A Downloadable Guided Inquiry Lesson for Grades 6-12 - Great for Gifted or Math Clubs

This lesson can be inserted anywhere throughout the school year and is perfect for students in a gifted program.

It would also be great for those last days of the school year, when exams are over, but you want to do something purposeful.

Get your students thinking critically about place value and the base ten number system by comparing it to another system.

Start by introducing the Mayan Number System.  This system uses base 20 and is great to work with because the zero acts as a place holder, just like our own!

After introducing the lesson, group students into pairs and hand out the Number Cards and worksheets.

Have students practice assembling two-digit and three-digit numbers using the cards.


The activity is great in pairs.  You will hear some awesome math talk about place value and digits.   It's so fun to see your students thinking more deeply about a fun new math idea. 

Extend the lesson by asking students to try another system.  Have them use base 8 (with standard numerals) to write numbers from 1 to 100. Click here to download the files for the Mayan Number System lesson.  Enjoy!

This structure for test corrections has been incredibly effective for me in EVERY secondary math class I have taught, from basic middle school math to Honors Algebra 2.  If you have not tried offering test fix-up opportunities, think about trying this procedure.

I know what your hesitations may be with allowing students to correct tests, but the procedure I use keeps everyone accountable.

I have students copy every step of the procedure into their notebooks at the beginning of the year.  I do not give reminders.  Completing test corrections is optional and the students hold themselves accountable for this.

This method cuts out all the problems of a typical "retake" system.  I have never liked the idea of a retake, but have yet to find a part of this test correction procedure that I do not like!

I allow students who complete test corrections to earn back half of the points that they missed on the test.  A student who did poorly, but is willing to go back and figure it out can make an appointment with me to go over the material together.  They can bring their test grade up just a bit, but not as much as if they had gotten the problems right the first time. 

This works out so that students who are top scorers also feel that it's fair.  They will usually correct their test even if they only missed one point, so they can get a half point back.  They still cannot earn a perfect score. 

Explanations must be in complete sentences.

This ensures that students who got help can demonstrate that they understand their mistakes.  They must write out a full explanation and show all re-done work.

When I first started offering this option, I was really surprised to see that sometimes, the students with the lowest grades chose not to bother doing corrections.  However, this is actually excellent evidence to provide parents and administrators.  When parents come in for a conference and hear that the student earned a D on a test and did not bother to do test corrections to bring the grade up, without fail, they turn to the student and go "WHATTTTT?" instead of blaming the teacher or curriculum.

The accountability is on the students. 

There is clear proof when a student is not putting in their effort.  I always say that since I give a full week for students to do their corrections, they have no excuse for not completing them.  There is plenty of time to come to me and go over what they still do not understand.  Then, when we move on, I know that I am not leaving them behind.

Students no longer give up and drop the graded test in the trash saying, "Oh well, I still don't get it."

Here is the full Test Correction Procedure available for download.  Feel free to use this in your own classroom.

This is specific to tests only.  I don't like to offer it for quizzes, because I do quizzes as stepping stones on the way to a test.  With a quiz, there is already an incentive to look it over, fix up mistakes, and prepare for the upcoming test.  I remind students to do this even though they will not be explicitly rewarded for it.  They know that they need to do it for their own improvement.

I also inform students that this procedure will not be in place for the final.  The final is an official cumulative assessment, and should reflect all learning up to that point.  (Also, I do not have time to offer a week for this after a final exam, when grades are due.)  There are no second chances at that point.

Please join in with us in the comments below to share your own experience with a similar strategy, or any questions you may have.  Take a minute to also browse through the great input that is already there from other teachers.

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