Days 82-86 – January 9-13

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, …
How can we describe the pattern?  How does it grow?What do they have in common?
(1)  As a team, initially sort the sequence strips into groups based on your first glance at the sequences.  Remember that you can sort the sequences into more than two families.  You will have a chance to revise your groups throughout this activity, so just sort them in a way that makes sense to start out with.  Which seem to behave similarly?  Record your groupings and what they have in common before proceeding.
(2)  If one exists, find a sequence generator (growth pattern) for each sequence and write it on the strip. You can express the sequence generator either in symbols or in words. Also record the next three terms in each sequence on the strips. Do your sequence families still make sense? If so, what new information do you have about your sequence families? If not, reorganize the strips and egroupwork-alg-sequencesxplain how you decided to group them.(3)  Get a set of resource pages, saving a copy of each of the tables and graphs for your team. Then record each sequence in a table. Your table should compare the term number, n, to the value of each term, t(n). This means that your sequence itself is a list of outputs of the relationship and the inputs are a list of integers! The first term in a sequence is always n = 1. Attach the table to the sequence strip it represents. Do your sequence families still make sense? Record any new information or reorganize your sequence families if nece
ssary.
(4) Now graph each sequence on a the graphs your teacher gave you. Include as many terms as will fit on the existing set of axes.  Be sure to decide whether your graphs should be discrete or continuous. Use color to show the growth between the points on each graph. Attach the graph to the sequence strip it represents. Does your sequence families still make sense? Record any new information and reorganize your sequence families if necessary.”
There was a lot of discussion on grouping, and some kids persevered on the rule and others had some troubles. We discussed the rules and I had students share how they figured out the harder ones. The next day they “learned the language” of sequences – arithmetic, geometric, sequence generator, common difference and were reminded of discrete vs continuous and domain.  It was also new to write the sequence as t(n) = 3n+4, and to understand that n is the term number, 1st, 2nd, 3rd. The next day was explicit equations vs. recursive equations. It’s the first time I’ve taught recursive equations as this didn’t used to be in algebra 1!  The kids didn’t see the point of it at first, why should they write an equation depending on the term before the current term if they could just write the rule? But…. a few days before we’d had the Fibonacci numbers in one of the sequences, so they remembered they couldn’t write a rule for it. However, they could write a recursive rule for it!  Another great CPM Algebra lesson. Today we had a quiz, that was all on review material (which is given daily in the homework). I told them if they don’t do well on the quiz it’s because they aren’t doing their homework very well (CPM has help for every problem, with hints, for free. Some check their work, some don’t…) I’ll grade the quizzes this weekend and see how they do!
Math 7 – We started our Probability Unit this week. We’re using the lessons from the 7th grade CPM book (CC2). If you buy a Black Line Master from CPM you can make as many copies of it as you like – so since I had one we could copy the lessons for the kids (it’s in ch 1 and ch 5). And, since the homework help is FREE, they can get help if we assign those problems…which we aren’t since we do the weekly hw page which is AWESOME.
We have worked on experimental vs. theoretical probability, we investigated probability by making a spinner and then having each student spin the spinner (bobby pin) 10 times. We totaled the spins by color and compared the class results to the theoretical results. Today we wrote about the difference between experimental vs. theoretical probability, and then calculated the theoretical probability for different things if it was possible.
“Look at the situations below and decide with your team if you can find a theoretical probability for each one.  If you decide that you can find the theoretical probability, then do so.

  1. Picking an Ace from a standard 52-card deck.
  2. Not rolling a 3 on a standard number cube.
  3. The chances of a thumbtack landing with its point up or on its side.
  4. Getting the one red crayon from a set of eight different-color crayons.
  5. 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!

 

Posted in Graphing, Groupwork, Patterns | 1 Comment

Days 78 – 81, January 3-8, 2017

Algebra – We came back from our Winter Break (aka Christmas Vacation when I was in school) and started chapter 5 in the CPM Core Connections Algebra Book. It’s on Sequences and I’m looking forward to teaching it because it’s so different from the 1 section that would be on sequences in the old Algebra book I’ve used.

