Yesterday my 5th period students were working on the Fort Hall Businesses activity from the IMP Meaningful Math Algebra books. Some of the groups in the class had #1 and some had #2. Each of the problems asked students to find the "starting point" for a situation. Anyway, I had "helped" the groups who had #2 first because it was a little more difficult. I had guided the students through how to take the two sets of data points and think through how to find the "starting point" which was the amount of money that a movie theater had started with in their cash register. We had "deduced" that they started with $10. What I didn't realize is that when I wrote down the two data points out of the problem I had written one of them incorrectly. Therefore although the students' reasoning in how they found the answer to be $10 was correct I had "led them astray" by writing down the wrong value.
So, my principal walks in and sits down for a minute. When he comes in I am working with the students who are doing #1 and writing on the back board. The problem that is still projecting on the front board is problem #2 so he finally asks me if we are doing different problems. He then goes and talks to a couple of the groups doing #2 and starts working on the problem. When I walk back to the front of the room he is telling the students that the starting amount of money in the cash register is $25. In my mind I am thinking, "O bless his heart! He is wrong and he is going to be embarrassed in front of all these students." Thankfully I didn't claim that he was wrong. I just asked him to explain his reasoning. He did a wonderful job explaining his reasoning and he was RIGHT - not bad for a former history teacher. My brain literally had a cramp in it because I was so confused why we had gotten $10 earlier. I KNEW we had used the right reasoning. After a couple of minutes looking back at the values I had written on the board we found the mistake. Needless to say my principal now thinks that he is a math expert!
I had a couple of students to throw their papers away because we had made a mistake. I tell them to never erase or throw away papers because I want to see their thinking on paper. I even had one student who graphed the 2 data points and extended the graph back to the y-axis in order to find the starting amount in the cash register. He had the correct points graphed and had $25 as the starting point until I went and "corrected" him because he hadn't graphed the points I had written down. I felt so bad! I told them to just write down "Owens was wrong" on that page in their notebooks instead of starting all over. I knew that they understood what was going on with the problem. I also used the situation as an "object lesson" about working in groups. I told them that this was an example of why you can't just accept everything that the "smart kid" in the group says. When you have different answers or ideas in the group you need to take time to explain and listen to each other's reasoning. Today they saw the mathematical practice standard #3 (construct viable arguments and critique the reasoning of others) acted out by me and my principal.
My principal and I are both former coaches and highly competitive individuals. I am sure he will never let me forget about the day he had to "set me straight" in my own algebra class.
Tuesday, January 27, 2015
IMP Cookies - Feasible Diets and Picturing Pictures
My students did Feasible Diets on this past Friday. The constraints that are needed for feasible diets were actually found during the Healthy Animals activity.
Today I used Picturing Pictures as a quiz but I added a twist to it. I allowed each student to ask me 3 questions (or get 3 hints). I actually wrote down their names and kept up with it. I encouraged the students to listen when others came up just in case they might learn from the questions/answers that other students have/get. I made the students use their "privacy fences" and did not allow them to help each other. I found that students were still struggling with graphing lines. The majority of the graphing we have been doing so far in Cookies have been easier to graph using intercepts. Once again I have found that students seem to understand the concept better since we have the context to tie it to.
I had a workshop today so I left "traditional" algebra problems where they practiced graphing using intercepts and graphing using slope-intercept form. I intend to give them a quiz on these 2 concepts this week.
Today I used Picturing Pictures as a quiz but I added a twist to it. I allowed each student to ask me 3 questions (or get 3 hints). I actually wrote down their names and kept up with it. I encouraged the students to listen when others came up just in case they might learn from the questions/answers that other students have/get. I made the students use their "privacy fences" and did not allow them to help each other. I found that students were still struggling with graphing lines. The majority of the graphing we have been doing so far in Cookies have been easier to graph using intercepts. Once again I have found that students seem to understand the concept better since we have the context to tie it to.
I had a workshop today so I left "traditional" algebra problems where they practiced graphing using intercepts and graphing using slope-intercept form. I intend to give them a quiz on these 2 concepts this week.
Monday, January 26, 2015
Cookies - A Simpler Cookie thru What's My Inequality
My personal life has been turned upside down. I enjoy blogging about our new curriculum. I look forward to being able to look back next year in order to help me when we go through a 2nd time. However, when I have to cut some things out because of a lack of time blogging is the first thing cut. The thing is...blogging just helps me to organize my thoughts and see where I have been and where I am going. I think I might could really be diagnosed with ADHD...I doubt that any of my colleagues would disagree. I am kind of joking but I really do think it is true. Forcing myself to focus and "verbalize" what I am doing with my classes helps me to reflect and think. So...here is a brief summary of what we have done so far in Cookies.
How Many of Each Kind? - The students brainstorm the number of dozens of iced and plain cookies that meet the 4 constraints that are mentioned.
A Simpler Cookie - This activity allows the students to only worry about prep time. They assume unlimited amounts of dough, icing and oven space. Then they are asked to try to find the most profit. We believed the max profit in this case was 150 plain and 0 iced.
Manipulating Inequalities - This activity allowed the students to "discover" the rules for solving inequalities. They also practice graphing inequalities in one variable. When going over #3 ask the students what would make the inequalities where you multiplied or divided by a negative "ok" again.
