Reflections of a High School Math Teacher: 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.