Instructional Week 10: March 7-11
ISTEP + 10 Mathematics
Focus Topic: Data Analysis plus Spiral Review
Paced Standards:
AI.DS.1: Distinguish between random and non-random sampling methods, identify possible sources of
bias in sampling, describe how such bias can be controlled and reduced, evaluate the characteristics of
a good survey and well-designed experiment, design simple experiments or investigations to collect
data to answer questions of interest, and make inferences from sample results.+
PS: 1, 2, 3, 4, 5, 6, 7, and 8 +
Process Standards to Emphasize with all standards
PS.1: Make sense of problems and persevere in solving them.
PS.2: Reason abstractly and quantitatively.
PS.3: Construct a viable argument and critique the reasoning of others.
PS.4: Model with mathematics.
PS.5: Use appropriate tools strategically.
PS.6: Attend to precision.
PS.7: Look for and make use of structure.
PS.8: Look for and express regularity in repeated reasoning.
Key Vocabulary
Sample - the part of a population that is surveyed.
Random Sample - a sample in which every individual or element in the population has an equal chance of being
selected.
Non-Random Sample – a sample that is often found using speed and convenience
Bias - a sampling error that causes one option to seem better than another
Infer - to conclude or decide from something known or assumed; draw as a conclusion.
Data
Analyze your classroom data from the weekly assessments and Acuity tests to determine where students are
struggling and why. Use the resources in the ISTEP+ plan, the resource documents, and online resources to
implement a new teaching plan.
Assessment
This week’s assessment is expected to take 10 to 15 minutes. Material will be spiraled through the
remaining assessment. .
Teacher Background: Examples
Sampling Bias
1. A survey of high school students was conducted to measure teenage use of illegal drugs. How might this
sample be biased?
2. Telephone sampling is common in marketing surveys. A simple random sample may be chosen from
the sampling frame consisting of a list of telephone numbers of people in the area being surveyed. How
might this sample be biased?
3. Distributing a questionnaire at the end of a 3-day conference. How might this sample be biased?
4. Interviews with people who walk by a certain location
4. Interviews with people who walk by a certain location. is going to over-represent healthy individuals or those
who live near the location.
Making Inferences from Random Samples
5. Cinemaniac Movie Channel randomly selected 30%, percent of its viewers and asked them how many
movies they watch per month. Of the viewers surveyed, 27 watch more than 10 movies per month.
Based on the data, what is the most reasonable estimate of the number of viewers who watch more
than 10movies per month?
6. Given the data in the table below from a random sample of 5000 registered voters, predict the outcome of the
election. What are some possible inferences?
7. In a company of 60 people, a random sample of 20 employees are asked if the job they do is satisfying. If 8
people say that they do not like their job, which statement is supported by the survey?
A. Since 8 is 12 less than 20, it can be concluded that 48 people are not satisfied with their job.
B. Since 8 is 12 less than 20, it can be concluded that 28 people are not satisfied with their job.
C. Since 8 is 40% of 20, it can be concluded that approximately 40 people in the company do not like their job.
D. Since 8 is 40% of 20, it can be concluded that approximately 24 people in the company do not like their job.
Teacher Background: Solutions
Sampling Bias
1. The sample does not include teenagers who are home schooled or those that have dropped out of school.
2. This method does involve taking a simple random sample, but it is not a simple random sample of the
target population (consumers in the area being surveyed.) It will miss people who do not have a phone. It
may also miss people who only have a cell phone that has an area code not in the region being surveyed.
It will also miss people who do not wish to be surveyed, including those who monitor calls on an
answering machine and don't answer those from telephone surveyors. Thus the method systematically
excludes certain types of consumers in the area.
3. The results are likely to include more people who are committed to the conference so their views would
be overrepresented.
4. The results are going to over-represent healthy individuals or those who live near the location.
Making Inferences from Random Samples
5. 90 viewers
6. Possible Inferences:
• Candidate B will most likely win the election.
• The winning candidate will have fewer than half of the votes.
• Candidates A and C are about tied.
7. D
Resources for AI.DS.1
 http://www.mdk12.org/share/clgtoolkit/lessonplans/SimpleRandomSamples.pdf
This is a worksheet with a key over random samples.

http://www.mathchimp.com/view.php?id=318
This is a video over sampling and population.
Week 10 Instructional Assessment
ISTEP+ Grade 10
Name________________________
1. Gina wanted to find out how many people in her town preferred a chocolate muffin to
a blueberry muffin. She conducted a poll of around 200 randomly selected people.
One hundred twenty people said they like the chocolate muffin more. What is the
best conclusion she can make about the total number of people in her town who
prefer a chocolate muffin over a blueberry muffin?
A. 80 people
B. 120 people
C. about 40% of the town's population
D. about 60% of the town's population
2. Sean wants to determine the effects of watching television for more than two hours
continuously. He performs an observational study by selecting 200 people from his
neighborhood and school. Based on the results, Sean concludes that everyone in
his town is likely to have a headache if they watch television continuously for more
than two hours. Which of the following is the best assessment of Sean's conclusion?
A. Sean is incorrect. His sample was not random and not representative of the
entire town, so he can not generalize his conclusion to the entire population.
B. Sean is incorrect because the sample size is too large to provide accurate
results.
C. Sean's conclusion is correct. The observational study results can be used to
predict the effects on the population.
D. Sean is incorrect. The participants in the study might be lying about their
headaches.
3. Reese wants to study the effect of soda intake on a person's blood pressure. She
chooses a random sample of 20 people in her neighborhood who drink soda and
randomly chooses another 20 people in her neighborhood who do not drink soda.
She then plans to measure their blood pressure and come to a conclusion about the
effects of drinking soda on blood pressure. Which of the following is true about
Reese's method?
A. Reese has chosen the best method to perform the study and achieve accurate
results.
B. Reese should have sampled only the people who drink soda because she
wants to study the effect of soda intake.
C. Reese should have sampled more people in each category.
D. Reese did not choose a random sample since she only studied people in one
neighborhood. Therefore, the results cannot be used to generalize an entire
population.
4. Solve for t.
- 9(5 - 7t) + 4 = 12t
5. Choose the equation you could use to solve this problem.
It took Ronaldo 34 minutes less to finish his test than Jonathan. Ronaldo finished his test in 47
minutes.
How long did it take Jonathan to finish his test?
A. 34 - n = 47
B. 47 + n = 34
C. n - 34 = 47
D. 34n = 47
6. The combined weight of Misa, Joshua, and their pet dog is 396 pounds. Misa weighs 55 pounds less
than Joshua, and their dog is half of Misa's weight. Choose the equation that you would use to find
the weights of Misa, Joshua, and their pet dog. Let x = Joshua's weight.
7. Solve the following inequality.
12y - (6 - 9y) > 12
A. y > 6
B. y > 6/7
C. y > 2
D. y < -4
Solutions to Week 10 Instructional Assessment
(AI. DA.1) 1 . D
(AI.DS.1) 2. A
(AI.DS.1) 3. D
(AI.L.1)
4. C
(AI.L.2)
5. C
(AI.L.2)
6. C
(AI.L.1) 7. B
All constructed response problems will be graded using the ISTEP+ Content Rubric