1. Limestone County 8 th Grade Math October 26, 2014 Jeanne Simpson AMSTI Math Specialist

2. Welcome  Name  School  Classes you teach  What do your students struggle to learn? 2

3. He who dares to teach must never cease to learn. John Cotton Dana 3

4. 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.

5. Agenda  8 th Grade Overview  Teaching Strategies  Activities Overview  You Decide! 5

6. acos2010.wikispaces.com  Electronic version of handouts  Links to web resources

7. Major Work of Grade 8 7

8. 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 8

9. Students:(I) Initial(IN) Intermediate(A)Advanced 1a Make sense of problems Explain their thought processes in solving a problem one way. Explain their thought processes in solving a problem and representing it in several ways. Discuss, explain, and demonstrate solving a problem with multiple representations and in multiple ways. 1b Persevere in solving them Stay with a challenging problem for more than one attempt. Try several approaches in finding a solution, and only seek hints if stuck. Struggle with various attempts over time, and learn from previous solution attempts. 2 Reason abstractly and quantitatively Reason with models or pictorial representations to solve problems. Are able to translate situations into symbols for solving problems. Convert situations into symbols to appropriately solve problems as well as convert symbols into meaningful situations. 3a Construct viable arguments Explain their thinking for the solution they found. Explain their own thinking and thinking of others with accurate vocabulary. Justify and explain, with accurate language and vocabulary, why their solution is correct. 3b Critique the reasoning of others. Understand and discuss other ideas and approaches. Explain other students’ solutions and identify strengths and weaknesses of the solution. Compare and contrast various solution strategies and explain the reasoning of others. 4 Model with Mathematics Use models to represent and solve a problem, and translate the solution to mathematical symbols. Use models and symbols to represent and solve a problem, and accurately explain the solution representation. Use a variety of models, symbolic representations, and technology tools to demonstrate a solution to a problem. 5 Use appropriate tools strategically Use the appropriate tool to find a solution. Select from a variety of tools the ones that can be used to solve a problem, and explain their reasoning for the selection. Combine various tools, including technology, explore and solve a problem as well as justify their tool selection and problem solution. 6 Attend to precision Communicate their reasoning and solution to others. Incorporate appropriate vocabulary and symbols when communicating with others. Use appropriate symbols, vocabulary, and labeling to effectively communicate and exchange ideas. 7 Look for and make use of structure Look for structure within mathematics to help them solve problems efficiently (such as 2 x 7 x 5 has the same value as 2 x 5 x 7, so instead of multiplying 14 x 5, which is (2 x 7) x 5, the student can mentally calculate 10 x 7. Compose and decompose number situations and relationships through observed patterns in order to simplify solutions. See complex and complicated mathematical expressions as component parts. 8Look for and express regularity in repeated reasoning Look for obvious patterns, and use if/ then reasoning strategies for obvious patterns. Find and explain subtle patterns. Discover deep, underlying relationships, i.e. uncover a model or equation that unifies the various aspects of a problem such as discovering an underlying function. SMP Proficiency Matrix

10. SMP Instructional Implementation Sequence 1. Think-Pair-Share (1, 3) 2. Showing thinking in classrooms (3, 6) 3. Questioning and wait time (1, 3) 4. Grouping and engaging problems (1, 2, 3, 4, 5, 8) 5. Using questions and prompts with groups (4, 7) 6. Allowing students to struggle (1, 4, 5, 6, 7, 8) 7. Encouraging reasoning (2, 6, 7, 8)

