Measures of Central Tendency

Showing posts with label Measures of Central Tendency. Show all posts
Showing posts with label Measures of Central Tendency. 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.

Friday, November 3, 2017

Practice Finding Measures of Central Tendency past times Playing Tenzi

Disclosure: This postal service contains affiliate links. 

I dearest a expert die game.  I've blogged earlier near playing Farkle alongside my students.  I don't recall I've ever gotten some to blogging near it, simply my hubby as well as I dearest playing statistics course.  This year, I decided to contain Tenzi (and a variant of the game called Splitzi) into Algebra 1's unit of measurement on Data Analysis.  

So, what is Tenzi?  

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It's a die game that comes inwards a bully tube.  I received my Tenzi game for either Christmas or my birthday.  The subway scheme contains 4 sets of 10 dice.  Each laid of die is a dissimilar coloring to brand them easily differentiated.  This volition allow 4 people to play.  

Tenzi also produces a Party Pack version that volition allow vi people to play at once.  

   

One of the things I dearest most near Farkle, I discovery myself explaining as well as re-explaining as well as re-explaining again.  With Tenzi, my students are ready-to-go afterward a unmarried explanation!    

Every histrion is playing at the same fourth dimension which keeps the game fast-paced.  This agency students don't convey fourth dimension to goof off or acquire distracted!  After i of the players says "Go!" all of the players coil their 10 dice.  The goal of the game is to acquire all of your 10 die to exhibit the same number.  Players examine their die to determine what value to coil for.  Dice showing that value are laid aside.  Dice showing a dissimilar value are re-rolled until all 10 die exhibit the same number.  The firstly histrion to acquire all 10 die showing the same number yells "Tenzi!"  That ends that round.  

Even though the game's rules are super-simple, the game is withal fun as well as quite addictive!  I've played the game alongside groups ranging from my husband's describe of piece of job solid unit of measurement to a grouping of middle-aged women at a Bunco number to my students.  It's e'er sum of fun as well as laughter.  

To spice the game upwards as well as continue you lot on your toes, the makers of Tenzi convey created dissimilar variations of the game.  There is an entire page on their website dedicated to these variations. 

Here are some of them:  (Image Source) 



I decided to run the master copy Tenzi game as well as the Splitzi variant to aid my Algebra 1 students do finding the mean, median, mode, as well as arrive at of a information set.  

To aid them organize their data, I created a sail for them to gum into their interactive notebooks when nosotros were finished.  


To brand the game suitable for information collection, I had my students non solely race to attain Tenzi earlier the other people inwards their group, simply they had to count the number of rolls it took them to attain Tenzi.  Some of my students would acquire as well as therefore caught upwards inwards trying to win that they would forget to count their rolls!  


Students played 8 rounds as well as recorded the number of rolls they required to attain Tenzi each round.


Another alteration I had to brand to Tenzi to acquire far piece of job for information collection was to require every unmarried histrion to continue rolling until Tenzi was reached.  In the actual game, game play ceases afterward soul yells "Tenzi!"


After students finished playing 8 rounds, they had to discovery the mean, median, mode, as well as arrive at of their data.


Of course, my VERY competitive students had to compare their measures of key style alongside i another!


Next, I taught my students the Splitzi variant.  Instead of rolling your die until all 10 exhibit the same value, you lot must coil your die until v of your die exhibit i value as well as the other v of your die exhibit a dissimilar value.


I asked my students to predict if it would live easier or harder to attain Splitzi than Tenzi.  


My students were pretty divide on their opinions near this matter.  Some insisted Splitzi would live easier.  Others insisted it would live much harder.  I told them that nosotros would discovery who was correct past times analyzing our data. 


In the future, I would add together a writing assignment to this activity.  I would convey my students write a hypothesis earlier start to play Splitzi. 


Then, they would demand to write a paragraph describing their findings.  Students would demand to include prove for each finding.  


I won't spoil the fun as well as portion our findings.  You'll convey to play for yourself as well as discovery out!  


After doing this action alongside 3 dissimilar flat periods, I learned a few tricks as well as tips I should in all probability share.  

Put each laid of 10 die inwards a plastic cup.  These cups volition stack as well as rest semi-organized throughout the day.  Students tin forcefulness out run the loving cup to aid them coil their die if they choose.  



For large flat sizes, the audio of the die hitting desks tin forcefulness out live almost deafening.  We played Tenzi at the terminate of i flat catamenia as well as Splitzi at the start of the adjacent flat period.  To continue myself from losing my hear from the audio of the dice, I had my students play Splitzi on the floor. 


