Honors Geometry; 5/31

Our lesson today focused on how to use the coordinate grid without numbers to prove various properties about figures.  We went over the concept of how to do coordinate proofs together as a class, focusing on making a drawing that is advantageous to doing the proof.  We worked through a few examples together before getting started on the assignment.


Assignment:  section 13-8 / 13-9;   page 558-559;  WE  #1-8;  page 561,  CE #1-4;  page 562;  WE #1-2

Geometry; 5/30

We continued our work with coordinate geometry today by taking a look at how to work with slopes of lines.  We reviewed the concepts of positive, negative, zero, and undefined slopes.  We also went over how to use the coordinates to calculate the slopes of various segments.  Being able to graph lines using points and slope values was also something we reviewed.


Assignment:  section 13-2;  page 532-533;  WE #1-24 all  (skip 20, 21)

Honors Geometry; 5/30

Welcome back from Memorial Day Weekend!  13 more days to go!  We spent a little time to begin the period reviewing the concepts from last week and going through some entry task practice.  The lesson today then focused on being able to work well with the three different types of line equations that are used in this unit.  The slope-intercept form, the standard form, and the point-slope form.  All three can be converted into the other two, and we went through some practice of how to do that.  We also went through 4-5 examples of how to write linear equations based on pieces of information that is provided to us.  The students then got started on their assignment.


Assignment:  section 13-7;  page 555-556;  WE  #1-34;  skip multiples of 3

Geometry; 5/26

We started our final chapter today!  Using geometry and putting it together with algebra is what we will be working on as we go through the final unit on coordinate geometry.  The topic today dealt with how to use both the distance formula and the formula for circles.  Both are based on the pythagorean theorem and will be used heavily in this chapter.


Assignment:  section 13-1;  page 526-527;  WE  5-12,  17-25,  27, 28. 31

Honors Geometry; 5/26

We continued on with coordinate geometry today by reviewing how to work with line equations.  We went over both the slope intercept form and the standard form of line equations together, emphasizing the need to be able to graph both types of equations.  We also went over horizontal and vertical lines, as well as how to graph and solve systems of 2 line equations.


Assignment:  section 13-6;  page 550-551;  WE  #1-34  (skip multiples of 3 except #6)

Geometry; 5/25

The students turned in their chapter 12 reviews and chapter 12 entry tasks to begin the period.  The rest of the period was spent taking the chapter 12 test.


Assignment:  none

Honors Geometry; 5/25

The students turned in their chapter 13 quiz reviews today before taking the chapter 13 quiz.


Assignment:  none

Geometry; 5/24

After going over the homework, we spent time today reinforcing how to work with volume and area ratio problems involving solid objects.  The main task is to determine the scale factor first, and then to set up an appropriate ratio to find the missing value.  We went over 3-4 problems together before spending the rest of the time working on the chapter 12 review assignment.  Chapter 12 test is tomorrow.

Assignment:  Chapter 12 review

Review sheet answers

1.  B = 276.3

     LA  = 650

     TA  =  1202.6

     Vol. =  2763

2.  B = 7.0

     LA  =  37.2

     TA  =  51.2

     Vol.  =  21.7

3.  B = 113.0

     LA = 286.4

     TA = 399.4

     Vol. = 527.5

     slant height = 15.2

4.  slant height = 17

     B = 256

     LA = 544

     TA = 800

     Vol. = 1280

5.   skipped

6.  B = 1808.6

     LA  =  3165.1

     TA = 6782.4

     Vol. = 37981.4

7.  slant height = 25

8.  height = 6

9.  skip

10.  skip

Similar Solids 

1.  a.  144 pi      b.  288 pi

2.  a.  9 pi          b.  9 pi / 2

3.  3

4.  32 pi / 3

5-6 skip

7.  yes

8.  a.  1:3      b.  1:9     c.  1:3      d.  1:27

9.  skip

Honors Geometry; 5/24

We didn't meet as a class today due to SBAC testing, but the review sheet answers are posted below.

