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## Content Deepening 8 th Grade Math

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**Content Deepening8th Grade Math**February 7, 2014 Jeanne Simpson AMSTI Math Specialist**Welcome**• Name • School • Classes you teach • What are you hoping to learn today?**He who dares to teach must never cease to learn.**John Cotton Dana**Goals for Today**• Implementation of the Standards of Mathematical Practices in daily lessons • Understanding of what the CCRS expect students to learn blended with how they expect students to learn. • Student-engaged learning around high-cognitive-demand tasks used in every classroom.**Agenda**• Square Roots • Pythagorean Theorem • Statistics • Exponents and Scientific Notation**acos2010.wikispaces.com**• Electronic version of handouts • Links to web resources**Five Fundamental Areas Required for Successful**Implementation of CCSS**Standards for Mathematical Practice**Mathematically proficient students will: SMP1 - Make sense of problems and persevere in solving them SMP2 - Reason abstractly and quantitatively SMP3 - Construct viable arguments and critique the reasoning of others SMP4 - Model with mathematics SMP5 - Use appropriate tools strategically SMP6 - Attend to precision SMP7 - Look for and make use of structure SMP8 - Look for and express regularity in repeated reasoning**SMP Instructional Implementation Sequence**• Think-Pair-Share (1, 3) • Showing thinking in classrooms (3, 6) • Questioning and wait time (1, 3) • Grouping and engaging problems (1, 2, 3, 4, 5, 8) • Using questions and prompts with groups (4, 7) • Allowing students to struggle (1, 4, 5, 6, 7, 8) • Encouraging reasoning (2, 6, 7, 8)**SMP Proficiency Matrix**Questioning/Wait Time Pair-Share Grouping/Engaging Problems Questioning/Wait Time Showing Thinking Grouping/Engaging Problems Grouping/Engaging Problems Encourage Reasoning Grouping/Engaging Problems Showing Thinking Questioning/Wait Time Grouping/Engaging Problems Pair-Share Questioning/Wait Time Grouping/Engaging Problems Showing Thinking Questions/Prompts for Groups Grouping/Engaging Problems Showing Thinking Grouping/Engaging Problems Grouping/Engaging Problems Encourage Reasoning Showing Thinking Allowing Struggle Questions/Prompts for Groups Encourage Reasoning Allowing Struggle Grouping/Engaging Problems Allowing Struggle Encourage Reasoning**Critical Focus Areas**Expressions and Equations Represent, analyze, and solve a variety of problems Linear equations, systems of equations, linear functions, slope, bivariate data Standards 7-10, 25-28 Functions Define, evaluate, compare Use to model relationships Standards 11-15 Geometry Transformations, similar triangles, angles formed by parallel lines, Pythagorean theorem, volume Standards 16-24 Other Irrational numbers, radical, integer exponents Standards 1-6**Square Roots and Pythagorean Theorem**Chapter 6**Work with radicals and integer exponents.**• 8.EE.2 – Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.**Connected Mathematics**• Coordinate Grids • Squaring Off • The Pythagorean Theorem • Using the Pythagorean Theorem**Looking for Pythagoras**• Relate the area of a square to the side length • Estimate the values of square roots of whole numbers • Locate irrational numbers on a number line • Develop strategies for finding the distance between two points on a coordinate grid • Understand and apply the Pythagorean Theorem • Use the Pythagorean Theorem to solve everyday problems**Understand and Apply the Pythagorean Theorem**• 8.G.6 – Explain a proof of the Pythagorean Theorem and its converse. • 8.G.7 – Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. • 8.G.8 – Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.**Use two different colored squares of paper.**• Student 1 completes Steps 1&2 and Student 2 completes Steps 3&4. • Students label the area of rectangles, squares and triangles in terms of a and b. • Students then cut out shapes. The triangles should fit perfectly on the rectangles leaving the squares a2 and b2 (of one color) = to c2 (of other color). Pythagorean Tile Proof**Understand and Apply the Pythagorean Theorem**• 8.G.6 – Explain a proof of the Pythagorean Theorem and its converse. • 8.G.7 – Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. • 8.G.8 – Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.**Understand and Apply the Pythagorean Theorem**• 8.G.6 – Explain a proof of the Pythagorean Theorem and its converse. • 8.G.7 – Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. • 8.G.8 – Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.**Mathematics Assessment Project**• Tools for formative and summative assessment that make knowledge and reasoning visible, and help teachers to guide students in how to improve, and monitor their progress. These tools comprise: • Classroom Challenges: lessons for formative assessment, some focused on developing math concepts, others on non-routine problem solving. • Professional Development Modules: to help teachers with the new pedagogical challenges that formative assessment presents. • Summative Assessment Task Collection: to illustrate the range of performance goals required by CCSSM. • Prototype Summative Tests: designed to help teachers and students monitor their progress, these tests provide a model for examinations that may replace or complement current US tests. http://map.mathshell.org/**MARS Tasks**• Lines and Linear Equations (8.EE.6) • Identifying Similar Triangles (8.EE.6) • Systems of Equations (8.EE.8) • Interpreting Time-Distance Graphs (8.F.4) • Modeling Situations with Linear Equations (8.F.4) • The Pythagorean Theorem: Square Areas (8.G.6)**The Pythagorean Theorem: Square Areas**Projector Resources The Pythagorean Theorem: Square Areas**Jason’s Method**“I drew a square all round the tilted square. I then took away the area of the four right triangles.”**Kate’s Method**“I divided the tilted squares into four right triangles and little squares inside.”**Simon’s Method**“I found the area inside the bold line is the same area as the tilted square and used that.”**Projector Resources**The Pythagorean Theorem: Square Areas**Data Analysis and Displays**Chapter 7**Investigate patterns of variability in bivariate data**• 8.SP.1 – Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.**Investigate patterns of variability in bivariate data**• 8.SP.1 – Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.**Investigate patterns of variability in bivariate data**• 8.SP.1 – Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.**Removing the outliers from the data set, make a new**scatterplot of the remaining animal body and brain weights. • Does there appear to be a relationship between body weight and brain weight? If yes, write a brief description of the relationship. • Take a piece of uncooked spaghetti and use that spaghetti to informally fit a line to the data. Attempt to place your line so that the vertical distances from the points to the line are as small as possible. • How well does the spaghetti line fit the data?**Illustrative Mathematics**• Illustrative Mathematics provides guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students experience in a faithful implementation of the Common Core State Standards, and by publishing other tools that support implementation of the standards. http://www.illustrativemathematics.org/