CURRICULUM GUIDE

Jennifer Zagofsky ñ Mathematics - Professor J. Cooks - SED 720 - Spring 2003

Article Reviews * Lesson Plan Reviews * Original Lesson Plans * Resource Review

 

Article Reviews

Citation or URL

Summary

Connection to Literacy

Significance

Thompson, D.R., Austin, R.A., Beckmann, C.E., (2002). ìUsing Literature as a Vehicle to Explore Proportional Reasoningî. National Council of Mathematics, 2002 Yearbook, 130.

The article explores a few studies that used literature to engage students in both informal (grades 3-5) and formal proportional thinking (grades 6-8).ÝÝ The results of three stories, Jim and the Beanstalk, Biggest, Strongest, Fastest and Gulliver in Lilliput are examined.Ý After reading each story, students where asked to use the information in the story to examine or solve mathematical problems. For example, after reading Gulliver in Lilliput, students investigated the 2:1 ratio presented (2:1 thumb to wrist, wrist to neck, neck to waist). The students took measurements to determine the accuracy of the hypothesis and then used ratios to estimate other measurements.Ý The study found that the students were more engaged in this type of lesson and better comprehension of the concepts.

Reading and then discussing the mathematics in each story stresses reading comprehension and reading strategies. In addition, the context of a story makes the mathematics less abstract and more concrete. This helps the student relate the material to something he/she knows.Ý As with all types of learning this will increase the probability that the student will be able to make a connection with the concepts.

In mathematics, it is more common to create a story around the math, which students often think is contrived and unrealistic. However, in this case, the mathematics was expanded from an existing story with which the students were familiar.Ý The ideas in this article are very constructivist and are aimed at engaging more students in mathematical problem solving.Ý I thought that these ideas could easily be incorporated into my classroom and will attempt to use this in one of curriculum guide lesson plans.

Click here for URL

Math, Computers and the Internet: Better Opportunities for Persons With Disabilities by Stoddard, Susan; Nelson, Jeannette

This article researches methods for helping disabled persons and students become a participant in technology by helping to develop their numeracy (mathematical literacy). The researchers assert that numeracy involves more than basic arithmetic. The article quotes the National Institute for Literacyís seven themes, which serve as the foundation for adult numeracy standards and goals for disabled students.

…     find relevance or make connections between mathematics and other disciplines;

…     use math to solve problems, reason and make decisions;

…     communicate mathematical ideas;

…     have a conceptual understanding of numbers;

…     interpret data;

…     understand number sense and measurement (geometry); and

…     recognize patterns and relationships (algebra).

Success is met when the relevance of math literacy is linked to everyday life and students are able to meet the above objectives. The article also discusses the effectiveness of tools like MathPad(TM) which helps physically disabled students work through math problems with a minimum of keystrokes.

The researchers state that half of the students the Vocational Rehabilitation Services population read at grade 9 or above, but have math reading skills only above grade 7.Ý For physically disabled students, they show that their math is at grade level until the math lessons become too difficult or abstract to complete without the use of pencil and paper.Ý Without the ability to properly (or quickly) use these key tools to problem solving, these students begin to fall behind in their math literacy.

 

As I have not yet taken the mainstreaming class, this article alerted me to the challenges and opportunities for disabled students who will be in my classroom.Ý I have observed in classrooms with physically challenged students, but I have never seen them using any of the techniques or tools that the researchers reviewed.Ý I will definitely review this article when I have students that could benefit from these tested approaches.

Click here for URL

Creating Cultural Relevance in Teaching and Learning Mathematics by By: Leonard, Jacqueline, Guha, Smita

 This researcher shows the importance of and provides examples of culturally relevant mathematics teaching.Ý The article analyzes an exercise from Ms. Toliverís class to incorporate the studentís environment in mathematics.Ý The students take photographs in the local neighborhood and then create math problems.Ý These problems become a springboard to reinforce the use of mathematical operations and the strategies needed to solve non-routine mathematics problems. However, the article also explores how teacher involvement stifled some of the creativity and problem solving as the teachers pushed the students to create convergent problems with single solutions.

The connection to literacy in this article is tied to culturally relevant pedagogy. The article stresses the importance of making the material relevant to studentís lives so that they will be more interested and engaged in the learning.

