Springboard Mathematics Course 2 Unit 7 Pdf
© 2 0 1 5 C o l l e g e B o a r d . A l l r i g h t s r e s e r v e d .
Unit 7
Planning the Unit Planning the Unit
Vocabulary Development
The key terms for this unit can be found on the Unit Opener page. These terms are divided into Academic Vocabulary and Math Terms. Academic Vocabulary includes terms that have additional meaning outside of math. These terms are listed separately to help students transition from their current understanding of a term to its meaning as a mathematics term. To help students learn new vocabulary: Have students discuss meaning and use graphic organizers to record their understanding of new words. Remind students to place their graphic organizers in their math notebooks and revisit their notes as their understanding of vocabulary grows. As needed, pronounce new words and place pronunciation guides and definitions on the class Word Wall.
Embedded Assessments
Embedded Assessments allow students to do the following: Demonstrate their understanding of new concepts. Integrate previous and new knowledge by solving real-world problems presented in new settings. They also provide formative information to help you adjust instruction to meet your students' learning needs. Prior to beginning instruction, have students unpack the first Embedded Assessment in the unit to identify the skills and knowledge necessary for successful completion of that assessment. Help students create a visual display of the unpacked assessment and post it in your class. As students learn new knowledge and skills, remind them that they will be expected to apply that knowledge to the assessment. After students complete each Embedded Assessment, turn to the next one in the unit and repeat the process of unpacking that assessment with students.
I
n this unit, students study normal data distributions and solve problems using tables and technology. An examination of bias provides students with a reason to develop simple random samples from a population of interest.
Students create simulations with and without technology to test conjectures about data.
Margin of error is applied to population proportions and an informal understanding of statistical significance is developed.
Normal Models, Surveys, and Experiments,
Researching Readers
Properties of normal distributions Sampling techniques in studies Characteristics of experimental studies Characteristics of observational studies
Embedded Assessment 1 Unpacking the Embedded Assessments
The following are the key skills and knowledge students will need to know for each assessment.
Simulations, Margin of Error, and Hypothesis Testing,
Psychic or Just Hot Air?
Embedded Assessment 2
Simulation of random processes Testing the truth of a conjecture Statistical significance Margin of error
AP / College Readiness
Unit 7 continues to develop student understanding of statistical methods by:
Exploring properties of normal distributions. Applying random sampling to experiments and observational studies. Using simulations to support or refute conjectures. Establishing margin of error with population proportions. Developing the concept of statistical significance.
Unit 7
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Probability and Statistics
551a
Additional Resources
Additional resources that you may find helpful for your instruction include the following, which may be found in the Teacher Resources at SpringBoard Digital.
Unit Practice (additional problems for each activity) Getting Ready Practice (additional lessons and practice problems for the prerequisite skills) Mini-Lessons (instructional support for concepts related to lesson content)
Suggested Pacing
The following table provides suggestions for pacing using a 45-minute class period. Space is left for you to write your own pacing guidelines based on your experiences in using the materials.
45-Minute PeriodYour Comments on Pacing
Unit Overview/Getting Ready
1
Activity 36
3–4
Activity 37
3–4
Embedded Assessment 1
1
Activity 38
2–3
Activity 39
2–3
Activity 40
2–3
Embedded Assessment 2
1
Total 45-Minute Periods15–20
© 2 0 1 5 C o l l e g e B o a r d . A l l r i g h t s r e s e r v e d .
Planning the Unit
continued
551b
SpringBoard
®
Mathematics
Algebra 2
EMBEDDED ASSESSMENTS
This unit has two embedded assessments, following Activities 37 and 40. These assessments will allow you to demonstrate your understanding of the relationships between data and models of real-world situations.
Embedded Assessment 1:
Normal Models, Surveys, and Experiments p. 591
Embedded Assessment 2:
Simulations, Margin of Error, and Hypothesis Testing p. 631
Unit Overview
In this unit you will investigate whether a normal distribution is an appropriate model for data and, if it is, how to use the model to analyze and understand the data. You will learn the importance of impartiality in surveys and experiments, as well as use simulations to decide whether data are consistent or inconsistent with a conjecture. You will also investigate how to use data from a randomized experiment to compare two treatments and decide if an observed treatment effect is statistically significant.
Key Terms
As you study this unit, add these and other terms to your math notebook. Include in your notes your prior knowledge of each word, as well as your experiences in using the word in different mathematical examples. If needed, ask for help in pronouncing new words and add information on pronunciation to your math notebook. It is important that you learn new terms and use them correctly in your class discussions and in your problem solutions.
Academic Vocabulary
7
Probability and Statistics
ESSENTIAL QUESTIONS
Math Terms •
density curve
•
z
-score
•
normal distribution
•
normal curve
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sample
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survey
•
response
•
bias
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simple random sample
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experiment
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explanatory variable
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response variable
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completely randomized design
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randomized block design
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matched pairs design
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single-blind study
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double-blind study
•
observational study
•
confounding variable
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simulation
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statistic
•
margin of error
•
simulation
•
sample proportion
•
sampling distribution
•
critical value
•
statistically significant
What role does a random process play when conducting a survey? What role does a random process play when conducting an experiment with two treatments? How can a simulation help you decide if a set of data is consistent or inconsistent with a conjecture about the world?
•
placebo
•
simulation
551
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© 2 0 1 5 C o l l e g e B o a r d . A l l r i g h t s r e s e r v e d .
Developing Math Language
As this unit progresses, help students make the transition from general words they may already know (the Academic Vocabulary) to the meanings of those words in mathematics. You may want students to work in pairs or small groups to facilitate discussion and to build confidence and fluency as they internalize new language. Ask students to discuss new academic and mathematics terms as they are introduced, identifying meaning as well as pronunciation and common usage. Remind students to use their math notebooks to record their understanding of new terms and concepts. As needed, pronounce new terms clearly and monitor students' use of words in their discussions to ensure that they are using terms correctly. Encourage students to practice fluency with new words as they gain greater understanding of mathematical and other terms.
Unit Overview
Ask students to read the unit overview and mark the text to identify key phrases that indicate what they will learn in this unit.
Key Terms
As students encounter new terms in this unit, help them to choose an appropriate graphic organizer for their word study. As they complete a graphic organizer, have them place it in their math notebooks and revisit as needed as they gain additional knowledge about each word or concept.
Essential Questions
Read the essential questions with students and ask them to share possible answers. As students complete the unit, revisit the essential questions to help them adjust their initial answers as needed.
Unpacking Embedded Assessments
Prior to beginning the first activity in this unit, turn to Embedded Assessment 1 and have students unpack the assessment by identifying the skills and knowledge they will need to complete the assessment successfully. Guide students through a close reading of the assessment, and use a graphic organizer or other means to capture their identification of the skills and knowledge. Repeat the process for each Embedded Assessment in the unit.
551
Springboard Mathematics Course 2 Unit 7 Pdf
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