For our in-class review day, the students will be doing the chapter review section #1 – 3 and 6 – 11. While they are working on that, I’ll be calling kids up one at a time to talk about their homework that they have turned in and encouraging many to stay after school or to come in the morning for help.
2008-2009: I made a worksheet for homework based on the review (since the answers to the book’s review are in the back of the text and kids just copy them)
Chapter 3 Review (A: Classwork B: Homework)
3.1 Recursive Sequences
3.2 Linear Plots
3.4 Linear Equations and the Intercept Form
3.5 Linear Equations and Rate of Change
3.6 Solving Equations Using the Balancing Method
Day 1:
After a weekend thinking about it, I’m going to try to do drill and kill first before I teach the kids what the pan balancing method really is. Since I’ve shown the students how to show their work “properly” while solving equations, I’m going to try to get them to do it tomorrow with the help of “undo tables”.
First, I’ll put two or three examples on the board for students to help me solve. Examples such three-step equations. Using an undo table off to the side, I’ll have the students help me solve the equation using the standard written method for solving the equations. Second, I’ve prepared a notes worksheet which the students will do and then cut up into four parts. I’ll put them underneath the document camera and discuss what is good and what isn’t. Lastly, I’ll send them home with a homework assignment with six equations to solve.
Day 2:
I never got to the homework on day 1. Lots of time was spent going over five examples and then giving them time to do the class notes was enough. The second day I went over their notes on the camera and then gave them a short quiz at the end of the period. Then I finally gave them the homework with six equations to solve on it.
I also never taught the multiplicative inverse, I think that I’ll wait on that.
I began the lesson going over “real world meanings” of the slope and y-intercept of linear equations using the equations in the box on page 187 which I had on the overhead as slides since they’ve had difficulty with these for days. I also continually asked them what types of equations they are (intercept rule) so that it would lead into the next part of the lesson.
I then gave them tables of data and had them write the intercept rule (also in the notes link below) on a piece of paper while I walked around the room to check their work.
The first one is a simple one in which the x-values increase by one each time, so the rule could be done by the majority rather easily.
The second one has the same y-values as the previous but the x-values increase by two.
The third one has decimal figures and the x-values increase by 5.
The fourth one has large x-values that increase at varying intervals and the y-values only increase slightly. It also does not include a y-intercept, so the “starting value” has to additionally be found.
This exercise took a great deal of time, but next year I would like to make the problems in the lesson a bit easier so that much of it could be done without calculators, which seemed to take away from the flow of the lesson.
For the homework on the first day, I gave them #1, 2, 5, 11, and 14. On the second day I gave them the “Extra Practice” worksheet after we went over the previous night’s homework.
Day 1:
As the students entered the room, I had them write on their notes what I had on the board:
I then had them copy down a simple table from the board which was really the first few lines of the sports car’s distance from Flint from the previous section.
| Time in minutes | Miles from Flint |
|---|---|
| 0 | 35.0 |
| 1 | 35.8 |
| 2 | 36.6 |
| 3 | 37.4 |
And we changed the data into the other three forms. I spent a lot of time explaining that given any of the four forms, students should be able to change it to any of the others.
I made sure that students saw the relationships between the four forms, such as the starting value is the y-intercept, or that the table is increasing by the same amount that appears in the rules. We talked about slope a little because kids brought it up.
The second problem that I gave them was with a graph (of y = -2x + 5) that needed to be converted to the other three forms. Then I gave them the 3.4 Notes, which involved more of the same, but I wanted them to be as successful as possible with the “boring” stuff before we add stories to the list of things we should be converting situations into. So I’m planning on doing the investigation on day 2, then assigning the homework (#1, 3, 4, 5, 6, 7)
For the first day, I gave them the worksheet from the Extra Practice materials on 3.4 to do.
Day 2:
I gave a warmup that took quite a long time, but I think that it was beneficial. Helping kids move from the explicit formula straight to the table was difficult for them. Once they began, they did pretty well, although there are still numerous issues with scales on graphs when the data jumps from 2000 to 5000. I spent the rest of the day going over the previous day’s homework in preparation for the quiz, which is below.
The amount of money that Gladys makes each week selling furniture is
y = 200 + 0.10x
where y is the amount of earnings and x is the amount of furniture sold.
This investigation takes a lot of time.
Day 1:
After going over the previous night’s homework, I spent a good deal of time going over how to use the calculator to get arrays of sequences into their calculator with a good number of examples. I tried to make sure that they understood the calculator’s method of working with the sets of numbers, particularly mentioning that you must think of each term in the set as a column for the Ans(1) or Ans(2) part. I did this by first putting data on the board in x, y, z, columns, then writing the rules using recursion. Then I added the columns in parentheses so that they were on the board as I was doing them on the computer’s calculator to be shown on the screen.
When it was time to make the tables from the investigation, which took the remainder of the period, many didn’t transfer the calculator exercise over. The students did okay turning the speeds from miles per hour to miles per minute, but the table confused them by going up by 1 to begin with, then up by 3, then by 5, then by 10s. They were writing the values as if the table was going up by 1 each time. Note: make extra copies of tables for next year! By the second time that I taught the lesson, I was much more careful about pointing this out.
Day 2:
I went over the table from the previous day (many were absent due to a student war protest (skipping, really)) which took awhile. I then had the students work on the graph and for some of them, answering the questions on the bottom of the page (steps 6 to 12). About 1/3 of them finished.
Day 3:
I was gone for a district meeting but had the students finish the questions from the investigation and work on 3.2 numbers 1-5, 7.
Day 1:
Short day because of a late-start.
I gave a short introduction about recursion. I brought back “recursive rules” from fractals and told them that we will be writing recursive rules once again, although for sequences of numbers.
I did investigation 1 by having them draw the triangles in their notebook. I was sure to tell them that the perimeter of the figure is the distance around the shape and did not include the toothpicks in the interior. (But this didn’t stop some of them!) I had them fill out the table for step 2, and then used the calculator to do the routine. We then wrote how to correctly write out a recursive routine.
I then had them do the same steps for the toothpick squares.
I then did example B from the textbook on the board – I just put the sequences up on the board and let them go. Then they came up to the board to do them. Once again, I pointed out that every term was a previous term added to some constant number. I also made sure that the students put the recursive rules up on the board next to their lists.
In order to work backward, I then erased the lists of numbers of the board and left the rules up. Then I changed the number of the first term, so that there was a new rule up, and we wrote down the first five terms of the sequence.
I gave questions 1 – 4, and 6 for homework on this short day. Depending on how well they do at it, I may come back to this section, but from what I saw today, I’ll probably be done with it.