The authors state that most studentsí first teachers will be white, middle-class women. This cultural discontinuity can create a mismatch between the cultures of the home and school, resulting in poor academic performance.Ý Thus, the authors offer some ideas for helping to reach different ethnic groups.Ý Incorporating this type of culturally relevant pedagogy in ìmathematics problems is one way to avoid the cultural deficit model and help students and teachers value the culture of the community.î

This article touched on one of the key concepts that I will take away from this course ñ I must ìhookî my students! They must find the information I am teaching relevant to something in their lives or something that they already know.Ý

 

This article mentioned a couple techniques for engaging students, linked to race (Native Americas ñ games, African Americans ñ rhythm, church and social perspectives). I think these are interesting ideas for all students, but I believe that my students will have multiple cultural influences, only one of which will be their race. However, I must find something in my studentsí lives with which to connect the learning or it will remain in my classroom and not with my students.

Whitin, D.J. & Whitin, P., ìExploring Mathematics through Talking and Writingî. National Council of Mathematics, 2002 Yearbook, 213.

This article discusses the importance of ìinviting everyone into mathematical investigations.î The teacher asking the right questions, participating in the process of exploring mathematics and playing devilís advocate to challenge students, can facilitate this.Ý The article showed how a student could use his/her experience with stories to help their mathematical thinking.Ý After reading a story, the students were questioned about the plot of the book and choices the author made. The students discussed the topic and then wrote their own stories with different numbers or examined other options the author could have chosen. Through this type of exploration the students learned about remainders, factors and prime numbers.

With this approach, students are encouraged to use their own cultural and linguistic experiences to change the storyís attributes.Ý The students write new stories, changing the plot based on mathematical lessons.ÝÝ The article also stresses that writing and talking should be part of the regular classroom activities and teacher guided activities to facilitate the learning of mathematics.

This article stresses the importance of teachers asking the right questions to move class mathematics forward.Ý The other role of ìlearnerî is equally important. The teacher should be viewed as a co-learner, not math authority, working in a classroom community to discover new ideas.Ý The other significant attribute of this technique is that it creates differentiated learning within the same lesson because students will delve into the problem to their own capability.Ý These are all concepts that I have been learning about in my math C&I class and plan to incorporate into my teaching.

http://www.leeds.ac.uk/educol/documents/00001634.htm

ÝThe UK researchers in this article analyze four seventh-grade mathematics classes as they studied the question ìCan we develop a school algebra culture in which pupils find a need for algebraic symbolism to express and explore their mathematical ideas?îÝ Each researcher examined one strand -- metacomments, teacher strategies, algebraic activity, student perspectives and classroom cultures.

They concluded that the teacherís behavior was contingent on the pupilís responses and student creativity is supported when they are engaged in asking their own questions.Ý When followed, these behaviors created a situation where students were able to articulate complex structures and patterns supporting algebraic descriptions.

 The focus of this research is numeracy or the development of mathematical literacy, as students develop the algebraic language.Ý Some of the approaches, like metacommenting are very similar to techniques like metacognition which were studied in our class. These and other techniques can be used to increase the mathematical literacy of my class.

This article gives teachers even more support, encouragement and research to show that constructivist, self-discovery results in deeper and more lasting learning for the students.Ý In this article, the students develop the algebraic language. Although the teacherís guidance is minimal, the teacherís questioning and involvement in structuring the activities is key to the studentís learning.

 

 

Lesson Plan Reviews

Note to Cooks ñ I focused both my reviews and my lesson plans on Geometry because it is most relevant to my student teaching.

 

Lesson Plan URL

Summary of Lesson Plan

Positive Aspects

Development Areas

How would you adapt this lesson for your classroom?

Critique 1

(Ask Eric)

 Students create scale models of a box and find surface area and volume. Then, the students compare the original and scaled drawings. Finally, students discuss occupations and techniques involving scaled drawings.

 The hands-on portion of the activity will keep students interested and give them a deeper understanding of ratios and scale.

This lesson could benefit from a student ìhook.î Measuring, drawing and cutting out boxes are not innately interesting.Ý Second, this activity and discussion may take more than 50 minutes to complete. Finally, I believe that 6-8th graders could definitely participate in this activity (vs. HS only).

 I would have the students bring in (or I would purchase) their own boxes (candy, cards, everyday objects). Then, I would have them make larger or smaller scaled representatives. I would have them use the grid paper to duplicate the designs on the box, as well as the dimensions.

