Factoring with a>1
Common Core Standards Addressed:
- F.IF. 8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
How can we factor a quadratic with a>1?
How can we prove that two forms are equivalent?
3 x 50 minute class periods
Day 1: 5 minutes to explain the different types of notes students can choose
20 minutes working on notes
10 minute whole class discussion
10 minutes of practice and 1 on 1 teacher help
5 minute exit slip
Day 2: 2 minutes to assign groups
48 minutes for stations (Teacher help, Makey Makey, Math Lib x10)
Day 3: Wrap up any further questions (10 minutes), if needed more time for any of the stations (5 minutes), self assessment, and a learning check (20 minutes).
*The rest of the class period will begin a new lesson that will use these skills learned.
Makey Makey Kit
Puzzle 24 piece or less
Slip and Slide Notes
Day 1 Exit Slip
Math Lib (teachers pay teachers)
Self Assessment/Learning check
Before this Lesson:
Students learned how to factor a quadratic trinomial with an “a” value equal to one (ax^2+bx+c). Where they learned how to watch the signs of the “c and b” values when creating the two binomials. Students will need this prior knowledge in order to continue factoring trinomials with an “a” value greater than one.
- Students will come in the class to find three different “note” options to choose from. A youtube video, a worksheet with explanations, or a nearpod guided notes.
- Students will choose which they would like to complete and take a laptop if they are watching the youtube video or nearpod notes. If students are on a laptop they will have a sheet of paper to have to take their own notes. If the student is doing the worksheet they will have this paper in front of them.
- Once students have completed their notes, the teacher will bring the whole group back together for discussion and questions. This conversation will help the teacher see how well notes were taken and if any additional information needs to be covered.
- Make sure that students understand how they can check their answers through distribution.
- After the whole group discussion the teacher while hand the students problems to complete individually, and the teacher will walk around to help students.
- The last few minutes of class ask students to complete 3x^2+2x-5 on a half sheet of paper. Once completed they will put a 4(I can teach it!),3,2, or 1 (I need help!) for their level of understanding and explain why they placed themselves there before turning in the exit slip.
- The teacher will take the exit slips to organize the students based on which part of the problem they are needing help on either by their work or through explanation.
- Assign students to their groups of two or three. I am grouping students based on responses from their day 1 exit slip (making sure that in each group one student could teach the other a key point/step of what they learned from day one)
- Students will go to assigned group number to work in specific stations. Stations 1-3 is part of the Math Libs, 4 is the Makey Makey, 5-8 is the Math Libs, 9 the students are working with me on the favorite no, and 10-12 will finish the Math Libs.
- The Makey Makey station will need a laptop so the students will know if they correctly solved the puzzle or not. Directions on how to make this are here.
- The “My Favorite No,” is a formative assessment where the teacher takes their favorite wrong answer and the students fix the mistakes.
- Students will work at each station for 3.5 minutes and rotate. Each student is responsible for answering every station’s question.
- Collect the stations worksheet in order to see where students left off if they need more time, or if students are still having misconceptions.
- Allow students additional time at any of the stations that they have not finished (about 5 minutes)
- Wrap up by giving the answers to the Math Libs activity.
- Complete a discussion about going through the maze with the Makey Makey, it will help by looking through the student work collected from day 2 to ask questions like:
- When were you sent back to start?
- What happened if you missed a step?
- What does this order matter? How does it relate to the maze?
- Give the students a self assessment worksheet that also has to wrap up questions for their learning check.
For this lesson students will be assessed formatively every day. Each day I am collecting student exit slips or daily work and can see where their understanding is based on the explanations provided. I am also using the student self assessment to interpret what they believe they are understanding and can explain through writing, or what they still are needing help on.
During day 2 I am able to work with the individuals in a very small group to here the key terms learned throughout the notes on day 1, and see how they can explain what went wrong in another student’s work, which show a higher level of understanding. I will also be able to hear a few conversations during the stations work to see which groups are working well together and having good discussions to call on when we wrap up the lesson.
The makey makey puzzle station I will be able to assess what the student are still struggling with based on their response of how they made it through the maze. It can be challenging for a student to understand where they are “stuck,” so if they could explain that they were sent back to start at a certain point of the maze it will tell me exactly which step of the process they are struggling with.
