Homeschool Math Newsletter, Vol. 35, December 2009

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In this month's newsletter:

1. My Gift To You: Geometry videos
2. Ratio word problem solved with block model and algebra
3. Mixture problems (for algebra 1)
4. Fact families on a whiteboard

1. My Gift To You: Geometry videos

As a little "gift", I made some geometry videos that kind of tie together. I hope they are useful & enjoyable!

First of all, this video shows how to use a protractor to measure angles. I show where the "base line" of the protractor is for three different protractors, and use it to find out the angle measure of different kinds of angles (including a reflex angle).

Then, the next video shows an easy way to PROVE to students that vertical angles are equal. That way, you don't have to just "hand it on a platter" and expect them to believe you:

Next, finding out about the angles in a parallelogram. I start out with two parallel lines and a transversal (line that intersects them both). We explore the angles formed, which some of them are corresponding angles, some are vertical angles. I draw a new line, and get a parallelogram.

Lastly, here is a short and easy proof about the angle sum in a triangle.

I appreciate you letting me know if the videos are helpful (just reply to this email).

2. Ratio word problem solved with block model and algebra

Two numbers are in the ratio of 1:2. If 7 be added to both, their ratio changes to 3:5. What is the greater number?

We can model the two original numbers with blocks. 1 block and 2 blocks makes the ratio to be 1:2.

|-------|

|-------|-------|

Now add the same thing to both (the 7):

          7
|-------|---|

|-------|-------|---|
                 7

Continue reading the solution.

3. Mixture problems (for algebra 1)

A merchant made a mixture of 150lb. of tea worth $109.50 by mixing tea worth $1.25 a pound with tea worth $.65 a pound. How many pounds of each kind did he use?

Organizing the information in a table or chart is usually very helpful in dealing with mixture problems. Other than that, it helps to study several examples and practice solving them yourself. After a while, it gets easier and patterns begin to emerge.

The first problem has two unknowns. Let x be the amount of more expensive tea, and y the amount of the cheaper tea (in pounds).

In our table, we will look at the amounts of tea (in pounds), price per pound, AND the amount the tea is worth, which is (the amount) times (the price).

Continue reading.

4. Fact families on a whiteboard

I just found this picture that I took of the fact families my 4-year old wrote on the whiteboard - totally on her own.

There was a time she loved writing fact families like this every day. Being able to choose different color markers plus it being on the whiteboard seemed to be the main motivating factors, because she didn't want to write them on blank paper... Kids are funny.

Then again, it allows us teachers to use colorful markers as a "motivational tool" : )

Anyway, I was really happy that she had grasped the concept.

Click here in case you cannot see the image in your email.

I wish you peaceful holiday times...
Till January,
Maria Miller

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