## Tuesday, February 2, 2016

### Day 93: Scale factor & Fractional Exponents

Today's estimation was a garden hose. I was getting tired of the tape measurers as I'm sure my students were too. Most had seen this sized hose and some made estimates based on the number of coils.

The last section of Chapter 6 has a great scale factor problem. I encouraged students to draw a picture model, after explaining what the gauge of a railroad track meant (the width).

As you can see below, the clues were the real measurements of the track and the wheel, and the width of the model track. You had to find the scale factor and the size of the model wheel. To get more participation, I reviewed how to the scale factor of 5/4 was found in previous days.

When students divided 3/4 by 36 they got 1/48. This told them that the model was 1/48th the size of the real train.

Students tend to want to use decimals, and when they have to divide 44 by 48 they think they should use a calculator. When they do, it gives a really long decimal. Some students see the connection to write it as a fraction, and then simplify to 11/12. We also reviewed multiplying fractions and fewer students said cross multiplication and said cross canceling or simplifying the fractions before multiplying.

 Here was one of the most complete answers to an assessment question on similar and congruent figures that I saw.
Here you can see a student's picture model that he created.

 While the model is good, you can see the student multiplied 3/4 by 36 inches to get 27 inches, which doesn't help in this problem. They need to be divided to get the scale factor.

In accelerated we worked on how to prove using algebra how to cube root a number by raising it to a certain exponent. Basically, they cube 17 and raise it to the x power, and set it equal to 17 to the 1st power. What must x be to get the exponent back to 1? Students reasoned 3x=1 so x is 1/3.

The main idea of making sense of raising a number to the 3/2 power is to use your reasoning of a power of a power. We reviewed this concept on whiteboards before students practiced it. I think I want to take some notes on it later this week to consolidate the concept.