Activity 2: Graphing
(Teacher Copy)

• transparencies of Activity 2 Reference Sheets

Students will learn to read and construct bar, line, and circle (pie) graphs, including double and triple bar and line graphs, in learning about the Food Guide Pyramid, recommended daily food servings for various categories of people, and proportions of protein, carbohydrates, and fat that comprise a healthful diet. Use with Activity 2 Student Copy and Reference Sheets.

• To read and construct single, double, and triple bar graphs.
• To read and construct single, double, and triple line graphs.
• To read and construct circle (pie) graphs.
• To become familiar with the Food Guide Pyramid and the recommended daily food servings for various categories of people.
• To become familiar with the recommended daily proportions of protein, carbohydrates, and fat that comprise a healthful diet.

Introduction

• Who has heard of the Food Guide Pyramid? What is it? (It is a chart prepared by the U.S. Department of Agriculture and the U.S. Department of Health and Human Services that names food categories and tells what proportion of the daily diet each should comprise.) What did it replace in recent years? (the "four food groups")

• Which food group makes up the largest proportion of a good daily diet? (breads/grains) the smallest? (fats/sweets)

• How do you think the "typical" American diet compares to the pyramid? (probably includes more food from the fats/sweets and meat groups and less from the lower levels than is recommended)
• What do you think a food pyramid of your daily diet would look like?
• Why do you think there is a range listed in the number of servings recommended within each food group? (Upper and lower limits show that there is a bit of flexibility in some cases in number of servings included from a group but mainly serve to include the different types of diets needed by different people, as dictated by age, height, body frame size, body composition [fat vs. muscle], activity level, gender, etc.)
• What do you think counts as one serving of: bread (1 slice), ready-to-eat cereal (1 ounce), rice (1/2 cup), vegetable or fruit juice (3/4 cup, or 6 ounces), milk (1 cup, or 8 ounces), meat (2-3 ounces of lean meat, poultry, or fish)

Note that this is typically called a bar graph, although it might also be called a column graph (usually on computer graphing software) because the bars are vertical. Ask:

• From which food group should the fewest number of servings come? (fruit; meat)
• How many servings of vegetables are recommended? (3)
• Besides the labels along the x (horizontal) and y (vertical) axes, what purpose do the other three labels (sets of words) serve? (The top one is the title that tells what the graph is displaying, the one on the left tells what the numbers by the tick marks on the y axis stand for, and the bottom label similarly categorizes the terms along the x axis.)
• What types of information do you think a bar graph is especially effective for showing? (the relative amounts/sizes of a set of items that may or may not constitute a whole)
• Could the labels along the x and y axes be reversed (all labeling on left exchanged with all labeling along the bottom)? (Yes; display Activity 2 Reference Sheet, page 3 to illustrate.)

• How is this graph like the bar graph? (Both have a rectangular format created by use of an x and a y axis. Both employ similar labeling, and the key data is found where the pertinent x and y descriptors/values meet. Both employ length in reaching a graphed value.) How is it different? (The values for each column are represented only by a point rather than by a thick bar that extends along its entire length, and plotted data are connected with adjacent data.)
• What types of information do you think a line graph is especially effective for showing? (values over a period of time)

• How is this graph like either or both of the other two graphs? (Displays the same information graphically; shows values in a relative manner, which especially compares to the bar graph.) How is it different? (It is circular rather than rectangular; it does not have two different sets of labels that are set up along axes; data is displayed as fractional parts of a single whole.)
• What types of information do you think a circle graph is especially effective for showing? (fractional parts or relative proportions of a single whole)

Part A

1. 1. The bars are grouped in pairs with each of the two bars representing (in a consistent manner) the same type of information for a different category.
   2. Two (for a total of 6 oz.)
   3. Fruit-girls, milk-girls and boys, meat-boys
2. 1. A double line graph
   2. Two servings
   3. Milk
3. 1. A legend (or key)-an explanatory list of the symbols on a map or chart
   2. Maps...
4. Because each of the two sets of information-girls, boys-is a separate complete entity, and a circle graph can only show one "whole" at a time.
5. Probably Figure 1, the bar graph, because the adjacent bars nicely show direct girl-boy comparisons, and the full length shown for each bar gives a better sense of the relative size of the values than is gained by looking at single points. Also see the discussion following the above note.

Part C

1. 1. 360°
   2. fraction-1/2, percent-50%, # of degrees-180°
   3. fraction-1/4, percent-25%, # of degrees-90°
   4. fraction-1/3, percent-33 1/3% ( %), # of degrees-120°
2. 1. Equivalent fractions: 30/120 = 1/4 (divide both terms of fraction by greatest common factor); four 30s in 120 means four equal parts, of which 30 is one (and so forth)
   2. Equivalent fractions: 30/120 = 1/4 = 25/100 = 25%; division to the nearest hundredth (30 ÷ 120, or dividing the numerator of any fraction equivalent to 30/120 by its denominator)
   3. Proportion: 30/120 = x/360; division: 360 ÷ 120 to find how many degrees each number in the 120 represents, then multiplying that times the number of units of interest (each unit of the 120 is "worth" 3 degrees, so 30 times 3 degrees each is 90 degrees)-in other words, "inflating" both numbers to put them on a scale in 360ths (essentially, finding a proportion).
3. Elicit names of first two types of graph: triple bar graph; triple line graph.
   
   Graph 1
   Graph 2
   Graph 3, 4, and 5

4. Use decimal form of percent and multiply it times 360, as in 64% of the circle would be 230.4° (0.64 x 360); use equivalent fractions or proportions after converting a percent to its fraction form (see earlier explanations, as in #2B).
5. Probably the bar graph for the same reasons given in Part A #5, although other answers may be reasonable.
6. Proteins
7. Chinese, because if any proportions are to deviate from those that are recommended, it is better to be lower in fats and higher in carbohydrates than the reverse.
8. 
   

   	a value of 0	a negative number
   Bar Graph	no bar shows beyond axis	bar goes below x axis for vertical bars, left of y axis for horizontal bars
   Line Graph	point is on x axis	point goes below x axis
   Circle Graph	can't be shown	can't be shown