North country UHS March 18, 2013

1. North country UHS March 18, 2013 Focus on Geometry in the CCSSM

2. North country Inservice outline • Review with Agreed Upon Expectations from 2-15-13 Inservice – Share Experiences • Review of CCSSM Practice Standards – Share Experiences • Presentation of How Geometry Unfolds over K – 12 in CCSSM • Focus on Volume Standard in HS Geometry • Develop one unit focusing on HS Volume Standard and Practice Standards

3. Agreement # 1 • Students will show steps that make it clear the process used. (units included, diagrams) • Turn to a partner and discuss how you have implemented this expectation and your experiences, both good and bad. • Be prepared to share out with whole group.

4. Agreement # 2 • Teachers will encourage discourse within their classes by: • Asking “why” or other similar question to dig deeper into students’ thinking • Providing multiple opportunities daily for students to communicate their work and the process they used • Turn to a partner and discuss, report out

5. Agreement # 3 • Teachers will intentionally teach and encourage perseverance skills. • Turn to a partner and discuss how you have implemented this expectation and your experiences, both good and bad. • Be prepared to share out with whole group.

6. North country Inservice outline • Review with Agreed Upon Expectations from 2-15-13 Inservice – Share Experiences • Review of CCSSM Practice Standards – Share Experiences • Presentation of How Geometry Unfolds over K – 12 in CCSSM • Focus on Volume Standard in HS Geometry • Develop one unit focusing on HS Volume Standard and Practice Standards

7. CCSSM Practice Standards • On your own, write down numbers 1 – 8 on a sheet of paper. • Try to fill in as many of the Math Practice Standards you can without looking. (Don’t worry about getting the numbers exact at this point) • When you run out of the ones that you know, turn to a neighbor and compare your lists, adding on when necessary. • Be prepared to report out.

8. Accountable Talk Teacher Moves • Look at the Handout “Teacher Moves from Accountable Talk” • Turn and talk to your neighbor and discuss which of these moves you have used in your classroom with success. • Be ready to share out with large group.

9. North country Inservice outline • Review with Agreed Upon Expectations from 2-15-13 Inservice – Share Experiences • Review of CCSSM Practice Standards – Share Experiences • Presentation of How Geometry Unfolds over K – 12 in CCSSM • Focus on Volume Standard in HS Geometry • Develop one unit focusing on HS Volume Standard and Practice Standards

10. K – 6 GEOMETRY • STUDENTS BECOME FAMILIAR WITH GEOMETRIC SHAPES • THEIR COMPONENTS (Sides, Angles, Faces) • THEIR PROPERTIES (e.g. number of sides, shapes of faces) • THEIR CATEGORIZATION BASED ON PROPERTIES (e.g. A square has four equal sides and four right angles.)

11. K – 6 GEOMETRY • COMPOSING AND DECOMPOSING GEOMETRIC SHAPES • The ability to describe, use, and visualize the effects of composing and decomposing geometric regions is significant in that the concepts and actions of creating and then iterating units and higher-order units in the context of construction patterns, measuring, and computing are established bases for mathematical understanding and analysis. • K-6 GEOMETRY PROGRESSIONS

12. SPATIAL STRUCTURING AND SPATIAL RELATIONS in Grade 3 • Students are using abstraction when they conceptually structure an array understand two dimensional objects and sets of objects in two dimensional space as truly two dimensional. • For two-dimensional arrays, students must see a composition of squares (iterated units) and also as a composition of rows or columns (units of units)

13. SPATIAL STRUCTURING AND SPATIAL RELATIONS in Grade 5 • Students must visualize three-dimensional solids as being composed of cubic units (iterated units) and also as a composition of layers of the cubic units (units of units).

14. Classify triangles in Grade 4 • By Side Length • Equilateral • Isosceles • Scalene

15. Classify triangles in Grade 4 • By Angle Size • Acute • Obtuse • Right

16. ANGLES, • IN GRADE 4, STUDENTS Understand that angles are composed of two rays with a common endpoint Understand that an angle is a rotation from a reference line and that the rotation is measured in degrees

17. Perpendicularity, Parallelism • IN GRADE 4, STUDENTS Distinguish between lines and line segments Recognize and draw Parallel and perpendicular lines

18. Coordinate Plane • Plotting points in Quadrant I is introduced in Grade 5 • By Grade 6, students understand the continuous nature of the 2-dimensional • coordinate plane and are able to plot points in • all four quadrants, given an ordered pair • composed of rational numbers.

19. Altitudes of Triangles • In Grade 6, students recognize that there are three altitudes in every triangle and that choice of the base determines the altitude. • Also, they understand that an altitude can lie… • Outside the triangle On the triangle Inside the triangle

20. Polyhedral solids • In Grade 6, students analyze, compose, and decompose polyhedral solids • They describe the shapes of the faces and the number of faces, edges, and vertices

21. Visualizing Cross Sections • In Grade 7, students describe cross sections parallel to the base of a polyhedron.

22. Scale Drawings • In Grade 7, students use their understanding of proportionality to solve problems • involving scale drawings of geometric • figures, including computing actual • lengths and areas from a scale drawing • and reproducing a scale drawing at a • different scale. • Scale: ¼ inch = 3 feet

23. They partake in discovery activities, and form conjectures, but do not formally prove congruence until HS. Unique Triangles • In Grade 7 students recognize when given conditions will result in a UNIQUE TRIANGLE

24. impossible Triangles • In Grade 7 students recognize when given side lengths will or will not result in a triangle • The triangle inequality theorem states • that any side of a triangle is always • shorter than the sum of the other two sides. • If the sum of the lengths of A and B is less than the length of C,then the 3 lengths will not form a triangle. • If the sum of the lengths of A and B are equal to the length of C, then the 3 lengths will not form a triangle, since segments A and B will lie flat on side C when they are connected.

25. Grade 7 Formulas for Circles • Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.   • C = 2πr A = πr2

26. Grade 7 Angle Relationships • Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

27. Grade 7 problems involving 2-D and 3-D Shapes • 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.   • Find the volume • and surface area

28. Grade 8 Transformations • Understand congruence and similarity using physical models, transparencies, or geometry software.   • Verify experimentally the properties of rotations, reflections, and translations: • Lines are taken to lines, and line segments to line segments of the same length. • Angles are taken to angles of the same measure. • Parallel lines are taken to parallel lines.

29. Grade 8 Transformations Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.  

30. Grade 8 Congruence via Rigid Transformations • 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 figures, describe a sequence that exhibits the congruence between them.  

31. Gr. 8 Similarity via Non-rigid and Rigid Transformations • 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. Enlarge PQR by a factor of 2.

32. Grade 8 Angles b a c • Use informal arguments* to establish facts about: • the angle sum and exterior angle of triangles, • the angles created when parallel lines are cut by a transversal • the angle-angle criterion for similarity of triangles. • *For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.