Critique 2

(Math Archives)

Through a series of class discussions, group work and resource pages, students will see how simply understanding prefixes can help them interpret the meaning of unfamiliar terms in and out of mathematics.

 The lesson is comprehensive, including all the needed materials and many good probing questions.Ý It brings creativity and language arts into the mathematics. Time is rarely devoted to this topic, but this learning can help students outside of mathematics.Ý

All these resource pages in one period could be ìboring.îÝ If I did this in one period, I would change pairs and groups throughout the period.

I would like to take the students to the computer lab and/or have a student(s) use a class computer(s) for an online dictionary. I might also break up the lesson into several days and build on the information, using it as a warm-up and increasing the chances that the students will retain the information.Ý

 

If my students were grouped in other classes, I would work with their teacher to link this lesson to their language arts class.

Critique 3

(Awesome Library)

 Students use measurement to find tree height, circumference and crown. Students find the height by walking away from the tree until a studentís ruler is equal to the tree height. Students then regroup inside and create bar graphs of the data.

Getting out of the classroom, this lesson will give the students hands-on learning. It uses many intelligences ñ visual, kinesthetic, nature and a few more!

 I think this lesson could be applicable for grade 7 as well. It would be helpful to find information on why this technique.

 First, I would make sure enough trees in area, especially in an urban environment. Also, I would allow a block period for the activity and re-write the directions more clearly for the students.

Critique 4
(Math Forum at Drexel)

 

 This lesson takes students from area of rectangles to areas of any parallelogram.Ý The students divide and reposition a trapezoid to make a rectangle and discover theorems about areas of parallelograms.

 This is a constructivist activity and builds on previous learning. The lesson also includes all needed overheads and student worksheets for a 40-minute class period.

 The activity seemed to lack depth and might take less than 40-minutes.Ý

 I would recreate the resource page because the dividing line is in the middle of the grid and thus will make the studentís calculation/measurement of the area of the recreated rectangle.Ý Also, I would create more examples and have the students do a similar activity to discover the area of triangles.

Critique 5
(Smile Program Math Index)

 

 Students discover area using constructivist methods.Ý Students find a square foot on the floor and determine the number of students who can comfortably fit in the square.Ý Then the students are asked to find the number of students that could fit in a larger area. The students then work individually to measure various surface areas in the room and then get ìdrywallî from the teacher to fit the space.

 This lesson gives students the opportunity to learn about area for themselves.Ý Area can be a very abstract concept when learned in a book by calculations. I think the students will find the ìconstructionî work interesting. The assessment portion of this lesson also incorporates some writing components by asking students to show a calculation and explanation of how they found the areas.

 None. Great lesson!

 Class size may be a challenge in a class of 30 students. Thus, I might have the students work in pairs, but submit the write-up individually. Also, once a student correctly turns in an assignment, I may put him/her in charge of distributing additional materials.Ý Also, I would probably use paper and tape for the ìdrywallî and ìdrywall tape.î

 

Original Lesson Plans

Note to Cooks ñ I focused both my reviews and my lesson plans on Geometry because it is most relevant to my student teaching. The lessons are in no order.

LESSON PLAN 1: Triangle Symmetry Postulates.

GRADE LEVEL:Ý 6 ñ 7
CONTENT SUBJECT AREA: Geometry
NUMBER OF STUDENTS: 20-30 students
TIME LENGTH OF CLASS: 50 minutes

OBJECTIVE:Ý Students will be able to state the Triangle Postulates and solve triangle problems using the postulates.

CA STANDARDS:

2.3 Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle).

3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures.

MATERIALS & RESOURCES: Notebook, Pencil, Construction Paper (Blue, Red, Green, Yellow), Scissors, Protractor, Rulers

NOTES FOR TEACHER:Ý Setup table with materials and instructions on overhead/board before class starts.

