algebra

Showing posts with label algebra. Show all posts
Showing posts with label algebra. Show all posts
Saturday, November 4, 2017

Can You Level the Towers?

Recently, I've been trying to notice a agency to organize many of the amazing resources I've flora online hence I tin role them to a greater extent than easily inwards the future.  Don Steward's blog is an absolute treasure trove of activities as well as interesting problems for whatever mathematics classroom.  A few weeks ago, I went through every unmarried 1 of his weblog posts as well as took greenback of all of the activities that aligned alongside my Algebra 1 standards.  There were Influenza A virus subtype H5N1 LOT of them!  


One of the activities that caught my oculus was called "Equal Sharing."  Students are given a gear upward of towers as well as asked to brand all of the towers possess got the same height.  You must maintain the same issue of towers.  The only affair you lot tin alter is the organization of the blocks.  

I took Don's activeness canvass that featured 10 problems, stuck it inwards a publisher file, enlarged it to fit on 11" x 17" paper, as well as added a championship alongside a cute font.  I printed the puzzle on unopen to 11" x 17" cardstock (affiliate link) that is amazing for creating activities that tin easily locomote worked on past times multiple students at the same time.  It also makes pretty awesome posters!     


Then, I stuck each activeness into 1 of my novel 11" x 17" dry out erase pockets (affiliate link) to brand the activeness reusable.


I allowed students to locomote on this activeness inwards groups of ii or 3.  A few of my students chose to locomote alone.  The bulk of students were inwards pairs.


I didn't give them many details earlier I permit them loose.  I instructed them that their challenge was to rearrange the blocks hence that each tower was the same height.  They had to terminate alongside the same issue of towers that they started with.


Even though I told students earlier nosotros started that they had to terminate upward alongside the same issue of towers that they started with, I silent flora myself answering that enquiry over as well as over as well as over.


It was interesting to sentinel students examine to convince their partners that they had a superior strategy equally I circulated.


Influenza A virus subtype H5N1 few minutes into the activity, I saw students changing upward their strategy.  At the outset of the problems, the students were mark out boxes as well as moving them 1 at a time.  This worked, but students shortly flora it tedious.  Instead, the students started counting all of the boxes inwards all of the towers.


I stopped past times a grouping merely afterwards they reached the determination that in that place were 28 blocks inwards the towers.  With a perplexed hold back on my face, I asked them why that data was useful.  The grouping informed me that because they knew how many towers they needed to terminate upward alongside that they could accept the issue of blocks as well as merely split past times the issue of towers.


I exercise possess got to acknowledge that non all of my groups made this realization.  Some were enough happy to maintain using the same method that worked over as well as over as well as over.

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When my students got to enquiry 6, they began to choke confused.  Really confused.


My students who were rearranging the blocks 1 at a fourth dimension flora themselves left alongside 4 extra blocks as well as 8 towers.  How does that work?


Some groups decided to cutting the 4 blocks inwards one-half as well as distribute 1 one-half block to each tower.  The groups that were adding upward the blocks as well as dividing past times the towers seemed to possess got less problem alongside this problem.  Many groups, however, got frustrated as well as gave upward when the employment didn't locomote out evenly.

After the groups had fourth dimension to effort MOST of the problems, I began a course of written report discussion.  I asked the groups to portion their strategies.  One educatee inwards each course of written report would select upward the fact that they had flora a shortcut.  They hence proceeded to push clitoris how they had added upward all the blocks as well as divided past times the issue of towers.

After they finished explaining, I asked them what mathematical concept matched upward alongside what they had merely done.  It was hence exciting to encounter their eyes lite upward equally they realized they had merely flora the mean!

I promise that my students walked away from this lesson alongside a meliorate agreement of what the hateful is instead of merely knowing the steps to choke far at the mean.

Thanks Don Steward for this awesome activity!

I possess got uploaded my eleven x 17 sized file of Don's activeness here.

Thursday, November 2, 2017

Always, Sometimes, Never amongst Measures of Central Tendency

Recently, I tried out the Always, Sometimes, or Never? exercise construction amongst my Algebra 1 students.  We used this equally a last-minute review earlier our quiz over finding measures of key tendency.  

I gave students this laid of xi problems.  They were allowed to dyad upwardly to function through the problems.  I laid a timer on my telephone for five minutes.  Students worked inwards pairs without whatever aid from me during these five minutes.  


After the timer went off, nosotros went through each problem.  Groups shared their initial thinking, as well as thence the disagreements started!  I dear when my students disagree inwards math degree because it way they are thinking as well as explaining their thinking.

