Quadratic patterns

For this lesson I hand students a slip of paper as they enter in the door, one that has a quadratic pattern printed on it.  Their 1st task is to make a guess, no calculations, how many squares/circles/shaded squares with the 50th term have?

All the patterns used for this lesson were taken from http://www.visualpatterns.org/

Then I will take a few answers and put them up on the board to incite some competition and buy-in from the students.

At this point I may show them how to do it, or remind them if they already know.

They have some time to work, most of the students can accurately find the equation using the table and the process I trained them with to find the equation from the table, but fewer of them can look at the pictures and write an equation relating x to side lengths and so forth.

Here are the patterns that we have been using:

Here is some student work that shows the process of finding the equations:

some students can look as the figures and relate the parts to x, but it is more common that they use the table approach as it is more formulaic.

Drawing the next picture is crucial to getting enough data for using a table.  It allows students to get the 2nd differences and work backwards to find the y-intercept.

Most of the questions that I received, or the students that I helped that were stuck had miscounted the squares, thus finding no pattern.

After they have done the work to generate the equation they use it to find the value of the 5th term, and at the end of the hour we look to see whose guess was the closest.

Students then go home with this practice Hw.  The first pattern is actually linear, and although it confuses students because that's not the unit we're in it is a good connection to make.

Monday 3/25/13 - Last day of review

Learning Target: students will have their note sheet and be ready for the test tomorrow.

Probability review solutions:

Polynomial review solutions:

Quadratic review solutions:

Friday 2/8/13 -quadratics quiz 2

Skills on the quiz:

multiplying imaginary numbers
factored, vertex, general form of a quadratic
finding real roots using the quadratic formula
finding imaginary roots using the quadratic formula

Tuesday 2/5/13 - Quadratic formula and imaginary roots

Learning target: students can apply the quadratic formula to find the roots of a parabola.

Homework: quadratic formula recital, you must accurately recite the quadratic formula to 10 people and they will sign off saying that you recited it accurately.

Monday 2/4/12 Quadratic formula

Learning target: students can apply the quadratic formula to find roots.

Notes:



Homework (due Wednesday)

You must accurately recite the quadratic formula to at least 10 people, where at least half of them are adults.   Give this sheet to the person that will quiz you, they can use the equation below as a reference.  If you recite the formula correctly then they will then sign off acknowledging this.

1.)     

2.)     

3.)     

4.)     

5.)     

6.)     

7.)     

8.)     

9.)      

10.)  

Wednesday 1/30/13 will it go in?

Learning target: students can solve for the roots of a parabola when given the vertex form.

Homework pg 382 #1-3 pg 388 #1-4

Tuesday 1/22/13 - Introduction to quadratics

Learning target: review of final from last week, and introduction to quadratics unit.

Procedure for folding an oragami parabola:

Interactive oragami parabola simulation:

Homework: pg 364-365 #1,5,6, pg 372-373 #1,7 (due Friday)
Classroom for success (due Monday)