Before I even get started I want to say that I’m so excited because I received Tracy Zager’s book: Becoming The Math Teacher You Wish You’d Had in the mail yesterday! I can’t wait to start reading it. Go buy it if you haven’t already!!
Algebra 1 – We are continuing with sequences this week. I love this first problem the kids had to do (this was 2 day lesson):
“Samantha and her teacher have been busy creating new sequence generators and the sequences they produce. Below are the sequences Samantha and her teacher created.Your Task: Working together, organize the sequences into families of similar sequences. Your team will need to decide how many families to make, what common features make the sequences a family, and what characteristics make each family different from the others. Follow the directions below. As you work, use the following questions to help guide your team’s discussion.
|a. −4, −1, 2, 5, …||b. 1.5, 3, 6, 12, …|
|c. 0, 1, 4, 9, …||d. 2, 3.5, 5, 6.5, …|
|e. 1, 1, 2, 3, 5, 8, …||f. 9, 7, 5, 3, …|
|g. 48, 24, 12, …||h. 27, 9, 3, 1, …|
|i. 8, 2, 0, 2, 8, 18, …||j. , , 5, 10, …|
- Picking an Ace from a standard 52-card deck.
- Not rolling a 3 on a standard number cube.
- The chances of a thumbtack landing with its point up or on its side.
- Getting the one red crayon from a set of eight different-color crayons.
- The likelihood that you will run out of gas on a long car trip.”
Initially the kids said #2 was 1/6, then some said NO, it’s Not rolling a 3! so 5/6.
After that we worked on what would happen if we “modified the sample space”. They had a bag with different colored blocks in it and calculated the theoretical probability for drawing the different colors (naturally 1 bag was missing a green, and that was the group I called on for their first probability…. so it was 4/11 rather than 4/12… so i had to run across to where I’d left the box ‘o blocks to get another green!). Then I gave them another (identical) bag and they calculated the probabilities again. They were the same!
The initial questions in the lesson were “If you want to have the best chances of getting a red gumball from a gumball machine, is it better if the machine is full of gumballs or half empty? How do the chances of getting an ace in a deck of playing cards change if you have three or four decks of cards to choose from instead of only one deck? In this lesson, you will think about the size of the sample space (the collection of all possible outcomes of an event).” We will talk about this again on Tuesday (Martin Luther King, Jr. day is Monday) because it’s natural to think that if there are more you have a better chance. It was a fun start to the unit.
Math 7 Accelerated – We are finishing up chapter 4 in the CPM CC3 book so we were putting together the pattern, table, rule and graph. They graphed a line without an xy table. There was a lot of discussion on the “growth” (we haven’t said slope yet), and why if the pattern increases by 4 each time you graph that as up 4 and over 1. I wrote “change in y / change in x” then introduced it as delta y/delta x and we talked about and drew the “growth triangles”. It’s hard for me to remember to do the actual drawing “up and over”, I’m so used to just “counting” up and over. But I think it pushed the kids and that was good. Yesterday we went to the computer lab and the kids did Desmos’ Marble Slides-Lines. Last year we had done this at the beginning of the unit and the kids figured out “how” to make the lines move, but didn’t know “what” they were doing. This year it was better, but some were still not sure how to move the lines up and down. We’ll be doing a lot more with the lines, and I think we’ll go back and do Marble Slides again because most of the kids didn’t get to the “hard” ones. It was a great way to review slope and y-intercepts though! Today they had their group quiz. One of the problems gave them an equation then a tile pattern from a different equation. They needed to write the rule, draw 3 or 4 patterns, make a table and graph the line for each of the patterns, then tell me if they thought the 2 patterns would ever have the same number of tiles. Yep – we looked at it and said, “these are great!” So last night I did the quiz – and looked at the answer key. The second pattern was triangular (okay) and decreased (okay), removing one layer, or column each time. So pattern 0 had 7 columns, with 7, then 6, then 5, then 4 etc. tiles per column. Pattern 1 had 6 columns. I told them they needed to draw the pattern first – at least 3 more – then do the other representations. If they didn’t know how to write the rule they could describe what was happening. This is because the rule is [(x-8)(x-7)]/2. Yep. I think I’m going to change the instructions to tell them to describe the rule because I like having them do this problem….but so many were starting in slope intercept form, with -28 as “b”, since pattern 0 had 28 tiles! I’ll grade those this weekend too.
That was the week!