It was awesome to run across students alter their minds equally their immature human being students shared sets of numbers that disproved their hypotheses.

I definitely desire to contain this exercise construction into my classroom on a to a greater extent than regular basis.

One of my twitter friends suggested that I ready 3 sections of the room to signify Always, Sometimes, as well as Never.  Instead of having students but say their answers, they convey to physically movement to stand upwardly inwards the department that represents their thinking.  Then, students percentage their thinking.  Students maintain to percentage their thinking until the degree comes to a consensus as well as is standing inwards the same area.  Doesn't that audio awesome?!?

I've uploaded the file for this activeness here.  The Always, Sometimes, Never statements are non original.  I establish them on page 135 of this PDF.  I volition likely modify the questions earlier using them again.  My students were quite miffed that in that place ended upwardly beingness thence many "Sometimes" equally the right answer!  


Factoring Trinomials Question Stack - Updated alongside GCFs!

I wasn't quite certain what to weblog nigh today, as well as then I started looking through my drafts folder inwards Blogger.  I ran across this post service on a enquiry stack I created for factoring trinomials during Algebra 1's unit of measurement on polynomials.  

I start blogged nigh this activity inwards Nov of 2015.  Here's the link to my master post.  

I generally kept the same questions, but I edited around of the problems to brand my students possess got to ingredient out the GCF first.  

Here are the questions: 



Here are the answers; 


I intentionally added 2 questions amongst a GCF of 2 as well as 2 questions amongst a GCF of x^2.  This meant that students wouldn't survive able to automatically figure out the right reply merely past times identifying the GCF.  

So, how does a enquiry stack work? 

Students are given a double-sided deck of 10 cards.  One side of the bill of fare features a question.  The other side features the reply to a DIFFERENT enquiry  Many people mistakenly assume that the reply printed on the dorsum is the reply to the enquiry on the front.  These may await similar flash cards, but they are definitely non flash cards.    

Students start the activity past times turning over all of the cards to break ALL of the answers.  I say my students this is their reply bank.  

Then, students flip over 1 bill of fare of their choosing.  This volition survive their start occupation to solve.  When students discovery the solution, it should survive inwards the reply banking concern if they possess got done everything correctly.  They option upwards the solution bill of fare as well as flip it over to break the side past times side question. 

I dearest enquiry stacks because they are self-checking.  This way I tin focus my tending on the groups struggling the most.  The reply banking concern gets smaller as well as smaller amongst each enquiry which helps gear upwards pupil confidence.  

Here are around pictures of my students inwards activity spell doing this activity: 









Want to acquire to a greater extent than nigh the box method for factoring polynomials?  I propose that y'all read these 2 posts: Post 1 as well as Post 2.

Printable file to practice this activity is uploaded here.

Wednesday, November 1, 2017

New Timers Thanks to a Generous Donor

Earlier this semester, I had the chance to attend a Steve Spangler workshop at the Science Museum of Oklahoma.  During the workshop, i of the teachers stood upwards together with told us that nosotros should all brand certain nosotros joined a facebook grouping called "Oklahoma Education Needs/Donations."  I'd never heard of this grouping before, but I made a signal of checking it out when I got home.  

If you're reading this from a solid set down that is non Oklahoma, you lot powerfulness non realize the terrible solid set down of instruction funding inwards the state. 

Check out this graphic: 

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Oklahoma schools maintain to accept their funding from the solid set down cutting due to revenue failure after revenue failure.  The coin for basic classroom needs only isn't in that place anymore.  

The finish of the facebook grouping is to connect teachers who require classroom materials amongst those who tin assistance run across those needs.  

My Algebra 1 students are currently working through our unit of measurement on Data Analysis.  We accept been using iii OERB workshop. 


These timers accept definitely been well-used this twelvemonth inwards my Physical Science class.  But, iii timers inwards a cast of twenty some students isn't enough.  

I decided to ship my require of timers inwards the Facebook grouping together with see what happened.  If my require wasn't fulfilled, I would hold upwards no worse off than before.  


Influenza A virus subtype H5N1 yoke of days later, I got a message that a gear upwards of half dozen timers had been purchased together with would before long hold upwards delivered to my school.  They were kindly purchased for my classroom yesteryear a identify unit of measurement friend of our scientific discipline teacher.  

Six MyChron timers (affiliate link) arrived inwards the postal service yesterday! 




