02-Math 7a-CC2 Ch8

In Section 8.1, students revisit concepts of measurement, data display, and analysis. Students have done a series of pre-problems in Chapter 7 and completed Checkpoint 7 in preparation for this work. Use this work to determine if your students need additional support or review. In Section 8.1, students will use two different tools to measure a dimension of their classroom and then use a technology tool to display and compare the two sets of data. This will lead them to draw conclusions about which data set appears to display the more accurate measuring tool. They will also look at how to compare samples and make inferences based on the median and the interquartile range (IQR) of each sample.

The two lessons in Section 8.2 introduce surveys and sampling methods. Students will also draw inferences and gauge the variation in sample statistics by creating multiple samples of a given population. In doing so, they continue to investigate the limitations of samples and statistics in accurately describing an entire population.

Section 8.3 begins by having students look at angles; students will do an activity that has them physically spinning 360° and creating their own “angle rulers.” They then look at how to classify angles of different measures and in relationship to other angles, such as complementary or vertical angles. Next students move to building triangles and quadrilaterals with given conditions. Finally, they discover what requirements are necessary to create a unique triangle.

Many of the mathematical practices are woven through this chapter. Students will use various graphs and statistical measures to make sense of problems. Reasoning, both abstractly and quantitatively, will be critical in analyzing the data. They will also construct viable arguments will be required to justify their conclusions. It will be important that students attend to precision throughout these lessons as they build vocabulary and justify conclusions.

7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.