Math 7 Unit 1

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Several mathematical topics are introduced or reviewed in Chapter 1: perimeter and area, proportional relationships, finding unknowns, repeating and terminating decimals, probability, fraction addition and subtraction, and equivalent fractions.

This chapter is designed to:

• Introduce students to some of the mathematical ideas on which this course is based.
• Establish class norms that will continue throughout the course, such as having students reflect in Learning Logs and using focus questions to drive learning.
• Provide an opportunity for the teacher to assess students’ skills and provide students an opportunity to review prerequisite material.
• Establish collaboration in teams of four and/or pairs.

These lessons, especially those in Section 1.1, are only meant as an introduction to the course! By no means should you expect students to have proficiency or mastery of these concepts by the end of this chapter. Instead, stress each day that students will need to apply their previous learning to solve new problems and that as they continue in this course, they will build a better understanding of these new ideas. These lessons will also allow you to informally assess your students’ prior knowledge. This will be helpful for guiding the level of scaffolding in future lessons when these topics are revisited.

Section 1.1 includes five engaging activities that set the stage for student work through the course. While these problems are not intended to bring closure to any major concept, they are intended to launch major ideas, such as identifying unknowns and the study of probability.

The overarching goal of this text is to stress Standard 1: Make sense of problems and persevere in solving them. Even when not specifically mentioned, your goal in facilitating these lessons is to encourage understanding through your introductions, questioning and closure activities.

In this chapter it is suggested that you do not yet introduce the practices explicitly, but rather encourage students to begin engaging in these practices through your directions and your questions. In the lesson notes for Chapter 1, seven of the practices are identified:

• Standard 1: Make sense of problems and persevere in solving them.
• Standard 2: Reason abstractly and quantitatively.
• Standard 3: Construct viable arguments and critique the reasoning of others.
• Standard 5: Use appropriate tools strategically.
• Standard 6: Attend to precision.
• Standard 7: Look for and make use of structure.
• Standard 8: Look for and express regularity in repeated reasoning.

After focusing on one practice per day in the first few lessons, you might begin to encourage the use of more than one if it is appropriate. More standards will be introduced in Chapter 2. It is suggested that if you plan to make these practices explicit in your classroom, that you begin Chapter 3 with a formal introduction to all eight of the mathematical practices.

7.SP.5. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

7.SP.6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predictthat a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

7.SP.7.Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

a) Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

b) Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

a) Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

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