Math Mysteries

One of the main goals of our homeschool is to help our children become critical thinkers.  It is our belief that math is something that doesn't or shouldn't revolve around memorization of facts, formulas and procedures.  Rather, math should focus on developing a deep understanding of concepts and seeing how they build and connect to one another.  We have chosen to approach the teaching of mathematics with a focus on critical thinking, problem solving, and modeling.  A variety of tools will be used to create an environment in which our children can explore and manipulate in order to develop their mathematical skills and see connections to other disciplines.

Resources

Main Text: Singapore Math  (text, workbook, intensives, and challenging word problems)

Math Analogies by The Critical Thinking Company

Math Detective by The Critical Thinking Company

Time 4 Learning

National Library of Virtual Manipulatives

Wolfram Demonstrations Project

 

Tuesday
13Oct2009

Lego Math: Area and Perimeter

Who doesn't love playing with Legos?  I have been trying to think of ways to incorporate our children's love of Legos with mathematics.  As an application of multiplication, I developed this lesson on area and perimeter.  It is geared for elementary students and takes an investigative approach to developing the concepts.

Grade Level: 2-4 grade

Main Goal: Use prior knowledge about multiplication to develop the concepts of area and perimeter.

Introduction:

Congratulations!  You have been selected to join an elite team of engineers to build a fortress for our great city. There is rising conflict in the Republic and we need to protect this outpost from invasion.  We are fortunate in that we have recently discovered a new material that appears to be stronger than steel. Hopefully, it will hold against the Empire's latest weapons.  You will use this as your building material.  Good luck!

Math Background:

  • addition
  • multiplcation

Mission: 

(printable version)

  1. Using Legos, create a model of your rectangular fortress.
  2. Determine in units of Legos, the measurements of your fortress.
  3. How many Legos are needed to "fill" your figure?
  4. If you were to patrol the outside of your fortress, how many Lego bricks would you pass?
  5. Create a mathematical model for your responses to questions 3 and 4.
  6. Let's test your model for another figure and see if it works.  Repeat steps 1-5 and record your responses.

Conclusions:

Using the evidence from your investigation, generalize your findings to write a formula for area and perimeter.

Area:

Perimeter:

What do you notice about the difference in area and perimeter between the two fortresses you designed?  You should see that the more spread out the fortress, the larger the area and perimeter.

Additional Online Games and Resources:

 


Monday
21Sep2009

Calculating Kinetic Energy

Main Goal: Apply mathematical concepts to explore the relationship between mass, speed, and kinetic energy. 

Introduction:

After viewing the BrainPOP movie on kinetic energy as well as completing a lab during our science class, we have discovered several things.

  • Kinetic Energy is associated with objects in motion.
  • Mass and speed can affect the amount of kinetic energy released.
  • Energy can be transferred and stored, but never created or destroyed.
  • Kinetic energy can be transferred fromone object to another when the objects collide.

Math Background:

  • Order of Operations'
  • Exponents
  • Multiplication and Division
  • Fractions

Mission

Which gives off more kinetic energy:  a cheetah or an elephant? 

  • Take a guess!  Which animal do you think?
  • Research the average mass of each animal and average speed. Record on your investigation sheet.
  • Using the fomula to calculate kinetic energy, KE= 1/2(mass * velocity<sup>2</sup>), determine the kinetic energy released for each animal.  Record your findings on your investigation sheet.
  • Now, assume that 2 cheetahs of the same mass are moving at different speeds.  Which cheetah releases more kinetic energy?

Conclusions

Was your initial guess correct?  What have you discovered through this investigation?

The amount of kinetic energy an object has depends on its mass and speed.  A fast moving object with a lot of mass wil have a lot of kinetic energy.  If two objects have the same mass, the one moving faster will have more kinetic energy.

Monday
21Sep2009

Singapore Math 3A- Ch. 2

This quiz covrs material from Singapore Math 3A Chapter 2 which includes addition and subtraction applications.

Quiz 1 in Google Docs

Monday
21Sep2009

Singapore Math 5A- Ch. 2

This quiz covers material from Singapore Math 5A Chapter 2 which includes multiplication and division by a 2-digit whole number.

Quiz 1 in Google Docs