Day 79: Trapezoids

6th Grade Math Standards: 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. MA.1.a. Use the relationships among radius, diameter, and center of a circle to find its circumference and area. MA.1.b. Solve real-world and mathematical problems involving the measurements of circles

Objective: Calculate the area of a trapezoid

Agenda:

1. Visual Pattern #72 
2. QSSQ 
3. Pepper & Review homework
4. Trapezoid Notes
5. Trapezoid Practice

Assessment: Students did a problem on their own after the notes had been completed. They were then able to start the homework on their own. Since the trapezoid notes were given relatively quickly, students were able to fix their weekly quizzes too this class.

Glass Half-Full: I liked a couple of things that were discussed as part of the notes. First, we had a brief introduction to using 4 (9) to multiply. We even touched on the distributive property.

I also think it is beneficial to discuss the order of operations and eliminating the term PEMDAS. There are always misconceptions and plain ignorance of the order of operations, and it is something that we eventually cross with numerical and variable expressions later on in the year.

Finally the idea of base meeting height at a right angle is revisited. Students struggled to identify what numbers were bases and which were height.

Regrets: For the second straight day, I went over homework for too long. There just is not enough investment from the students during this time and I need to give them more opportunities to try rather than just listen to me. Most of them will take the easy way out and just listen to me instead of exploring on their own, so it's just something I constantly need to be reminded of. Even if it is just to change the numbers of a problem we did five minutes before and let students try it on their own.

Day 78: Formula Application

6th Grade Math Standards: 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. MA.1.a. Use the relationships among radius, diameter, and center of a circle to find its circumference and area. MA.1.b. Solve real-world and mathematical problems involving the measurements of circles

Objective: Find the missing side or height of a triangle, rectangle, and parallelogram given the area and another dimension; correctly input the dimensions of a triangle and parallelogram; find the area of a polygon shaped garden while not including a portion that is also a polygon; determine how the area is changed when both dimensions are doubled

Agenda:

1. Open Middle Pocket Change 
2. QSSQ 
3. Review Triangle HW and Pepper
4. Exit Ticket: If the base of a triangle is 4 yards and the height is 5 yards, what is the area of the triangle in square feet? 
5. Stations. Missing side, find the area or perimeter, weekly quiz 14, what formula and what are the proper numbers to substitute, and determine what happens to the area when the base and height of a rectangle are doubled 

Assessment: Exit Ticket; homework check; finding the missing side

Glass Half-Full: Stations was effective use of group work and getting students to try problems that have multiple steps and multiple layers of thinking. I stayed at the group that needed to find what formula to use and what numbers to use with that formula. No matter how many times I say, "The base meets the height at a right angle," students still need to apply this concept and fail at it in my presence to recognize how to do these problems. I also noticed students dividing the parallelogram by two because they were in the habit of using the triangle formula.

Regrets: I took too long going over the homework and not enough time administering the exit ticket. Going over the homework was too much of me talking. Students took a back seat and did not have to think. The exit ticket involved thinking and in almost the case of every student, it was not a problem that could be solved without my help. If students were paying attention, they would have been fine, but what student pays attention? I'm not complaining. I'm being realistic. I need to give students more opportunities to work things out and fail at them. That's when I'm at my best. Not when I'm telling them exactly what needs to get done.

Day 77: Area of Triangles

6th Grade Math Standards: 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. MA.1.a. Use the relationships among radius, diameter, and center of a circle to find its circumference and area. MA.1.b. Solve real-world and mathematical problems involving the measurements of circles

Objective: Determine the area of a triangle; summarize how the area of a triangle formula is related to the area of a rectangle

Agenda:

1. WODB #21 
2. QSSQ 
3. Recap from yesterday about why the formula is A = b x h for a parallelogram and a rectangle
4. Pepper and HW review
5. Area of a triangle notes
6. Area of a triangle exit ticket
7. Area of a triangle practice/homework

Assessment: The notes were essentially me circumventing the room as students discovered for themselves how to get the area of a triangle. The exit ticket was done with turning point clickers. The homework was started in class.

Glass Half-Full: The exit ticket was a new feature this year on this lesson. I wanted the students to utilize the clickers because it had been a while and I also wanted to have some form of transition from notes to homework. The problem with this exit ticket is that it is all about the answer and not about the process for how that answer is found. As experience with sixth grade has taught me, students will find a way to "muff the punt" when it comes to going back and forth with area formulas of triangles and quadrilaterals.

Regrets: Students had a hard time finding the base and height of the triangles, so perhaps giving them the first homework problem's base and height would save some aggravation on their part. I also did not show them a problem in which the perimeter of a triangle is given in addition to the height of the triangle.