11. Students:(I) Initial(IN) Intermediate(A)Advanced 1a Make sense of problems Explain their thought processes in solving a problem one way. Explain their thought processes in solving a problem and representing it in several ways. Discuss, explain, and demonstrate solving a problem with multiple representations and in multiple ways. 1b Persevere in solving them Stay with a challenging problem for more than one attempt. Try several approaches in finding a solution, and only seek hints if stuck. Struggle with various attempts over time, and learn from previous solution attempts. 2 Reason abstractly and quantitatively Reason with models or pictorial representations to solve problems. Are able to translate situations into symbols for solving problems. Convert situations into symbols to appropriately solve problems as well as convert symbols into meaningful situations. 3a Construct viable arguments Explain their thinking for the solution they found. Explain their own thinking and thinking of others with accurate vocabulary. Justify and explain, with accurate language and vocabulary, why their solution is correct. 3b Critique the reasoning of others. Understand and discuss other ideas and approaches. Explain other students’ solutions and identify strengths and weaknesses of the solution. Compare and contrast various solution strategies and explain the reasoning of others. 4 Model with Mathematics Use models to represent and solve a problem, and translate the solution to mathematical symbols. Use models and symbols to represent and solve a problem, and accurately explain the solution representation. Use a variety of models, symbolic representations, and technology tools to demonstrate a solution to a problem. 5 Use appropriate tools strategically Use the appropriate tool to find a solution. Select from a variety of tools the ones that can be used to solve a problem, and explain their reasoning for the selection. Combine various tools, including technology, explore and solve a problem as well as justify their tool selection and problem solution. 6 Attend to precision Communicate their reasoning and solution to others. Incorporate appropriate vocabulary and symbols when communicating with others. Use appropriate symbols, vocabulary, and labeling to effectively communicate and exchange ideas. 7 Look for and make use of structure Look for structure within mathematics to help them solve problems efficiently (such as 2 x 7 x 5 has the same value as 2 x 5 x 7, so instead of multiplying 14 x 5, which is (2 x 7) x 5, the student can mentally calculate 10 x 7. Compose and decompose number situations and relationships through observed patterns in order to simplify solutions. See complex and complicated mathematical expressions as component parts. 8Look for and express regularity in repeated reasoning Look for obvious patterns, and use if/ then reasoning strategies for obvious patterns. Find and explain subtle patterns. Discover deep, underlying relationships, i.e. uncover a model or equation that unifies the various aspects of a problem such as discovering an underlying function. SMP Proficiency Matrix Grouping/Engaging Problems Pair-Share Showing Thinking Questioning/Wait Time Questions/Prompts for Groups Pair-Share Grouping/Engaging Problems Questioning/Wait Time Grouping/Engaging Problems Allowing Struggle Grouping/Engaging Problems Showing Thinking Encourage Reasoning Grouping/Engaging Problems Showing Thinking Encourage Reasoning

13. 13

14. Expressions and Equations Work with radicals and integer exponents Understand the connections between proportional relationships, lines, and linear equations. Analyze and solve linear equations and pairs of simultaneous linear equations. 14

15. 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. 15 http://map.mathshell.org /

16. Applying Properties of Exponents 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.

17. Applying Properties of ExponentsProjector Resources Powers of 2 P-17 B: 16 ÷ 8 = 2 A: 8 × 4 = 32 D: 8 ÷ 8 = 1 C: 8 ÷ 16 = ½

18. Applying Properties of ExponentsProjector Resources Working Together P-18 Take turns to: 1.Select an expression card and find all other cards that have the same value as the one you have chosen. 2.Explain your matching to your partner. 3.Your partner must check your matching and challenge your explanation if they disagree. 4.Once agreed, glue the cards onto the poster and record your explanation for each match. 5.Continue to take turns until you have ten groups of cards.

19. Applying Properties of ExponentsProjector Resources Sharing Work P-19 One person in your group: Write down your card matches on your mini-whiteboard. Go to another group’s desk and compare your work with theirs. If there are differences in your matches, ask for an explanation. If you still don’t agree, explain your own thinking. The other person(s) should: Stay at your desk, and be ready to explain the reasons for your group’s decisions.

20. Estimating Length Using Scientific Notation  8.EE.3 - Use numbers expressed in the form of a single digit times a whole number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.  8.EE.4 - Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology.

