TRUTH or SNARE: A Math Equivalence Game

TRUTH means equivalent

SNARE means not-equivalent (but really close) 

This game is the reverse of a Number Talk.  In a number talk the teacher gives a problem and students find different ways to come up with the answer.  With TRUTH or SNARE, the teacher gives an answer and the students create potential equivalent possibilities (truths) or non-equivalent possibilities (snares).  The rest of the class has to find ways to determine if the possibilities are a truth or snare.

Let's give an example

Teacher:  Let's play TRUTH or SNARE with the theme being exponents and order of operations.  Remember that SNARES are NOT-EQUIVALENT but are really close to being equivalent and very tricky.  Create at least 2 TRUTHS and 2 SNARES for the following answer:  16      (Teachers resist the urge to give examples.  Don't do it.  Instead, encourage the students to create a problem that has an answer of 16.  Remind the students that it won't matter if their problem is equivalent or non-equivalent...they will not be wrong)

Students:  Work in groups of 2-4 to accomplish the task.  (Teachers  make sure each group has at least one example of either kind)

Teacher:  Pick groups at random to present their possibility.  Students will not be telling the rest of the class if it is a truth or snare yet.   Have the groups put their problem on the board or have the group give them to the teacher to put on the board.

Teacher:  Now take some time in your groups to decide which ones are TRUTHS or which ones are SNARES.  (Allow enough time for all groups to get through at least half of the examples given)

Students:  Work together in your group or with your partner to determine if each problem is a TRUTH or a SNARE.  Be ready to defend your work.

Class Discussion: Take a vote for each example.  Thumbs Up (Truth), Thumbs Down (Snare), and Thumbs Middle (Unsure).  (see my voting thumb pictures below)  Have students walk through the reasoning and or the teacher walk through the reasoning for each example.  Be open about the fact that this activity is meant to push your understanding and that you might make mistakes on what is a TRUTH or SNARE.  These mistakes are helpful for us to recognize equivalencies in the future.

See the example below that we did in class.

Here are a few examples of what the students made.

Group B,C and D are TRUTHS and A and E are SNARES.

The beauty of the game is that students do not fear creating a wrong answer.  Actually, they like to create answers that are SNARES.  Students like to trick their classmates.  

Here are some other examples that we have done.

This is what I have been doing when I have my students voting.

This game is a work in progress.  Do you have any suggestions for me?  What has worked for you?  Please let me know.

Measuring to find the Slope of a Line

Slope is so cool.  But I have made it so boring in the past.  I don't want SLOPE to be boring.  So this is what I tried.  I took some blue tape and made a big line across the front of the room on the wall.

Starting the Lesson (we have not covered anything to do with slope yet)

Ask the question:  What is your guess for the slope of this line?  I had the students think about the question and talk with their partner.  Then I picked a few students at random.  Here are a few of their guesses.

The most interesting thing that came out of this was that some students wanted to know the rule before they guessed.  I then asked if anyone would like to share what they know about slope.  The rule of slope is the rise of the line over the run of the line came out.  Also the word steepness came out.  We did some discussing regarding the fact that the rise "looked" smaller than the run and how that might look with numbers and decimals.

Refine your guess:  I told them that all of their guesses were too high.   Someone also noted that the slope was positive.  So we talked about the fact that it had to be greater than zero.  Then I told them that since all the guesses were too high that m=1 was too much.  I asked them to talk with their partner and come up with a new guess.  Here is the second round of guesses.


Measure Yourself: We were definitely getting closer.  The discussion shifted to the equivalent numbers of 0.13 and 13/100.  Also 0.7 and 7/10.  I told them about the fact that you could measure the rise by starting at any point on the line and going straight up to any other point, and measure that.  Then the rise would be from that end point all the way across horizontally to the line, and measure that.  Now I asked that they come up to the line and actually measure the slope.  I only had half the class to this because of space.  The rest of the class were asked to be thinking of how and where they wanted to measure the line.

This first round of measurements came on with some amazing accuracy.  The slopes came in at 0.269 as the lowest and 0.3125 as the highest.  I thought this was spectacular.  

Also, I had one group that measured in wrist width.  They measured 4 wrists high and 13 wrists long.  This was an answer that was very close to the middle answers.   We used inches, cm, and wrists as our measurements.  I never told them what to use before the activity.   

By the way, I measured the whole triangle height over the width and got 67 inches over 210 inches.  So the actual slope turned out to be approximately 0.319.

The homework for the tomorrow is to measure the slope of 5 things.  Give all the measurements.  Take a picture if you need to.  We will see what they bring to class tomorrow.

Take Aways
Here are some reasons that I was excited about today's lesson.

1. Taking a guess at the answer helps students to try without the fear of failure.  It is only a guess.
2. Refining the guess helped them to continue to think about what exactly slope is.
3. They had to measure something.
4. They used different unit measures.
5. Today students were Active and Participating in learning Slope
6. We also compared multiple equivalencies.   0.5 was the same as 1/2 or 5/10
7. Learning a math concept always takes more time than I think.  This took 25-30 minutes.