Category Archives: foldable

Function Families & Why’d It Do That?

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We began our week in Algebra I with Function Families.

This old task… here are the New link to files.

We eventually end up here as a wrap up. Students come to the board and share their sorts.

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The following day we summarize their findings on a foldable…descriptions of the equations and graph shapes from their groups.  The inside of the foldable contains an example of each type of function, table of values and a graph.

I began with quadratic because I see the most mistakes here. Students will use their calculators and jot a number down without pausing to ask if it’s reasonable.  We had 10, -8 and -27 for the first table value.  Hmmm? How’d they get those?  I actually used an entire set of wrong calculations and graphed, then asked, Is that what you expected it to look like?  No. So we need to check our work and find the mistake.

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We completed the first table and they were asked to write about what they noticed in the numbers. And we shared.

Next, we looked at the first differences. They wrote about their noticing again.  “Oh,” a girl says.  “That let’s me see what’s happening in the graph!”

And we finished with the second differences.

I went to the absolute value next.

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One student claimed, it’s doing the same thing as the first but with different numbers. Another student disagreed because the numbers were constant and not changing like the first.  But the directions were the same.  I explained that different operations would cause the graphs to look differently and we were creating a guide to help us sort through the patterns and learn to recognize them.

In both cases, I heard students mention reflection, symmetry, matched – up referring to numbers in table, not the graph.

We continued with linear and the exponential. 

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I began with 4^1 on this table and asked, can I write this 4*1 and it’s still 4?  Yes.  So, 4^2 would be 1*4*4 and 4^3 1*4*4*4.

Which means 4^0 would be 1* (zero 4s)…or just 1.

We had done simple function inverses prior to fall break.  I had used the -1 exponent to represent inverse.  So our discussion went back to 4^-1.  Student ask, “well, if exponents are repeated multiplication, would an inverse exponent be dividing?”  And we continue with that discussion. 

We ended the day with some reflection on our learning.  They were asked to tell which 2 functions were most alike and why.  Which 2 functions were most different and why.  Very eye opening to read some of their thoughts.

At the end of one class, a couple of students we still discussing something.  He shared, “I was wondering what I’d get if I graphed y=x^-1” and he showed me the graph.  Why does it graph that way he asked.  Why does it graph that, I asked him back.

His group mate shared, well, I graphed y=x^-2 and instead of reflecting into the 3rd quadrant, it’s like it reflected across the y-axis.  Why did it do that?  I replied, why do you think it did that? 

I told them both, that was my goal…to let them start asking their own questions…and to keep pondering their graphs, we would talk more about them next week.  It was a good way to end the week.

Week 2 Sunday Summary #MTBoSchallenge & #made4math

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Week 2 is complete.  I am still trying to find my groove with having 1st hour prep.  I am a morning person, so I am ready to interact with students as soon as we arrive.  Sitting down for plan time, I lose my momentum.   Paired with having to be out of our building by 3:00 due to renovations, I have no time to sit and process the day’s events.
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3 Things That Happened This Week
I finally got my anchor chart board with sentence starters and questions completed.  I am very pleased with it and have been trying to model/give students opportunities to practice in class discussions.  Here is a link to a file of the starters.

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I giggled when I saw Sarah saying she “totally stole” from me…that’s what #MTBoS is all about. Sharing and making our classrooms better for our students!

I am using visualpatterns.org as one of my daily tasks to begin class.  I wanted students to have a page in their INBS to record these…

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Here is the file.  Print 2 up and front/back for a booklet for your INBs. 

I shared Thursday how I was a bit hesitant to allow my students to go with their process of locating the midpoint given coordinates of endpoints.  I know.  There are those that say just tell them the midpoint formula.  I could but this is the method they are owning.  Basically, they are finding the distance between the coordinates, then “moving” half the distance will put them at the midpoint. 

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But then I got to thinking about the actual standard:

CCSS.MATH.CONTENT.HSG.GPE.B.6
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Midpoint is the most common and yes, we’ll use it in proofs later.  But if I go in Monday and ask them to find 1/3 point which would be a 1:2 ratio, or a 2/5, 2:3? Will their method actually prove more efficient because it is actually the same process for both?

