Outlin e of Fo cuse d Math fo r 6 th Gr ade
6th grade Focused Math will address all topics required by the California State Standards in an experiential, project-based manner. Daily lessons will incorporate hands-on investigations where students have the opportunity to make discoveries and then are guided in connecting their findings to established definitions and properties. Daily lessons are organized into a series of projects, so that principles learned are not something simply contained on the pages of a textbook, but instead have real-world relevance. The plan shows state mathematics standards being addressed by late March, and then the school year concluding with a series of cumulative projects that require application of most of the material previously addressed. The following outline is a suggested plan. In the event students need additional time for mastery of topics initially addressed, one or more of the cumulative projects can be eliminated.
Topic
Beginning-of-the Year Essentials: Properties, Decimals, Fractions, Integers Solving Equations
Duration
7 weeks 2 weeks
Associated Project
Students produce hands-on learning tools and activities to be offered to similar-leveled math classes serving ELD students. An understanding of the method of solving equations is developed as students generate and follow reverse direction tables to retrace their steps to the origin after following a map to some destination in downtown Half Moon Bay. Students use information from The World Village Project to proportionally reduce the world’s population to a village of 1000 inhabitants. Students make discoveries such as of the village, 520 inhabitants are women and 480 are men. Only 86 villagers would speak English and just 52 would be North Americans. Students continue to examine other demographics such as how many villagers can read, how many die from lack of food, and so on. Students present their results using both tables and circle graphs. Students develop and conduct their own survey for a driving question they find relevant. Probability is studied by conducting a number of hands-on experiments. Project to be determined; hands-on investigations are planned. Students use the properties learned in this unit to design and paint their own stained glass window panel. Project to be determined; hands-on investigations are planned. Following a series of hands-on experiences where students learn about volume and surface area of cylinders and prisms, understanding of 3-d figures is enhanced as students design and build birdfeeders from nets they develop for the figures studied.
Ratio, Proportion & Percent
3 weeks
Probability, Statistics & Data Analysis Circumference and π Properties of Angles, Triangles & Quadrilaterals Area in the Plane Geometry in Space
3 weeks 2 weeks 3 weeks 2 weeks 4 weeks
Topic
Cumulative Project: Small-Scale Models of Theater Sets Cumulative Project: Bird Station Rate Analysis
Duration
3 weeks
Associated Project
The concepts of proportional analysis and scale are revisited in this unit as students design smallscale models of play sets for upcoming performances at the Coastal Repertory Theater. Students address the question “does the height of a bird feeder affect the amount of birdseed eaten?” by monitoring the amount of seed eaten from feeders built during the Geometry in Space unit, then using proportional analysis to determine a unit rate for each feeder. Findings are presented using various display formats learned during the Statistics and Data Analysis unit. During this unit, students design aircraft wings using various two-dimensional shapes studied during the Properties of Angles, Triangles & Quadrilaterals unit. After building their planes, students perform multiple flight tests to form a sample, and collect measurements for time and distance traveled. Students use algebra to determine speed. Data is compiled into statistics, graphs and charts to make deductions about how various wing shapes affect flight. Groups of students are given a surface area and volume limit as well as a budget, and are tasked with designing and building a wheeling cart that a person might use to wheel their purchases home from the store. This project requires students to use concepts geometrical concepts for 3-d figures, solve equations, use ratio, proportion, and percent of discount and sales tax, as well as perform extensive computation using both decimals and fractions. Completed wheeling carts will be offered to Lesley Gardens for resident use.
1 week
Cumulative Project: Wing Design & Rate
2 weeks
Cumulative Project: Wheeled Carts
4 weeks