Test 52

1.  a.  2 radical 5    b.  1/2      c.  (5, 1)
2.  a,  radical 61     b.  -5/6     c.  (-2, -7.5)
3.  a.  16                 b.  undefined     c.  (4, 0)
4.  a  radical 26      b.  -1/5          c,  (3.7, 5.2)
5.  (x-4)2 +  - 5)2 = 121
6.  (7, -2);  2
7.  perpendicular
8.  vector
9.  equals
10.  (e + g)/2 ,  (f + h)/2
11.  ( 9, 8)
12.  (5, -5)
13.  5 radical 2
14.  ( -15, 15)
15.  graph of vector
16.  a.  (3, 4)    b.  graph
17.  a.  both slopes are -2/7
       b.  perpendicular slopes,  opp. reciprocals,  -2/7 and 7/2
18.  same midpoint for both AC and OB;  (2, 2.5)
19.  midpoint of AB  (8, -4)
       slope of AB = 4/1;   slope of PM is -1/4;  opp. reciprocals so perpendicular


Test 51

1.  undefined
2.  0
3.  negative
4.  1/2
5.  1
6.  a.  3/5;   b.  radical 34
7.  a.  -1      b.  4 radical 2
8.  a.  -5/2    b.  2 radical 29
9.  a.  0         b.  7
10.  x2 +  (y + 3)2 = 36
11.  (x - u)2 +  (y - v)2 = a2
12.  a.  2      b.  (0, 0)
13.  a.  1/2      b.  (2, -2.5)
14.  graph of circle with radius 3 and center (-2, 1);  shaded inside
15.  graph of line
16.  a.  -2/3   b.  -2/3     c.  3/2
17.  a.  -1       b.  -1       c.  1
18.  2 radical 13
19.  a.  all three slopes of AB, BC, and AC are = 1
       b.  B is between A and C   (graph points to verify this)
20.  a.  all sides are = radical 10
       b.  slope of GA = 1;  slope of RM = -1
                 slopes are opp. reciprocals so they are perpendicular lines

Geometry; 5/23

Due to the SBAC testing schedule, the class did not meet today.

Honors Geometry; 5/23

We answered any questions that the students had concerning how to work with vectors to start off the period.  We then reviewed the equations that are required for the quiz on Thursday as well as going over one multi-step problem involving graphing, slope, and distance formula.  The students then got started on their review assignment for the chapter 13 quiz.


Assignment:  Chapter 13 quiz review


check the posting for 5/24 to see the answers to the review sheet

Geometry; 5/22

We finished our last topic in chapter 12 today in dealing with solid objects.  We went over how to work with similar solid objects and how to determine their scale factor.  Once we found the scale factors, we were able to find both the volume ratio and area ratio between the shapes.  These ratios can then be used to solve for unknown quantities.  We went over 2-3 examples before getting started on the homework assignment.


Assignment:  section 12-5;  page 510;  CE  6-11;  page 511-512;  WE  #1-8, 10, 11, 17

Honors Geometry; 5/22

The topic of today's lesson involved seeing how vectors work and how they are related to various applications from navigation and physics.  We went through the basic definition of what a vector is  (measures both magnitude and direction) and then went over how to work with vectors mathematically.  We found the slope of vectors and the magnitude of vectors.  We also went over how to add and multiply vectors, each time graphing the results.


Assignment:  section 13-4;  page 541-542;  WE  #1-9 odd,  10-25 all

Geometry; 5/19

We continued our work with solid objects today by taking a look at the volume and surface area of spheres.  These two formulas are ones that we just use to plug in the various numbers that we are given.  We also took a look at how to work with hemispheres, and the differences that exist between these and spheres.  The students then got started on their assignment.


Assignment:  Spheres worksheet

Honors Geometry; 5/19

We added to our coordinate geometry skills today by determining how to use the midpoint formula in a variety of problem types.  We used this concept to prove that diagonals bisect each other in a variety of types of figures.  After going through a few examples together, the students then got started on their assignment.


