Completing the Square Lesson Plan

Completing the Square Lesson Plan

  • Complete the square
  • Use completing the square to find maximum and minimum values (A-SSE.3b)
  • Derive the quadratic formula using the form (x-p)2 = q

Day 151 - Visual Understanding

Day 152 - Maximum and Minimum Values

Day 153 - Derive the quadratic formula using the form (x-p)2 = q




Just in case  you did not know about this website, I thought I would share it with you. My colleague reminded me of it today. I use this website to generate quizzes, tests, and homework. We do not use books in my classroom so it is nice to have this resource. It allows you to access different types of problems that other states use as their state and chapter tests. Very handy to have as a bookmark and it is free even though you will have a log in. They update their problems at least twice a year and will send you an email of any changes!


Remembering 9/11

Image adapted from Flicker:

Image adapted from Flicker:

I remember the librarian coming to my door telling me to turn on the tv.
I remember the look of fright in her eyes.
I remember the horror as I watched, trying to be calm in front of my eighth-grade students.
I remember watching the second plane and thinking this does not happen in America.
I remember watching the smoke and people jumping.
I remember the goosebumps that covered my skin.
I remember thinking that the top of the building fell off and realizing I did not want to believe that it collapsed on all of the firefighters running in.
I remember thinking, "What the hell is going on?" as another plane hit the Pentagon.
I remember the look of horror as I looked at my students, and realized that at least 3 of them had parents flying that day.
I remember helping them call home.
I remember praying.
I remember us coming together as a country.
I remember, for the first time, leading my classes in the Pledge of Allegiance.
I remember giving blood.
I remember praying for those searching for loved ones.
I remember the few that were pulled from the wreckage.
I remember the stories of strength and sadness.
I remember that it did not end in a day, or a week, or a year.
I remember that they stopped putting the pictures on tv.
I remember our country healing.
I remember feeling sad for the loss and proud of my country.
My ninth-grade students will not remember because they were too small, but I will give them memories. Because we all must understand and remember.
Feel free to use the slideshow provided with discretion. Some of the slides are not appropriate for students depending on the maturity and characteristics of the class. Please use judgment and delete the slides that will not be appropriate for your classroom. I used all the stats to give you the option to cater it to your class.

A.CED.1 How to Break it Down

The Common Core State Standards do not allow us, as teachers, the luxury of a checklist. Each standard has to many components. This is my attempt to be sure that I am teaching each standard to the full extent that is expected and that will help my students be successful.

A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.*

To break this down, I began listing all the components students would need to understand to master this standard. I checked sample problems and online resources to be sure that I was not overlooking  anything.

I then assigned everything on this list to a unit, being sure nothing gets missed. You will notice on my lesson plans for each unit I will only list the part of the standard being covered to help keep my focus on the skills for that unit and how they are part of my Big Picture Lesson Plan.

  • Order of operations - Unit 1
  • Distributive property - Unit 1
  • Translate expressions and equations, verbal to algebraic - Unit 1
  • Solve one variable equations
    • Simple two step equations - Unit 1
    • Variables on both sides - Unit 5
    • Complex linear equations - Unit 5
    • Quadratic equations - Unit 12
    • Rational functions - Unit 11
    • Exponential functions - Unit 8
  • Solve one variable inequalities
    • Compound conjunction inequalities - Unit 5
    • Compound disjunction inequalities - Unit 5
In a nutshell, the Common Core Standard A.CED.1 is asking students to be able to create and solve equations in one variable to answer questions.

Please feel free to take a look at these Common Core sample problems, all A.CED.1, and see how they will progress in difficulty throughout the Algebra 1 course.

Create your own Playlist on MentorMob!I hope this helps everyone understand how I created my skills list for each unit. Please take a minute and let me know if this is helpful. I would love to get your feedback.

Common Core Assessment Examples for High School Math

Common Core AssessmentWe have all been told to begin with the end in mind.

What do the kids need to learn? What is important? Needed? Imperative for future success?

We then create the lessons to support that end.

But what is the end according to the Common Core? It seems to be a grand idea, gives the kids problem-solving skills to apply to real-world problems. This is what most teachers have wanted to do for years.

Having an idea of what these future Common Core assessments will look like will give us the best chance to prepare our students for success.

Understanding the Assessments

  • Gotham Schools posted a sample of slides showing old and "new" assessments to compare and contrast. It would be great to see more examples, but it is helpful to see the transition side by side to get a better understanding of the standards.
  • For a more in-depth understanding of the new assessments, you may consider downloading a webinar from ASCD. One that I have found helpful is by Susan Brookhart, Common Core: Assessment Shifts.

Sample Performance Tasks

I love the idea of performance tasks. I want kids to do well in life, not just on a bubble test. But who has time to come up with and write all these tasks?

  • PARCC has released sample tasks for their assessments.
  • This is a wonderful collection of performance tasks to get started with. Balanced Assessment is a collection of tasks created by the Harvard Graduate School of Education.