2 Things on My To-do List
I have 3 tubs that still need to be unpacked from our renovation move.  I have my shoe boxes on the shelves, but I need to get those labeled correctly.

Finish an Intro to Matrices Unit, I hope will work as  flipped/blended learning unit.

1 Good Book to Read
Thanks to @mathymeg07 for sharing Wonder by RJ Palacio. 

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Megan said it is a book everyone from 9-99 should read!  Right now, the Kindle version is on sale for $2.50.  I am making posters of Mr. Browne’s Precepts for my classroom, such great lessons to live by.

Setting Personal Social-emotional Goals pt. 2 #julychallenge Post #17

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This morning as I responded to a commented from @bpagirls on my post about an Essential Questions Board, a thought hit me, so I typed it in my reply so I wouldn’t forget…

… I have just realized as I type, why not add a spot for personal-social goal-setting on my organizer for each student to set, write and reflect.

It stems back to this post and one of the 14 ways to think about good teaching post, 3. Include social-emotional learning goals as well as academic goals.

I got that I needed to do this, but I was not quite sure how to set and record these goals.  My plans are to include a place on the back of our unit organizer students receive at the beginning of each unit.  These are formatted in a booklet style to fit our INBs.  Students can set a personal/social goal to focus on for the duration of the unit. Ideally, following the SMART goal format.  Commit to it by writing it on their organizer.  I will ask to see it, but they may choose whether to share with a peer.  Wouldn’t it be great to have accountability partners for the unit? 

Throughout the unit or even at beginning of class, ask them to read it to themselves.  Maybe even allow someone to share their progress.  Revisit them as we end the unit and write a brief reflection:  How did I do?  Did I meet my goal?  If not, did I at least move toward it? What do I need to modify?  Follow the format: 2 stars and a wish for their quick-write reflection.  Celebrate their progress, maybe through our Shout-Out Board (more on that later).

I realize this type of goal setting may be tough for students… I am hoping after completing this task, it will allow for students to generate ideas.

Initially, I think goals can range from:
Improved / good attendance
Be to class on time
Being prepared for class
Completion of assignments
Asking for help
Asking questions or participating in class discussions.
Attend tutoring if needed
Work in a group with people I don’t know.
Share my ideas in class
Share my assessments and progress with parents/guardian
Choose better practice/study options
Listen to others ideas
Evaluate how my choices are impacting my learning.

Here is a sample of the back of my unit organizer.  I plan to insert personal goals below the unit reflection.  Here is an updated version of a complete unit organizer and student assessment tracker. Feel free to modify for use in your personal classroom. Thanks to Crazy Math Teacher Lady and Math = Love for inspiring through their posts?

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My next task is to locate a fill-in the blank for a SMART to include on the first unit.  Kind of a madlibs style to get us started.

If you have a system in place or use LIM or AVID in your school, I welcome input and suggestions.

INB Unit Organizer

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I wanted to create a unit organizer than encompassed several aspects but would also be narrowed to one page, fiting in to the INB.  Here’s a list of what I wanted:

vocabulary
unit overview/schedule
learning targets
record of assignments
track their own assessments/learning
place to record questions/big ideas
opportunity for end of unit reflection

Here is what I arrived at for a first attempt, copied front to back and folded in half, this is the order students will see the booklet. 

The vocabulary pre-assess was a great tool.  I saw this idea over at Math = Love earlier in the summer.  It went so well. It only took students a couple of minutes to self-assess their vocabulary knowledge.  As I walked around, I was able to see several terms had 3s & 4s.  We compiled a list of our 1s & 2s words.  I explained, as they learned a word or gained better understanding, they should go back and put a +.  Before the end of class, students were asking if they could go ahead and update their chart.

If possible, maybe completemthis part a day before beginning a unit, in order to make needed adjustments based on student responses.

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I included the correlated CCSS # for each target.  Eventually, these may be beneficial when looking online for a resource on a specific standard.

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I am not fully satisfied with this chart yet. Assignments made for specific targets can be listed, a note if completed (stamp) and place to monitor their assessment for each.  A second line has been included in case RTI/enrichment is needed.