We started out by representing exponential growth by looking at bunnies reproducing. There were several different situations that we looked at, drew patterns for and graphed. Next came dropping a bouncy-ball from different heights and seeing what the rebound rate was (it was raining that day, so we had to go into the “Jungle Hallway” – see the pics). We calculated the “rebound ratio” and figured out that this was the slope of the line.

The next day we used the bouncy-balls again, except this time they caught the ball at the top of the rebound, recorded that height, then dropped it from there again. This graph was ball bounce to bounce height – and showed exponential decay! It was pretty cool.

Math 7 – We decided to finish up proportions and come back later to equations again. We (awesome co-teacher-Maddy and I) need to do more work with using inverse operations to solve equations that have fraction answers. Our kids are really good at “undoing” or “looking inside” the equations to find the answer when it’s an integer, but we want to work more on just “using inverse operations to solve the equation” so they have another resource when the equation isn’t as “nice”. So… we did big white board review of proportions – we gave the kids a situation and they had to write the proportion from it and solve it – and equations, and some area and perimeter. (We started reviewing area and perimeter in homework, so put a perimeter question on our test.) Wednesday we used Mr. Orr’s awesome post on a site he found “Internet in Real Time”. The link to the original site wasn’t working so I found another one that showed the numbers changing (go look at his post!), then froze it at one second. The kids made up problems on the white boards (if there are 214 tweets per second, how many tweets would there be in a day?) and then walked around the room looking at the different questions. Then I called on a few kids and they picked one of the problems and we all solved it – and explained how they solved it. I NEVER had to explain how to figure out how many seconds were in a day! They said 60 x 60 x 214 because there are 60 seconds in a minute and 60 minutes in an hour, then times that by 24 for the hours in a day. WooHoo!!  On Thursday we did some more proportion problems and then on Friday they took a team test. We started out by having the kids work in pairs, then they could check their results with the pair across from them. And, a lot didn’t finish, so they’ll finish today.

I think the reason they didn’t finish is because we are still discussing the homework everyday, but that is so great! This week one problem was to write a situation for 157 – 162 and the student that was explaining it said he lent his mom $157 and then spent $162  ( so -157 – 162) and got -319. Hands went up. He called on a student who said it wasn’t -157, just 157. The boy explaining said, “But you can’t take away 162 from 157, it doesn’t make since. You can’t spend more than you have.”  I said “What if you reversed the problem?” So then he wrote -162 + 157 and said, “Oh, it’s -5.”  I loved that 1) kids questioned his answer, and 2) he thought about it making sense when writing his story and 3) realized he could have reversed it. This is the best homework, and use of homework I have ever done.

Math 7 Accelerated – We also started a new chapter, Chapter 4 in the CPM Core Connections 3 book. It’s on patterns and equations, tables and situations, and tying them all together. The groups all had patterns that were all quadratic, and we were working on “seeing the pattern number in squares and rectangles in the patterns”. It was pretty cool seeing the different ways the kids “saw” the patterns. We spend a few days doing it – and used Fawn’s site www.visualpatterns.org for some extra examples. On Friday we started talking about y=mx+b and where the m and b are shown in the patterns.  It is so much fun watching the kids “see” the growth.

Posted in Graphing, Large White Boards, Ratios & Proportions | 1 Comment

Days 73 – 77 Dec 12-16, 2016

The last week of school before winter break!

Algebra CP – We finished chapter 4. The week started by choosing the best method to solve systems problems, and writing systems from word problems. We had the group quiz on Tuesday, then went over it and did some more review and had the test on Thursday. Friday the kids did some test corrections and then did the Stacking Cups Activity that Fawn wrote about. Some of the kids remembered it from last year – everyone got the equation really well, I think it was better here than in 7th Accelerated (note to self).

