Geometry Gap Summary In order to eliminate gaps that will occur under the new core standards, we recommend the following changes be made in the 2012-13 and 2013-14 school year: (This material is not required under our current curriculum, but all material is available in our current textbook). 2013-14 will be the year for full implementation of the common core.

Proof: Integrated into curriculum 12-13 Construction: Integrated into curriculum 12-13 Probability: Integrated into Accelerated curriculum 12-13 TransformationApplication: Integrated into curriculum 13-14 CoordinateGeometry: Integrated into curriculum 13-14 Conic Sections (Circles & Parabolas): Integrated into curriculum 13-14 Modeling: Integrated into curriculum 13-14

Geometry Gap Committee Recommendation for PROOFS in 2012-13

Introduction to Proofs *As a class, work 3 to 4 proofs from sections 2.6 and 2.7. This will serve as an introduction to proofs. Use the textbook/worksheet problems.

Parallel Line/Angle Pair Relationships *Prove Theorem 3.1 in class (Pg. 134) *Have students prove Theorems 3.2 and 3.3. Assign pg. 137 #39,40 *Prove Theorem 3.5 in class (Pg. 152) *Have students prove either Theorem 3.6 or 3.7. Assign pg. 155 #32 or 33.

Triangles *Informally prove Theorem 4.1 (Triangle Sum Thm). Use technology (TI nSpire, Geomtry Sketchpad,etc), hands-on paper activity, protractor, etc. *Prove triangles congruent using SSS, SAS, ASA, or AAS. Assign proofs similar to those on Pg. 204, 211. May supplement with worksheets. *Prove Theorem 4.9 in class (Pg. 217) *Have students prove Theorem 4.10. Assign Pg. 220 #33 *Have students prove Theorem 5.1. Assign Pg. 243 #10 *Informally show the points of concurrency for medians, altitudes, angle bisectors, and perpendicular bisectors. (i.e. have students construct, use TI Nspire, Geometry Sketchpad, etc.) *Informal proof/demonstration of trigonometric ratios (see activity pg. 365)

Parallelograms *Prove Theorem 8.4 in class (Pg. 412) *Have students prove Theorems 8.4-8.8. Assign pg. 415 #41-45 (pick 2)

Circles *Derive arc length formula in class using Key Concept box on pg. 532 *Derive area of a sector formula in class using Key Concept box on pg. 623

Geometry Gap Committee Recommendation for CONSTRUCTIONS in 2012-13

Construction *Copy a Segment Page 15 (#48, 49 Page 18) Use compass/straightedge *Bisect a Segment Page 24 (#2 Page 25) Use compass/straightedge *Copy an Angle Page 31 Use compass/straightedge *Bisect an Angle Page 33 Use compass/straightedge *Perpendicular Line Page 44 (#1, 2 Page 44) Use compass/straightedge, calculator, software (you choose) *Parallel Line Page 151 Use compass/straightedge, calculator, software (you choose)

*These constructions can be covered again when discussing Proof of Median, Altitude, Angle Bisector and Perpendicular Bisector Using compass/straightedge, calculator, software

Geometry Gap SummaryIn order to eliminate gaps that will occur under the new core standards, we recommend the following changes be made in the 2012-13 and 2013-14 school year: (This material is not required under our current curriculum, but all material is available in our current textbook). 2013-14 will be the year for full implementation of the common core.

Proof: Integrated into curriculum 12-13Construction: Integrated into curriculum 12-13Probability: Integrated into Accelerated curriculum 12-13TransformationApplication: Integrated into curriculum 13-14CoordinateGeometry: Integrated into curriculum 13-14Conic Sections (Circles & Parabolas): Integrated into curriculum 13-14Modeling: Integrated into curriculum 13-14Geometry Gap Committee Recommendation

for PROOFS in 2012-13

Introduction to Proofs*As a class, work 3 to 4 proofs from sections 2.6 and 2.7. This will serve as an introduction to proofs. Use the textbook/worksheet problems.

Parallel Line/Angle Pair Relationships*Prove Theorem 3.1 in class (Pg. 134)

*Have students prove Theorems 3.2 and 3.3. Assign pg. 137 #39,40

*Prove Theorem 3.5 in class (Pg. 152)

*Have students prove either Theorem 3.6 or 3.7. Assign pg. 155 #32 or 33.

Triangles*Informally prove Theorem 4.1 (Triangle Sum Thm). Use technology (TI nSpire, Geomtry Sketchpad,etc), hands-on paper activity, protractor, etc.

*Prove triangles congruent using SSS, SAS, ASA, or AAS. Assign proofs similar to those on Pg. 204, 211. May supplement with worksheets.

*Prove Theorem 4.9 in class (Pg. 217)

*Have students prove Theorem 4.10. Assign Pg. 220 #33

*Have students prove Theorem 5.1. Assign Pg. 243 #10

*Informally show the points of concurrency for medians, altitudes, angle bisectors, and perpendicular bisectors. (i.e. have students construct, use TI Nspire, Geometry Sketchpad, etc.)

*Informal proof/demonstration of trigonometric ratios (see activity pg. 365)

Parallelograms*Prove Theorem 8.4 in class (Pg. 412)

*Have students prove Theorems 8.4-8.8. Assign pg. 415 #41-45 (pick 2)

Circles*Derive arc length formula in class using Key Concept box on pg. 532

*Derive area of a sector formula in class using Key Concept box on pg. 623

Geometry Gap Committee Recommendation

for CONSTRUCTIONS in 2012-13

Construction*Copy a Segment Page 15 (#48, 49 Page 18) Use compass/straightedge

*Bisect a Segment Page 24 (#2 Page 25) Use compass/straightedge

*Copy an Angle Page 31 Use compass/straightedge

*Bisect an Angle Page 33 Use compass/straightedge

*Perpendicular Line Page 44 (#1, 2 Page 44) Use compass/straightedge, calculator, software (you choose)

*Parallel Line Page 151 Use compass/straightedge, calculator, software (you choose)

*These constructions can be covered again when discussing Proof of Median, Altitude, Angle Bisector and Perpendicular Bisector Using compass/straightedge, calculator, software

Additional ResourcesTI Nspire

SketchPad

www.Geogebra.org

http://www.mathopenref.com/tocs/constructionstoc.html