The library of over 300 mathematics assessment tasks developed during the project remains freely available through this web site. Teachers may use these materials in their own classrooms at no cost.

  • 101questions  is a great site for peeking student interest in questions that they come up with themselves. This was started by Dan Meyer. 101qs is very powerful, and I would encourage you to try this in your classroom. This is an extension of 3 acts; you may want to start there.
  • PARCC aligned interactive tasks from CSS toolbox. Online interactive questions that will help you understand which direction the writers are heading in...
  • Another great resource is Map Assessment Tasks. These tasks are written as formative assessments. They come complete with lesson plans, leading questions, scoring rubrics, and sample student work.
  • This set of practice tasks can be found on the CCSS Toolbox website under the standards for mathematical practice tab. These assessments are aligned with CCSS, and I find the accompanying notes helpful.
Most of us will begin coming up with our ideas to motivate our kids once we have some samples to get us comfortable with the presentation of the ideas.

Sample Common Core Assessment Questions

These can be hard to find for the high school level. But there are a few great resources out there.

  • Smarter Balanced Assessment examples. This is a large file to download, but if you want to see the beginning of the creation of these assessments it is worth your time and computer "space." Be sure to scroll down to mathematics; it is near the bottom of the page.
  • Illustrative Mathematics has been updated. If you have not been there lately, they have added tasks to almost every standard. This is a great place to start, and I use their ideas in my assessments.
  • The sample assessments put out by the NYSED only goes up through eighth grade. But I will be teaching some of the Common Core seventh and eighth grade standards until the transition is done in our district. This is also a great way to stay up on what our students "should" be able to do when they enter ninth grade.

What's Next?

This post will be updated as new updates are published, or new resources are found. Please feel free to bookmark it to find later.

There is also a template for creating your performance task. Please feel free to take a look.

How can you help?

Please let me know if you know of any resources for the Common Core Assessments that I have missed. I would love to keep this as current as possible.

Blended Learning in the Algebra 1 Classroom

What is Blended Learning?

There are so many definitions of blended learning. If you search it online, no two definitions match. In the math class most examples online use KhanAcademy. I find that extremely limiting. If traditional lecture and examples worked, our math program would not be in the state it is currently. We must find the best ways to teach, whether it is on the computer or with a teacher. With that in mind, I found a definition that I can embrace:

Blended learning combines online delivery of educational content with the best features of classroom interaction and live instruction to personalize learning, allow thoughtful reflection, and differentiate instruction from student to student across a diverse group of learners.

Where to begin?

As I have continued to research and read, I am drawn to the concept of blended learning. Our school is slowly moving towards a 1 to 1 ratio of computers to students. What a wonderful opportunity to combine the very best of traditional and online learning! I have decided to attempt to keep this extremely simple to make this format of learning valuable instead of intimidating my students. They should feel like experts when they leave my class. I want to be sure to add technology because it is useful, not because it is there. And therefore, I have limited myself to the following sites to use with my students. (I reserve the right to change my mind and with MentorMob I can add different sites with out my students having to learn something completely new.)

Google sites -

This will be the main hub for my students. I already use this platform and find it extremely easy to edit and add my lessons. Click here to see my sample page, but please note that this is still under construction.

Edmodo -

Our school district uses Edmodo across grade levels, and it will be an easy transition and allow my students a place for safe discussion. I also value the online learning community on that site.

thatquiz - I love this free, easy, equation formatting, quiz creator. It allows me to assign assignments; it grades them and allows students to move ahead as needed The common core has a focus on open-ended story problems as opposed to traditional multiple choice problems.  This site allows you to create and edit story problems to better align with the standards.

GeoGebra -

This must be one of the best free resources for math educators. The number of quality resources created by educators for the site only adds to its value.

Mangahigh -

This game based, math education site gives students the practice they need and is wonderful for number sense practice. The lessons are useful to check for understanding of the math content.

MentorMob -

This is a great way to present information (videos, manipulatives, and applets) or embed it into the class website without all the surrounding advertisements, and it gets rid of all the outside info from places like YouTube. I see this being very useful in implementing the 3 acts idea.


How do I see a typical day in my blended algebra 1 classroom?


The students come to class with their netbooks and begin with a bellringer that I have assigned to them using The students know their assignments because they are organized on Google sites, and they may be at different places in the curriculum. It may even look a little bit like the stations we are used to seeing in elementary schools. The students will all have differentiated small group time with me, where they could be presented with problems to work through or introduced to projects that they will need to complete with their assigned groups. The time with me will not be more examples, but an intriguing question for them to answer. I really like the 3 acts model by Dan Meyer. They will be able to discuss their thoughts and ideas on Edmodo and will be required to do so on a regular basis. I am hopeful that with careful planning, all students will be able to thrive in this atmosphere.