Math 7CP – I didn’t get to post some of the “If I Were One Inch Tall” poems my kids wrote, so I want to post them now…

This week we worked on writing proportions from word problems, writingultimate-tictactoe a little “word ratio” so it would be easier to see which numbers were representing which items. I still need to work more with them on why cross multiplying works – we did examples like 1/2 = 2/4 so they could cross multiply and see the results were the same, but I think next week I want do more with it – I think if we reduce them to the lowest terms it’s easier to see that we are multiplying the same things, so that’s why we get the same answers. We had a quiz on proportions this week and then on
Friday I had 2 different activities – Ultimate TicTacToe and Area Puzzles from a book I had bought (after seeing it on Twitter)…

 

 

Math 7 Accelerated – This week we had the chapter 3 group quiz, chapter 3 closure and the chapter 3 test. What a fun week! It was on equations so was really a review of the work we’d done at the beginning of the year, but there are still too many kids not thinking about what they’re doing and not distributing correctly or other errors. We’ll keep solving equations!  On Thursday we did Robert Kaplinsky’s In and Out Burger activity and I think they liked it. On Friday the kids worked together to do problems from the Area Puzzles book (see above) and these problems definitely get challenging!

This was a short post because 1) I’m writing it 2 weeks late so don’t remember some of the things we did, and 2) it was the week before the break so it was tests and quizzes before the break! I did like that I found puzzles and fun math activities for the last day, I didn’t want to “have a party and show a movie” this year. This is the end of 2016!

 

Posted in Ratios & Proportions, Systems of Equations | 3 Comments

Days 68-72, Dec. 5-9

Algebra 1 – We’ve been working on solving systems of eqsystems-problemuations using the elimination method for part of the week, then the lesson was on picking the most efficient way to solve a system based on the system. It was good because the kids had to say WHY they chose their method. On Thursday I gave the kids some puzzles I had saved. I really like the rectangle puzzle – but it was a little frustrating for period 2. They wanted to divide by 5. We talked about what the perimeter is of a rectangle, then labeled the sides with length or width. They got the first equation, then one group saw the second equation of comparing the sides and shared that with the class, so eventually everyone solved it.

The second problem was the problem with Ivan, Acrobats and Grandmas. It doesn’t need to be solved with systems, but it can be solved with systems. It’s just a fun problem.

Math 7 CP – We continued working on Barbie Proportions, calculating what Barbie’s measurements would be if she was the height of the person measured. Then we compared the person’s measurements to Barbie’s to see if Barbie would look “realistic” or not! It turns out her neck would be too long, and her feet would be too small – way too small! On Wednesday we went over the homework from Monday and Tuesday (the kids go up and explain how they did each problem and we need to make corrections sometimes but I think it’s totally worth it) and then I read them the poem “If You Were One Inch Tall” by Shel Silverstein. Their assignment was to write a similar poem, but using a different measurement with similar comparisons. Finishing the poem was their homework for 2 nights, I collected it today (Monday). On Thursday we did Double Clothesline Math by Andrew Stadel & Chris Shore. The kids worked on the questions then we talked about the different ways they solved them. We did several problems – I think it worked really well. On Friday I was out of town at a memorial for my Aunt in Virginia and the kids worked on solving proportions – they had to tell me if they used a relationship or cross-multiplied to solve them, and what the relationship was. Hopefully it made them think a little and not just be a robot!

Math 7 Accelerated – This was the final week of chapter 3, solving equations. I really wish we hadn’t done that big equations unit at the beginning of the year – it was really hard and this chapter was on equations…and it was well done and had great mixed practice homework so we didn’t want to skip it!  Next year we’ll change it to just starting with this book I think.

The class worked on figuring out how many solutions the equation would have, and wrote equations to solve problems. On Friday they did a review on showing an problem as a graph, tile pattern, table and the equation. Today I walked around and looked at their graphs – too many kids need to remember to use a ruler, use the space accurately – when should they make a 1 quadrant vs 4 quadrant graph, and to label!

 

Posted in Area & Perimeter, Ratios & Proportions, Systems of Equations | 3 Comments

Days 63-67, Nov 28 – Dec 2

I have 15 minutes so this will not be very thorough!