The learning check that goes with the self assessment is a formative assessment, but will give the students an idea how they will do for the summative assessment at the end of the unit and if they need additional help/time before moving to the next lesson. Since the students have only worked on this type of factoring for two days, there is still more learning to take place before the end of the unit when students should know what type of factoring to use for a given problem.
Factoring is a topic throughout algebra that students have a hard time understanding. By allowing students to pick their method of note taking is my way to help students personalize their learning. Culatta (2013) presented how students were given the opportunity to choose how they wanted to learn during the day whether it was watching videos practicing problems, and I thought this would be an interesting way to start this lesson. My hope is to create a blended learning environment that Childress and Benson (2014) explained in their article that the math teacher presented the topic and the material that followed were based on the students’ needs. I am hoping that by the student picking their type of notes and by me selecting the groups, during day 2, that I am able to help the “exercise” implementation for each individual. Although my goal for the lesson may be simple, factoring with a>1 is very challenging and I am hoping through formative assessment, personalized learning, and simply time, the students will have a better understanding with these additional resources versus the standardized text.
My puzzle prototype is to help break up the Math Libs work, and to re-enforce how to factor by quick feedback when I am not available. I do not want the students to go through the entire activity and find that they were getting every single station incorrect. The puzzle will help the students see which step they are solving incorrectly and can move forward as a group with a better understanding of what questions that the student/group still has. Then they will be able to go back to the Math Lib and focus on that part of the problem to see if they can overcome their misunderstanding. I am also a part of the stations activity to partake in a scaffolding exercise, which the students will be able to have a conversation about math with their teacher. I will be able to question the student and see how they are developing through the work day and if I need to help re-explain a topic, ask a questions for clarification, assign a harder problem to check if they are understanding, and to make sure they are working as they should through the activity. By splitting the Math Lib with the two other activities I feel that I can reach every student as an individual throughout the class period versus only giving the students a worksheet which is how the topic is usually presented.
Since I am still learning on how to adapt my curriculum and use my maker tools, I know that I have more work to come. In order to truly personalize the learning for each individual Garrity and Burris (2007) explains that it takes teacher’s years to truly develop a program and includes specific professional development to make improvements. With my lesson I was able to have an end goal in mind (with the help of Understanding by Design written by Wiggins and McTighe 2005), and I need to remember that when first implementing this lesson that my end goal is to personalize students learning and where I can make those changes and adapt the lesson, my students can be more successful achieving my end goal.
How-to and Additional Support:
Instructions for the Makey Makey Maze:
- If you have questions on how to create your own maze here is a how I created my Makey Makey Maze
- Have the outside edges of my puzzle together in order to save time since the students only have a few minutes at the station.
- Connect the alligator clips to the specific answer to each step of the problem that will also align with how to successfully move the ball through the maze.
- Have a laptop set up with the scratch.mit.edu maze open for students to use.
- Click the green flag to start and if needed to this will restart the maze as well.
- Remind students to hold the earth tin foil in order to complete the circuit when pressing their answer.
- If there are any problems when completing a circuit remind students to push the puzzle pieces firmly together and that the alligator clips stay connected.
Teachers Pay Teachers worksheet (Math Libs) and notes for the self guided lesson require
you to purchase a license, therefore I cannot post these items entirely.
Link to Youtube Video for note taking
Link to Nearpod Notes
Self Assessment/Learning Check worksheet
Link to my Google Doc of the original lesson Plan
Childress, S., & Benson, S. (2014). Personalized Learning for Every Student Every Day. Phi Delta Kappan, 95(8), 33-38. doi:10.1177/003172171409500808
Garrity, D. T., & Burris, C. C. (2007). Personalized Learning in Detracked Classrooms. School Administrator, 64(8), 10-16.
L. (2012). Quadratic Expressions – Factoring with Slide and Divide – Just the Practice Problems. Retrieved June 12, 2016, from https://www.youtube.com/watch?v=B8-Q4F2DVmo
Polynomials and Factoring (Algebra 1). (n.d.). Retrieved June 12, 2016, from https://www.teacherspayteachers.com/Product/Polynomials-and-Factoring-Algebra-1-426662
Reimagining Learning: Richard Culatta at TEDxBeaconStreet. (2013, January 10). Retrieved June 2, 2016, from TEDx Talks, http://tedxtalks.ted.com/video/Reimagining-Learning-Richard-Cu
Wiggins, G., & McTighe, J. (2011). The Understanding by Design guide to creating high-quality units. Alexandria, VA: ASCD.