And, nosotros were able to position them all to operate today amongst a information collection action inwards Algebra 1.

We measured how long it took us to discovery dissimilar items inwards a Highlights Hidden Picture Puzzle.  Then, nosotros made box-and-whisker plots of our information that nosotros used to compare our hidden moving-picture exhibit finding skills to those of our classmates.





I'll ship to a greater extent than close this action SOON!

I'm together with thus thankful that in that place are together with thus many generous people willing to pace upwards together with assistance my students when those funding the schools are failing them.


Always, Sometimes, or Never? Resources for Math Class

After successfully using Always, Sometimes, or Never? to assistance my students hit a ameliorate conceptual agreement of the measures of fundamental style (link to spider web log post), I began to wonder what other math topics I could utilisation the Always, Sometimes, or Never? construction with.


I spent utilisation of an even out googling for resources.  I idea I should part my findings alongside yous guys equally well.  Have yous used Always, Sometimes, or Never? to review other concepts?  Please piece of job out a comment!

Algebraic Properties


Angles


Miscellaneous


Negatives


Number Sense


Parallel together with Perpendicular Lines


Points, Lines, together with Planes


Quadrilaterals


Rational together with Irrational Numbers


Similarity


Transformations


Trig


Tuesday, October 31, 2017

How good tin you lot approximate thirty seconds?

How good tin sack yous approximate thirty seconds?  This is the inquiry I posed to my Algebra 1 students a duo of weeks agone every bit purpose of our unit of measurement on information analysis.  

My master computer program together with the computer program I carried out during get-go menstruum was to projection an online stopwatch on my SMARTBoard.  


I had all of my students unopen their eyes.  I told them the exact instant that I pressed "Start" on the timer.  Their task was to opened upwards their eyes when they *thought* thirty seconds had passed together with to tape the amount of fourth dimension that genuinely passed.  

This would in all likelihood have got worked only fine if my students hadn't been then excited past times this activity.  One of my students get-go hr opened his eyes, saw that he was at precisely thirty seconds, together with yelled out a scream of glee.  This, of course, caused my other students to opened upwards their eyes together with also orbit near-perfect results.  Not precisely what I was going for!  

For my ii afternoon classes, I pulled out my develop of OERB workshop.  I received an additional 6 timers from a local donor through the OK Education Needs Facebook group.  


Students were instructed to accept turns estimating thirty seconds inward PAIRS.  This took a chip to a greater extent than than twice every bit long every bit doing it every bit an entire class, but the information was then much to a greater extent than accurate!  



One pupil would unopen their eyes together with approximate thirty seconds spell their partner timed how long their approximate genuinely was.  Then, they would switch.  


Here's the information collection shape I gave students to gum inward their interactive notebooks: 


Silly me gave students a box titled "Your Time." In retrospect, this should have got been titled "My Time!"  Earlier inward this unit, I didn't give students a designated infinite to tape their information value.  This led to lots of confusion later on on.  Lesson learned!  


Another alteration I demand to brand for side past times side twelvemonth is to give students a specified house to write the information inward order.  I had to squelch this in, together with it would expect meliorate if it had a box of its own.


Students copied downwards the information from the other students inward their shape every bit I recorded it on the SMARTBoard.  We ended upwards rounding our times to the nearest 2d to brand calculations together with pretty much everything easier!  


After putting our information inward companionship (see above!), I had students abide by the 5 release summary, IQR, together with cheque for outliers.

sixth hr discovered that 49 was an outlier.

For side past times side year, I would add together a inquiry to the bottom that asks if at that spot are whatever outliers.  When my students took this quiz, many of them struggled when I asked them to write a judgement explaining if at that spot were whatever outliers.  I demand to brand certain my students are writing downwards a judgement to justify the presence or absence of outliers each fourth dimension nosotros practice!

On the within of our booklet foldable, students were given infinite to brand a box-and-whisker plot, point plot, stem-and-leaf plot, together with histogram.


See that annoying trouble that the school's re-create machine position through my page?  My students were genuinely really excited virtually it because many of them used it to shape the release trouble for their box-and-whisker plot.  In the future, I volition give students a pre-printed release line.  Then, they volition entirely have got to produce upwards one's heed how to release their release trouble to capture all of the data.  This should relieve a chip of precious shape time!


I would render a pre-printed release trouble for the point plot, too.


I intend I mightiness genuinely have got them brand the point plot on top of the release trouble together with brand the box-and-whisker plot nether the same release line.  I did this amongst a Tenzi (affiliate link) activeness I have got notwithstanding to weblog about, together with it worked pretty well!