Algebra CP – We are working on Systems of Equations, we just started chapter 4. It starts with the “Equal Values” method, which the students also did in 8th grade  (assuming they had 8th grade math, and not Boost Camp). This is when the equations are both in slope intercept form and you just set them equal to each other since the “y’s” are equal.  Then we saw how it’s not always efficient to put the equations into slope intercept form, you get fractions for M and B, so another method is solving by substitution.  We were also writing the 2 equations from a situation. Today we put it all together – wrote the equations from the situation (yodelers with xylophones on a gondola…)and solved them, then graphed the lines – hey! they cross at the same solution, then made tables from the equations and saw that they both contained the same points! The kids worked on the white boards on the walls one day solving the systems.

Math 7CP – We are starting a new unit – proportions and more equations. We started the week with a Desmos Activity – Marcellus the Giant – to introduce proportions. Then we created Ratio Tables from examples in the book Building Powerful Numeracy for Middle and High School Students, which I think worked pretty well. I need to do more though!  Then we wrote proportions from “If the World was 100 People” – we made a worksheet from this YouTube video.  I want the kids to write one on their own at the end of the period, and a lot picked 30 would have the internet, 70 would not.  Then they wrote the proportion as 30/70 = …. I’m going around saying “is the world 70 people?”  Yeah, need more work on those! We ended the week doing Barbie Proportions – but it was too soon in retrospect. We need to work on solving equations by cross multiplying first, and how to logically set up a proportion more before we do this.  I’ll try and put all of the material for it in next week’s blog.

Math 7 Accelerated – We are continuing with chapter 3, and spent the beginning of the week looking at graphs and deciding what made a complete graph – labels, title, proper increments, lines with arrows and also looked at graphs and found the common errors. Then we reviewed some and took a quiz on chapter 3 that had “the silent board game” in it as well as equations, simplifying expressions and “graphing, tables, rules” – I gave them one and they had to do the other 2.  For homework after the quiz they had do solve 10 equations that had distributive property, combining like terms, etc.  This should be TOTAL REVIEW since we’ve been doing equations since September.  It was amazing to me how many kids were saying “I didn’t get that” and I’d start the problem with them and they’d have messed up on distributing, negatives, written the problem wrong.  I haven’t finished correcting the test – hopefully those equations are better!  Today we worked on solving equations and checking with the formal check – showing the substitution of the value for the variable and showing the equation is equal.

I’m also getting Maddy and Karen signed up for Jo Boaler’s Mathematical Mindsets conference at Stanford…in my spare time. I think it will be amazing, but getting the check from the district (Stanford won’t take a PO) is a ton of paperwork.  Fingers crossed that we’ll get them registered before the session is full!

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Days 58-62, November 14-18

This year (and apparently this year only) we have a week off for Thanksgiving. And this is the week before that week, it’s the end of Trimester 1, and the kids are READY to be out of school. So of course EVERYONE is giving tests this week! Lucky kids.

Algebra 1 – Monday we had the Group Quiz – which was too easy I think. I had looked it over, but didn’t do it (why won’t I learn??), and then when I did the key I thought it was too easy. But, that means all of the  grades were good! We did the closure problems on Tuesday, and the kids had the option of doing them on the large white boards, then whatever they didn’t finish in class was homework, to be done in their spirals. Most of the kids did them on the whiteboards, and I walked around. I liked it a lot because they could pick how they wanted to work – sitting or standing, alone or with a partner. It went really well. Wednesday we went over some of the closure problems that they wanted more help with – a LOT of exponent work. Thursday they had their chapter 3 test (which I haven’t looked at yet so have no idea how they did) and today we worked on graphing parallel and perpendicular lines. The kids that had Math 7 Accelerated (had the 8th grade standards already) remembered they’d done it before so they could help the kids that just took Boost Camp and got to be in Algebra instead of Math 8CP. I collected the papers as One More Grade.

