Something Old, Something New…

I used to keep a large poster up for our INBs table of contents.  For whatever reason, I got away from that last year and did not even do it last fall with those classes.  However, the poor attendance, numerous snow days have demanded I do it again…  to help students get / stay organized / catch up and for my own sanity!  When they ask…I can point to the poster…

Something new…  I am a believer in literacy strategies.  Students often are not taught how to take notes from what they read.  Most of us vomited highlighter all over our textbooks…  without discerning the needed, important information, we would just learn ALL of it.

So, here is what I did…  Students are 4 to a table, so I cut the review / summary notes into 4 sections.  I asked students to divide their pages into 4 sections with labels.

Each person at the table gets a different section of summary notes / examples.

This was over domain and range of continuous graphs.  With a snow day making a long weekend, I thought it was a great way to review.

1 minute to read.  1 minute to jot down important BIG ideas.

Rotate summary notes.

Repeat.

Some may think 1 minute was not enough time – but since this was a review of last week’s work, I felt it was fine.  If introducing new material, I may feel differently.

After the first round, I observed students writing during the reading time.  I shared my reasoning – the first time was to read – no worries about grabbing information to remember.  The second time was to skim / write big ideas… that way they were accessing the information at least twice.

After every student has read / written for all 4 sections.  They share out 1 BIG idea they wrote down with their table.

I asked for questions, but none.  So, I think next time I will have a post-it available to reflect…  something I learned, realized, was reminded of OR still have a question about…  they tend to ask when its written and anonymous.  I get that.

What summary, literacy, reading strategies do you use in math class?

 

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Function Families & Why’d It Do That?

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.

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.

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.

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. 

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.

Flip Chart Review

This review tool from Math Teacher Mambo

and this formative assessment/student engagement reminder tool form Stat Teacher

inspired a chat with @druinok & @gwaddellnvhs during spring semester and led to this flip chart review for AP Statistics.

Ours started at bottom right corner and worked up, then over to bottom of left hand side.  That seems weird to me now, but I think my initial idea was to build the flipchart as we go along, adding cards after each completed unit.

We ended up creating ours late in spring, just weeks prior to AP Exam.  We will create them in one setting, then go back and add information as we complete units.

This was a tool several of my students stated was beneficial to them.  A couple even went on to say, they closed their eyes to visual the flip chart on the exam – which helped ensure all steps on a test or specific details on a response.  They only wished we had created them earlier.

Start with cardstock folded in half.  Wow. That’s exciting.

We attached 26-28 index cards.  Tape first card at bottom.

Next card is placed up just enough to leave space for Chapter & Title.  If using lined cards, you can turn upside down and used top line to add Chapter & Title.

If using pens, make sure ink  won’t bleed through.

The idea is not to include every single detail – but quick reminders, mnemonics, anything they struggled with on the assessment.  I encouraged them to spend 10 minutes each day leading up to the exam.

I also like how Math Teacher Mambo created a flipped video for students to know important things to include.

If I get them started earlier, I will encourage them to spend 10 minutes reading through 3 or 4 times per week.

This envelope attached to inside of INB back cover is perfect for storing the Review Flip Chart.

Week 2 Sunday Summary #MTBoSchallenge & #made4math

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.

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.

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…

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. 

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. 

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

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?

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.

#5things to Do with Sticky Notes #julychallenge

2-Minute Assessment Grid ideally is for the end of a learning task, but is a great reflection tool used toward the end of an entire unit.  Each student gets 4 sticky notes to respond on for each prompt as seen in the picture.  I like it 3 or 4 days before a unit assessment.  I am able to create a chalk talk with the questions they still have-which allows students an opportunity to respond/learn from one another before I intervene.  Read post here.

12×12 Sticky Notes These were a treasure from our local Mighty Dollar store.  25 large sheets for $1.  Yes, I bought all 10 packs!  I basically cut apart a pre-assessment and tape one question to each giant sticky then distributed them to pairs of students.  They responded to the question, then hung the sticky on the wall.  Students carouseled around…responding they agreed or disagreed with suggestions.  I believe this particular one had 9 stations and I asked that they visit at least 5 or 6 in the alloted time.  We then discussed their responses and arguments as needed. Full post here.

Post-It Note or Stop Light Quiz has been around for several years, post here.  The basic idea is for students to place their name on the back side of the quiz.  They respond on the front side, self-assess to determine their level of understanding/confidence and place it in the corresponding space.  Its a nice visual for me yo scan as they leave the room in determining what’s next the following day.  I have RYG folders for them to drop their papers into when we aren’t using stickies.  Red – needs some help, most of the time these are the students who have been absent.  Yellow – still lacks confidence, maybe a little more practice.  Green -Got it! Ready to move on.

