Supporting Questions are being added throughout the unit as I am seeing what the bigger picture is. I have added a few supporting questions, but they are definitely being changed as I move through. Using some of the "Higher Order Thinking Skills" Problem for Supporting Questions.
Points, Lines, Planes (1.1) (This lesson took 3 days, but I think it was because of problems with visualizing a 3-D situation, see below)
- Hard lesson to start on. Lots and Lots of vocab words. Do not really want students to address vocab words on their own; trying to set norms for how students should be taking notes on vocab words and notations as part of their journal. I feel like I am not going fast enough, and afraid that I will be questioned on my lack of rigor in the classroom.
- Also I am finding it hard to have warm-up problems as part of the beginning of class. Maybe I should start putting a time limit and letting students know when that limit ends.
- Students had a hard time visualizing the 3-D image of intersecting planes. For the next class I made a card-board representation of the intersecting planes. It definitely helped most student see what was happening.
- Some of the more advanced students struggled with the idea that there were only two planes defined, they understand that there are an infinite number of planes, but they are not understanding that only 2 are defined. I have told them that if there are 3 or more that it will be clear and that I will not try to trick them.
- Exercises: #54 students struggled with the directions of "Satisfying an equation", so got tripped up on the entire problem; #51 d is not necessary; #50 students did not know what a vanishing point was; #52, many students did not using a problem solving technique, they just assumed that they did not have enough info to solve the problem.
- Spiral Review of Algebra Skills: Radicals, Solving systems of equations, Graphing points to create geometric figures, metric conversions
Linear Measure (1.2)
- Students are struggling with the fact the definitions are to for their use to be prepared for the next lesson, they are not HW, I will not be collecting them.
- Needed to clarify to students that lines and segments will/can have the same name, with the different designation symbol over it.
- Quickly running through examples 1 & 2, w/ the assumption that students at this level should be able to use and read a ruler to measure a line segment.
- Students are lazy about writing the "betweenness equation", needed to remind them of practicing notations with simple problems, so that we encounter more difficult problems we are clear about the notations. For example: writing it using subtraction.
- Spiral Review of Algebra Skills: Solving Inequalities, Evaluating Expressions
Distance & Midpoints (1.3)
- When I introduced the distance formula through theory first, it was a disaster!
- Stepped back to teach it again, first talking about the Pythagorean Theorem and finding the distance by drawing a right triangle between the points. Then talking about how a and b in the theorem could be replaced with the name of the segment. Then talking about how we would find a and b without drawing a picture (i.e. subtracting the values of our coordinates). Talking about a general form of the equation we end up with. And then ending with the Supporting Questions: "How do are the Pythagorean Theorem and the distance formula related?"
- Students are fighting the need to write formulas on every problem. Trying to stress to students that there are so many more formulas in Geometry than in Algebra, and many more packed into 1 lesson. Also trying to explain to them the need to do it because of proofs, and that is the make up of Geometry.
- Spiral Review of Algebra Skills: Solving Equations
Angle Measure (1.4)
- Short quick lesson. 1 day on content, spent another day on (short day Tuesday) on constructions: Copying of angles and Bisecting of Angles.
- No need to do 2 examples on naming vertices and all the angles with that vertex.
- Stress the need to use the notation for congruent angles and measures for congruent angles are equal.
- Starting to get away from the solving of the variable together. Continuing to set up the problem for them (progress check = having a student give me the steps), but focusing my talking time on the concept at hand, not the algebra 1 content of solving for 1 variable.
- Gave students hand-out with figures because of the complicated nature of the figures, saved on class down time.
- Use the example from "Personal Tutor" for example 3. I felt as though the one in the original ppt was too wordy for the concept to be addressed, and the REAL-World situation was not relatable.
- Questions #41 & 39 were difficult for the students to visualized. Stressed the need to sketch the figure. WOrked through 1 or the other with the class, but NOT both. They are essentially the same problem except for the algebraic expressions given for angle measures.
- May want to suggest that students distribute the 2 in the expression representing the measure of angle ABE, so they are working with 2s + 11. Some students are not doubling the angle, rather assuming the angle is doubled because the original expression is 2(s + 11)
- Questions 30-35: Have students copy the figure from the book (gave them a blown up copy) using a straight edge and compass only to practice copying an angle and bisecting. The figure is not drawn accurately, so when doing this, the right angle symbol should be IGNORED!!!!
- Gave the students a copying the angle sheet, as well as step by step instructions on copying and bisecting an angle.
