Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
7th Grade Mathematics Quarter 3 Curriculum Map 2013-2014 Unit 4: Geometry 3rd 9 Weeks Suggested Instructional Days: 20 Unit Summary (Learning Target/Goal): Draw, construct, and describe geometrical figures and describe the relationships between them. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. CCSS for Mathematical Practice: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Unit Timeline 1 day Geometry Draw, construct, and describe geometrical figures and describe the relationships between them. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 2 days Standards 7.G.2: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles rom three measure of angles or sides, noticing when the condition determines unique triangle, more than one triangle, or no triangle. 7.G.5: Supplementary, complementary, adjacent, and vertical angles Learning Expectation & Example Activity Lab: Drawing geometric figures Vocabulary line segment; triangles; rhombus Resources Prentice Hall Mathematics 6-1a Use understandings of angles and deductive reasoning to write and solve equations Angles acute; right; obtuse; straight; complimentary; supplementary; adjacent vertical; congruent Prentice Hall Mathematics 6-1 trapezoid; area Prentice Hall Mathematics 6-2a Example If angle G and angle H are supplementary and the measure of angle G is 4 times the measure of angle H, what are the measures of angle G and angle H? .5 day 7.G.6: Solve real world and mathematical problems involving area, volume and surface area of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Activity Lab: Generating formulas for area 7th Grade Math Quarter 3 1 7th Grade Mathematics Quarter 3 Curriculum Map 2013-2014 1 day 1 day 2.5 days 3 days 1 day Prentice Hall Mathematics 6-2 triangle base; height Prentice Hall Mathematics 6-3 Area of a parallelogram, relating perimeter and area 7.G.6: Solve real world and mathematical problems involving area, volume and surface area of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Area of triangle, relating side lengths and area Example A carpenter has blueprints for a wooden, triangular patio. The base is 5 m and the height is 7 m. What is the area of the patio? tri = 𝐴 = 𝑏ℎ 7.G.6: Solve real world and mathematical problems involving area, volume and surface area of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Area of other figures (trapezoids, irregular figures) trapezoid base; height Example trap = 𝐴 = Example A playground has the shape of a parallelogram. If the base is 30 ft., and the corresponding height is 25 ft., what is its area? The top of a trapezoid is 17 in long, and the bottom edge is 39 in long. The distance from the top edge to the bottom edge is 16 in. What is the area of the trapezoid? 7.G.4: Know the formulas for the area and circumference o a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Circumference and are of a circle 7.G.3: Describe 2-d figures that result from slicing 3-d figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Drawing and naming three dimensional figures Example Example Find the circumference and area of a circle with a given diameter or radius. Identify the number of faces, edges, and vertices a hexagonal pyramid has. parallelogram base; height rect A = lw parr A = bh 7.G.6: Solve real world and mathematical problems involving area, volume and surface area of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. ! ! ! ! Prentice Hall Mathematics 6-4 ℎ(𝑏1 + 𝑏2) circumference; diameter; radius; pi; circle; C=πd C=2 πr A= πr2 3-D figure; face; edge; prism; base; height; cube; cylinder; pyramid; vertex; cone; sphere; center; 3-D Prentice Hall Mathematics 6-5 Prentice Hall Mathematics 7-1 7th Grade Math Quarter 3 2 7th Grade Mathematics Quarter 3 Curriculum Map 2013-2014 2.5 days .5 day 3 days 7.G.6: Solve real world and mathematical problems involving area, volume and surface area of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 7.G.6: Solve real world and mathematical problems involving area, volume and surface area of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 7.G.6: Solve real world and mathematical problems involving area, volume and surface area of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 1 day 1 day 7.G.3: Describe 2-d figures that result from slicing 3-d figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Determine the dimensions of the figures given the area or volume, surface area of prisms and cylinders, drawing nets surface area net Prentice Hall Mathematics 7-2 Example The diameter of the base of a cylindrical can is 4 in. The height of the can is 6.5 in. Find the can's surface area to the nearest tenth. Activity Lab: Patterns in 3-d Figures Students determine the dimensions of the figures given the area or volume. Prentice Hall Mathematics 7-2b volume; cubic unit Prentice Hall Mathematics 7-3 Example Mrs. Sanchez has a can of concentrated orange juice, 8 cm tall and with a diameter of 7 cm. What is the volume of the can in cubic centimeters? Word problem practice Describe the resulting face shape from cuts made parallel and perpendicular to the bases of right rectangular prisms and pyramids. Prentice Hall Mathematics Pp. 269-270 cross-section plane Prentice Hall Mathematics 7-4 Example Jorge and Patti are eating sushi rolls shaped like cylinders. Jorge cut his sushi roll vertically. Patti cut her sushi roll horizontally. What is the shape of each cross section? 