Math 7CP – We were finishing up our equations unit – we aren’t done with equations, but we really worked on ones that they could figure out “by thinking about it”. I was a little sad yesterday when the kids took their test and one of my kids had no idea what to do to solve the equations – I’m going to ask him if he can stay after school on Wednesdays and work with me for 1/2 an hour. He needs some 1 on 1 time I think. We will do more equations that have division in them, and ones that have fraction answers next trimester. So Monday and Tuesday we did more work with equations, and Wednesday we reviewed. Maddy (my awesome fellow teacher) had made a list of the topics that would be on the test (study guide for her website, I don’t put one up) and assigned each table one of the items to create a problem on that topic. After we had gone over the homework (That is working SO well. I’m still assigning the problems to the different tables and then a student from the table goes up and presents how they solved the problem, they answer questions from the class, then they “get a clap on 3”. This is another thing I got from Maddy – she does hers on white boards and I used the document camera, but it’s really working well – I think one of the reasons is all of the problems are on different topics so it’s not 12 of the same thing!) I assigned (yes, I’m still on the original sentence) each table one or two of the topics and had them work together to make up a question. Then with about 10 minutes left each table sent up one person to write down their problem in my spiral – and these problems were the homework for the test review. (there were 8).equation-test-review

I collected them on Thursday before the test, after we went over the correct answers. Thursday we had the Equations Unit Test, and today we are going to go over the homework (Wednesday’s since I hadn’t planned on the Awesome Review Homework), then play MATHO (yep, Bingo but to get the number they have to do a math problem-the link is for the book). The book is cool because it has a bunch of games with the problems already made, and the problem number is the answer.

Math 7 Accelerated – We decided to give the Math 7 Accelerated Benchmark to our classes even though we are using supplemental material (CPM). There were 3 questions we changed because they were on inequalities which we haven’t done yet. So, we worked on chapter 3 – completing tables, drawing graphs, finding the equations for the tables for Monday and Tuesday, then reviewed on Wednesday. We talked about a few things that they hadn’t done but could figure out – consecutive integers, how to write an inequality from a situation (which I’m pretty sure they did in 6th grade) such as “you must be at least 16 years old to get your drivers license” and a few other things, then I put up the list of topics and assigned each group a topic. They had about 4 minutes to work in their groups, then they read the question aloud and I wrote them down (we didn’t have as much time as Math 7CP did) and these questions were their homework. Number 5 below is 1) not a good question because it doesn’t work out to whole cookies, so that group didn’t do the problem and 2) has shown to be really hard for the kids because my TA is checking their problems and they’re not doing it correctly. So, we’ll be doing a lot more of these problems!

benchmark-review

Thursday they did a short performance task and started the Benchmark (most of them) and today they finished the Benchmark and worked on a KenKen (did you know you can subscribe to KenKen and get puzzles emailed to you each week? They had a choice of a “no-op 7×7 puzzle” or “twist 6×6 puzzle”) or a HUGE dot to dot puzzle.

I’m definitely looking forward to next week – even though I have a lot of tests and work to grade! Happy Thanksgiving!

 

Posted in Equations, Review | Leave a comment

Days 53 – 57, November 7-11

I was absent the first 2 days of this week – I had a little R & R with my friends in Puerto Vallarta. The only problem with leaving school is preparing! I was working until 9:20 on Friday grading all the tests and quiz corrections but at least I didn’t need to do anything when I returned. I had forgotten to write my blog for that week though! It did get written though 🙂

Algebra CP – We had started rewriting equations, solving for a specific variable. We finished the lesson on Monday, then had a review sheet with more examples on Tuesday. I could tell on Wednesday that the review sheet was really worthwhile. On Wednesday we did a summary of solving equations – the kids were at the large white boards and I would put up a variety of equations for them to solve – they worked in pairs taking turns being the solver and helper. I think some of the helpers were really talkers with other helpers, but overall it was good. We did a few more Absolute Value Equations, then at the end of class I had them all write up “How to solve |4x – 3| = 12 for a person that had never seen an absolute value equation before, include WHY there are 2 solutions!” I told them I would like it on Thursday, but if they had a lot to do they could turn it in on Monday. I don’t have all of them in yet! One interesting thing I found in both classes is a few kids changed the equation to be  |4x + 3| = 12 instead of writing it twice with the equations being  4x – 3 = 12 and  4x – 3 = -12. I’m glad I gave this assignment so I could find this misconception.  Thursday we did a review of multiplying monomials and binomials, some kids used the generic rectangle and some are doing the distributive property twice. NO ONE is doing FOIL!