Flip for Answers -I like having sttudents create their own problems.  When they enter class the following day, they can exchange, work each other’s problems, then check.  The sticky can serve as a cover-up for the solution. 

Notice & Wonder The last suggestion came during our ppschat last winter Powerful Problem Solving by Max Ray, his post here.  If you aren’t familar with it, you need to look it up!  His Ignite talk is great too!   With student work displayed, either patterns, data collection, graphs, various models or solution approaches…give each students 2 stickies, preferably 2 colors.  One is for something they notice, the second is something they wonder while viewing other student approaches, etc.  They attach it to the samples.  Continue to visit each station, reading others notice and wonder postings.  This should be a nice springboard for class discussion. 

HW Part 2 #MTBoS30 Post 9

It was a conversation I read on Twitter last night linking this article that got me to thinking…

Where is the balance?  I have students at both ends of the spectrum…those who are college-bound & those who are not; those who have highly involved parents & those who are practically raising themselves; those who are intrinsically motivated & those who are a warm body in my classroom by court order;  those who do not work & those who go to work directly afterschool…not because they want to but because they are helping their family’s income; those who are college/career ready and those in the 15th percentile…all in the same class.

Pretty straight forward indicators of who will and who will not completed lengthy assignments.  Those who are progressing continue to progress, so its up to me to get the content infused during the class period…otherwise, its amiss.

HW/Practice is a small percentage of the overall grades reported.  However, I still see that it makes a huge impact on so many of my struggling students.  I am perfectly fine for students who don’t need it to not do it and master any quiz/test on the concepts.  But if they are able every single time, then do I need to up the level of my assessments?

Students who are not “grade getters” are satisfied with good enough.  This is my struggle.  If I set my mark at 80% and they get 60% or even lower…I require a wrong answer analysis, which gets completed IF I allow time in class, but beyond my 50 minutes…usually not.  They must show proof of practice, some action-tutoring, meeting with me, completing/redoing a previous assignment.  But if they are content with their score…there is little effort to make improvements.

After some in class intervention, I pull them out of elective classes for RTI (because after school tutoring interferes with their work schedule).  Its usually about 50/50…appreciating extra help vs. Mad at you for making them miss their electives.

When I assign HW, I attempt to make it purposeful.  Some may have more skills practice, while others are geared toward contextual problems.  If its skills practice, I choose so many and they choose so many-with suggestions based on their performance on a quick quiz in class. (Ex. If you need more practice like #3…choose from problems 11-15) Self-reflection and student choice. 

Other times, it may be to write a summary or reflection of the discovery activity / small group task of the day.

I attempted to flip using some video lessons provided by out textbook nut that was a flop.  I like the idea, but to me what I was seeing was no more than direct instruction….here copy what I do…Which is appropriate at times, just not all of the time.

There are students who simply copy someone else’s work.  Duh. Seriously.  But I see educators do it to when it comes time to submit a PGP or other documents for program reviews…and those are usually the ones who complain about students not trying/thinking on their own.  Yep. Cheating, how could teenagers do such a thing. 

I attended a session at NCTM Louisville last fall by Samuel Otten @ottensam on twitter.  The focus was on SMP but I had so e great take a ways as pertaining to HW.  Rather than the standard dry check most of us grew up doing…try some reflection.  These will easily fit in the LHP of your INBs:
Which problems were most alike? Different? Why/Explain.
Which problem was easiest? Most difficult? Why?
Give them the answer(s) and let them create the problems.

For me, its key to walk around skimming their responses, carefully select a few to share and sequence them appropriately.  I definitely am a fan of pair-share then share with whole class something you heard (not what you actually wrote) or saw from your partner.

I have even tried a question board…as students enter the room, they list problem #s that gave them some struggle.  Use this to guide our HW discussion.

As HW…assign problem to a student…they must create 2 possible student responses…one with correct reasoning, one not. Post them on chart paper for a carousel activity and students walk around Chalk Talk responding with stars (things they agree with) or  delta (questions they might ask to help student change/improve their response).  Each student gets 3 stars and 3 deltas which means they would visit 6 different responses from other students.

Another favorite assignment which actually serves as a review…
At end of lesson, they create a 3 question quiz to share the following day.  With complete solutions /explanations on back.  This can be modified to use high DOK questioning with a bit of guidance.
Or at the end of a unit, allowing students to compose their own assessment addressing each of the learning targets allows them to revisit various lessons/tasks.

