Linear Equation Sorting Update

On Sunday, I posted my plan for a set of cards that I wanted my students to sort. We started sorting them yesterday. I gave each group about 5 minutes to sort the cards. I asked them at that point to share out their strategies. They continued sorting until at least a few groups were finished. Most teams started with 5 groups, not 4 as I'd expected. They separated the equations by form and then separated the graphs by positive or negative slope. A few groups sorted by y-intercept (where they could decipher one). Only one group actually started down the path they eventually needed to be on. I interrupted to tell them that I actually needed 6 equal groups of cards. With that direction, about 2/3 of the groups figured out what to do, even if they had some trouble with how to accomplish it. I still had several groups in the proverbial woods, though. I asked, "I wanted six groups. Do you have six of anything?" Each time, I got a version of, "Oh, there are six graphs!" Sorting took off quickly then. It took quite some time for the groups to sort the cards into the six groups. I'm glad that I included both positive and negative 3/2 as a slope because I was able to catch some misconceptions there. It also helped that repeated a y-intercept for the same reason.

Once the students had six groups each containing one graph and its equation in three forms, I challenged them to match the numbers in the point-slope form (which they hadn't learned yet) to the features of the graph.  They figured out the slope quickly and were likely aided by how many of the slopes were fractions.  I was happy to hear many of them explain that they knew which number was the slope because they knew they would distribute the number outside the parentheses to the x, which would make it the slope in slope-intercept form.  The "point" of "point-slope" form was an enigma.  I pushed them for 20-30 minutes.  My first class didn't quite get there.  One boy saw it, explained it to me and his group, and then got picked up early.  His explanation got completely lost in translation because his group member tried to explain it to the class and even had me confused as to what he was trying to communicate.   I ended up giving it away to this class.  I wish I'd had a few more minutes to push them to list ordered pairs to make the connection.  The second class went better because I saw how a few of my lines of questioning didn't work and how others worked well.  I had over half of the class get the meaning of the point without me giving it away and I was able to get those students to clearly explain it to their classmates. 

The reason I wrote this post was to remind myself that being less helpful is hard, but good.  The students were having incredibly good, productive discussions today, using their vocabulary and their reasoning to work on what was a challenging but possible task.  We spent a full hour in groups having these discussions and sorting the cards.  I was aiming to be done this part in about 15 minutes, but my students' engagement convinced me to hang in there until they had gotten all the way through, even though it look longer than I had anticipated.  The first group to whine, "We can't get this!" was actually the first group to fully understand and articulate the meaning of point-slope form.  Now, will they remember how their perseverance paid off?  I hope so! 

How do you scaffold exploration activities with questioning so that students are successful?

Mathematically yours,
Miss B

Matching Three Forms of Linear Functions

My students have worked on slope-intercept form and standard form in Algebra.  I want them to also learn point-slope form. 
I'm trying to avoid making that into a direct instruction lesson, and I am going to use these cards to help students make some observations about point-slope form.
I'm planning to give pairs students this stack of cards and have them sort them into meaningful piles.  I suspect they might start by sorting the graphs into one pile, the slope-intercept form into another, etc.  I'll then suggest they try to make 6 piles so that they try to match the graphs to the functions. 
Once students have the six piles, I'll ask them to explain why they put each pile together. I'll ask what the numbers in point-slope form represent. And we'll go from there. This feels like something Cindy Johnson (the Conic Card Lady) would do; I hope I'm keeping with the spirit of her activity.


*The graphs are taken from a Math-aids.com worksheet and I just added the forms of equations below.  What's your favorite card sorting activity? Mathematically yours, Miss B

Integer Rules

Noticing how my students struggle with their integer operations, I put together these simple posters. Hopefully, they'll serve as enough reminder for some of my students who are almost to proficiency. How do you address integers in the later grades? Mathematically yours, Miss B

Vertical Number Line

I should have been typing up lesson plans.  That's boring.

Instead, I read Sarah's blog post about using vertical number lines.  My students this year are worse than ever at integers.  Ugh.  How does that keep happening?  I suppose this group's problem might be from elementary school because they're also having trouble with 8x3 and 12-7.  Anyway, rather than complain, let's give them tools to get past the hurdle.  Sarah's individual number lines are a good start.  She mentioned in her post that she wanted a wall version.  I've gotten quite adept at MS Word tables lately, so I made one.

Enjoy.  I think I'm going to make mine neon green. 


EDIT: In a couple of minutes I made a horizontal version too.  If, like me, you ordered a number line only to find out it was discontinued (really?), you might need one of these as well.


EDIT 2: I shouldn't do school stuff late at night. In the first version, I managed to make the vertical number line upside down. It's fixed now. I could really use a proofreader! :)
How do you approach students' misconceptions with integers?

Mathematically yours,
Miss B

A Happy Thought Worth Recording

This morning, my assistant principal did an informal observation in my class at the end of first period.  He walked in around the time I had decided the kids were not really grasping the introduction of negative exponents we'd done.  They had a really hard time seeing a pattern emerging.  I knew their number sense was poor, but I'd underestimated how poor when they had trouble seeing that 32, 16, 8, 4, 2, 1, 1/2, 1/4,... was a sequence of numbers divided by two from one term to the next.   

We were working on whiteboards.  Questions like "write x^-3 with a positive exponent" were mostly successful, but God forbid I give them x^2 • y^-5.  That wasn't flying.  We worked them through step by step, had students explaining their reasoning, etc.  At one point, I told them to stop and erase; we needed to go back because we were lost. 

