Embedded Files
Chapter Overview
Chapter Overview
Chapter 9 consolidates and extends a couple topics of study that were introduced earlier in the course: portions (in this case, percentages), and area.
Chapter 9 begins with a development of volume as another quantity (beyond length and area) that can be measured. Students build prisms from nets and fill them with cubic units, generalizing to cases in which they would need more cubes than they have. They learn that the volume of a right prism can be calculated by multiplying the area of its base by its height. Students will practice visualizing three-dimensional shapes based on two-dimensional representations by analyzing nets and considering how their parts fit together, as well as by drawing and building their own nets.
In Section 9.2 students work with percent applications. Students develop strategies for calculating percents of amounts. Students will use diagrams and fluency with portions to help them find 10%, 5%, and 1% of given amounts and then combine these known portions to calculate discounts, sale prices, tips, and simple interest.
Finally, Section 9.3 offers several class activities to help pull ideas from the entire course together. These activities are designed to enable students to reflect about what they have learned as well as draw connections between different topics. It also offers students an opportunity to review the mathematical ways of thinking (math practices) developed and used often in this course. See the Course Closure notes below.
Standards for Mathematical Practice
Standards for Mathematical Practice
The six lessons in Chapter 9 present your final opportunity to work with your students on abstract and quantitative reasoning. By this time, making sense of problems and persevering in solving them and attention to precision should be a habit for students.
If you have spent time this year explicitly teaching the 8 Standards for Mathematical Practice, you might split the class into teams that create a presentation or poster with examples culled from their experiences throughout this year. If so, note that even though you have worked to develop these in your course this year, Practices 7 (look for and make use of structure) and 8 (look for and express regularity in repeated reasoning) are difficult for students at this age to comprehend. Your explicit focus might be on only the first 6 Mathematical Practices.
CA Content Standards
CA Content Standards
6.G.2. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
6.G.4. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
6.RP.3c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
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