The Algebra Toolbox

If the only tool you have is a hammer, you tend to see every problem as a nail. – Abraham Maslow


My Best Number

73 The Best Number in the World

73 The Best Number in the World

One of my many goals this year is to increase number awareness and number sense in my students.  This open-ended get-to-know-you assignment was a good start.

First, I showed the students this 1:00 minute video clip from youtube to introduce the idea of the “best” number. (Use caution if you just search for Sheldon Coopers best number on youtube. One version explains Raj’s favorite number 5,318,008 because it spells boobies when you turn a calculator upside down!)  After watching the video, we talked about the types of numbers that Sheldon mentioned (palindrome, prime,  binary, product). I asked what other “types” of numbers they knew. Descriptions such as odd, even, perfect squares, whole numbers, etc were brought up.

I gave each student this  My Best Number recording sheet. (I left room for more “best” numbers so students could add other cool numbers to their recording sheet as they year goes on).  They had to come up with one  Best Number for them and at least 2 reasons why it was the best. The reasons could be mathematical, historical,  or personal to them.  I gave them a couple days to think about it. On Friday of that week, each student shared his/her best number and the reasons behind it. It was a great way to get to know the students. One girl said 10 was her best number because that was how old she was the first time she met her real dad and that’s how many fingers she had to count how much she loves him.  WOW – deep for a high school freshman.  Many students chose their birth date, sports jersey number, etc. but many were very personal.

As we worked through our unit on solving equations, the students substitute their best numbers into equations that had “all real number” solutions to check the validity of the solution really being all reals. They loved that their best number was a solution. As they check their solutions to linear inequalities in the next unit, they will do the same thing.


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Super Bowl Math 2013

SB pic

In preparation for Super Bowl weekend, I updated a lesson I used a couple years ago where my Algebra I students calculated the quarterback passer rating for their favorite quarterbacks.  They really enjoyed it!  For a little history on the QB Rating, this is a good article.

I provide the data they need since most NFL sites include the rating in their usual stats for each player.

Quarterback Passer Rating Worksheets guide the students step-by-step through the calculations

Quarterback Statistics for 2012 season gives the answers

Quarterback Stats for 2012 seasion WITHOUT the QB Passer Rating is the data sheet to give to students

I am a new fan of which also has had some great Super Bowl prep activities on their site, including How Have the Super Bowl Ads changed (graphing points, recognizing an exponential function, predicting future costs of ads), Super Bowl Scores 2013 (predicting Sunday’s score, finding mean, median, mode, and range and determining which measure best represents the data), 4th Down (using data to decide whether to go for it, attempt a field goal, or punt on 4th down), Super Bowl Numerals (Roman numerals, number sense), Losing Teams in the Playoffs (ratios, percents, and proportionality) and NFL Home Team Advantage (using an inforgraphic to compare NFL home and away wins).  This site provides FREE pdfs of their activities which are linked to the Common Core State Standards, or you can purchase a $15/yr membership and have access to editable documents and solutions. Well worth the $15 a year to be able to personalize the already great activities.

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Christmas Price Index


With three days of school left before break and an impending snow storm on Thursday evening, it’s time to do some holiday activities.

Today, we used PNC Bank’s Christmas Price Index website (interesting FAQs). I gave the students a recording sheet. First, I had the students estimate the cost of each of the gifts in “The Twelve Days of Christmas,” while I told my story about how upset I would have been if my “true love” had sent me all those pooping birds, dancing ladies, men in tights, and loud drummers while I was trying to get my house decorated and cookies made for Christmas.  I would have kept all those golden rings and sent him packing.

After they make their estimates, we head to the computer lab and they go to the PNC site. This year it’s really cool. Each gift is “hidden” somewhere in the world and they have to follow clues and do little puzzles to find them before each price is revealed. Great geography tie in. Looks like google earth images may have used in the creation.  I had them record the location and the price of each gift as it is revealed. There is a link at the bottom of the screen where they can click and immediately get the prices of the gifts without the puzzles, but I wanted them to see the sights.  The website also gives the percent increase or decrease in price since last year.  Great activity for working with percents…they can figure out last year’s prices.  We talked about which costs surprised them the most, why some prices went up while others stayed the same, and some of the places they “visited” on the journey.  They got really excited when their estimate was close.  I only wanted to spend one day on this, so that’s all we did. So many options for additional activities though.  CAUTION: I don’t know if it was the site or our computers, but it got really slow sometimes. “Patience” was our word of the day.

Tomorrow, I’m trying the Auction from Math=Love. I’ve never done it before, but will give it a go. I wrote 12 auction questions with 9 correct answers and 3 incorrect. I kept score using an excel spreadsheet which I displayed on the board.


My Favorite Sub Plan

My favorite plan to leave for a sub is the FACEing Math  activity.  It takes most of my students two 42-minute periods to complete, is self-explanatory and easy for classroom management, provides review for students of concepts we’ve previously studied, and gives me great pictures to put on my walls!

Students complete 27 problems. Each problem is multiple choice with 2 answer choices so it’s moderately self-checking.  The answer choice tells students what feature to draw on the face template or what color to make each feature.  There are numerous FACEing Math books for all different levels, but my favorite is the “Create” books which are blank templates so you can put in the problems you want your students to do. 

I know we are only supposed to put free resources on here, but this is money well spent.  The author allows people to download the first lesson from each book for free, so I’m hoping not to violate any copyright laws by posting one of the templates from Create Book #2 for view.  In honor of World Series Season, here is a FACE template that makes a Baseball player ( page 2)  with the answer key (Lesson 16).  You just need to look at the answer key to see which letter (A or B) the correct answer choice needs to be for the face to come out correctly. 

My students really love this activity. They can talk quietly as they work.  I require them to show work either on the worksheet or on another sheet.  Even though all the students’ drawings should have the same facial features, each face will look unique.  We have contests to see who has the silliest, neatest, most unique, etc face when finished.  Students will need access to colored pencils or crayons and a pencil. I keep copies for emergency sub plans of content we’ve already studied so students can complete it independently.

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Universal Design for Learning

One of my favorite planning tools is this UDL (Universal Design for Learning) wheel.  Even though all good teachers do these things in their lessons all the time, my district is requiring us to list the specific UDL principles and learning supports in each of our lessons, so this is a convenient way for me to access them.

According to “Universal Design for Learning is a set of principles for curriculum development that give all individuals equal opportunities to learn.  UDL provides a blueprint for creating instructional goals, methods, materials, and assessments that work for everyone–not a single, one-size-fits-all solution but rather flexible approaches that can be customized and adjusted for individual needs.”

The wheel can be found at  Click the arrows to the right or left of the viewing window to rotate the wheel to the desired Principle of UDL.  Principle 1 is to Provide Multiple Means of Representation (presenting content in a variety of ways). Principle 2 is Provide Multiple Means of Expression (how students express what they know). Principle 3 is Provide Multiple Means of Engagement (how students are engaged and how they interact with the content).

Picture of UDL wheel