PROCEDURES AND STEPS (TIME):

ANTICIPATORY STEP:Ý Ask students what they learned yesterday (Triangles, 180 degrees in triangles, labels sides/angles, etc).Ý Show two pictures of large triangles and ask students if they are the same? Students should have dissenting opinions. Tell students that we will investigate some methods for investigating this today. (5 min)

  1. Get students in groups of 4 (and one or two groups of 3 if needed). Each group gets one piece of each colored paper.
  2. Ask student to please create triangles as indicated on overhead/board. (10 min)
    1. Blue ñ Create a triangle with the following side lengthsÝ - 2 cm, 5 cm, 3.5 cm.
    2. Red ñ Create a triangle with the following angles ñ 40, 60 and 80 degrees (p.s. this triangle is Acute!).
    3. Green ñ Create a triangle with two sides with the included angle of 2 cm, 40 degrees, 6 cm.
    4. Yellow ñ Create a triangle with two angles and the included side of 20 degrees, 3 cm, 100 degrees.
  3. In each group, one student should collect all blue triangles, another all red, etc. Ask students to look at the cutouts and the criteria for the triangles they collected. Ask them to come to some conclusions and/or check the cutouts if needed. (5 min)
  4. Ask all students to regroup with other students that have the same color cutouts.Ý These students should discuss their finding and summarize their findings and conclusions on a poster or overhead to present back to the group. (10 min)
  5. Students present back (hopefully results as below or teacher will need to look at cutouts to see if there was a mistake.) (15 min)
  6. Teacher summarizes postulates for studentsí notes and defines ìCongruentî or asks students to define congruent. (5 min)
    1. Blue ñ SSS (Side, Side, Side) - Congruent
    2. Red ñ AAA (Angle, Angle, Angle) ñSIMILAR, but not congruent!
    3. Green ñ SAS - Congruent
    4. Yellow ñ ASA ñ Congruent
  7. Assign homework and allow students to start homework with any remaining time.

FOLLOW-UP ACTIVITY/HOMEWORK: Assign students homework problems in book that will have them justify congruency of triangles.

LITERACY ASPECT:Ý Students will discuss in groups, create a slide and present.Ý For homework they will be writing responses to show congruency.

ASSESSMENT: Students will be assessed during class for understanding, their participation in-group discussion and presentation.

REFLECTION/RESPONSE/DEBRIEF: TBD, but additional timing may be needed for this activity due to its constructive nature.

LESSON PLAN 2: Circles ñFinding PI

GRADE LEVEL: 6 or 7
CONTENT SUBJECT AREA: Geometry
NUMBER OF STUDENTS: 20-30
TIME LENGTH OF CLASS: 50 min

OBJECTIVE:Ý Students will discover pi and be able to measure circumference and diameters for a given circle. Students will also be able to calculate C or D, given the other measure.

CA STANDARDS: ÝÝ

1.0 Students deepen their understanding of the measurement of plane and solid shapes and use this understanding to solve problems:
1.1 Understand the concept of a constant such as p; know the formulas for the circumference and area of a circle.
1.2 Know common estimates of p (3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements.

MATERIALS & RESOURCES: Notebooks, Pencil, String, Scissors, Ruler, Large white piece of paper

NOTES FOR TEACHER:Ý Previous day ask students to bring in a circular object from home. Be sure to have a number of different circular objects in the classroom for students to easily access and measure circumference and diameter (CDs, records, jars, etc.). Post procedure on board/overhead before class starts.

PROCEDURES AND STEPS (TIME):

ANTICIPATORY STEP:Ý Ask students to take out their circular object(s). This was assigned for homework yesterday. Ask one or more students to BRIEFLY describe their object and why they brought it. (5 min)

  1. Demonstrate instructions below and post an example at the front of the room.Ý (5 min)
    1. Encourage them to use any type of measure (metric, English, etc.)
    2. Show students how to measure diameter of circles using the string and ruler. Make sure they measure through the center. Students should measure twice for same circle to ensure correct measurement is taken.
    3. Remind students to ìbudgetî their string to the 3 circles!
  2. Assign students to pairs and give each pair of students a piece of string. Each pair will find 3 circles in the classroom (and objects brought) and follow the instructions below.Ý (20 min)
    1. Cut the first piece of string to measure the circumference of the circle.
    2. Tape the string to the paper and label with the name of the object.
    3. Use the string/ruler to measure the diameter of the circle and record it next to the circle.
    4. When finished, students should be seated and measure the circumferences and individually make the chart below.

Circumference

(Measure string)

Diameter in decimal

(Measure)

Ratio of Circumference to Diameter (c:d, c ½ d or c/d)

7.2 in

2.3 in

 

25.12 cm

8 cm

 

15.7 in

5 in

 
  1. Ask pairs of students to compare ratios within table groups. They should find that all ratios are similar. (5 min)
  2. Teacher should summarize findings for studentís notes and show the formal calculation and symbol for p. (7 min)
  3. Now that we know there is a constant relationship for all circles between circumference and diameter, ask students to think about how we could find (7 min):
    1. C if we know D?
    2. D if we know C?
    3. C if we know radius?
  4. Assign homework and allow students to start homework with any remaining time.

