Mathematics Geometry and Measurement Geometry

Geometry In the Area of: Geometry & Measurement
1	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Interpret, draw 3-D objects.	-Present visuals and have question and answer session. -Ask students the question, "how many regular solids are there in the world?"	- Build their own 3-D object. -See the video- 5 Platonic Solids, then show various modells and discuss the models in groups.		-DGT Resource book p. 213, 'similarity in geometric creatures.' -Make some of the solids.	- Discovering Geometry, p. 527, Investigations 11.1. - Video:5 Platonic Solids.
Geometry In the Area of: Geometry & Measurement
2	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Classify, sort, analyze figures in terms of congruency and similarity.	-Lead discussion about where 'similarity' fits in real life. -Have student discover SAS, ASA, and SSS. -Discuss the shadow measure of a tree or pole and method to use (similar triangles).	-Make a mural. -Cut out triangles so they can see SAS, ASA, and SSS. -Measure the flagpole by the shadow method. Follow up on overhead in class.	- Journal entry on this activity in student portfolio. - Student portfolio.	-Project on discovery ratio: surface area to volume (i.e., 'why elephants have big ears') DGT p. 619. -Measure a tree/ pole in their yard or neighborhood.	- Discovering Geometry, p.593. - Patty Paper. - Tape measure.
Geometry In the Area of: Geometry & Measurement
3	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Use basic properties of logic & deductive reasoning.	- Explain, show students how to solve logic problems. - Show the use of Venn Diagrams as problem solving tool.	- Write their own logic puzzle. - Perform a variety of Venn diagramming scenarios in groups.		Math Applications.	Zounds!, p.216.
Geometry In the Area of: Geometry & Measurement
4	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Identify, analyze congruent and similar figures using transformations and coordinates.
Geometry In the Area of: Geometry & Measurement
5	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Analyze properties of Euclidean transformations.
Geometry In the Area of: Geometry & Measurement
6	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Develop, deduce properties and relationships between figures from given assumptions.	- Introduce geometry sketchpad to students. - Have students discover theorems on triangles, lines, medians, quadrilaterals.	- Use geometric sketchpad to discover properties and relationships of figures. - Use the Geometric Supposer in the math computer lab.	Journal entry describing class activities.	Star polygon project- DGT p. 317.	-Discovering Geometry. -Program in on the computer in lab.
Geometry In the Area of: Geometry & Measurement
7	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Use a variety of proof formats (i.e. paragraph, two column, etc.).	Demonstrate the indirect method by giving the green-purple people problem.	- Do the green- purple people indirect proof. - Perform the ZEBRA problem.	Submit worksheet.	Act out the characters in the green-purple people problem (have a play).	See green-purple people problem.
Geometry In the Area of: Geometry & Measurement
8	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Use a variety of techniques of proof (i.e. transformational, synthetic, coordinate, etc.).	Show connection between paragraph proof and flow chart proof.	Create a flow chart from other students' paragraph proofs and vice versa.
Geometry In the Area of: Geometry & Measuremen
9	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Use inductive and deductive reasoning through real world applications.	- Provide excerpt from, The Adventure of Duncan's Men, by Doyle. - Show how alternate interior angles were used to measure the earth.	- Read and answer questions to examine the two forms of logical reasoning. - See how Erastothenes measured the earth.	Compare class activity with 'original work'.	Extend the problem to a cube with edges: 4, 5, ..., 10.	- Discovering Geometry, p. 687 -Geometry - Moise & Downs, p. 299.
Geometry In the Area of: Geometry & Measuremen
10	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Translate between synthetic and coordinate representations.	Introduce the painted cube problem. &emdash; edge 3&emdash; paint all 6 faces&emdash; How many blocks painted on 3 sides, 2 sides, etc.	Complete the chart to generalize for a cube with N edges.	Submit a journal write up for the activity.	- Stained glass project DGT resource book. - Try to trisect an angle . Investigate what regular polygons cannot be constructed.	Geometry resource book.
Geometry In the Area of: Geometry & Measuremen
11	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Develop compass & straight edge constructions in context of geometric theorems.	- Demonstrate construction in small groups. - Show students the BASIC constructions	- Do the packet of constructions. - Go on a,''treasure hunt.' Make a map and students will use constructions to find treasure.	Create their own piece of geometric art.	Sets goals/parameters for art activity.	Discovering Geometry, pp. 3-33.
Geometry In the Area of: Geometry & Measuremen
12	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Demonstrate and understanding of geometric concepts based on polygons. (i.e. triangles, squares, rectangles, pentagons, hexagons, etc.)	Explain, explore various polygonal shapes and their properties with students.	- Write children's story illustrated with 'tangram' pictures. - Make the TRI-HEXAFLEXAGON in class.	Rubric scoring and sharing of the story book.	- Geometry scavenger hunt.- DGT p.325. - Make the rest of the flexagons.	Martin Gardner's Puzzle Books.
Geometry In the Area of: Geometry & Measuremen
13	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Demonstrate an understanding of geometric concepts based on circles. (i.e. tangents, chords, arcs, etc.).	Have students explore concepts through manipulatives.	- Carry out various investigations of circle for audience. - Use the Geometric Supposer on circles.	Folding paper circles.	Racetrack geometry. DGT , p. 360.	-Discovering Geometry, p. 201. - Computer program in lab.
Geometry In the Area of: Geometry & Measuremen
14	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Understand concepts of areas and volumes.	- Have students discover the circle theorems. Demonstrate the volume formulas. - Use plastic models.	Use water to show that a cone is 1/3 its cylinder, etc. Use 3-D plastic models.	Building a home project.	- Discover through measurement the theorems on central angles, inscribed angles, etc. - In groups, discover the biggest box (volume) that can be made from a 9 x 12 piece of paper.	-Discovering Geometry, p. 209. -3-D set of pyramids, cones, etc.
Geometry In the Area of: Geometry & Measuremen
15	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Perform various activities involving areas and volumes.	- Introduce various formulas and an example of exploration of formulas. - Have students discover Pic's Formula.	- Give presentation on how to derive one of the area or volume formulas using posters and visual aids. - Be given a worksheet to discover the formula.	Work with group to write test items and application problems.	Project: Archimedes principles, DGT, p. 562.	Use any Pic's formula worksheet or any geoboard investigation of such.