Day 76 Area of Parallelograms

6th Grade Math Standards: 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. MA.1.a. Use the relationships among radius, diameter, and center of a circle to find its circumference and area. MA.1.b. Solve real-world and mathematical problems involving the measurements of circles

Objective: Determine the area of a parallelogram

Agenda:

1. Find the first number that is not a multiple of four, a multiple of five, and a multiple of six. The number is also not prime nor is it a square number. 
2. QSSQ
3. Review the homework on rectangles
4. Parallelogram my favorite no 
5. Area of parallelogram notes
6. Let students start the homework with about 20 minutes left in class
7. Give students feedback on their weekly quiz and let them fix the weekly quiz 

Assessment: The my favorite no was a question that asked students to find the area when there were three different dimensions given for a parallelogram. It forced students to utilize the "base meets the height at a right angle" instruction. Only one student answered it correct of all of my students. This was the most popular wrong answer:

Glass Half-Full: Getting the feedback to students on the weekly quiz was crucial because the percentage of a number concept is still an issue for more than half of my students. I also wanted to give them feedback on the quality of their writing. Some students are still writing nothing but the math on open responses. It would have still been ideal to have more time to provide this feedback, but I made the most of twenty minutes and the students worked well enough in partners that it was not a classroom management issue that took me away from the goal of helping students on the weekly quiz.

Regrets: I doubt that students have mastered how to find the length of a square when the area is given. We went over one homework problem about that concept, but it is still something that they struggle with. It was a little helpful that the term square number was accidentally glossed over by us again as part of the warm up.

Day 75: Area of Rectangles

6th Grade Math Standards: 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. MA.1.a. Use the relationships among radius, diameter, and center of a circle to find its circumference and area. MA.1.b. Solve real-world and mathematical problems involving the measurements of circles

Objective: Calculate the area of a rectangle

Agenda:

1. Visual Pattern #53 
2. QSSQ 
3. Pepper and Review HW 
4. Area of Rectangles HW Models
5. Index Card Activity from Laying the Foundation
6. Area of Rectangle Practice

Assessment: Students did a homework model problem on their own; I checked their homework and collected weekly quizzes; the index card problems were done in partners

Glass Half-Full: The index card activity was a genuine measurement activity. Too often I rely strictly on worksheets for something that is very much a hands on math skill that my students even at twelve years old can completely wrap their heads around. We used rulers to measure an 8 inch by 5 inch index card. Students then got the area and perimeter of that index card.

Next, they cut the index card in half so that the five inch side stayed intact. To help them I had them lightly shade this side with a pencil. Again they found the area and perimeter of the index card. We kept repeating this process four times. At which time students could see that every single time the area was cut in half and the perimeter was also getting smaller obviously. I then did out the work for the next several areas and had the students say the word "limit" three times and told them that this was their first Pre-AP Calculus class.

Regrets: Time goes by quick today. The perimeter homework had many good problems on it, but some problems I would do with out. The second to last and third to last problems are among those problems. That being said the interleaving problem of a tape diagram was beneficial for many students and is featured again tonight on the homework.

Day 74: Intro to Perimeter

6th Grade Math Standards: 4.MD.3 Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Objective: Determine the perimeter of a polygon

Agenda:

1. Estimation 180 Days 81 through 83
2. QSSQ 
3. Pepper
4. Perimeter Notes
5. Perimeter Staircase
6. Perimeter Practice 
7. Weekly Quiz

Assessment: Circumventing the room as students began the homework as well as while they worked on the perimeter staircase problem.

Glass Half-Full: The question on the perimeter staircase that really forced students to struggle was the question, "How many toothpicks are in the tenth staircase?" In one class, I put the timer on for four minutes and let the students work. One of my students worked it through with me in a way that I had not even anticipated. He said that each staircase had a certain amount of toothpicks that were not counted as part of the perimeter and that this along with the perimeter was done in a pattern. By combining the number of toothpicks in both patterns he got the number of toothpicks altogether.

This lesson got better as I went on in class. I started out by having students write down the first two stairs in their notebook and then physically constructing those two staircases in partners using paperclips which I have in surplus because of the Dan Meyer lesson we always use.

Next, I had them find the perimeter of those two staircases. Inevitably there are groups that calculate the inside of the second staircase, so we need to have an argument about whether the perimeter is 8 units (as it should be) or 10 units (which includes the two paperclips inside the staircase.).

Third, we construct the third and fourth staircases on paper and using the paperclips.

Fourth, we find the perimeter of those. Fifth students get the rule. Sixth, they apply the rule to staircase ten. Seventh, I overwhelm them by asking for how many toothpicks (or paperclips in our case) are required to make staircase ten. As I already stated, that question tripped everyone with one exception.

Regrets: I never explained today's weekly quiz which is an open response. I have had issues with the students writing this year in terms of very basic concepts. I'm not the best writer (I don't need to tell you, you're reading this...), but I learned at a young age to start a sentence with a capital letter. The students are not doing that with consistency this year. I'm not sure if this is a texting thing or a writing in math issue, but I actually had to write on the rubric that points will be deducted for lack of capital letters at the start of sentences.