My Simplest Inequality - In Part I the students practice solving inequalities in one variable. We supplemented with an additional worksheet on solving and graphing one-variable inequalities. In Part II we investigated equivalent inequalities. Then in #3 we took inequalities and wrote them in simpler ways.
Simplifying Cookies - In this activity you take the Cookies Constraints and write them as simpler inequalities. We did not spend much time on this but I did write the simpler inequalities on chart paper.
Picturing Cookies - In this activity students take the constraints and use 2 colors to indicate ordered pairs that either work or do not work for the cookies constraints. They will hopefully recognize a "dividing line" that halves the graphs into correct solutions and incorrect solutions. I gave each group one constraint to test and had them put it on chart paper after they did it individually on graph paper.
Inequalities Stories - I gave this as a bonus opportunity...
A Hat of a Different Color - This POW was assigned when I had a sub. I think it would be a good idea to use hats or objects and act out the situation a few times in class before the students try to figure out the color of Carletta's hat. Her hat is blue. If Arturo couldn't tell then the 2 girls could NOT have both had red hats. One of them must have been blue. If Belicia had opened her eyes and seen a red hat on Carletta she would have known her hat was blue. However, since she passed Carletta must have been wearing a blue hat.
Healthy Animals - You create 3 inequalities - one for fat, one for protein and one for total amount. I did not have my class graph this activity.
**Picturing Cookies - Part II - We used this to "reteach" graphing using slope-intercept form. We used Desmos to show the graphs but I don't know if I should have waited on the technology... Anyway, it is extremely important to have each student to graph these correctly and identify the feasible region. They will need it to solve the unit problem. I did the graph on chart paper and left it hanging in the room.
What's My Inequality - I really liked this activity to help us tie the work in the unit to "traditional algebra problems." This is the first time the text mentions the differences in when to make the line solid and when to make the line dashed.
How Many of Each Kind? - The students brainstorm the number of dozens of iced and plain cookies that meet the 4 constraints that are mentioned.
A Simpler Cookie - This activity allows the students to only worry about prep time. They assume unlimited amounts of dough, icing and oven space. Then they are asked to try to find the most profit. We believed the max profit in this case was 150 plain and 0 iced.
Manipulating Inequalities - This activity allowed the students to "discover" the rules for solving inequalities. They also practice graphing inequalities in one variable. When going over #3 ask the students what would make the inequalities where you multiplied or divided by a negative "ok" again.
My Simplest Inequality - In Part I the students practice solving inequalities in one variable. We supplemented with an additional worksheet on solving and graphing one-variable inequalities. In Part II we investigated equivalent inequalities. Then in #3 we took inequalities and wrote them in simpler ways.
Simplifying Cookies - In this activity you take the Cookies Constraints and write them as simpler inequalities. We did not spend much time on this but I did write the simpler inequalities on chart paper.
Picturing Cookies - In this activity students take the constraints and use 2 colors to indicate ordered pairs that either work or do not work for the cookies constraints. They will hopefully recognize a "dividing line" that halves the graphs into correct solutions and incorrect solutions. I gave each group one constraint to test and had them put it on chart paper after they did it individually on graph paper.
Inequalities Stories - I gave this as a bonus opportunity...
A Hat of a Different Color - This POW was assigned when I had a sub. I think it would be a good idea to use hats or objects and act out the situation a few times in class before the students try to figure out the color of Carletta's hat. Her hat is blue. If Arturo couldn't tell then the 2 girls could NOT have both had red hats. One of them must have been blue. If Belicia had opened her eyes and seen a red hat on Carletta she would have known her hat was blue. However, since she passed Carletta must have been wearing a blue hat.
Healthy Animals - You create 3 inequalities - one for fat, one for protein and one for total amount. I did not have my class graph this activity.
**Picturing Cookies - Part II - We used this to "reteach" graphing using slope-intercept form. We used Desmos to show the graphs but I don't know if I should have waited on the technology... Anyway, it is extremely important to have each student to graph these correctly and identify the feasible region. They will need it to solve the unit problem. I did the graph on chart paper and left it hanging in the room.
What's My Inequality - I really liked this activity to help us tie the work in the unit to "traditional algebra problems." This is the first time the text mentions the differences in when to make the line solid and when to make the line dashed.
Thursday, January 8, 2015
My purple sky is very cloudy
Ever since December 24th the forecast at my house has been cloudy. My husband hurt his back and can't sit or walk without crutches. He can't teach or coach. He has only left the house for doctor's appointments and literally has to lie in the floor of the waiting rooms. It is crazy how I just can't seem to function when he isn't himself. My world is turned upside down. We have 3 children and 2 of them play sports (the 3rd one is 3) so we are always on the go. Our schedule is hectic when we are both 100 percent. The hardest part though is leaving him laying there by himself knowing he will be by himself all day...frustrated and discouraged. I am so thankful to have an incredible network of family and friends to help support us. Blogging about teaching has become very unimportant to me right now... I hope to have a desire to continue soon. This too shall pass. We are praying for God's guidance as we seek a way to help him to be pain free again.
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