In Math 7 we’ve been working with adding and subtracting integers. Before we can move into multiplying and dividing, we had to tackle the topic of adding and subtracting rational numbers. Having just worked through a unit that required a familiarity with adding, subtracting, multiplying and dividing positive fractions and mixed numbers, I knew we had the potential for struggle with this topic.

I have kids still relying fully on slow strategies to multiply things like 9×8 making finding common denominators very challenging. I was working with a student while he slowly skip counted, 9, 18, 26 … “wait I said, it is 27” and I thought, “adding and subtracting positive and negative fractions is daunting for students who have to rely on these slow methods.” Once he finally got a common denominator he was tired out!

My answer for Module 2 Lessons 7-9 in particular was to give only 3 examples for class each day and to have them then do several with support on our class notes. We checked in after those and then I set them loose with the cards.

View the Rational number cards and A-U Card answer page. I just used regular index cards and hand wrote them. If you plan to use them over and over, take time to laminate them.

#### What and why cards?

I took problems from the modules that could have been put on a worksheet or printed out straight from the module. I set the activity up like this.

- You may work alone or in pairs. No groups of 3. Please select a partner that is at a similar level to you unless you would like to spend some of your time teaching your partner. It is ok if you want to teach your partner because we learn by teaching.
- Get the answer sheet and have a pencil out. There is room on the answer sheet for calculations but you may also use extra scrap paper.

The cards are labeled A-U and there is a spot on the answer sheet for the work for each card. Each card has a problem on the front and an answer on the back. Your directions:

- Write down the problem from the card.
- Show all your work.
- Circle your final answer.

Then, check the back of the card. If your answer isn’t the answer on the back of the card, look back and your work and see what could have gone wrong. Try to figure out your mistake and if you can’t, then call Mr. Rocco or me over. We’ll help you.

To help make things feel more attainable, I leveled the cards. A-K are the “easier” ones. They involve smaller numbers with easier to find common denominators. They also don’t involve parenthesis and grouping. They are located in one part of the room on a table. Problems L-U are more challenging, involving grouping, larger numbers and are generally more daunting looking. All are from these modules.

#### The activity in action

I wasn’t sure how they’d enjoy this. I wasn’t sure if I would collect it. Truth be told I didn’t want to. I wanted them to be motivated to do the work without a grade having to be attached. They had the answers, all they had to do was roll up their sleeves and commit to practicing and seeking help when they needed it. “Will you collect this?” I heard. “I don’t know yet. Maybe.” I said. “Will we finish today?” “No but we’ll circle back to these on Friday.”

This style activity is much like going to hockey when you can’t really skate yet. Suddenly the focus is on the hockey instead of the step by step “how to skate.” Guess what? The skating comes pretty quickly! In our case, the focus is suddenly on doing ONE problem at a time and seeking ONE correct solution. The student has control over the type of problem done first and can feel success or challenge. I was SO happy when two of my strongest students went for the challenging cards and were stumped on several. To challenge the kids that need it while supporting the kids that need support – that was the goal of this!

What about the students who struggle to find common denominators? They were finding them. It is satisfying to get the correct answer and know instantly that you have it. It is also satisfying to get up out of your seat and go get another problem. The slow starters? We had some of those too. The truth of the matter is that each successful problem counts. That was one of the reasons I didn’t want to collect this to grade. Some kids will not finish and I don’t want to put the focus on finishing. The focus needed to stay on doing. But, I didn’t want to tell them either because I felt I needed to inject a healthy level of stress in the equation for success.

**What about kids who just copied the answers? **Luckily there were very few of them in the grade. Grade 8 is where our school really focuses on integrity so these guys haven’t had that opportunity to discuss that in detail .. yet. But, most kids followed the directions with at least some enthusiasm.

#### Who is this best for?

I think an activity like this works well for most students. It is especially good for active kids who need built in move breaks. Having the option to work alone is really nice for introverts who are stressed as soon as they hear the word “partner or group.” It is hard for students who “just want to be done.” They have to get up every few minutes for a new problem and wait for a problem if it is not available. I think it is a good growth opportunity for this type of student.

#### What did the kids say?

I asked one class about what they thought of this and some of the comments included:

- I loved that the problems weren’t too hard for us.
- I liked picking my partner.
- I liked having music to work to.
- I liked getting up out of my seat.
- I was proud that we were able to stay focused and quiet.

There were surely negatives but this crew was super polite with their commenting. One thing I noticed is that when I gave students extra time to work on them in math lab they stayed on task for the entire time. No one gave up or lost focus. In a class of 5 students late in the day I found this notable. They knew full well they’d have more class time to do it but chose to plow forward for almost an entire period on them.