1 day All standards taught Review Formative Assessment Lesson: Using Dimensions- Designing a Sports Bag http://map.mathshell.org/materials/lessons.php Formative Assessment Lesson: Estimations and Approximations http://map.mathshell.org/materials/lessons.php?taskid=220&subpage=problem 7th Grade Math Quarter 3 3 7th Grade Mathematics Quarter 3 Curriculum Map 2013-2014 Formative Assessment Lesson: Maximizing Area- Gold Rush http://map.mathshell.org/materials/lessons.php?taskid=415&subpage=problem INTERIM ASSESSMENT 3: JANUARY 21-FEBRUARY 6 Suggested Instructional Days: 10 Unit 5: Statistics and Probability 3rd 9 Weeks Unit Summary (Learning Target/Goal): Use random sampling to draw inferences about a population. Draw informal comparative inferences about two populations. Investigate chance processes and develop, use, and evaluate probability models bar graph Prentice Hall Mathematics Central tendency measures, plots, pie chart Supplemental Materials and various graphs and charts histogram Example scatter plots Assessment Task: Jason wanted to compare the mean line plots Temperatures height of the players on his favorite line graph http://map.mathshell.org/m Statistics and basketball and soccer teams. He thinks mean aterials/tasks.php?taskid=3 Probability the mean height of the players on the median 84#task384 basketball team will be greater but mode Use random doesn’t know how much greater. He range sampling to also wonders if the variability of draw inferences heights of the athletes is related to the about a sport they play. He thinks that there population. will be a greater variability in the 7.SP.3: Informally assess the degree of visual heights of soccer players as compared overlap of two numerical data distributions with Draw informal to basketball players. He used the 5 similar variability’s, measuring the difference comparative rosters and player statistics from the between the centers by expressing it as a multiple inferences about days of a measure of variability. team websites to generate the two populations. following lists. Investigate chance processes and develop, use, and evaluate probability models. Basketball Team – Height of Players in inches for 2010 Season 75, 73, 76, 78, 79, 78, 79, 81, 80, 82, 81, 84, 82, 84, 80, 84 Soccer Team – Height of Players in inches for 2010 73, 73, 73, 72, 69, 76, 72, 73, 74, 70, 65, 71, 74, 76, 70, 72, 71, 74, 71, 74, 73, 67, 70, 72, 69, 78, 73, 76, 69 To compare the data sets, Jason 7th Grade Math Quarter 3 4 7th Grade Mathematics Quarter 3 Curriculum Map 2013-2014 creates a two dot plots on the same scale. The shortest player is 65 inches and the tallest players are 84 inches. 2 days 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. 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. 1.5 days 7.SP.5: Understand that the probability of a chance event is a number between 0and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 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. Data variability (comparing populations and interpreting data. Example: The two data sets below depict random samples of the management salaries in two companies. Based on the salaries below which measure of center will provide the most accurate estimation of the salaries for each company? • Company A: 1.2 million, 242,000, 265,500, 140,000, 281,000, 265,000, 211,000 • Company B: 5 million, 154,000, 250,000, 250,000, 200,000, 160,000, 190,000 Solution: The median would be the most accurate measure since both companies have one value in the million that is far rom the other values and would affect the mean. Recognize that the probability of any single event can be can be expressed in terms such as impossible, unlikely, likely, or certain or as a number between 0 and 1. Example There are three choices of jellybeans – grape, cherry and orange. If the probability of getting a grape is and the probability of getting cherry is , what is the probability of getting box-plot lower quartile upper quartile interquartile range variability mean absolute value Prentice Hall Mathematics 8-4 outcome event Prentice Hall Mathematics 9-1 theoretical probability complement favorable outcomes possible outcomes unlikely likely 7th Grade Math Quarter 3 5 7th Grade Mathematics Quarter 3 Curriculum Map 2013-2014 orange? 1.5 days 7.SP .8: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 7.SP.8b. 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. Solution The combined probabilities must equal 1. The combined probability of grape and cherry is . The probability of orange must equal to get a total of 1. Use tree diagrams, frequency tables, and organized lists, and simulations to determine the probability of compound events. Example How many ways could the 3 students, Amy, Brenda, and Carla, come in 1st, 2nd and 3rd place? Solution: Making an organized list will identify that there are 6 ways for the students to win a race A, B, C Sample space counting principle Prentice Hall Mathematics 9-3 A, C, B B, C, A B, A, C C, A, B C, B, A Formative Assessment Lesson: Estimating- Counting Trees http://map.mathshell.org/materials/lessons.php?taskid=422&subpage=problem 10 REVIEW for state assessments All standards taught days NOTES/REFLECTIONS: 7th Grade Math Quarter 3 6