Mean

Showing posts with label Mean. Show all posts
Showing posts with label Mean. 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.

Mean, Median, Mode, as well as Range Notes for Interactive Notebooks

You may convey caught a sneak peek of these notes over finding mean, median, mode, together with make inwards my blog post service well-nigh creating pockets for your interactive notebooks.

When my Algebra i students constitute out that our adjacent unit of measurement was starting out amongst a review of finding mean, median, mode, together with range, they promptly informed me that nosotros didn't remove to review it because they've been learning well-nigh it since the 5th grade.  Given how frequently I convey had students reference these notes, I volition nation that I create recollect they needed the review!



Our notes for mean, median, mode, together with make were placed inwards a nifty pocket.  Some students chose non to brand a steal together with instead stapled the pages together at the overstep together with glued inwards the bottom sheet.  I told them that they could seat them inwards their notebook using whichever method they preferred.


Notes for Finding Mode:


Notes for Finding Median:


Notes for Finding Mean:


I had my students create a Don Steward activeness to conk them thinking well-nigh hateful earlier nosotros started these.  Of course, the puzzle didn't elevate the give-and-take hateful anywhere on it.  You tin read to a greater extent than well-nigh this puzzle here.


Notes for Finding Range:


Files are uploaded 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!  


Saturday, October 28, 2017

Monday Must Reads: Volume 2

It's difficult to believe it's already been a calendar week since my first mass of Mon Must Reads.  Since the final mass was received thence positively, I'm dorsum today amongst mass 2!  The finish of this weblog serial is to highlight some of my favorite weblog in addition to twitter reads that I cry upwards are worth sharing.

  

Last week, I discovered the Pie Says No (@pie_says_no) Twitter account, in addition to it's definitely worth a follow.  The occupation organization human relationship regularly tweets cringe-worthy pie charts (and other information visualizations).  These are perfect for showing students what NOT to do!  Here's my favorite one:


Fawn Nguyen's recent post service near Solving an Equation amongst a Fraction has me thinking a lot near how I desire to construction my solving equations unit of measurement for side past times side year's Algebra 1 class.  I bespeak to focus less on mindlessly manipulating equations in addition to focus to a greater extent than on a conceptual agreement of what equations genuinely mean.

here.  I await frontward to genuinely having my students construct the towers side past times side year!      

Megan Lonsdale tweeted a moving painting of a display she had her students do amongst information from flipping a money in addition to finding the experimental probability of the money landing on heads.  I talked amongst my Algebra 1 students this twelvemonth how experimental probability approaches theoretical probability every bit the unwrap of trials is increased, but I honey how Megan SHOWED this to her students instead of simply telling them.  I peculiarly honey the role of record to demo where the theoretical probability lies in addition to the role of private stickers to stand upwards for experimental probabilities.  Definitely stealing this side past times side year!   Want to run into the poster inward greater detail?  Check out this link.  


Karl Lippa has me really intrigued amongst this tweet about having his students participate inward Opposite Hand Olympics inward Algebra 1.  You MUST click through the link to a higher house to sentry the video of students trying to residual marbles on a textbook.  It looks similar thence much fun!  The screenshot I'm posting below simply doesn't capture the awesomeness of the entire video.    


Teach180 tweets!  I honey this punch carte du jour activity that she created for trigonometric equations.  I've used punch cards i time before, in addition to they worked well.  I bespeak this reminder to seat punch carte du jour activities into my normal pedagogy rotation. 


    
I likewise honey Sarah Newton's role of a Venn Diagram to practise polynomial vocabulary!  My Algebra 1 students convey been struggling a chip amongst Venn Diagrams inward our probability unit, thence I cry upwards that incorporating them before inward the twelvemonth would live on genuinely helpful to them.


I don't learn geometry, but Kerri Sustich's Circumference or Area? activity that she posted on Twitter definitely caught my eye.  So often, nosotros practise all of i type of occupation thence all of some other type of problem.  This activity gets students thinking near 2 types of problems at the same time.  I tin transportation away definitely run into applying this same practise construction to other math topics!

  

dry erase templates for pedagogy polynomials using the box method!


That's it until side past times side week!  Read whatever "must reads" lately?  Share them inward the comments!

Monday Must Reads: Volume 5

It seems similar it was simply yesterday that I decided to laid about Mon Must Reads every bit a weekly characteristic to highlight the awesomeness I run across daily through the blogs I read as well as the inspiring teachers I follow on Twitter.


Rick Barlow's tweet caught my oculus non because of what the pupil had written on the board but because of the poster hanging higher upward the dry out erase board. I intend this poster belongs inward every math classroom.  This is definitely on my listing of posters to exercise for my classroom for adjacent year.


set of dry out erase pockets, yous demand to exercise as well as then now! Check out this awesomeness:






most recent number of Mon Must Reads, I featured a visual representation for solving equations.  I wondered how it powerfulness piece of work alongside equations that accept variables on both sides.  Yah Lee answered my inquiry alongside a visual model that does simply that!  I've played or as well as then alongside it, as well as I similar it.  The alone affair I can't figure out how to exercise at in 1 trial is illustrate an equation that involves subtraction 1 one side of the equal sign as well as add-on on the other side.


I was outset introduced to Conway's Rational Tangles occupation through a summertime immersion programme hosted past times the Tulsa Math Teachers' Circle.   interactive notebook pages for angles formed past times secants as well as tangents.  I dearest how she encouraged her particular students to hold out 2 small-scale pieces of newspaper to improve visualize the arcs as well as angles.  I intend this is a strategy that all students could exercise goodness from!

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Image Source: 
I also dearest the vinyl ornamentation she created for her mug!


Maths teachers inward the U.K. accept been honouring the belatedly Malcolm Swan's contributions to maths pedagogy past times using his resources inward their classrooms on #malcolmswanday.  Pip Mathematics shared a dandy Swan chore that I await forrad to incorporating when my Algebra 1 students tackle evaluating expressions inward the fall.




Theressa Engel shared students' results to a problem-solving chore I would dearest to endeavour out alongside my ain students: exercise the longest chain possible from a unmarried canvass of paper.  I'm thinking this would brand a dandy outset calendar week of schoolhouse activity!  


Sam Shah late shared a brilliant introduction to the unit of measurement circle inward trigonometry using every shape but a circle!  

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Image Source: https://samjshah.com/2017/05/25/an-prelude-to-unit-circle-trigonometry/

Susan Russo took the traditional spaghetti activity for graphing sine as well as cosine curves a laid upward further past times hanging them side-by-side to exercise a beautifully long graph. 


Andrew Jensen shared a vivid geometry chore regarding wasted packaging space.  




Until adjacent time, proceed sharing!