I approximate that's why the instructor I did my pupil education alongside vi years agone had foam dice!  

The makers of Tenzi convey created a deck of 77 variations of the game.  I expect forrard to using some of these variations when nosotros start our science on comparison information sets.


I desire to convey my students motion through stations that each characteristic a dissimilar version of the game.  They volition count the number of rolls needed to attain the goal.  Then, I volition convey them house a sticker on a point plot for that version.  This volition allow us easily compare the dissimilar versions of the game.  So excited to come across what nosotros discover!

The file for this Tenzi/Splitzi action is 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!  


Goodies from the Makers of Tenzi

Today I desire to hand a shout-out to the awesome creators of Tenzi!  After I tweeted together with blogged nearly using Tenzi inwards my classroom to exercise finding measures of key tendency, I received an awesome bundle inwards my mailbox.  

Here's what I received: 


Disclosure: Affiliate Links Below

Tenzi Party Pack - I received the original Tenzi set for 4 players for either Christmas or my birthday.  So, this is the perfect add-on to my Tenzi collection.  The political party pack includes die for upward to half dozen players at once.

77 Ways to Play Tenzi -  This deck of cards provides 77 dissimilar ways to play Tenzi.  One of the cracking things nearly Tenzi is that at that spot are SO many ways to play.  I dearest that yous tin role this deck to modify upward the game from circular to round.  Just flip over a novel bill of fare together with follow the directions.  This keeps the game from getting monotonous without requiring the players to come upward up amongst novel ideas during the game.  I fifty-fifty used some of the cards from the deck to innovation my lesson for tomorrow on comparison information displays inwards Algebra 1.

Want a sneak peek at tomorrow's lesson?

Students volition circulate approximately the room together with play 1 circular each of nine dissimilar Tenzi variations.  Students volition tape the reveal of rolls it took them to consummate each variation together with score it higher upward the reveal trouble to create a dot plot.


Once all the information is collected together with dot plots are created, students volition interruption into groups.  Each grouping volition acquire the information canvas from 1 of the variations.  Groups volition notice the 5 reveal summary, IQR, together with banking concern check for outliers.  Then, each grouping volition create a box-and-whisker plot BELOW the reveal line.
Students volition brand predictions nearly the similarities together with differences betwixt the variations earlier nosotros start out collecting data.  Then, students volition write statements comparison the information sets afterward nosotros complete making the box-and-whisker plots.

So excited!

Slapzi - I had never heard of the game Slapzi earlier receiving it inwards the mail.  Given my dearest for Tenzi, I fully expected to dearest this game.  And, it did non disappoint!  My married adult man together with I played the basic version of the game 1 afternoon presently afterward receiving it.  I intend inwards the hereafter we'll play 1 of the to a greater extent than advanced versions to brand things a flake to a greater extent than difficult.

The cracking affair nearly this game is that it's super slowly to learn.  (I audio similar I'm describing Tenzi therefore far...)  Each actor gets 5 double-sided motion painting cards.  You lay your 5 cards out inwards front end of yous amongst the side of your selection facing up.  The stack of description cards is kept inwards the middle of the table.


One actor flips over a description card.  Each actor looks at their motion painting cards to endeavor to notice a motion painting that matches that description.  The get-go actor to "slap" their motion painting bill of fare on the description bill of fare gets to run out that bill of fare inwards the pile.  The destination of the game is to survive the get-go actor to acquire rid of all of their motion painting cards.


The game play is simple, only the contest is fierce!  If the bulk of players concur that the bill of fare yous played does non jibe the category, therefore yous get got to get got dorsum your bill of fare plus an additional penalization card.


I had a span of instances concluding calendar week where therefore many of my students were absent inwards a shape menstruum that nosotros couldn't motion on amongst the planned lesson.  We played Slapzi instead, together with my students LOVED it!


I constantly heard them say things similar "This is fun!  You should allow us play this again!"  Anytime yous tin entertain a teenager amongst something that doesn't need the electrochemical cell inwards their mitt is a winner inwards my book!


All of the classes I used this game amongst had vii or less inwards attendance.  Students played inwards 2 groups.  I gave each grouping one-half of the motion painting cards together with one-half of the description cards.  After a few rounds, the 2 groups would switch motion painting together with description cards to proceed the game fresh.

  

To the makers of Tenzi, give thank yous you therefore much for the bundle of goodies!  My students together with I greatly appreciate them!  Thanks for making cracking games that are perfect for using inwards my classroom!

Wednesday, November 1, 2017

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