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Finally, the back side has a place to record reflection.  Ideally, I would have them complete the reflection at least 2 days prior to unit assessment, allowing to address any needs the following day, prior to assessment.

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As always, this is a work i  progress, suggestions and ideas are welcomed!
PDF:  http://db.tt/DWfJUqLL
Foundations in Geometry doc

Intro to Matrices:

Intro to Matrices pdf
Intro to Matrices doc

Interactive Notebooks

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INBs were introduced to me at TMC12 last summer by Megan Hayes-Golding.  It was consistently the #1 response students stated on their evaluations as something I should continue doing in my classrooms.  They are not bulky, students like the conciseness of the information we place in them, they helped students stay organized. 

Using CWP (color with purpose), foldables, graphic organizers for note-taking allow students to develop skills that can carry over to future coursework. 

By creating assignments that require students to ‘interact’ with information helps them develop connections and retain the knowledge.  Often times, we would complete an inquiry task in-class, then together create a summary of what we saw/learned. By using a variety reflection tools after completing a task, students are able to self-asess any questions that remain and we can address those misconceptions either individually or in-class.

The TOC is imperative.  For teacher accountability 🙂 and it allows students to quickly locate info in their INBs.  One change I plan to make this year, is the addition of tabs as suggested in this post by Mrs. Hester.  The only change I plan to make to her suggestion, is to use the unit title. 

I really like the EOC Review glossary she shared in the post.  I believe using different techniques which allow students to interact with the vocabulary helps students develop deeper understanding of the words.  I appreciate the complete glossary, but do I dedicate several pages at the end of the INB for this?  What are some ways you incorporate literacy/vocabulary into your INBs? 

A KAGAN structure I used often in geometry this year  was Developing Definitions.  Examples/non examples of each term were posted around the room and students would carousel to each, creating their own definitions.  There was a pair-share, then whole class follow up to discuss how they defined terms to ensure we were all on the same page.  After the first time we used this task, students requested that we do it again.  They said by having to come up with the definition on their own, they were able to have a real understanding of the terms.  For a left-hand page assignment, we would often play “Draw What I Say” – another task from KAGAN.  Students would play pictionary of sorts by using a prescribed statement incorporating specific terminology.

I wonder if by having purposeful assignments within each unit of study focusing on specific terminology, then as a review prior to the end of a unit, allow students to complete those entries in the glossary, if this would have greater impact?

Another idea that developed as the year progressed, were pockets.  We began by having one pocket at the front of the INB.  However, a student suggested to have other pockets throughout.  This coming year, my intenions are to have a pocket at the beginning of each unit.  Here is an example of a pocket.  You still have room to place information.  Possibly your essential questions for the unit, a concept map-brainstorm at the beginning, then revisit as a reflection and modify it at the end of a study?

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This pocket is super easy to construct!  One of my favorite things I learned at TMC/Global Math!  Simply fold top left hand corner down on a page.

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Place glue or add tape to the bottom and left edge of that page.

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Flip pocket top to the right and adher to the back of pocket.

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These pockets are much sturdier than I gave them credit to be.

Another idea I plan to develop before the school year begins are unit organizers to attach to the back of the pocket.  I just need to figure out how to modify this

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into a folded-booklet style which also includes a place for students to record their own learning progress.

I am super excited about continuing use of INBs in my classroom and look forward to developing an even larger basket of ideas to make them even better learning tools for my students!

Pam Wilson, NBCT
Currently Reading
5 Practices for Orchestrating Productive Mathematical Discussions, Smith & Stein
Teach Like  a Pirate, Dave Burgess
From Ashes to Honor, Loree Lough

#Made4Math Monday – Parallelogram Foldable

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Its been a while since I’ve sumbitted #made4math Monday post.  I really like the idea of foldables – a kinesthetic graphic organizer…I believe they have a positive impact on student learning when used purposefully.

This one (found here parallelogram foldable) for parallelograms, rectangle, square and rhombus.  I wanted a foldable that somehow showed all were all in the parallelogram family, but still kept them separate – I chose a trifold.

