# Indirect Measurement #mtbos #made4math Monday!

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In reading Building Thinking Classrooms and considering how to defront my classroom, I’ve found I need to purge lots of stuff! Getting ready for year 27, well, that means I’ve got a lot of stuff!

Several shoe boxes, most labeled correctly with what they contain, but a few are in disarray. I have run across many items from early years of having little to no money to spend, but I have always said, these are the times you are most resourceful and creative.

I always said Geomtey was a favorite to teach because there are so many hands on tasks you can implement. I feel like this task likely came from a lesson in Discovering Geometry, Michael Serra.

I remember using one with a protractor attached in later lessons. And also having a mirror students placed on the ground to sight the top of their object to measure, and then shadows… we would use multiple approaches to measure then compare our results.

Even way back when it was obvious to me to allow students a time to reflect. Which tool was easiest, most challenging to use? Within their groups, they would discuss which meathod(s) seemed most accurate.

I always remember during these tasks students struggling with setting up their proportions. Reasong if their answer made sense within the context. It was a great opportunity to allow them to figure out corresponding parts as they would sketch the scenario on their recording sheets.

I loved these measurement tasks, then later using the protractor to make connections back to our previous indirect measurement tools. It gave them prior knowledge to have a foundation as we began a new way to measure with angles.

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Sharing an idea today that reminds me of my Ice Cube Gum container that became my paperclip holder in my teacher bag, an idea I shared on my 3rd #made4math post ever.

I still use it today! And I have another I use to store random dice.

This spring I noticed students with these fancy gum containers.

Empty…..

Are perfect to store card sort, flashcards, matching activity.  Cards are about an 8th of a sheet of standard paper, so smaller than standard index cards.  But one could easily print 8 cards to a page.

I asked students to donate the empty gum containers to their favorite math teacher. And several did.  I actually bought a pack today.  \$1.98 for 35 pieces of gum and a super cool container vs. \$0.96 for 15 pieces in a throw-a-way package.  In my opinion, a no-brainer bargain!

What other ideas for these cute containers?

# Planning for Post-It Note Assessments #made4math

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Let me just say I love Post-It notes.  @druinok questioned me last spring, “Just how many do you go through in a year?” The answer, I have no clue.  I use them once week or so on average, because like anything else, kids can get bored with them.

About 4 years ago, it was my curriculum specialist B.Wade and colleague J.Jessie who introduced me to Post-It note quizzes as a quick exit ticket tool to gauge where students thought they were.

@tbanks1906 blogs about it here as well.

So last year, I was introduced to this site called Pinterest, not sure if you’ve ever heard of it. 🙂  Anyway, I ran across this great reflection tool, 2-minute Assessment Grid,

that I shared here and a follow-up Chalk Talk #makthinkvis activity here.

This issue I ran into this past spring, I didn’t have time to read/reflect on each class’ responses before the next class was filing in.  So, my #made4math for this week… I am laminating full size, color posterboards.  I already color-code my classes, 1st red, 2nd orange, 3rd yellow, 4th green, 5th blue.  I will leave one side of each board blank, but on the other, I will draw out my grid with icons before laminating.

Snipping some reinforced holes at the top so I can hang it on the wall using command hooks. (Thanks @solvingforx for this idea!) Students place their responses on, then I can remove their poster and replace with the next class’ for their responses.  During my planning, I can sit down and review each class separately.  Since, they are poster boards, it will be easy to store between 2 file cabinets or behind a shelf.

I can easily attach other color-coded stickies on the back side to create my Stop-light or any other formative assessment involving post-it notes, and this will allow me to keep each class section separate until I can sit down for some quality time to analyze and reflect.

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

# Happy Birthday #Made4Math !!! Formative Assessmemt Reminder Cards

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First, just let me say a big THANK YOU to @druinok for beginning #made4math and to all of the generous folks who have openingly shared their classroom ideas, lessons, tips over the past year.  I was overwhelmed with how quickly it took off!  Still, today, I am amazed at the generosity of this community.  I have learned so much and my classroom was definitelh impacted by your awesome ideas!