Again, only some ideas of things I have found useful in my classroom…hopefully at least 1 take a way you can tweak for your students.

Give them a box…take it home, redesign/construct a more efficient box. 

Student Reflection on HW

When I get back from a conference, I have the best intentions of sharing, but its nearly 3 weeks later and I am just starting to get caught up…only to realize there are less than 3 weeks of instructional time before Christmas break. 

Starting to stress in my Geometry blocks classes…similarity (although I tied in some with our congruence unit and they used dilations in our transformations unit…) right triangles and circles…then a super dooper quick approach to modeling via 3-d problems.  Anyone have an amazing project that ties circles and right triangles together?  Anyway, a bit off topic, because the stress causes me not to focus.

  I attended a session led by @ottensam sharing different approaches to ensure we are integrating the SMPs in our instruction.  He was very engaging and shared some simple, research-based strategies.

A great idea he shared was to change up the way we approach homework.  One simple suggestion was to ask students to eflect on the problems…which were most alike? Most different?  Why? Which one did you think was easiest? Most difficult, why?  I had students to do a quick write using this idea this past week.  Once they were finished, they had to meet with someone they did not sit next to and share their responses.  Finally, I called on students, asking them to share -not what they had written- but something they had heard. 

I am always amazed at student responses when I use startegies similar to this and could kick myself for not being more intentional, more often.  Several shared exact similar/different pairings but for totally different reasons.  I love it, being able to see and hear their ideas and thinking. 

Purple Circle Card Sort

Last spring, I placed equations of circles after distance between 2 points.  The idea came from a mini-investigation in my Discovering Geometry book (formerly Key Curriculum, now Kendall Hunt). 

Earlier in the semester a new colleague shared the success her students experienced with the Formative Assessment Lesson Equations of Circles 1.  I decided to use this lesson…

In my early geometry class yesterday, we literally stared at circles.  It felt like a wasted class.  No matter what example I referred back to, or what question I asked, it just didn’t work.  Thankfully, I had planning immediately following and I was able to reflect very quickly.  For my last geometry class of the day, I adjusted my sequence of leading examples.  Reviewing our previous work from last week. 

The remainder of the lesson went smoothly.  A quick white-board quiz at the beginning of class today allowed me to address some small errors.  Once again, I had them create their own notes/examples in their INBs.  Yes, a few are still lacking, but the majority are very thorough in what they are including.  Asking questions about specific what-ifs, like one student brought up none of our examples today had a center located at the origin, so I asked the class if they could remind her.  Several went on to include a similar example on their page.

The lesson continued with a collaborative pair.  They were given 12 equations to sort by center and radius.  There were 4 blank blocks in their grid that required them to create their own equations.  At the beginning, some were “cheating” so I stopped them to remind them 1 person picked a card, explained why they were placing it, the other person had to agree and understand before taking their turn.  They are getting better at disagreeing and telling why when their partner is making a mistake.

Their assignment was to create an artistic picture incorporating 5 different circles and listing their equations on the back. Short, sweet, simple.  Can’t wait to see them.

Pythagoras, His Formula and a Teacher Who Didn’t Teach

So a simple lesson today. 

A segment on a grid and asked students to find the length of it. Yep, most sketched in their right triangles and pulled out the Pythagorean Theorem.  But what if we don’t have a grid? How can you find the distance between the two points without graph paper? Or if one of your points is (543, 97)? 

After their sharing, while practicing, some wondered, “Is it okay to use the slope if its in lowest terms?”

Good question.  Does it matter?  What could you do to determine if it matters?

And their suggestion:

…with their finding.  Makes me smile when they answer their own questions.

Best part of lesson today?  Their INB notes.  A post by @justinaion made me wonder how I could be more purposeful in student notes.  Today’s notes…after completing the lesson, students put their whiteboards away, and created their own notes.  Some had step by step instructions.  Others had pictures drawn, paragraphs with a couple of examples.  But in the end, they wrote what was important to them. 

I loved the question a student asked while walking out the room.  “How am I supposed to find the distance with three coordinates in space?”

My response, How are you supposed to find the distance with three coordinates in space?  A smile with an a-ha look on her face…you just…yes, child, you knew how all along.

A day when I didn’t teach a thing but my students left knowing something new (well, except for the kid who sulled up because I wouldn’t TELL them ‘the formula’, use your device) …its been a good day.

Even better, a FB post from a former student-