21. Estimating Length Using Scientific NotationProjector Resources What’s the Number? P-21 30,000 × 10 −1 3 × 10 3 0.3 × 10 4

22. Estimating Length Using Scientific NotationProjector Resources Scientific Notation or Not? P-22 30,000 × 10 −1 3 × 10 3 0.3 × 10 4

23. Estimating Length Using Scientific NotationProjector Resources Which is Greater? P-23 8 × 10 −3 4 × 10 −1

24. Estimating Length Using Scientific NotationProjector Resources Matching Card Set A 1.Take turns to match a card in scientific notation with a card in decimal notation. 2.Each time you match a pair of cards explain your thinking clearly and carefully. Place your cards side by side on your desk, not on top of one another, so that everyone can see them. 3.Partners should either agree with the explanation, or challenge it if it is not clear or not complete. 4.It is important that everyone in the group understands the matching of each card. 5.You should find that two cards do not have a match. Write the alternative notation for these measurements on the blank cards to produce a pair. P-24

25. Estimating Length Using Scientific NotationProjector Resources Matching Card Set B 1.Match the objects in Card Set B with the corresponding paired measurements from Card Set A. You may want to put the objects in size order first to help you. 2.It is important that everyone in the group agrees on each match. 3.When you have finished matching the cards, check your work against that of a neighboring group. 4.If there are differences between your matching, ask for an explanation. If you still don’t agree, explain your own thinking. 5.You must not move the cards for another group. Instead, explain why you disagree with a particular match and explain which cards you think need to be changed. P-25

26. Playing Catch-up  8.EE.5 - Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationship represented in different ways. 26

27. Dan Meyer  Math Class Needs a Makeover Math Class Needs a Makeover  Three Act Math Tasks Three Act Math Tasks  Blog Blog

28. 8.EE.8 - Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cased by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. 28

29. Cell Phone Plans Company A charges a base rate of $5 per month, plus 4 cents for each minute that you’re on the phone. Company B charges a base rate of only $2 per month and charges you 10 cents for every minute used. How much time per month would you have to talk on the phone before subscribing to company A would save you money? P-29

30. Classifying Solutions to Systems of Equations

31. Projector Resources Card Set A: Equations, Tables, Graphs P-31 1.Share the cards between you and spend a few minutes, individually, completing the cards so that each has an equation, a completed table of values and a graph. 2.Record on paper any calculations you do when completing the cards. Remember that you will need to explain your method to your partner. 3.Once you have had a go at filling in the cards on your own: Explain your work to your partner. Ask your partner to check each card. Make sure you both understand and agree on the answers. 1.When completing the graphs: Take care to plot points carefully. Make sure that the graph fills the grid in the same way as it does on Cards C1 and C3. Make sure you both understand and agree on the answers for every card.

32. Classifying Solutions to Systems of EquationsProjector Resources Card Set B: Arrows P-32 1.You are going to link your completed cards from Card Set A with an arrow card. 2.Choose two of your completed cards and decide whether they have no common solutions, one common solution or infinitely many common solutions. Select the appropriate arrow and stick it on your poster between the two cards. 3.If the cards have one common solution, complete the arrow with the values of x and y where this solution occurs. 4.Now compare a third card and choose arrows that link it to the first two. Continue to add more cards in this way, making as many links between the cards as possible.

33. Functions 33 Define, evaluate, and compare functions. Use functions to model relationships between quantities.

34. Illustrative Mathematics 34  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/

35. Foxes and Rabbits Given below is a table that gives the population of foxes and rabbits in a national park over a 12 month period. Note that each value of t corresponds to the beginning of the month.