My share for today was initially a result of a convo with @rachelrosales and @druinok, brainstorming ways to organize reminders for the numerous formative assessment techniques…something simple, at your finger tips.

I loved @druinok’s post today and her Student Engagement Flipchart.  Very.Nice.  It will definitely be on my to-do list for a future project.  However, I am choosing to share a similar idea, just a bit different format.  I cut down index cards to fit sports card pages… pack of 10 for \$1.  I am able to display up to 90 of these reminders ranging from formative assessment techniques to various strategies for student engagement, reflection, etc.

Front side of card has title, with some information…

Back side of cards has description, suggestions, reminders…

I have placed the pages in a small 3 ring binder which can easily hold more pages.  Currently, I am trying to include summaries/reminders of techniques I have used or see being easily modified for math class.

Looking forward to learning and sharing more FA techniques with my amazing PLN!!!

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

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Through the years, I’ve seen students struggling trying to remember which Trig Ratio is which.  I have a colleague who draws a big bucket with a toe dipped into the water.  She says she tells the students “Soak-a-Toe” to help them recall SOH-CAH-TOA.  Another has described the “Native American”  SOH-CAH-TOA tribe as the one who constructs their teepees using Right Triangles.  The most entertaining though is the rap from WCHS Math Department “Gettin’ Triggy Wit It” on youtube.

I wanted to use an inquiry activity to help them develop the definitions of the Trig Ratios.  Basically, they constructed 4 similar triangles, found the side measures, then recorded ratios of specific side lengths.  Next, I had them measure the acute angles, then we used the calculator to evaluate the sin, cos and tan for each angle measure.  Students were asked to compare each value to the ratios they had recorded in the table and determine which ratio was closest to their value.  Here’s the file https://www.dropbox.com/s/gfvhnictujfj2ik/similar%20triangles%20intro%20trig.docx?dl=0 Similar Triangles Trig Ratios.  Anyway, its not a perfect lesson, but a starting point.  If you use it, please comment to let me know how you modified it to make it a better learning experience for students.

In the past, students sometimes struggle trying to decide which ratio they need to use when solving a problem. I put together an activity adapted from a strategy called  Mix-Pair-Freeze I’ve used from my KaganCooperative Learning and Geometry book.  This book offers numerous, quality activities for engaging your students.

You can make copies of this file, Trig Ratio Cards File, then cut cards apart to use.

Each student gets a card.  They figure out which Trig Ratio is illustrated on their card (& why).  They mix around the room (with some fun music would make it better), then pair up with someone.  Each person tells which Trig Ratio and why (can be peer assessment, if one is mistaken).  They swap cards, mix and pair with another classmate.  This continues for several minutes, allowing students to pair with several different people.

When I call “Freeze!” Students are to go to a corner of the room which is designated Sin, Cos or Tan.  Within the group in each corner, students double check one-another’s card to determine if they are at the right location.  Again, peer assessment, if someone is wrong, they coach to explain why, then help them determine where they belong.

Students swap cards, mix-pair-freeze again.

I like this activity for several reasons:

• 1. Students are out of their seats and active.
• 2.  Students are talking about math.
• 3.  It allows them to both self-peer assess in a low-stress situation.
• 4.  I can listen to their descriptions and address any misconceptions as a whole-class as a follow-up.

To clarify, the intent of this activity is for students to determine what information they are given in relation to a given angle, then decide which ratio it illustrates. It is meant to help students who struggle deciphering what information is given.

# Writing Equations of Lines – with Some Novetly

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So I picked up some packs of foam number cubes at Mighty Dollar last week.  I sat wondering – what could I do with these?  Finally, during supper one night – an idea came across.  I’d use them to generate coordinates of points and students could write equations of lines.  Hmm.

But as is, all points would fall in Quadrant I.  On half of the dice, I added a negative to 1, 2, 3 and the other half, onto 4, 5, 6.  So, have students roll the dice…thanks to ROY G BIV, we’ll know what order to place them for some consistency.

Students record the coordinates of 3 points.