FOLLOW-UP ACTIVITY/HOMEWORK: Students will duplicate the activity at home and answer questions above.

LITERACY ASPECT:Ý Students will record information, discuss in groups and write explanations for homework.

ASSESSMENT: Students will be assessed during class work for understanding and their homework will be reviewed.

REFLECTION/RESPONSE/DEBRIEF: TBD, but I think the students will find the self-discovery of pi interesting, as well as using their own objects. Again, timing and class management of a constructivist activity can be challenging.

 

LESSON PLAN 3: Finding Area of Circles

GRADE LEVEL: 6 - 7
CONTENT SUBJECT AREA: Geometry
NUMBER OF STUDENTS: 20-30 students
TIME LENGTH OF CLASS: 50 min

OBJECTIVE:Ý Students will derive and apply the formula for area of a circle.

CA STANDARDS:

1.0 Students deepen their understanding of the measurement of plane and solid shapes and use this understanding to solve problems:
1.1 Understand the concept of a constant such as p; know the formulas for the circumference and area of a circle.
1.2 Know common estimates of p (3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements.

MATERIALS & RESOURCES: Notebooks, pencil, resource page, scissors, tape/glue, Rulers

NOTES FOR TEACHER:Ý

PROCEDURES AND STEPS (TIME):

ANTICIPATORY STEP:Ý Ask students what they learned yesterday? (Circumference = pd, d = 2r = r+ r, p is constant, p is ~3.14)

  1. Tell students we are going to find area of a circle and ask questions below. (15 min).
    1. ÝIf no response ask them definition of area? What does it mean?
    2. How do we find area of other shapes?
    3. How would we find area of a (draw a rectangle and triangle)?
    4. Ask students how they would find area of a circle?
    5. If they give formula, ask them why or to explain why.
  2. Handout resource page (has 3 identical circles with a center and diameter marked).
  1. Ask students to find the following in centimeters (and get consensus on each). (7Ý min)
    1. Radius
    2. Diameter
    3. Circumference of the circles
  1. Ask students to cut one circle into four equal pieces and tape them to their notebook as below. (5 min)

  1. Ask them to do the same for the second circle, but into 8 equal pieces. (5 min)

  1. Ask students what shape the circle now looks like? (15 min)
    1. What if we cut it into 32 pieces?
    2. Rectangle
    3. So what would the area be if this were a rectangle? LxW. Ask students to point to L and Width on their diagrams.
    4. What is the width? (Radius)
    5. What is the length? (Half of the circumferenceÖ students may need hints or prompting)
    6. Summarize formula for Area of a circle = p r2
    7. Ask students to find Area in terms of diameter.
  2. Assign homework and allow students to start homework with any remaining time.

FOLLOW-UP ACTIVITY/HOMEWORK: Ask students to find Area in terms of diameter. Some area problems in the books will also be assigned.

LITERACY ASPECT:Ý Students will discover mathematics through a logical sequence and formulate a theorem.

ASSESSMENT: Students will be assessed during class work for understanding

REFLECTION/RESPONSE/DEBRIEF: TBD.

 

LESSON PLAN 4: Angles -- Complementary and Supplementary

GRADE LEVEL: 6 - 7
CONTENT SUBJECT AREA: Geometry
NUMBER OF STUDENTS: 20-30 students
TIME LENGTH OF CLASS: 50 min

OBJECTIVE:Ý Students will solve problems using knowledge of complementary and supplementary angles.

CA STANDARDS: Ý

2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.
2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle.

MATERIALS & RESOURCES: Notebooks, Pencil, Protractor

NOTES FOR TEACHER:Ý Teacher will need to setup stations before class. Students must already know how to use a protractor.

