Monday, October 15th
1.12 Samples and Surveys
Getting Started – 5 min
Mental Math and Reflexes – Smartboard Notebook file using Responders.
Students make ballpark estimates for products. Volunteers share strategies if time
permits.
Suggestions:
26 * 33
59 * 94
12 * 224
157 * 319
900 (30 * 30) or 750 (25 * 30)
5400 (60 * 90) or 6,000 (60 * 100)
2,400 (12 * 200) or 2,250 (10 * 225)
45,000 (150 * 300) or 60,000 (200 * 300)
Math Message – 2 min
Complete the Math Message on journal page 40 with a partner
Math Message Follow Up – 5 min
Student Math Journal, page 40
Have students share how they would find the percentage of cookie weight that is
chocolate chips. Many students might suggest breaking up the cookies, removing the
chocolate chips, and weighing the chips. Some students will need help taking the
problem to the next step, which involves dividing the weight of the chips by the total
weight of the cookies (20 ounces). Provide students with examples such as the following.
If the weight of the chocolate chips in a 20-ounce bag of cookies is 13 ounces, then
Weight of chips
= 13
Weight of the sample
20
= 0.65 * 100 = 65%
Because a 20-ounce bag of cookies represents a part of all the chocolate chip cookies the
manufacturer makes, the bag can be considered a sample. A sample is part of the
population that is chosen to represent the whole population. In this case, the sample is
the 20-ounce bag of cookies; the population is all the chocolate chip cookies the
manufacturer makes.
Draw a Venn diagram to show the relationship between a sample and a population.
Because the population is very large, it would be impractical to collect data about every
chocolate chip cookie. Therefore, data are collected from a representative sample of the
population. The data from the bag approximate the data from the entire population.
Determining Representative and Biased Samples – 10 min
Student Math Journal, page 40
A sample should always be examined to determine whether it is representative of the
population. Sample is a word that has multiple meanings, including a mathematical
meaning. To support English language learners, write sample on the board and discuss
its meaning in this context. A representative sample can be provided by a random
sample. A random sample gives all members of the population that same chance of being
selected. The bag of cookies described in the Math Message is a random sample. It is
assumed that the cookies in the bag were randomly selected. Cookies with few chips and
those with many chips had an equal chance of being included.
A biased sample is a sample that does not truly represent the total population from which
it was selected. A sample is biased if some members of the population have a greater
chance of being selected than others. If the cookie manufacturer were to hand select
cookies for the sample, for example, it’s likely that the manufacturer would select
cookies with a generous amount of chips. To support English language learners, write
random sample and biased sample on the board. Discuss the meanings and write some
examples of each type of sample.
Circulate and assist as students work on journal page 40 to identify samples as random or
biased. Discuss students’ responses.
Analyzing a Newspaper Article – 10 min
Student Math Journal, page 41
Surveys are often used to gather data from a sample of people. A recall survey is a
survey used to collect information about past behaviors, habits, or activities. The
individual pieces of information gathered in such a survey are usually not precise.
However, estimates based on combined survey data are often worthwhile. To support
English language learners, write recall survey on the board. As you discuss examples of
recall surveys, list them on the board.
The U.S. Department of Agriculture (USDA) conducts nationwide food consumption
recall surveys. The data used in this activity are based on the USDA Continuing Survey
of Food Intake by Individuals from 1977 – 1978 and 1994 – 1996. Data are collected by
interviewing people who know a lot about the food that members of their households eat.
A food list is used to help respondents recall kinds, quantities, and costs of food used
during the seven data prior to the interview.
To support English language learners, discuss the meaning of the words consumption and
preferences. Have students read the newspaper article “What Kinds Are Drinking” on
journal page 41 and answer the related questions.
Pose discussion questions such as the following:
-Why do you think side-by-side bar graphs were used in this article?
They make it easy to see the changes in drinking habit between 1978 and 1994
-Why are there separate data for children and teenagers?
Their drinking habits are different
-Why do you think there is a difference in data collected from 6 to 11 year olds and from
teenagers?
Teenagers usually have more control over what they drink than young children
-Why might milk consumption have decreased and juice and soft drink consumption have
increased over the years?
Sample answers: Soft drink and juice machines are in more places now. Juice is now
available in juice boxes, which are convenient for lunches and snacks. Allergies and
other medical problems are now associated with milk consumption.