Directions will be:

1. i. Find the slope between RO & YG.
2. Write an equation of a line that passes through RO & YG in slope-intercept form.
3. Write an equation of a line parallel to ROYG and through the 3rd point IV.
4. Write an equation of a line perpendicular to ROYG and through the point IV.
5. Find the midpoint coordinates.
6. Calculate the distance between RO & YG.

Yes, skill and drill – but with a bit of novelty, hopefully to engage the students a bit more than a black & white worksheet.

I’ve read several posts about activities similar to this – they are not easily assessed.  Students in the group – hold each other accountable.  I prefer same ability grouping – this allows students who are able to move along – while I can spend time with a student who has been absent/struggling to catch them up.  I purposefully walk around the room and spot-check each group to ensure they are on the right track.  If students are recording their coordinates/work/equations – its very easy to take up their work and spot check 2 or 3 sets to ensure correctness.

Sometimes when working in small groups  such as this – I like to have the stop light cups out – If students are okay, the green cup is showing, if they have a question – but can keep on going, the yellow cup and finally, if they need my help – the red cup showing.  I can easily glance around the room for a quick look to see how everyone is doing.

# Linear Equations Card Match #made4math

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Let me first say – I did NOT create this set of cards.  I received them in a session at KCM about 3 years ago.  Kudos to whomever they belong.

I was looking for resources to use during my RTI and ran across a box I had used in the past.

LinearEquationsMatch – the file of the cards.

You can do several different sorts with them.  POINTS-SLOPE, POINTS-EQUATION, GRAPHS-EQUATIONS, etc.

I have each complete set on different colors of cardstock, so I can have several sets out at once, but none of them get shuffled.

# #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.

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.

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

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.

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!

# Made4Math #5 Polynomial Station Activities

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Its been one of those busy weeks, so I’ve not actually created anything “new” but decided to share something I used last spring.  The idea developed after @lmhenry9 tweeted a need for ideas to use with polynomial stations.  A month or so later – I decided to use a similar idea.

I purchased a bag of 8 wooden blocks from Hobby Lobby ~ \$3.  Used my sharpie to add expressions to the blocks.  Created instruction cards for each station.  Based on a pre-assessment, I grouped kids by similar struggles – those who were a step ahead could “play” more game-like activites – while I could spend time with groups who needed some extra support.  We spent a couple of days in class rotating activities.  I think most pictures are self explanatory.

1.  Collecting Like Terms

2.  Adding / Subtracting Polynomials* – let students know which “color” block is the first polynomial.  For a little discussion, ask if it really matters?  If so, when/why?

3.  Multiply Monomial x Polynomial

4.  Binomial x Binomial

5.  Factor Match – I didn’t have orginal copies with me to scan – but will get them posted here asap.

I also had a station utilzing a Tarsia-style puzzle with variety of polynomial multiplication expressions.

Tic Tac Times – Students pick 2 factos listed at bottom of the page and multiply.  Place game piece on the product.  First player to get 3 or 4 (you pick the rules) in a row, wins!  For more challenge, each player must use one of the factors just used by their opponent.

* A sidebar – while creating my blocks – my daughter asked what I was doing.  I replied – making a game for my students to play.  She asked – can I play it to?  My first instinct was to tell her No – but I bit my tongue.  And then I remembered a problem she had left on my board one day afterschool and my students had asked me what it was… (After school, she and a couple of other “teachers’ kids” hang out in my room and play school.) I realized it was very similar to how she had been adding and subtracting 3 digit numbers in class this year.  So I explained how the x^2 was like her 100’s, x was like the 10’s and the # was just one’s.  She rolled the blocks and did a few problems…I’m thinking – if a 2nd grader can do it – so can 9th graders, right?

So I went in the next day – and shared “her lesson” with the class.    I gave an example like the one above – referring back to the problem they had seen on my board.  They understood the process of decomposing the numbers to add/subtract.  I connected the example to (3x^2+4x+2)+(2x^2+3x+5) to get (5x^2+7x+7) – good to go.  Then I asked, WHAT IF we let x = 10…  you know – not one student missed these problems again…