PROCEDURES AND STEPS (TIME):

ANTICIPATORY STEP:Ý Tell students that on the count of three they will get up from their desks, take their protractor and find a station with an angle in the room. At the station ask students to measure the angle using their compass. (5 min)

  1. Go around the room and ask students to say their angle. (10 min)
    1. What are the most common angles? 90 and 180
    2. Ask students if they think that there are other angles in the classroom that they think are more common?
  2. 180 degree angle ñ Ask students who had these angles the questions belowÖ(10 min)
    1. What else do we commonly call a 180-degree angle? A line
    2. Have a student draw a line (in any direction) on the board/overhead.
    3. Have another student draw another line intersecting the line at any angle.
    4. Have a student measure and label one of the angles.
    5. Ask students to determine other angle.
    6. Ask student to summarize what happened and how they found the angle.
    7. Define supplementary angles.
  3. 90 degree angles ñ Ask students who had these angles the questions belowÖ (10 min)
    1. Do we have any special names for 90-degrees? Right angles
    2. Where else do we see 90-degree angles? Rectangles, squares, buildings, T-square (drafting tool)
    3. Have a student draw a right angle on the board, or use the corner of the board and draw a line between, creating two angles. Measure one of the angles and ask class if they can figure out the other angle.
    4. Ask student to summarize what happened and how they found the angle.
    5. Define complementary angles.
  4. Show pictures of different angles ask them if some look ìbiggerî than others? Break angles into acute and obtuse groups. Ask students to describe groups of angles or estimate angles. Lead students to fact that some are > 90 and some are <90-degrees. (7 min)
  5. Define acute and obtuse angles. (5 min)
  6. Assign homework and allow students to start homework with any remaining time.

FOLLOW-UP ACTIVITY/HOMEWORK: Students will develop problems for other students to solve, using supplementary and complementary angles.

LITERACY ASPECT:Ý Students will use measuring skills and deduction to find angles and learn theorems.Ý Students will also develop their own problems.

ASSESSMENT: Teacher will review homework and observe studentsí participation and class-work.

REFLECTION/RESPONSE/DEBRIEF: TBD

LESSON PLAN 5: Interior Angles in a polygon

GRADE LEVEL: 6-7
CONTENT SUBJECT AREA: Geometry
NUMBER OF STUDENTS: 20-30 students
TIME LENGTH OF CLASS: 50 min

OBJECTIVE:Ý Students will develop a formula for the sum of interior angles in a polygon. Students will solve problems using the theorem.

CA STANDARDS:

Geometry

10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.

11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.

MATERIALS & RESOURCES: Notebooks, pencils, protractor, resource page

NOTES FOR TEACHER:Ý

PROCEDURES AND STEPS (TIME):

ANTICIPATORY STEP:Ý Ask students to draw any shape with straight lines on the board. (5 min)

  1. Ask students how many angles there are in each shape? (5 min)
    1. What shapes do we know the sum or can calculate sum of angles? Handout resource page.
    2. Triangle (3-sides -> 180 degrees)
    3. QuadrilateralÝ (4 sides -> 360 degrees)
  2. Assign each group a polygon (7,8,9-sides). (15 min)
    1. They draw a large x-sided figure (depending on assigned polygon).
    2. Measure and sum total of all exterior angles to the nearest degree.
    3. Create a table on the board (name of shape, # sides, sum of interior angles).
    4. When they have their answer, they write it on the board.
  3. What pattern is established? Students should work in small groups. (10 min)
  4. As a class, can this same pattern be used to calculate the number of degrees in a decagon? or a 16 sided polygon? (13 min)
    1. Come to formula (n-2)180
  5. Assign homework and allow students to start homework with any remaining time.

FOLLOW-UP ACTIVITY/HOMEWORK: Selected homework problems and explanation of todayís discovery.

LITERACY ASPECT:Ý Students will use vocabulary (Latin roots) in working with polygons.

ASSESSMENT: Teacher will review homework and observe studentsí participation and class-work.Ý There will also be a test later in the chapter.

REFLECTION/RESPONSE/DEBRIEF: TBD

Resource Reviews

 

 

Resource (URL)

Summary of Resources

Positive Aspects


Development Areas


How would you use this resource your classroom?

1.  http://www.math.com/students/tools.html

 

This is an elegant, well-rounded math site geared toward middle and high school students.Ý There are numerous lessons, practice examples, math related online games and even study/test preparation tips.

There are many excellent components to this website so Iíve chose my three favorite to highlight. The Algebra worksheet generator gives ample options to specify the number and types of problems (number of variables, quadratics, negatives, etc.). It also offers the option of an answer sheet.Ý The on-line solver portion of the tools section will simplify, factor, differentiate, plot lines, solve equations based on the students ìentry.î Finally, the Wonders Of Math section has some cool math applications, like fractals and tessellations.Ý Within this section there are links for students (or me) to make their own.