Assignment:  section 13-5;  page 545-546;  WE  #1-20,  skip #13, 19

Geometry; 5/18

We continued our work with solid objects today by taking a look at cones and how these are related to both pyramids and cylinders.  We went over a few cone calculation problems together, as well as going through some of the previous formulas to show how algebra can be used to solve for different variables.  The students then got started on their assignment.


Assignment:  Cones and Various Shapes worksheet

Honors Geometry; 5/18

We continued our work with coordinate geometry today by going over how to use the slopes of perpendicular and parallel lines confirming the properties of certain types of figures.  We went over how to use both the slope and distance formulas in confirming figures.  The students then got started on their assignment.

Assignment:  section 13-3;  page 537-538;  WE  #1-14;  19, 20

Geometry; 5/17

We continued our work with solid objects today by taking a look at how pyramids are studied.  The new concept today involved finding what is called the slant height of a pyramid.  This is needed in order to figure out the lateral area of the triangle.  It is determined by using the pythagorean theorem, but the correct numbers from the diagram must be used in order to get it to work.  We went over a couple of examples together before getting started on the assignment.


Assignment:  Pyramids worksheet

Honors Geometry; 5/17

We reviewed the concept of slope today in class in terms of the types of slopes that lines can have and how to calculate slope the slope of a line from two points.  This topic is almost entirely a review from algebra, so most of the students were very familiar with what we went over.  The students also were shown how to graph lines using slope data and how to determine if points are collinear using slope data.


Assignment:  section 13-2;  page 532-533;  WE  #1-29  (skip multiples of 3)

Geometry; 5/16

We continued working with prisms today by taking a look at how to solve problems involving prisms with regular shaped bases.  We went over pentagons, hexagons, and circles (cylinders) together to show how the formulas can be applied to a variety of shapes.


Assignment:  prisms and cylinders worksheet

Honors Geometry; 5/16

We began our unit on coordinate geometry today by taking a look at how to determine the distance between two graphed points.  This distance formula comes from the pythagorean theorem and will be used throughout this chapter.  We also looked at how to use the distance formula to determine the equations of circles.  We worked with circles that were either centered at the origin or one with centers other than the origin.  The students then got started on their assignment.


Assignment:  section 13-1;  page 526-527;  WE 1-11 odds,  17-37;  skip multiples of 3 and skip #34

Geometry; 5/15

The students got their chapter 11 tests back today and were given an opportunity to go over any of the problems that they had questions on.  We then proceeded to start the next chapter that deals with the area and volume of solid objects.  We went through how to determine the base area, the lateral area, the total area, and the volume of prisms today.  We worked with rectangular and triangular prisms in our lesson today, and we will go over more shapes tomorrow.  The students then got started on their assignment.


Assignment:  section 12-1;  page 478;  WE 1-17 all

Honors Geometry; 5/15

The students turned in their chapter 12 reviews and entry tasks to start the period today.  I also collected the solid objects measuring activity that they had been working on last week.  The class then took the rest of the period to take the chapter 12 test.


Assignment:  none;  extra credit puzzle option

Geometry; 5/12

The students turned in their chapter 12 review sheets and chapter 12 entry task sheets at the beginning of the period.  They then spent the rest of the period taking the chapter 12 test.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 5/12

We wrapped up the activity on solid objects today and then spent some time reviewing for the test on Monday.  We went over 3-4 problem types that involve using the formulas backwards to find a particular dimension (radius, height, etc.).  The students then got to work on the second review sheet for chapter 12 and/or finish up their final measurements for the solid objects activity.


Assignment:  Chapter 12 Review Sheet #2

Similar Solids

1.  area = 9 pi;    volume = 9 pi / 2
2.  radius = 6;   volume = 288 pi
3.  radius = 1/2;   area = pi
4.  40 pi
5.  512 + 128 pi / 3
6.  yes
7.  a.  2/3       b.  4/9       c.  8/27
8.  a.  3/4       b.  3/4       c.  9/16
9.  a.  4/5       b.  16/25   c.  64/125
10.  100
11.  54

Geometry; 5/11

We spent some time reviewing the geometric probability concepts that we introduced yesterday with a few more sample problems together.  We then went over the 4 main types of problems missed on the chapter 11 test as a mini group review.  The students then spent the rest of the period working on the chapter 11 review sheet.

