Arrange students in groups of 2. Instruct the class that they will receive 4 cards with problems on them and that their goal is to create a solution to the problems.

For the first two cards they draw, students will alternate solving the equation by stating to their partner the step that they plan to do to each side of the equation—and why—before writing down the step and passing the card. For the final two problem cards, each partner picks one and writes out its solution individually before trading to check each others’ work.

To help students understand how they are expected to solve the first two problems, demonstrate the trading process with a student volunteer and a sample equation. Emphasize that the “why” justification should include how their step maintains the equality of the equation. Remind students to push each other to explain how their step guarantees that the equation is still balanced as they are working. For example, a student might say that they are combining two terms on one side of the equation, which maintains the equality because the value of that side does not change, only the appearance changes.

Distribute 4 slips from the blackline master to each group. Give time for groups to complete the problems, leaving at least 5 minutes for a whole-class discussion. If any groups finish early, make sure that they have checked their solutions. Then challenge them to find a new solution to one of the problems that uses fewer steps than their first solution used. Conclude with a whole-class discussion.

If time is a concern, give each group 2 cards rather than all 4, and have them do only the trading steps portion of the activity. In that case, make sure that all 4 cards are distributed throughout the class. Give 6–7 minutes for groups to complete their problems. Make sure that each problem is discussed in a final whole-group discussion. Alternatively, extend the activity by selecting more problems for students to solve with their partners.

Tell students to close their books or devices. Ask them to choose a positive number, but not to share the number with anyone else. Tell them that they will perform a sequence of operations on their number and then tell you their final answer.

Say each step of Tyler’s number puzzle, giving students time to calculate their new number after each step. Select 5–6 students to share their final number, and after each, tell them their original number as quickly as you can.

Pause here, and ask students if they know how you are able to figure out their number so quickly. If no students notice that each number you say is always 6 more than the number given at the end of the steps, you may wish to record and display the pairs of numbers for all students to see, or call on more students so that everyone can hear more pairs of numbers.

When the class agrees that you are able to figure out their original numbers by adding 6 to their final numbers, tell them that the number puzzle is really Tyler’s and that their task is to figure out how it works. Tell students to open their books or devices. 

Give 3–4 minutes of quiet work time for students to write their explanations, and follow that with a whole-class discussion. Select work from students with different strategies, such as those described in the Activity Narrative, to share later.