A couple of the links, like Ask an Expert and Grotesque Geometry, were outdated when I viewed the site (4/1/03).Ý I have seen a number of math websites and this is one of the best!

I would definitely recommend my students to this site to create practice problems and/or get more help outside of school. In addition, I might use this site to generate worksheets or exam questions (site permits duplication).Ý The on-line solver is a very quick way to find out if an equation simplifies ìneatly.î

 

With computer lab time, I could have the students work with the portions mentioned above or do a lab on one of the ìwonders of math.î

2.  http://campuscgi.princeton.edu/~mathclub/index.pl

 

The overall site is the Princeton Math Club.Ý The site is relatively easy to navigate and gives the math teacher an overview of what is happening in mathematics. The site also lists potential learning opportunities, internships and of course links.Ý The internships might be of interest to math teachers on sabbatical.

The part of this site that interested me is the puzzles and games piece. As a math club, I think these may be more updated than other sites.Ý These puzzles and games are divided into 5 levels, which can help in differentiating classes.

There are also excellent links to other pure math resources, like the Mathematical Association of America.Ý I learned that April is Math Awareness month!

Based on the type of organization, it is geared more towards the university level. The problems are a nice bridge towards lower level students.Ý It would be helpful to have more of these types of linkages to what they might consider prospective students who are currently in middle or high school.Ý On the other hand, it is helpful for math teachers to keep their mathematics current.

I will be giving my students ìchallengeî problems at least bi-weekly. I will need a variety of sources to find these challenge problems so as not to repeat the problems, which would allow students to get the answers from older peers or family members.

3. ÝMOVIES

http://world.std.com/~reinhold/mathmovies.html

There are a number of movies that contain mathematical concepts (to varying degrees of course!).Ý This site contains to find over 80 different movies with at least a little math content, and a list of movies featuring real mathematicians

The link to the NPR Math in the Movies recording is an excellent overview of what the site is about.Ý Otherwise, the site is a good resource to find a math related movie. The site also gives some idea of the movieís content (overall and math).

The format of this webpage is mostly text and not easily navigated and could be improved. There will be seen in the movies that are not appropriate to be shown in a school setting.

It would be a fun extra credit assignment or class reward to watch one of the PG movies and then do a brief research and write-up, or journal about the math in the movie, or solve some of the equations mentioned in the movie (if applicable).Ý This might also be an excellent source to find a movie for a math club meeting!Ý It gives a picture, though Hollywood style, of math in life.

4. MUSIC

School House Rocks! Rocks (CD)Ý

(words available at URL)

This CD has a collection of the famous 1970 School House Rocks songs played by updated artists such as Blind Melons and Lemonheads.

This is a really fun way to show math in a mainstreamed concept (like the movies) that the students may have seen on Saturday mornings because these were/are being replayed in the 90ís and 2000ís.

Since this project was from the 1970ís I doubt they will be updated, but they could enhance the series by covering higher math. The current math songs are for 3-4th grade levels.

I would play these songs to the class and then ask them to write a story, song, poem or rap about one of the math concepts that we are studying.

5.  http://matti.usu.edu/nlvm2/nav/vlibrary.html

(TOP RESOURCE!)

This is one of the only sources I have found that has activities for high school mathematics. Manipulatives are common in math classrooms, but this site takes the manipulatives on-line with over 40 activities for students in grades 6-12 in Algebra, Geometry, Data Analysis/Probability, Measurement and Number/Operations.

All of the tools that I used had great graphics and were well constructed. Many of the activities had additional information to the right and/or a lesson plan.Ý Each activity is also linked to the National Math standards.Ý

 

If students have access to computers, this site is like having a full complement of mathematical educational tools!

There were a few activities that I had difficulty using because I was not familiar with the math concept or manipulative.

Most likely I would use this tool projected on the front screen as part of a lesson plan.Ý Of all the on-line activates I have seen, this one would be the best to use with a class in a computer lab.Ý It allows each student to go at his/her own pace.Ý Also, because the graphics are so large, I could ensure that the students are on the correct webpage (and not surfing the web).Ý Also, the diverse mathematical content area would allow this site to be helpful throughout the year.

ÝOther ideas include Mathematics teacher magazines:Ý NCTM Math teacher and CA Math council Communicator magazines (http://www.cmc-math.org/).