- Spiral Review of Algebra Skills: Measurement Conversion, Solving Equations
MID CHAPTER QUIZ -- Gave students the distance formula and midpoint formula.
Angle Relationships (1.5)
- Day 1 (1/2 class): Gave students two tables, "Relationships do to Angle Positioning" & "Relationships due to Angle Measures". THis is how I addressed vocabulary (Adjacent, Linear Pairs, Vertical, Complementary, & Supplementary Angles). Used language from text book, but put it in less wordy terms. Stressed the importance of the notation formulas for Complementary & Supplementarty relationships, and the NEED to use them.
Chapter 2- Logic & Reason:
- I didn't have the kids write enough related conditionals.
- Students struggled with inductive vs. deductive. Need to do more practice with inductive/deductive statements together.
- I need to explain better the purpose of a Venn Diagram as related to Logic. i.e. the conjunction is the intersection of a circle, a disjunction is the union of the two sets (circles)
- Proofs: Why aren't these being taught? I know students struggle with them, but it is so important in their thinking process moving forward. The higher level students want to know where certain theorems come from, which they would understand from the proof process. Should probably teach as a fill in the blank process.
- need more practice on IDing angle relationships without parallel lines, understanding that there is no congruency or supplementary relationships unless the lines are parallel
- I like the paper folding activity to make the angle relationships
- do not do the making a cube again...students thought it was stupid and didn't see the point. Maybe bring in several cube boxes, maybe try to make a pyramid, and a pentagon prism for examples on skewed lines and parallel planes. Have them do a walk around activity and ID skew and parallel via hands on.
3.2- Angles and Parallel Lines
- Like paper folding activity to create parallel lines and a transversals. I think that the really could see the angle pair relationships.
- I need to do more practice on looking at relations created by parallel lines and those created by non-parallel lines. Doing now as an activity in the next chapter, will be quizzed over them. Using the Angle-Pair Relationship worksheet that I got from Math Teacher Mambo (under resources). Need to change the sheet to say that it is consecutive interior angles rather than same-side interior angles. Hoping to get the original word document from the author.
3.3 - Slope of Lines
- WOW...amazed at how many students struggle with slope.
- Need more practice on the slope relationship between parallel lines and perpendicular lines
- Wondering if worksheets would be better for students then bookwork. i.e. getting students to write down problems. What about having them graph every problem AND do it algebraically.
- What about a slope only quiz?
3.3 - Equations of Lines
- students only want to use slope-intercept form and fight the idea of using point-slope, although student forget what to do with the "b" once they find it and regularly put the point back in to y=mx+b and leave b and m as the variables.
- Would more practice be all they need? Why aren't they better with this skill?
3.5 - Proving Lines Parallel
- Some struggles with this chapter because we haven't really talked about proofs. Tried doing informal proofs, but students fight the requirement of writing reasons. Wondering if doing proofs in Chapter 2 would remedy some of this.
- I think because we didn't do enough related conditional statements, the students do not recognize that we are working with converses of the theorems.
3.6 - Perpendicular Distance
- students struggled because of the long problems. They are lazy and don't want to do all the steps. They want to find a short cut, but one does not exist. I wish they would trust me on the fact that there is not a short cut. DO they not trust me because of the informal proof process I am making them do? If we were doing formal proofs would I allow them to not do the informal proof process on every problem? Is the informal proof process to repetitive for every problem? Should I really make them show the steps of Def. of Congruency and substitution every time? OR would it be ok if they just stated the theorems they used at the end of the problems?
4.1 - Classifying Triangles
- Do I need to have a lecture on this section. Could I give the kids skeleton notes for classifying triangles by angles & classifying triangles by angles within in figures, and have the level of discourse in the class be raised a little? Creating more student-student discussions? Maybe do 1 problem where you have to find the missing value problem?
4.2 - Angles of Triangles
- Would love to have students discover the "Triangle Angle-Sum Th." on their own through a flow-chart graphic organizer from me. Do I have time? The flow chart could lead into a flow proof...two birds with one stone?
- The above statement could lead into the "Exterior Angle Th." discovery too.
- students are confusing Ext Ang Th (m<1>
4.3 - Congruent Triangles
- Need to be more clear to students that when writing congruent statements for segments that congruent angles need to match up (i.e. Segment AB is congruent to Segment DE, not Segment ED).
SSS, SAS, AAS, ASA, & SSA, AAA (4.4 & 4.5)
- Billy Bob's Road Kill Cafe - First attempt was ok, but I need to revamp it to see if it can go smoother.