Review for test 2

 

Logs and their Laws

Visible random groups and vertical non-permanent surfaces to work on logarithms and log laws.
First evaluating logs.

 

Dominoes - Relationships between the Number of the Dominoe and Various Variables

Students watched this video and then were examined the relationship  between the number of the dominoe and some variable. Here were the variables I assigned.

Once groups had their variable to examine I asked them to create a poster that had the following.

 

Dominoes - What are the Criteria for a Good Question?

Students looked at this picture and were asked to write down any questions or wonderings they had.

In visible random groups they shared their questions with each other and on mini whiteboards they wrote out their three best questions and why they thought they were the best questions. Here are them working on it.

Rational functions - Oblique Asymptotes

In visible random groups we explored rational functions where the degree of the numerator is one more than the degree of the denominator. For example, a cubic divided by a quadratic.

Before we did this we recalled factoring a polynomial using the area model. My work and some other groups work.

 Then we reviewed a rational function with y = 0 as the horizontal asymptote. Degree of numerator is less than degree of denominator. Two examples.



Then we reviewed a rational function where with a horizontal asymptote of y = some number other than zero. Degree of Numerator = Degree of Denominator. Horizontal asymptote is y = (Leading Coefficient of Numerator) / (Leading Coefficient of the Denominator).

Then we looked at Rational Functions where the degree of the numerator is one more than the degree of the denominator. This creates an oblique asymptote.

Example 1

 Example 2

 Example 3

 Example 4

 

 

Example 5



 Example 6

 



Rational Functions - Looking at Zeros, Vertical Asymptotes and Horizontal Asymptotes

The purpose of this whiteboarding activity was to look at zeros of rational functions - from the numerator - and significance of double, triple etc. roots. We also examined vertical asymptotes of rational functions - from the denominator - and significance of order two, three etc. of the factors in the denominator. Lastly we examined when the horizontal asymptote was y = 0 (degree of numerator < degree of denominator) or when the horizontal asymptote was y = some other number other than zero (degree of numerator = degree of denominator) so horizontal asymptote ended up being y = (Leading coefficient of Numerator / Leading coefficient of the Denominator).
Here are some photos from the whiteboards as we worked our way through this.
We started with something that would have lots of confusion - included a hole

 

Light It Up

I was away for this one.
Students were given this.

The Light It Up Game

 For this experiment, you will need:

• Laser pointer (or a small flashlight)

• Small, flat mirror

• Tape measures (2)

• Wooden block, about 10 cm tall (or a thick book)

• Tape

• Graphing calculator (optional)

Factoring Polynomials and Dividing Polynomials

We started by factoring a quadratic without any instruction. Here are some photos of student work and my work. Some used a "short cut" and others used area = length * width.



 

Next we divided a cubic by a linear function.

Volume = Length * Width * Height

This activity allows students to see the relationship between cubic polynomial equations in expanded form (volume form - y intercept form) and factored form  (length width height form - x intercept form)

Students were put in groups of 4 using visible random groupings.

Each group was given one of these equations.
y = x^3+4x^2+5x+2

Sucker Rates

This is an activity to look at average rates of change (AROC) and instantaneous rates of change (IROC). Students are asked to get a piece of dental floss, a tootsie pop and a measuring device.

Students then collect data every thirty seconds after being told to suck evenly and with the same enthusiasm each time. They then record the circumference at thirty second time intervals.

Here are some photos of "sucking"

Reciprocal Functions

The task today was to look at a function f(x) and its reciprocal 1/f(x). We were looking for connections between the two.

The first thing I asked groups (visible random) to do was graph y = x and the reciprocal y = 1/x. When they were done I had them graph y = x^2 and the reciprocal y = 1/x^2.

Here is what it looks like.