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Algebra

In this module you will explore activities and information related to algebraic thinking.

The objectives of this module are for you to:
1) Develop a deeper sense of algebraic thinking.
2) Examine students' misconceptions related to algebraic thinking.

 

Task 1- Task 2- Task 3

Task 1:
Write down 4 consecutive counting numbers- e.g., 1,2,3,4. Take the product of the 1st and last numbers and compare it to the product of the 2nd and 3rd numbers. What do you notice?

Try this with 3 different sets of numbers. What do you notice about the relationship between the product of the 1st and last numbers and the product of the 2nd and 3rd numbers?

If the 1st number you choose is x, try to explain the relationship in terms of variables.

Submit your solution/ideas through Moodle.

Task 2:
Visit the Pan Balance activity. Find out the value of each shape in relation to the square (see picture below). For example, place squares on the left side and circles on the right side. Keep placing objects on the scale until the scale is balanced. When the scale is balanced, the solution should appear in the box on the right. Clear the balance and continue this with squares-triangles and squares-kites.

When you have all three solutions (squares compared to circles, squares to triangles, squares to kites/diamonds), come up with a numerical value for each shape that makes each equation balanced. For instance, if 3 squares = 2 triangles, squares could have a value of 2 and triangles could have a value of 3. 3 squares = 3*2 = 6. 2 triangles = 2*3 = 6. You should be able to come up with numerical values for all four shapes that work for every solution.

Click Guess Weights and put your answer in...it will give you feedback.

 

 

 

 

 

 

 

 

 

For example, in the figure we know:

4 squares = 3 circles
2 squares = 3 triangles
5 squares = 3 kites.

If a square had a value of 3, then...
4 * 3 = 12 = 3 circles. Each circle = 4.
2 * 3 = 6 = 3 triangles. Each triangle = 2
5 * 3 = 15 = 3 kites. Each kite = 5

Therefore, square =3, circle =4, triangle =2, kite =5.

Read this article about using the Pan Balance to teach algebra.

Questions for Posterous:
What was your experience like using this technology and completing the task above?
How does this technology support students' algebraic thinking?
In the article, what role did the teacher have in supporting students?

Part 2: Respond to 3 of your classmates' Posterous blogs- the person before you, the person after you, and one other.

 

Task 3:
Revise Task Writing Assignment- due through Moodle 1 week after I give you feedback.

 

Task 4:
Watch the video from Chapter 11 and read that chapter in My Kids Can.
We will connect this video and chapter to Module 1 by revisiting the work we did then.

Revisiting Addition/Subtraction Errors- assignment explained and work done on class PBWorks page.

You will need work from Module 1 to help you!

 

Work due by the end of this module

Task 1: Submit through Moodle

Task 2: Pan Balance Activity, read article. Post on Posterous responses to the questions. Respond to 3 classmates.

Task 3: Final resubmission of task writing assignment.

Task 4: Work done on the course PBWorks page.