Assignment:  Chapter 11 Review Sheet

Answer key:

1.  361
2.  112
3.  area = 309.1;  perimeter = 70.6
4.  100 radical 3
5.  area = 405;  perimeter = 88
6.  384 radical 3
7.  area = 28
8.  area = 75
9.  area = 100 radical 3
10.  area = 96
11.  area = 615.4;  circumference = 87.9
12.  arc length = 2 pi
13.  25 pi - 50
14.  sector = 103.6
15.  central angle = 240
16.  r = 6
17.  4/49
18.  x = 98;  A = 24
19.  a. 1/100        b.  6/25
20.  a.  1/6;  .17;  17%          b.  1/2;   .50;     50%

Honors Geometry; 5/11

We continued our work on the solid objects activity today by measuring and calculating more objects.  The activity took most of the period.  The students got a chapter 12 review towards the end of the period that is the assignment for tomorrow.  We will go over the review in class tomorrow and then finish up the measuring activity / review for the chapter 12 test tomorrow.  The test on chapter 12 is Monday, May 15.


Assignment:  Chapter 12 Review Sheet #1

Geometry; 5/10

Our lesson focused on how to determine geometric probability today by using the area of various figures.  We went over the concept of probability and how it can be applied to lines, circles, rectangles, and other shapes.  Identifying the specific item studied and then dividing it by the total area of what could happen is the concept that we went over with the sample problems before starting the assignment.

Assignment:  Geometric Probability worksheet

Honors Geometry; 5/10

We continued our work with solid objects today by starting on a measuring / calculating activity that involves 16 different solid objects.  We will be using this as a review for the topics we covered in chapter 12.  We will work on this Thursday and Friday as well.  Our test on Chapter 12 will take place on Monday, May 15.

Assignment:  none

Geometry; 5/9

We incorporated similarity into our study of area of figures today by looking at how we can use the scale factor between two similar figures to determine both the area and perimeter ratios.  We went through the concept and wrote down the overall summary before applying it with 3-4 problems together.  The students then got started on their homework assignment.

Assignment:  Similarity of Polygons worksheet

Honors Geometry; 5/9

The students got back their chapter 12 quiz today and we went over any questions that they had on it.  This was the quiz that they had taken last Friday.  We then went through our next lesson today by taking a look at the ratios between similar solid objects.  The 3-4 examples we went over involved showing how the scale factor can be squared to determine any of the area ratios between shapes and also the volume ratio can be found using the scale factor cubed.  This is a concept we initially looked at in chapter 11, so hopefully the idea will still be fresh in the students' minds.

Assignment:  section 12-5;  page 511-512;  WE  #1-15 all, 17-19

Geometry; 5/8

I was out again from class today with an illness.  The students used the period to work on an assignment that dealt with shaded regions involving circles and rectangles.  These types of problems are ones that we dealt with earlier in the chapter and serve as a good review for the upcoming test.  They spent the period working on the assignment.

Assignment:  Shaded Regions worksheet

Honors Geometry; 5/8

I was out from school today with an illness.  The students worked through section 12-4 today on their own as they learned about the area and volume of spheres.  There were some examples in the book that they needed to read through in using the 2 formulas to help them in working on their assignment.


Assignment:  Section 12-4;  page 500-501;  CE #7-9;  WE 1-26 (skip multiples of 3)

Geometry; 5/5

I was ill today and not at school, so the students worked on a review packet from the previous 3 sections that we had been going over.  They corrected and turned in their homework assignment first, and then spent the rest of the period working on the assignment.


Assignment:  Chapter 11 Review Packet (trapezoids, circles, arcs, and sector areas)

Honors Geometry; 5/5

The students turned in their ch. 12 Quiz review sheets today at the beginning of the period before taking the chapter 12 quiz.  The students used the rest of the period to take the quiz.