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When I saw an example of the tri-cut Venn Diagram, I knew I wanted to incorporate it somehow to show squares as the overlap of rectangle and rhombus.  This picture does not show the cuts between rectangle/square and square/rhombus, but I think its visible in the last picture.

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The file is simply the skeleton, please feel free to make it your own (ha, just don’t go selling it as your own!)

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I am still debating what should go in the center – thinking of examples / non-examples.   Possibly even giving students a couple of example problems using properties of quadrilaterals.  Istuck area formulas in at the last second – but think it may be more effective to let students discover area of a rhombus on the own.  Suggestions are always welcome!

#made4math Monday! More Kagan, Triangle Center Foldable, Einthoven’s Triangle

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A couple of weeks ago, I shared how much I was enjoying some of Kagan’s strategies!  We’ve been working with triangle congruence this past week.  I am a fan of the sequencing they’ve placed within these lessons.  From recognizing missing information, to stating congruencies, justifying each part.  This is an informal way to introduce the proofs, but each activity leads one step closer.

Today, our activities involved more of the Boss/Secretary and Pairs Check formats.  Tomorrow we are doing Blind Sequencing.  The idea is similar to ones I’ve seen others post – I think @misscalcul8 did some proofs on popsicle sticks back in the summer and I loved that idea!

Color Coded Cards for Proofs

I printed the 4 sets of each “proof” on color-coded card stock…notice, I highlighted/circled problem # in corresponding color.  This way students can come up and exchange a set once they  complete it.

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Students are “forced” to talk about the math – the questions, discussions, (arguments) I’m hearing is wonderful!  They really like Boss/Secretary and even said they have to think about their choice of words – especially when the Secretary (Assistant) writes something completely different than what the Boss had intended.  The praise and coaching aspect is still a bit awkward for a few of them.  The questions they ask one another are so purposeful – they really want to know.  A great opportunity to observe learning / struggles.

Upon completion of the activty, I pop the answers on the overhead – allowing them to double check, a time for discussion, questions, clarifications.  Very interesting to hear students share different approaches to the same problem…and they want to know if its okay… 🙂

Triangle Centers Foldable

As we finished our triangle centers, students asked if I would make them “one of those cool charts” (aka foldable) to help organize all the names/sketches/special characteristics.  Its mostly blank, my first attempt at actually creating a foldable.  I printed it off, made copies and I had my sides reversed, but life goes on and my kiddos were okay with it.  Triangle Centers Foldable I only copied the front side and let them write the names on the inside of the flaps, so they can have “flashcard” style study tool.

Around the Clock

To fill in the center columns – I let them decide what was important.  I used the “Around the Clock” – is that Kagan or another book?  Sorry.  Students have a slip of paper, draw a circle and write in 12, 3, 6 and 9.  I give them 1 minute to go set up appointments with their classmates.  For example, if I made an appointment with Kelly at 3 – she would have my name on her card at 3 and I would have her name on my card.  I had a few stragglers, but it was a quick fix – asking who had an appointment at 6 open.  When they arrived at their appointment, I would write a specific topic, like median/centroid on the board and they were restricted to those topics at that appointment.  I gave them between 2 & 3 minutes to share discuss.  Time.  Move to your ___ appointment.

They loved it, I think.  And once again, they were TALKING about the math!

Cardiology Technician – application of Triangle Centers

While I was searching for some clipart for the foldable, I ran across a text problem from www.nexuslearning.com, about Einthoven’s Triangle for a person’s heart.  I tweaked it a bit, inserted a bigger graph, gave the students a piece of patty paper (how we’ve done the constructions they’ve needed) and assigned it for homework.  In Kentucky, we have program reviews of our accountability model – we must document/show student work samples that we are integrating Practical Living / Career Studies; Arts/Humanities and Writing/Communication…this will definitely be one of my samples for PLCS.

Cardiology Technician – assignment sheet

I left school today feeling successful for the first time this school year.  I know I’ll be back to treading water soon, so I’ll enjoy this small bit of time – smiling, because I loved what I was doing today!