Navigating a Table of Equivalent Ratios

Warmup

Activity #1

Navigate a Table of Equivalent Ratios.

Always keep in mind that in order to create equivalent ratios, you have to multiply or divide both sides of the ratio by the same number. To obtain that in a table of values, one pair is necessary and sufficient.

• Complete the table below. Enter as many pairs as you can.​

Activity #2

More about Tables of Equivalent Ratios.

Every 8 kilometers is 5 miles. So the ratio of kilometers to miles is 8:5. We are going to use the applet below to find other equivalent ratios.

• Change the names in the boxes below as follows; Label 1 to Kilometers, and Label 2 to Miles.
• In the first ratio box, enter 8. In the second ratio box, enter 5.
• Check the kilometers box to see whole number values for kilometers.
• Check the miles box to see corresponding whole number values in miles.
• To organize this data in table form, click “Table” at the top right corner. The data is displayed in table form.
• To organize the data ready for transferring to a graph, click “table” and “2nd table” at the top right corner.
• Now to obtain intermediate ratio values(values that are not whole numbers), click the remaining check box at the lower right corner. A blue vertical line which can be moved appears marking corresponding values.
• Move the blue scale slowly to see equivalent non-whole number ratios.
• To assist you in locating the precise points, click .
• Click the reset button to try using other ratios.

• Use the double number line above to find equivalent ratios for the following;

(1.) Every pint is 2 cups

(2.) Every Pound is 16 Ounces.

(3.) Every Gallon is 4 Quarts.

(4.) Every Quarter is 5 Nickels

Activity #3

Plot Equivalent Ratios on a Double Number Line

In 2016, 128 gigabytes (GB) of portable computer memory cost $32. Here below is a double number line that represents the situation:

One set of tick marks has already been drawn to show the result of multiplying 128 and 32 each by  .

• Label the amount of memory and the cost for these tick marks.
• Next, keep multiplying by and drawing and labeling new tick marks, until you can no longer clearly label each new tick mark with a number.

Here is a table that represents the situation. Find the cost of 1 gigabyte. You can use as many rows as you need.

Did you prefer the double number line or the table for solving this problem? Why?

Challenge #1

Priya collected 2,400 grams of pennies in a fundraiser. Each penny has a mass of 2.5 grams. How much money did Priya raise? If you get stuck, consider using the table.

Challenge #2

Kiran reads 5 pages in 20 minutes. He spends the same amount of time per page. How long will it take him to read 11 pages? If you get stuck, consider using the table.

Challenge #3

Mai is making personal pizzas. For 4 pizzas, she uses 10 ounces of cheese.