Math 7CP – While I was gone the class worked on the distributive property and combining like terms, and took a quiz on Tuesday. There are still issues with multiplying and dividing mixed numbers. Some of the kids want to multiply the whole numbers, multiply the fractions, then add the 2 answers together – so we’ve been doing MORE examples. I changed the fractions to decimals and tried to point out that they’d be just multiplying the “ones” and the “tens” if they did it the same way they were doing the fractions – maybe that clicked for some? I’ve also put problems on the homework that ask “what is the first step” in doing the problem (rewrite as a mixed number) and “what is the next step” (simplify!! if it’s multiplication) to hopefully help. We’ll also keep putting them on the quizzes and tests! Wednesday I had the class do quiz corrections – I had circled errors but didn’t put the score on the quiz so I could add back points for corrections. I discussed how to solve the mixed number problems, then gave another one for them to do to get credit for them. Some kids still aren’t simplifying first, so I’m going to put larger denominators on the test. I know they need to see WHY it’s beneficial for them to simplify first, I just though they would by now! Wednesday and Thursday we kept working on equations – writing down the thinking for what they were doing. So in the equation 3x + 8 = 32 I want them to think “what + 8 is 32?” 24! So 3x must equal 24. Now, “what times 3 is 24?” 8! So x = 8. I also what them to think about 4(x-5) =24 as “4 times what is 24?” 6! So x-5 must equal 6. We worked on the large white boards on Thursday solving these problems and writing the thinking.

Math 7 Accelerated – I made a worksheet for the lesson so the kids could more easily finish the problems without me being in class for questions – which they did on Monday. Tuesday I had another worksheet on patterns, they need to draw the 0, 4 and 5 figure, then find the rule, complete the table and graph the pattern. There were 4 patterns to do. On Wednesday we finished the lesson and talked about why it is important that the rule, or equation works for all numbers, you just can’t check it on one of the numbers. Thursday we worked more with patterns – this time the patterns were not linear!

Friday was November 11, Veteran’s Day, so we had no school.

Posted in Equations, Graphing, Large White Boards | 1 Comment

Days 48-52, Oct. 31-Nov. 4

Algebra – We started the week reviewing for a Quiz on Halloween, with no homework (which was appreciated by all of the classes!) and had the quiz on Tuesday. On Wednesday we started using Generic Rectangles to multiply monomials/binomials and binomial/binomials. It went really well – the kids combined the like terms without even really thinking about it since they had just been building the rectangles with algebra tiles and were used to seeing the x tiles in 2 places. On Thursday we worked with some basic Absolute Value equations also. I don’t think all of the kids understood why there are 2 problems to solve…yet!  Friday we began “rearranging” equations that have multiple variables…so “solve for t” in the equation d = rt types of equations.

Math 7CP – WooHoo! It’s Menu Math! We started teaching equations using Brad Fulton’s Menu Math Lessons. (This is on TPT, but it’s a free download.) These are wonderful lessons, the kids naturally add up the types of foods and can write an order from the variables so easily. The only issue we’re working on is when we “take away” more than one item. They’re fine when it says (2c + h + x) – c, but when it’s (2c + h + x) – (c + x) they aren’t subtracting the x (which is an extra large drink!). We’ll keep working on that. Go download that lesson! On Friday I gave them the “order” and they made up the “situation”.

Math 7 Accelerated – We started the week finishing the chapter and reviewing for a quiz on Halloween (sounds so familiar!). We had our Group Quiz on Tuesday, and the Individual Chapter 2 Test on Friday. Wednesday we started Chapter 3, which is extending patterns and finding rules. We did more of this on Thursday, using tables, graphs and rules to make predictions of what would happen next. I really like how CPM introduces their patterns – they start with words and shapes, then go to numbers.