Assignment:  extra credit puzzle option

Geometry; 5/4

We continued our work with arcs and sectors today by taking a look at how to determine the central angle in these types of problems.  We also went over how to work with what we called "shaded region" problems.  These are problem types that deal with a portion of a circle that is found by working with both a sector and a triangle.  The key thing is to determine what each area is individually and then either add or subtract the values to determine the final answer.  We did a few examples together before the students got started on their assignment.


Assignment:  Arc Length - Sector Area worksheet + page 454;  WE #13, 14, 16

Honors Geometry; 5/4

We went over homework questions regarding cylinders and cones today before spending some time reviewing for the quiz tomorrow.  The students made a note card of formulas that they can use on the quiz and test this chapter, and then we went over a couple of calculation problems involving cubes.  Both of these examples involve realizing that all sides of a cube are the same.  The students then spent the rest of the period working on their review sheet.


Assignment:  Chapter 12 quiz review


Important Solids 

1.  AX
2.  rectangles
3.  360
4.  480
5.  600
6.  a.  RSTU    b.  triangle VRS  (one example)
7.  vertex
8.  17
9.  544
10.  800
11.  1280
12.  make a sketch of a cone
13.  14 radical 2 or 19.8
14,  12 pi or 37.7
15.  16 pi or 50.2
16.  16 radical 2 / 3 time pi or 7.5 pi or 23.7
17.  make a sketch of a cylinder
18.  108 pi or 339.1
19.  270 pi or 847.8
20.  486 pi or 1526
21.  343
22.  600
23.  48 radical 3 or 83.1
24.  4, 4, and 8
25.  4
26.  a.  equal     b.  less than
27.  15:7

Geometry; 5/3

We continued our work with circle areas today by introducing the topics of arc lengths and sector areas.  These two new vocab terms are related to circles and use the concepts of area and circumference that we learned yesterday.  We went over 3-4 problems together to introduce the concept of what a fraction of the circle is before getting the students to practice a few problems on their own.  The students then got started on their assignment.

Assignment:  section 11-6;  page 453;  CE #1-4, 6;  page 453;  WE #1-12 all

Honors Geometry; 5/3

Our topic today including taking a look at the area and volume of cones and cylinders.  Both of these shapes are based on circles, so using the area of a circle formula was a constant throughout the problems.  We went over 2-3 examples together before getting started on the assignment.


Assignment:  section 12-3;  page 492-493;  WE  #1-19, 21, 25

Geometry; 5/2

We continued our study of area today by going over the area of circles.  We also reviewed how to find the circumference of circles in a variety of ways.  We did problems with exact values of pi and approximate ones (3.14 and 22/7).  We also did a few application problems that use the areas of circles in their overall solution.  The students then got started on the assignment towards the end of the period.

Assignment:  section 11-5;  page 447;  CE #1-12;  page 448-449;  WE #9, 11-13, 15-17

Honors Geometry; 5/2

We continued to work on solid objects today by taking a look at different types of pyramids.  The dimensions of pyramids include the slant height and lateral edge, which are new ones to us.  In order to determine the lateral area, total area, and volume of these shapes, we need to use the pythagorean theorem quite a bit.  We spent time studying the drawings of different pyramids before going through a couple of examples.  The students then got started on their assignment.


Assignment:  section 12-2;  page 485;  WE  #1-16;  (skip mult. of 3), 21, 23, 27

Geometry; 5/1

We spent the first few minutes of the period today taking a few questions from the chapter 11 quiz review sheet before turning it in.  The students then spent the remainder of the period taking the chapter 11 quiz.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 5/1

The students got back their chapter 11 tests from Friday and were able to ask questions about ones that they may have missed.  We then started the next unit of study that deals with the volume and surface area of 3-D objects.  We went through how to work with various types of prisms today.  We showed how to calculate the area of the bases, the lateral area, the total area, and the volume of various types of prisms.  Several of these calculations are closely related to what we were studying last chapter.  The students got started on their assignment during the last part of the period.


Assignment:  section 12-1;  page 478-479;  WE  #1-25;  skip multiples of 3