Math 7 Unit 5

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In Section 5.1, students will begin by looking at part-to-whole relationships and will connect them to percentages. Students will be introduced to a linear diagram that can organize the information in a problem. They will then find percentages and solve for missing values using equivalent ratios and by composing quantities on the diagram.

In Section 5.2, students return to probability. They will make predictions about how likely an event is and whether a game is fair. They will play number games that use a random number generator to create a data set of experimental results and analyze the games. They will also analyze how the chances of winning a game change when the sample space changes.

Then students consider probabilities of multiple events, beginning by differentiating between independent and dependent events, and then learning multiple strategies for calculating probabilities of compound independent events. Finally, students will learn how to create systematic lists, probability trees and probability tables to determine the probability of compound events, such as choosing a red shirt and black pants from a selection of shirts and pants. Students will also learn to calculate compound probabilities when events are not equally likely.

In Section 5.3, students will develop the 5-D Process as a method for solving situational word problems. The 5-D Process guides students through reading a situation, learning to: Describe/Draw important concepts from the reading, Define the terms involved and their relationships to each other, Do all the math operations, Decide if the answer is correct (and how to modify it if it is not), and Declare in a complete sentence the solution to the problem. The students will practice the process, develop strategies to interpret and represent relationships expressed in words with pictures and numbers, and learn to use a variable to represent quantities and relationships in the problems. Later in Chapter 6 students will write equations to represent the relationships and will use new equation-solving strategies to solve word problems.

At the end of this chapter there are opportunities for both chapter closure and mid-course reflection. The intent of chapter closure is to help students summarize their learning in the chapter, while the mid-course reflection activities enable students to consolidate their learning from the entire first half of the course as well as to make new connections. The mid-course reflection contains two separate activities, “Scavenger Hunt” and “Memory Lane.” Teachers can choose to use one or both activities. The mid-course reflection activities can be used after completing the chapter closure, or both can take place simultaneously by doing a mid-course reflection activity during class and assigning problems from chapter closure for students to complete at home.

In Chapter 5, students will be using various tools strategically to make sense of problems and persevere in solving them by modeling with mathematics.

Even when not mentioned specifically for a lesson, encourage abstract and quantitative reasoning, the construction of viable arguments and critiquing of others’ reasoning, and attention to precision in team discussions. One overarching goal of Chapter 5 is to really make sense of problems and persevere in solving them.

7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

7.RP.3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

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.

b) Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

c) Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

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