Lesson Plan Title : Drawing Nets of 3 Dimensional Objects

 

Age Range:

Grade 9 through Grade 12 (High School)

Overview and Purpose:

Students will be able to use concrete materials to help them understand the concept of nets. Being able to take an object and spread it out flat is much easier to see in concrete terms rather than in the abstract.

Objective:

The student will be able to draw a net of three different objects. Two of those objects will be able to be laid flat and one will not.

Resources:

One cereal box for each pair of students (cut off the six overlapping tabs, three on each end)
One ice cream cone wrapper (with the lid taped onto part of it) for each pair of students
One short round candle for each pair of students
Math journals

Activities:

Discuss that a net is a 2 dimensional representation of a 3 dimensional object. Give each pair of students a cereal box, ice cream cone wrapper, and a candle. Have them unroll the ice cream wrapper so that it lays flat. Explain that this is a net. If they close the wrapper back up it makes a cone. Have them sketch the net in their math journals.
Have the students work with their partner to turn the cereal box into a net and sketch it in their math journals. Point out that six of the extra flaps are missing since they overlap on the ends.
Explain that often you have to visualize what the net will look like since things cannot be laid flat. Have them try to do this by sketching the net of the candle in their math journals. Come back together and have some students show their drawings. Make sure they included the ends of the candle in their nets.

Closure:
Nets can be a very difficult thing for students to visualize. Giving them concrete examples that they can manipulate will help them understand the concept. If more practice is needed, students could create their own nets and 3-D objects out of paper and tape.

Percentages

Age Range:
Grade 9 through Grade 12 (High School)
Overview and Purpose:
Students will be able to apply percentages to real life situations by figuring the amount of income tax that will be withheld from a salary.
Objective:
The student will be able to
*calculate how much they will pay in federal, state, and local income tax for a year when they are paid for doing their dream job.
*research salary information on the internet.
Resources:
Internet access
Tax percentages for your area
Math journals
Calculators (optional)
Activities:
Have students look up the average salary for their dream job. Explain that they will have to pay taxes on that salary to the local, state and federal government. They can either research the tax percentages or you can give them to them. Have them calculate how much each week, month, and year they will pay in taxes and record the amount in their journals.
Graph the different amounts and have them draw conclusions about the amount of taxes people pay.
Closure:
Homework could include having students calculate and graph the amount paid in taxes for salaries at least $25,000 apart. More advanced students may also want to research the amount of other taxes withheld (Social Security, Workman's Compensation) and analyze how that affects salaries.

Lesson Plan Title : Math on a Map
Age Range:
Grade 9 through Grade 12 (High School)
Overview and Purpose:
Students will practice finding a variety of information using a satellite picture of their hometown. This would be a great activity to use for review or when there is a substitute.
Objective:
The student will be able to find information using a satellite picture of a given area.
Resources:
Satellite pictures from Google Earth of familiar areas in your town.
Include the following overlays on your map: Scale, push pins in various areas, roads, and terrain
Teacher created worksheets
Overhead projector
Satellite picture copied onto a transparency
Rulers
Protractors
Activities:
Pass out the satellite pictures and give the students time to look at them and to locate as many familiar areas as possible. Spend some time talking about the maps and pointing out any areas of interest.
Pass out the worksheet. The worksheet can contain math problems that ask students to find the area of a given place on the map, the square footage of a lake or park, the percentage of urban versus rural areas, angles that road intersect, or any other information that can be gathered from analyzing the map.
Come back together as a class and discuss the answers. Use the overhead and map to help students understand any problems they are struggling with.
Closure:
For homework, send home a different map and have students create five questions about it. This lesson can also be done on the computer. Students can use Google Earth to find information and answer questions

For Math, Click Calculate

The editorial writer of New York Times, Anna M.Phillips, discuss in her article, "For Math, Click Calculate," whether or not students should use the calculator while doing exams. I personally think that calculator only helps, and students still have to use their math skills to solve the problems. I don't think that students should memorize the formulas, too. All professionals such as engineers use softwares that contain all the formulas that they need. Cheek it out guys!!!!


http://www.nytimes.com/2012/01/22/education/edlife/for-math-click-calculate.html?_r=1&ref=educationandschools

Mathematics

Sum of interior angles of the triangle

* Michele France Viana Debus *
 Special to Page 3 Communication & Education

Objectives

Using a practical activity, leading the student to:
1) conclude that the sum of interior angles of the triangle is 180 degree.
2) recognize the characteristics of the external angle of the triangle.

Strategies

Before showing the properties of the angles of the triangle and the property of the exterior angle is important to explain to the class the following contents: angles (classification: acute, obtuse, shallow, etc..) And triangles (its elements).

Activities

1) Ask students to draw and cut out three equal triangles of any kind in waxed paper or in a role more firmly, yet easy to handle.

2)They should mark the angles with three different brands. All triangles should be identical.

3) At this point, the teacher can discuss the congruence of triangles or the concept of congruence in geometry.

4) Instruct the students to put together  one vertex of each triangle, so that the three angles are adjacent, two by two.

5) Ask students what are they concluding:

What are the forms of the three angles?

What is the measure of this new angle?

 Where those three angles come from?

 What happen if we exchange the angles of each triangle by putting them all together with the angles of the other triangles?

6) After this discussion, ask them to draw a line on paper, with the help of the ruler, and fix one of the triangles with the base on this line. After the triangle set, discuss the concept of the external angle.
7) On the line, it is possible to identify two external angles. Instruct the students to put one of the identified external angles, and other angles of the two other triangles, on the outer corner angle of each of the two triangles that haven't been set yet.  And ask:

Which angles fit perfectly in the external angle?

What does it means?

What relationship can be found between the external angle of the triangle and the other angles?

 

Michele Viana Debus France has a degree in mathematics from USP and an MA in mathematics education at PUC-SP.