Math 6a Unit 8

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In Section 8.1, students will revisit the Calaveras County frog-jumping contest first introduced in Chapter 1. Students will analyze contest data in greater depth, including comparing data sets from different years using measures of central tendency (mean and median). Students will construct histograms, stem-and-leaf plots, and box plots to determine the kinds of information each representation conveys. They will also learn methods to describe the shape and spread of data, both verbally in a graphical representation and numerically with mean absolute deviation.

Section 8.2 focuses on statistical questions – how to identify one, how to write one, and why they are important when collecting data.

In Section 8.3, students will explore the relationship between distance, rate and time as they learn how to write equations involving multiplication such as px = q. Students will find it necessary to convert units so that they are the same when they compare rates. In each of these situations, time can be thought of as a multiplier. For example, if you run 5 miles per hour (problem 8-12), then distance traveled in one hour is scaled based on time to find the distance traveled. So running for 2 hours scales the distance traveled in one hour by a factor of 2, while the distance traveled after running hours can be found by multiplying by . Situations will be represented using graphs, linear models, and words. Students will become familiar with each of these representations and use them to write equations using distance, rate, and time.

All of the mathematical practices are woven throughout this chapter. In Sections 8.1 and 8.2, practices 1 through 6 are prevalent as students engage with data. They will use various graphs and statistical measures to make sense of problems. Reasoning, both abstractly and quantitatively, will be critical in analyzing the data and constructing viable arguments will be required to justify their conclusions. As they identify important quantities in situations and map their relationships using graphs and statistical measures, students will be modeling with mathematics. In comparing different graphs and measures, making decisions about when each of these tools might be helpful and recognizing both the insights to be gained and their limitations, students will be using appropriate tools strategically. It will be important that students attend to precisionthroughout these lessons as they build vocabulary and justify conclusions.

In Section 8.3, students will model with mathematics while looking for and expressing regularity in repeated reasoning. They will also have the opportunity to look for and make use of the known structure of d = r · t. They will attend to precision by paying attention to units.

6.SP.2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

6.SP.3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

6.SP.5c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

6.SP.5d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered

6.SP.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots

6.SP.5a. Reporting the number of observations.

6.SP.5b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

6.RP.1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

6.SP.5b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

6.EE.7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

6.EE.9. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

6.RP.3b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

6.RP.3d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

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