbles). A part-to-whole ratio compares one part to the total (e.g., red marbles to all marbles).
A unit rate is a rate with a denominator of 1. Divide to find it.
A class has 12 boys and 18 girls. What is the ratio of boys to girls in simplest form?
You drive 150 miles in 3 hours. What is the unit rate?
A bag has 5 red and 8 blue marbles. What is the part-to-whole ratio of red marbles to total marbles?
Generate equivalent ratios using multiplication and division, and organize them in ratio tables and double number lines.
Equivalent ratios are ratios that express the same relationship. Multiply or divide both terms by the same number to find them.
A ratio table organizes equivalent ratios in rows or columns. A double number line shows two quantities lined up at equivalent values.
To check if two ratios are equivalent, simplify both ratios to simplest form or check that both terms are multiplied or divided by the same scale factor.
Which ratio is equivalent to 3 : 5?
In a ratio table, if the first row is 4 and 10, what pair comes next when you multiply by 2?
Are 6 : 9 and 10 : 15 equivalent?
Plot equivalent ratios on a coordinate plane, interpret the slope as a unit rate, and connect graphs to tables and equations.
Each equivalent ratio can be plotted as an ordered pair (x, y) on the coordinate plane. The horizontal axis is x (input) and the vertical axis is y (output).
A graph shows a proportional relationship (equivalent ratios) if and only if:
The point (1, r) reveals the unit rate r. In the equation y = kx, k is the constant of proportionality (unit rate). For every point on the line, y ÷ x = k.
| Hours (x) | Earnings (y) | Point (x, y) | Action |
|---|---|---|---|
| 0 | $0 | (0, 0) | |
| 1 | $15 | (1, 15) | |
| 2 | $30 | (2, 30) | |
| 3 | $45 | (3, 45) | |
| 4 | $60 | (4, 60) |
Question 1: Look at the graph below showing bicycle riding distance over time. What is the unit rate (speed in miles per hour)?
Question 2: On the paint-mixing graph below, what does the highlighted point (4, 8) represent?
Question 3: The graph below shows carnival ticket sales at a constant rate. Based on the graph, how much will it cost to purchase 6 tickets?
Question 4: Which of the three graphs below represents a proportional relationship (equivalent ratios)?
Starts above 0 (at y = 3)
Straight line through (0, 0)
Curved line
Compare ratios and rates using unit rates and equivalent ratios in tables to find better buys and make decisions.
To find the better buy or faster rate, calculate the unit rate for each option and compare.
You can also compare two ratio relationships by scaling both ratios in a ratio table until they share a common quantity, then comparing the other quantity.
Pack A: 6 pencils for $3. Pack B: 10 pencils for $4. Which is the better buy?
Recipe A uses 2 cups of sugar for every 3 cups of flour (2 : 3). Recipe B uses 5 cups of sugar for every 6 cups of flour (5 : 6). Which recipe has more sugar for the same amount of flour?
Car A travels 180 miles in 3 hours. Car B travels 220 miles in 4 hours. Which car is traveling at a faster rate?
Convert units within and between measurement systems using ratio reasoning and conversion factors.
A conversion factor is a ratio equal to 1 that relates two units (e.g., 12 inches / 1 foot).
Multiply by the conversion factor so the unwanted unit cancels out. For multi-step conversions, chain conversion factors.
How many feet are in 36 inches?
Convert 5 kilometers to meters. (1 km = 1,000 m)
How many inches are in 2 yards? (1 yard = 3 feet, 1 foot = 12 inches)
Tap a card to reveal the definition.