Posted in Equations, White Boards | 1 Comment

Days 43-47, October 24 – 28

Algebra  – We started Chapter 2 and have been working with algebra tiles for most of this week. Monday the lesson was on zero and negative exponents – I really liked how CPM has the kids think about the zero exponent. It asks them to write down what they know about x squared/x squared.  Some kids do the “division rule” they figured out, and end up with x to the zero power. Other kids see that it’s the same thing in the numerator and denominator so that simplifies to 1. We talked about if doing both things is correct then x to the zero power must equal 1.  I also expanded out from 2 to the 4th power down to 2 to the zero power – but instead of just writing 2 times 2 times 2 times 2, I put a 1 in front of it:  1(2)(2)(2)(2). So the exponent “4” tell you the number of 2’s to write. Therefore when you get to 2 to the zero power, you write the 1 and no 2’s!  I said Math People are Efficient (lazy lol) so we don’t want to write the “1” each time in front of the expansion, but if we did then it is easy to see why anything to the zero power is 1.

With the algebra tiles we solved equations using an equation mat so we could see it visually and then also wrote the equations algebraically so we could see how the “legal moves” of moving the algebra tiles compared to the written expressions. All of this was getting us to exploring the Area Model and multiplying binomials to create an area model. It was challenging and fun today  – challenging for me to not get frustrated when some kids want to do the minimum… but it all worked out.

Math 7CP – This has been an interesting week. Monday we had a Team Quiz to get ready for our Unit Test, which was Wednesday. Before we started I had the kids do the 100 Number Challenge, which promotes working together as a team.

I took pictures of all of the teams and they’re up at the front of the room to “show” what team work looks like – everyone participating, everyone engaged, helping each other.  (We talked about them on Tuesday before I hung them up – all of the other classes asked why THEIR pictures weren’t up!) So then on the Team Quiz I heard a couple of groups saying “okay, let’s each do one problem.” Later, when I thought about it I realized that technically, this is team work, they were going to share their answers, but when we have a Team Quiz we make the problems harder, so they need to work together and help each other do the problems. Apparently the 100 Number Challenge was one thing, and working on a Team Quiz was another on “how they did it”. So I had them take them home to finish….and they’re not good. On Tuesday I collected them and then we did all of the problems together in class and reviewed a little more for our Rational Numbers Unit Test.  The test wasn’t great either.  On the quiz I had highlighted all of the errors, and the kids could work together and do corrections (on a separate page, showing all the work) and improve their quiz grade.  I really don’t know if this helped – I know it helped that grade, but the test had the same mistakes. Huge problems with fractions and integers – which was the main part of the test. Today I’m going to do some fraction multiplication and division using rectangles with them – which could be either a disaster or helpful. Something has to help!  I’m passing back the tests today too…. at the end of the period I think. I don’t want to spend a lot of time correcting in class. I want to just keep teaching these concepts and then do a retake in a couple of weeks.

Thursday was fun because we worked on Balance Puzzles after we went over the homework. This time I assigned certain homework problems to a table and they had to go over them together, then decide who was going to come up and present their problem to the class, on the doc camera. It worked really well! If they were wrong other students raised their hand (I was sitting with the class) and I just said “someone has a question” and the other student would explain what was wrong and it got fixed. After each person we did one clap (a la Andrew Stadel). Here are the Balance Puzzle sample pages I have.balance-puzzles-and-more. They are from SolveMe Puzzles – and there is super fun app for your phones from the same place with fun balance puzzles and more on it!

Math 7 Accelerated  – They’ve also been working all week with algebra tiles and equation mats – in much more detail than the algebra kids. We’ve compared expressions, simplified and recorded the work, and solved equations.  There are 3 “legal moves” that can be used to remove the tiles from the mats to simplify or solve the problems: 1) remove “zero pairs” from one of the sections = combining like terms when doing the problem algebraically. 2) moving tiles from the “opposite” (negative) section to the positive section – the tiles need to be flipped over when they move from one section to the top/bottom. So if you had x + 3 in the “opposite” section, and moved it to the positive section you’d flip them over, and they’d become -x – 3 in the positive section. This is the same as distributing the negative algebraically. For example: -(x + 3) = -x – 3.  3) Taking the same tile away from 2 related sections. If there is an x-tile in the positive section and an x-tile in the opposite section (on the same side – left or right – you can’t go “across the equal sign” on the mat) you can remove them both, because x and the opposite of x is zero.  You can also remove two tiles that are the same in corresponding sections across the “equal sign” on the mat – so if you have 3 unit tiles in the positive section on both the left and right sides of the mat you can take them both off. Algebraically it’s combining like terms if they’re on the same side of the mat (left or right) and removing the same amount from both sides if they’re in the same section, but on opposite sides of the mat. Some kids want to combine everything in their heads and just write the problem and the answer (that’s a surprise) so while I’m walking around I’m asking them for their answer and just saying “right, wrong, wrong, right” – and telling them to show me their steps. Regardless of the materials some kids want to do the minimum (I can relate).