36. US Garbage, Version 1

38. Domino Effect

39. Nonlinear Functions 8.F.3 - Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.  Using your graph paper, create a set of axes for Quadrant 1 39

40.  Construct a T-table for the function that compares the steps in the pattern to the number of toothpicks used to make the pattern. Label correctly.  Graph steps 1-3.  Add more values to your T-table and to your graph. 40

41.  Construct a T-table for the function that compares the steps in the pattern to the number of toothpicks used to make the pattern. Label correctly.  Graph steps 1-3.  Add more values to your T-table and to your graph. 41

42.  Construct a T-table for the function that compares the steps in the pattern to the number of toothpicks used to make the pattern. Label correctly.  Graph steps 1-3.  Add more values to your T-table and to your graph. 42

43.  Construct a T-table for the function that compares the steps in the pattern to the number of toothpicks used to make the pattern. Label correctly.  Graph steps 1-3.  Add more values to your T-table and to your graph. 43

44.  Construct a T-table for the function that compares the steps in the pattern to the number of toothpicks used to make the pattern. Label correctly.  Graph steps 1-3.  Add more values to your T-table and to your graph. 44

45. 45

46.  8.F.5 - Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described verbally. 46

47. Bike Race 47

48. Geometry 48

49. Understand congruence and similarity using physical models, transparencies, or geometry software.  8.G.1 - Verify experimentally the properties of rotations, reflections, and translations.  8.G.2 - Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figure, describe a sequence that exhibit the congruence between them.  8.G.3 - Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.  8.G.4 - Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. 49

50. High School Geometry  Represent transformations in the place using e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). [G-CO2]  Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. [G-CO3]  Develop definitions of rotations, reflections, and translations in terms of angels, circles, perpendicular line, parallel lines, and line segments. [G-CO4]  Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. [G-CO5]  Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. [G-CO6] 50

51. High School Geometry  Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. [G-CO7]  Explain how the criteria for triangle congruence, angle-side-angle (ASA), side- angle-side (SAS), and side-side-side (SSS), follow from the definition of congruence in terms of rigid motions. [G-CO8]  Verify experientially the properties of dilations given by a center and a scale factor. [G-SRT1]  Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. [G-SRT2]  Use the properties of similarity transformations to establish the angle-angle (AA) criterion for two triangles to be similar. [G-SRT3] 51

52. Fishing for Points 52

53. Translation P-53 Where will the L-shape be if it is translated by −2 horizontally and +1 vertically?

54. Reflection P-54 Where will the L-shape be if it is reflected over the line x = 2?

55. Rotation P-55 Where will the L-shape be if it is rotated through 180°around the origin?

56. Matching Cards  Take turns to match two shape cards with a word card. Each time you do this, explain your thinking clearly and carefully.  Your partner should then either explain that reasoning again in his or her own words, or challenge the reasons you gave.  It is important that everyone in the group understands the placing of a word card between two shape cards.  Ultimately, you want to make as many links as possible.  Use all the shape card, and all the word the cards if possible. P-56

57. Starting point (1, 4) P-57 Show me the new coordinates of the point (1, 4) after it is: Reflected over the x -axis Reflected over the y -axis Rotated through 180°about the origin. Reflected over the line y = x. Reflected over the line y = − x. Rotated through 90°clockwise about the origin. Rotated through 90°counterclockwise about the origin.

58. General starting point (x, y) P-58 Show me the new coordinates of the point ( x, y ) after it is: Reflected over the x -axis Reflected over the y -axis Rotated through 180°about the origin. Reflected over the line y = x. Reflected over the line y = − x. Rotated through 90°clockwise about the origin. Rotated through 90°counterclockwise about the origin.

59. Aaron’s Designs P-59

60. 8.G.6 8.G.6 – Explain a proof of the Pythagorean Theorem and its converse.  Pythagorean Tile Proof  Proofs of the Pythagorean Theorem? 60

61. 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 a 2 and b 2 (of one color) = to c 2 (of other color). Pythagorean Tile Proof

62. Proofs of the Pythagorean Theorem 62 1 3 2

63. Statistics and Probability 63

64.  8.SP.4 - Understand that patterns of association can also been seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. 64

65. What’s your favorite subject? 65

66. Jeanne Simpson UAHuntsville AMSTI jeanne.simpson@uah.edu acos2010@wikispaces.com Contact Information 66

67. Feedback 3 things I learned 2 things I liked 1 thing I want to know more about 67