For today's Warm Up, I included two exponent problems that again expose common misconceptions with negative exponents as well as understood exponent of 1. I also included a division of scientific notation problem because students need additional exposure to this concept. Students understand the division concept, but sometimes struggle when translating the answer into appropriate scientific notation. My hope is that dialog about this problem will help students develop further understanding.
Finally, I include a real life scenario because I am interested to see if students are able to write a simple function rule given a context. This is the focus of today's lesson, so discussion about this problem will help launch us into the topic.
Using the fourth problem from warm up as a starting point, I introduce today's learning objective. I remind students that we have actually been writing function rules the past few days with Turtle and Snail. Today, however, we are going to focus on connecting the story to the table and the rule. (pictures and graphs won't be needed today).
I reveal the first scenario: A lawn service charges $20 plus $12 per hour to mow and edge your yard. Write a function rule that models this situation. I select students at random (from name sticks) to help me fill in the data table for this function. If a student is unsure, I allow them to "phone a friend" or seek someone who can help them. The friend must conduct a "whisper conference" where they have been trained to give tips instead of just telling the answer. Once the whisper conference is over, the student I called on originally gives the answer. I use this strategy to give appropriate support to my struggling students without letting them off the hook for the learning.
Once we have the table filled in, I give the table groups two minutes to look for a rule that would fit the table. I tell them they must be able to explain how they got the rule. I circulate through the room eavesdropping on student conversations so that I know which group to call on for the answer.
Once the time has expired, I call on a group who has the correct rule and ask a representative to explain their thinking.
I continue in the same manner for the next scenario. For the third scenario, I instruct the groups to fill in the table and find the rule.
For the fourth practice problem, I provide the function rule and ask the students to use it to help fill in the table. I demonstrate with the first table entry. Once we have filled in the table, I give student groups 2 minutes to write a story that matches the function I gave them. When the time sounds, I ask for a volunteer to share. I then verbally confirm their story matches by saying while pointing to the function, "Joe charges $5 per hour to babysit his cousin. He also gets $4 for gas money." For clarification, I ask, "So does Joe get $4 for gas every hour?" I want students to think about the purpose of the variables within the function. I ask for two additional stories to be shared. I want students to see that scenarios can change, but the same function can still be used because the relationship between the variables has not changed.
Once we finish the four guided practice problems, I survey my students on our learning scale. If they signal 5, that means they could teach someone else this concept. A signal of 4 means they understand the concept well; 3 means they beginning to understand the concept; 2 means they understand a little; and 1 means they do not understand the concept at all. If I see any 1s or 2s, I group those students together with me as the coach for the next activity, pairs coaching.
For the next activity, pairs coaching, I distribute a paper to each pair that has six functional scenarios, three on one half and three on the other. In pairs coaching, one student begins by explaining to his/her partner exactly what to write on the first problem, step by step. Once the problem is finished, the paper passes to the other partner who then coaches. This back and forth continues until all six problems are completed. If, at any time during coaching, a coach gets stuck, s/he may ask the other pair at their table for help.
For any student who signaled a learning level of 1 or 2, I partner with him/her (if there is just one) or group them (if there is more than one). I coach the students altogether on the first two problems, then I partner them to coach each other for the last four. This scaffolding typically provides just enough extra practice to build their confidence.
It is critical to teach procedures with this activity since faster processing students tend to get frustrated if their coaching partner is slow at giving directions. When I introduce this procedure at the beginning of the year, I make a point to students that the coach learns just as much, if not more than, the person being coached. Therefore, it is important that the coach not feel rushed.
Once teams finish their work, I ask them to turn their paper over to signal they are done.
For closure, I asked students to share any "a-ha" moments they had during the coaching period. One student volunteered, "I figured out that when I saw the work 'per', I should put that number with a letter." I re-coded his statement for the class by saying, "What I heard you say was that if you saw the word 'per' in the scenario, you knew to put that number with a variable, like '$4 per hour would be 4h. Is that right?" The student nodded in agreement.
I then explained that during the next lesson, we will continue to write functions, but that we will be using them to make decisions about how to spend money.