Today is the closure activity – they have to make up a problem, then on the Activity Page they have to explain the steps as if they were teaching it to a student that hadn’t used algebra tiles before. Then they make up a “test problem” for their student. When they finish, and I see it, they can start their Closure Problems (the chapter review). Which reminds me, we need to finish making the tests for this chapter – a group quiz and individual test!

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Days 38 – 42, October 17-21

Algebra – On Monday we finished the last lesson this chapter – and the kids used Desmos to graph the equations of the lines they’d written, along with domain/range restrictions to make the ‘logos’.

I thought they did a really good job! Tuesday I wasn’t here, Wednesday was a final day of clarification and review, Thursday was the chapter 2 test, and today we started chapter 3, “Simplifying and Solving” with the first section on exponents.  It was interesting because the problems had the kids factoring the exponential expressions so they had what they could simplify out written separately. So the second step was simplifying what they could to 1, then what was left they multiplied across the numerators and denominators.  A lot of them wanted to use the “rules” but this was teaching them WHY the rules work, and what is happening to the parts that are “cancelled”. I will pass back the tests on Monday.

Math 7CP continued working on the Rational Numbers Unit. We did a lot of problems together and in their groups – word problems that involved decimals and fractions. I really tried to have them draw pictures of the problems that involved fraction division.  (pic on left) We had a discussion today about subtracting with mixed numbers. The problem I was using said “the weight of the basket is 58/3 pounds”. I said, “This shouldn’t be written this way, who says 58/3 pounds?” It also had the weight of the fruit as improper fractions. So we changed everything to mixed numbers. Then wrote the problem – which was now a subtraction problem with mixed numbers. I asked “Who now wants to change everything back to improper fractions?” and several hands went up. After not shooting myself, I went up to the front of the class and had a big talk with them about how this is SO MUCH HARDER than just subtracting the whole numbers and subtracting the fractions (it wasn’t borrowing, thankfully – another topic). I asked them if they go to the store with a $5 bill and ask the cashier to change it all to nickels because they’re going to buy something for $1.25. I told them that I knew teachers taught them to do it the improper fraction way, because it would always work, but it was SO MUCH HARDER,and they could do it with mixed numbers. So we did the problem together. We all lived!

When I was gone on Tuesday they did “fraction squares”. I gave them a fraction and they had to represent it in a drawing (I’m irritated with myself that I forgot to have mixed numbers and improper fractions in it), on a number line, as a ratio written 3 ways, as a percent, decimal and then as 3 equivalent fractions. I had the first example drawing as a circle. One of my fractions was 1/6. When I came back I was checking their fraction squares and a few kids had drawn a circle, and made 5 vertical lines in it and colored in one section. Which was not the same size as the other sections! I asked the kids why they’d done it this way and they said, “The sub said we had to draw it as a circle.” I’m sure she didn’t notice that they’d drawn the lines like that! And interesting to know that some of the kids don’t understand that the pieces need to be the same size!  We’re having a group quiz on Monday, so I’ll see how much they know then.

Math 7 Accelerated – We started Chapter 2 in our supplelegal-movesmentary text, which is on expressions and equations, using algebra tiles. On Tuesday one of the problems had them writing the perimeter of a complex shape made with algebra tiles. We went over it again on Wednesday because they weren’t labeling all of the little sides, so were doing it wrong. Wednesday and Thursday we used Expression Mats and the algebra tiles and they were building them and simplifying them. Today we learned the “legal moves” that can be used to simplify the expressions, and used the Expression Comparison Mat to simplify then compare the expressions. We also wrote what was happening algebraically. It was confusing to some at first, but I think by the end everyone was doing it correctly.

Posted in Equations, Fractions, Graphing, Groupwork | 2 Comments