Grade Level: 10 / Date: November 15th, 2010
Topic: Quadratic Equation Transformations / Time (min): 70 mins
Learning Goals
- Students will be able to graph horizontal and vertical transformations of parabolas using vertex form
- Students will be able to look at a graph of y = x2 that is shifted horizontally or vertically and determine the equation in vertex form
1. Ministry Expectations
Strand: Quadratic Equations
Specific Expectation(s):
– identify, through investigation using technology, the effect on the graph of y = x2 of transformations (i.e., translations, reflections in the x-axis, vertical stretches or compressions) by considering separately each parameter a, h, and k [i.e., investigate the effect on the graph of y = x2 of a, h,
and k in y = x2 + k, y = (x – h)2, and y = ax2];
2. Pre-Assessment
- Students should be able to graph y = x2
- Students should understand the shape of a parabola
- Students should be able to use a table of values (determine y given x and an equation)
3. Required Resources
Each student will require access to a computer and Internet
www.mathwarehouse.com/geometry/parabola
www.math.hawaii.edu/lab/241/online-grapher.shtml
mathinsite.bmth.ac.uk/html/applets.html#slineAnchor
http://www.youtube.com/watch?v=0G00eni0vN0
http://www.greenglobs.net/
Each student will need 2 pieces of graph paper, pencil, and math notebook
SMARTBoard
Whiteboard and markers
4. The Main Lesson
a) Agenda
- Minds on – Match the graph
- Let’s move up and down!
- Shake side to side!
- Create your own graph
- Alien homework video
b) Introduction – Minds On Total Time: 10 min
Have four equations and graphs up on the board (with horizontal transformation and vertical transformation).
Have students try to match up each equation with each graph.
Hint: For students that may be having difficulty, ask them to create a table of values for each equation.
Summary: Have students justify why they choose each value.
c) Teaching Plan - Action Total Time: 50
Activity 1 - Vertical Transitions and Comparison to y = x2 (18 minutes)
If you can hear me clap once, if you can hear me clap twice.
On the MathWarehouse Website, www.mathwarehouse.com/geometry/parabola
Get students to complete the webpage, interactively graphing y = x2 and y = x2 + 1
Have students write down a comparison between the two graphs on a piece of paper.
As students are completing the webpage, go around and ask students their comparisons between the two graphs and ensure all students are on task. Remind students that they have one minute left.
If you can hear me clap once, if you can hear me clap twice.
Once students have completed the online activity, present to them a new formula on the board:
Y = x2 – 2. Provide graph paper to all students (have one student distribute graph paper to class)
Ask students to draw on the graph paper what the graph of the function would look like. Students are to complete this individually (5 min).
Circulate fast to make sure students are on tasks
Consolidate this activity by having one student come up to the SMART board and draw the graph of the function. During this time, students would follow along and if they did something different, they can address the issue to the teacher and the rest of the class.
Activity 2 – Horizontal Transformations (15 minutes)
Demonstrate how to use online grapher to students. www.math.hawaii.edu/lab/241/online-grapher.shtml
Write two equations on the board (eg. y = (x + 2)2 and y = (x – 2)2
Have students graph two examples on computers (one with a transformation right, and one left).
Give them another two formulas and ask them to Think-pair-share of what they think the graphs will look like. Allow them to graph the formulas using the online graphers to check their predictions.
Circulate fast to make sure students are on tasks.
For students that complete task early, provide them with a second website and mathinsite.bmth.ac.uk/html/applets.html#slineAnchor and select “Parabola”.
Change the values of a, b and c and observe how the vertex formula is changed in comparison with the graph.
Activity 3 – Direct Instruction (6 minutes)
In class discussion, have students come up with a general formula combining vertical and horizontal transformations. Write on whiteboard. Have students copy this formula into their notes.
Activity 4 – Create your own graph and challenge partner (13 minutes)
Tell students that they are going to make a graph now and challenge their partner.
Give instructions to create their own equation and graph that has both a vertical and horizontal transformation. Students will have chart paper that they can use from before. Let them know that they have 8 minutes to complete the graph and with the equation. After this, they will switch with a partner the graph with a partner and see if the partner can come up with the same equation to the graph. If they do not come up with the same equation, they should discuss and figure out why.
d) Consolidation & Assessment Total Time: 8 minutes
If you can hear me clap once, if you can hear me clap twice.
Summary
Today we talked about vertical and horizontal transformations of parabolas.
What does the operation sign (+ or -) indicate about the transformation in each part of the formula?
Show http://www.youtube.com/watch?v=0G00eni0vN0
Ticket out the door: Summarize using a general formula (give example of a general formula using letters instead of numbers)
At Home Activity:
Challenge them to play green goblet for 10 minutes and come back with the highest score.
http://www.greenglobs.net/
Students will need password that can be provided by you once subscribed.
May also start to come across stretches and parabolas opening down if they get far enough into the game which can lead into next days lesson.