Since our information was then unopen together, my students together with I chose to brand a separate stem-and-leaf plot.  Originally, I idea my students would survive genuinely opposed to this alteration of the stem-and-leaf plot, but they popular off along suggesting fourth dimension after fourth dimension that nosotros separate the stems.  Many of them fifty-fifty chose to separate the stems on their quizzes!

Next year, I desire to position some graph newspaper inward the background to aid students trouble upwards their digits.  This volition also ensure that all of the digits goal upwards taking the same amount of space!


Finally, my students made a histogram from our information of estimating thirty seconds.  In the future, I would also position graph newspaper inward the background.  This should aid students brand all of their equivalent towers equivalent heights.

The file for this activeness tin sack survive downloaded here.

Dry Erase Workmat for Finding Five Number Summary, IQR, in addition to Outliers

My Algebra 1 students are inwards the midst of our next-to-last unit of measurement of the year: information analysis.  This is my showtime twelvemonth of teaching Algebra 1 where my students do non conduct keep to conduct keep an end-of-instruction examination inwards Algebra 1.  This way that I don't conduct keep to rush through concepts inwards club to conduct keep plenty fourth dimension to review for a essay inwards Apr fifty-fifty though schoolhouse doesn't exit until May.  Usually, our unit of measurement on information analysis is super-short equally a result.  

This year, I conduct keep plenty of fourth dimension to genuinely prepare my students' science at reading information displays together with creating their ain information displays.  Today, I desire to portion an action I created to give my students do alongside finding the v number summary together with IQR of a laid upward of data.  Students together with therefore used this information to cheque for together with position outliers.  

I started past times creating a workmat template inwards Publisher.  I purpose Publisher to do most all of the resources I postal service on my blog.  



I titled it "Identifying Outliers Practice," but it also gave my students do alongside finding the v number summary together with IQR.  Not certain what I could championship it to include those equally well...


I printed this workmat on 11 x 17 cardstock (affiliate link) that I slid into 1 of my 11 x 17 dry out erase pockets (affiliate link).  I conduct keep a laid upward of smaller, 8.5 x xi dry out erase pockets (affiliate link), too.  But, I prefer the 11 x 17 size (affiliate link) for partner work.      

I also created a laid upward of information value cards (1-36) that jibe just into the information laid upward boxes on the operate mat. 


Each laid upward was cutting apart together with placed inwards a tiny bucket from Dollar Tree. 


These stacked upward real nicely betwixt classes!



Like many activities I create, I ended upward modifying the action throughout the 24-hour interval to improve it together with become far to a greater extent than effective.  Originally, I had planned for each couple of students to curl a 12-sided move past times (from this set of polyhedra dice from EAI Education - affiliate link) to decide how many information values they should delineate from their bucket before starting.   


My idea behind having them curl a move past times was that I wanted them to larn used to how to bargain alongside quartiles when in that location are an fifty-fifty number of values together with an strange number of values.  

But, together with therefore my students were ending upward alongside information sets of 3, together with the information do only wasn't rigorous enough. 


For my afternoon classes, I did away alongside the die together with had each couple of students delineate 12 information values from their buckets.  This ended upward working soooo much better!  


As students worked, I circulated the room together with checked for errors.  In the motion-picture demonstrate above, the IQR should genuinely live 18.5.


As pairs finished, they would heighten their hands to conduct keep their calculations spot-checked.


One of the issues I didn't foresee alongside this action was that the bulk of students did non respect whatsoever outliers inwards their data.


It ended upward beingness okay because afterwards I cheque each pair's work, I would challenge them to do their ain information laid upward that had outliers.


This ended upward beingness the perfect extension activity!


I dear how much collaboration I tin terminate come across alongside my students inwards these pictures!


There are a few changes I would similar to brand inwards the time to come to this activity.


After students delineate their information values together with before they laid about doing whatsoever calculations, I would similar to conduct keep my students brand a prediction re: outliers.


Then, afterwards they complete all of their calculations, I would similar them to write a judgement explaining why or why non the information contains outliers.  My students genuinely struggled alongside writing a judgement to justify their outliers on their quizzes.  Need to start practicing that earlier!  


Additionally, I would similar to do a laid upward of "challenge cards" for students to operate through.  For example, each bill of fare would state them how many cards to select from the bucket.  Students mightiness randomly choice cards, or they mightiness choice specific cards to effort together with orbit a specific thing.


The file for this action has been uploaded here.