Food for Thought

Teacher Notes:

• You may want to have students write the measures as ordered pairs (ounces, grams) and compare the rate of change or slope for these pairs.
• As an extension, have students enter the data into a graphing calculator and find a linear regression for the data.

Procedure for the Activity

Answers:

Sample answers are given using six canned food items.

Steps 1–3   Sample using 6 items:

Step 4    Sample answer using table above: stew (524, 18.5); shrimp (120, 4.25); rate of change for stew and shrimp: (18.5 – 4.25) ÷ (524 – 120) = 14.25 ÷ 404 » 0.0353

Step 5    Sample answer using table above: onions (170, 6.0); beans (454, 16.0); rate of change for onions and beans: (16 – 6) ÷ (454 – 170) = 10 ÷ 284 » 0.0352

Step 6    The rates were almost equal.

Step 7    Sample graph using table above:

 
Step 8   Sample answer: Draw a line through the data points. Find the number of ounces on the y-axis. Locate the corresponding point on the x-axis and read the number of grams.

Step 9    It is a conversion factor between grams and ounces. For example, if you know that the number of grams, multiply by 0.035 to get the approximate number of ounces.

Wrapping Up the Activity

According to the World Almanac, one gram is 0.035 ounce and one ounce is 28.3495 grams. The graph in this activity shows that one gram is 0.035 ounce. The reciprocal of 0.035 is about 28.57, which is very close to 28.3495. If you know the number of grams, multiply by 0.035 to get the number of ounces. If you know the number of ounces, multiply by 28.3495 to get the number of grams.