So, the lesson was tanking.  There was no way the students were ready to be independent and they were reaching or at their frustration point.  Mercifully, we got to the end of class with a few of the easier problems.  I didn't give homework knowing it would just lead to bigger problems. 

You might be wondering why I called this a "happy" thought.  I dismissed the class and let out a disgusted sigh when the kids were all gone.  My AP asked why.  I explained I'm frustrated when they need more time to get a concept than I hoped because it puts me further behind in the unit schedule that I didn't establish but must adhere to.  He reminded me, "But your instruction was good."  I knew this logically but I hate that I'm going to have to finish this unit in a week and I'm roughly a week behind.  Still feeling bummed, I checked my mailbox 15 minutes later to find a personal note thanking me for the lesson and telling me negative exponents aren't so scary anymore.  The write-up was complimentary.  And when I saw my AP tonight, he told me that he was glad that's how he'd started his day. 

This was a happy thought because my AP helped me feel good about my teaching in spite of the results in the moment.  He pointed out that I was using good strategies.  If I remember this as a "not yet" moment, I can be happy with it. 

In writing this up, I've decided that tomorrow I'll have the students make additional charts on powers of 3 and 4 like we did for powers of 2.  That should help them solidify the pattern.  Then I'll tell my story of happy positive exponents and sad negative exponents.  And I'll use this cartoon to seal the deal. 

What made you happy today?

Mathematically yours,
Miss B

Back to Back

Today was a busy review day for my Algebra I class before their first quiz tomorrow.  We started with "Problem Master" which is really my name for Kate Nowak's speed dating.  I can't use that name in middle school!  They had great success with the structure on the first time.  In one class, it was an absolute God-send because I was able to sit with a student who had missed the last two days and get her caught up on the lessons she'd missed in just a few short moments.  This time, students had to write the equation for a linear function.  The cards I used are linked in this post. 

Later in class, we did a "Back to Back" activity that I took from MissCalcul8.  Except, her activity is for finding midpoint.  Lucky for me, I could just swap out the directions and use everything else as-is.  I had the students either rearrange desks or sit on the floor back to back while they were solving so they couldn't see their partner's solution until they were done the question.  It was a fun structure that I'll use again. It was also the first time I got to use the clipboards from my redditgifts Santa.  Thanks mystery donor! 

What are your favorite review activities?

Mathematically yours,
Miss B

Two weeks down!

How is it possible that I've already been in school for two weeks?  I am not really sure, but I know that time is passing by at a rapid speed.  I have a few things that have changed this year. 

1. I moved to a different classroom.  The new room is many times superior to the old room.  My school was originally open concept with large areas for 4 classes that have since been divided with metal walls.  Two interior classrooms are on the hallway with no natural light and act as a hallway to the exterior classrooms that actually have windows and outside doors. I moved from a large interior classroom shaped like a trapezoid with no closet to an almost-as-large rectangular classroom with natural light and no one passing through my room.  It's been great so far.  I miss two things about my old room: my amazing next door neighbor who was great to talk to between classes for a moment of sanity after a rough class and being on hall duty so as to get to see all of the students passing by. 
2. I took on the role of grade level team leader.  This means I get to organize our weekly meetings and act as a liaison to the administration.
3. Curriculum.  There will be a year, eventually, when none of the curriculum changes from one year to the next.  I'm on year 7 and that's not happened yet.  I would just like to get better at one curriculum instead of constantly changing what I'm doing.
4. I am buying a house this month.  I saw it and put in a contract the weekend before school started.  I will close at the end of the month.  So, I'm packing boxes every weekend until then! 

On a totally different note, I wanted to say how much I'm enjoying my students this year.  I have confidence it is going to be a great year.  Unfortunately, they've already realized I'm nice.  Crud.  Can't I have them fooled just a little bit longer?

I assigned my students the “Numbers About Me” project that I first heard of from Sarah at Everybody is a Genius. This is my second year giving the project and I feel like my students’ creativity came out much more this year.  Last year, I got a lot of “my birthday is…” and “my soccer jersey number is…” but this year the kids have stepped up the game and gotten creative, some actually doing math to figure out facts. 

Here are some of the clever ideas I’ve seen:

·      BMI

·      Name ranking based on Social Security information

·      Birth weigh

·      Height as a portion of a mile instead of feet and inches

·      Ethnic heritage

·      Food consumption (“I once ate 5.5 tacos” or “I usually eat 3/8 of a pizza.”)

·      Fraction of the population (“I am 1/x of the people to live in our town.”)

·      Age in decades instead of years

·      Sports stats like batting averages

·      “Once I spent 3 hours straight on FaceTime.”

·      Number of minutes spent in an airplane this summer

·      Miles from home to favorite summer vacation destination

One reason I love this project is that I get to know what students want to tell me about themselves.  If they're not comfortable sharing a certain statistic, they don't have to.  Said differently, I learn what my students value.  Many of them had photos of their siblings on their notebooks; those are students whose family is really important.  I had a student lose a family member the week before school started.  It was heartbreaking to see "There are x people in my family" on that notebook because I know how painful it must have been for the student to write that sentence. Other students focused on their sports stats; I know they're serious about being athletes. 

How do you get to know your students at the beginning of the year?

Mathematically yours,
Miss B