# Chapter 4: Basic Geometry TE - Differentiated Instruction

**Introduction**

In this Teacher’s Edition, we will help the educator adapt our Basic Geometry FlexBook for all learners. Differentiated Instruction involves providing students with different avenues to acquiring content, involving processing, constructing, and making sense of ideas. This text develops teaching materials so that all students within a classroom can learn effectively, regardless of differences in ability.

Each lesson is split up by the type of learner: visual, kinesthetic, or auditory. Not every lesson will have a suggestion for every type of learner. There are also modifications for the English language learner (ELL) and the learning disabled student.

Several students who claim they do not like math really enjoy creative writing. Every couple of lessons there is an alternate journal entry that can be used as a warm-up. These journey entries are somewhat math related, but really draw on the creativity of the student. Have students keep these entries in with their Review Queues and collect all warm-ups at the end of each chapter.

The low-achieving or basic level student needs all the incentives you are willing to give in your classroom. One suggestion is to grade everything. Give students a participation grade, worth 5-10% of their total grade. Have a checklist of student names and for each day give them points based on completing notes, the Review Queue, investigations, and certain class work. Each day is worth 2 points; 2 = they did everything, 1 = did half, 0 = did nothing. Even though it does not seem like a lot, the points will add up. This is a great incentive for the basic level or EL student who has a hard time understanding math, but are good kids who want to try. Then, occasionally collect class work and give a separate grade for these assignments. You can also collect the Review Queues and journal entries at the end of each chapter and give students a grade or extra credit toward the test.

Collaborative learning can be a very rewarding experience for basic students as well. Allow your class room to be “flexible.” At the beginning of class and during note-taking, organize the desks in rows. Then, when students are doing group work, allow them to rotate their desks into groups of four. Change seats every 1-2 chapters. On the first day of new groups, have students practice going from rows to groups and back to make the process more efficient.

Groups can be picked a number of different ways. Three suggestions are: one student from each grade achievement: 1 A, 1-2 B/C, 1-2 D/F, the students may pick their own groups (this should be used sparingly and as a reward for students), or picked totally at random by a grade program or Excel. However you pick the groups, the grading should be uniform. One way to grade group work is to staple all the work together and grade one student’s work out of each packet; the second paper in each group, for example. Another option would be to grade everyone’s paper and the “group grade” would be the average of the member’s scores. Both methods will encourage students to double-check everyone’s work and make sure that everyone has the same answers, so that everyone gets the best grade. Explain these repercussions to the class. You can decide if you would like to tell the class which grading method you are going to use before they begin working or after you have collected the assignment.

Testing can also be a cause of high anxiety for all levels of students. This text will present alternative assessments as a final chapter. There are options for group testing, projects, alternative set-ups for quizzes and tests, as well as alternative grading rubrics.

## Chapter Outline

- 4.1. Basics of Geometry
- 4.2. Reasoning and Proof
- 4.3. Parallel and Perpendicular Lines
- 4.4. Triangles and Congruence
- 4.5. Relationships with Triangles
- 4.6. Polygons and Quadrilaterals
- 4.7. Similarity
- 4.8. Right Triangle Trigonometry
- 4.9. Circles
- 4.10. Perimeter and Area
- 4.11. Surface Area and Volume
- 4.12. Rigid Transformations