Sunday, November 5, 2017

Organizing my Desk Drawer

I'm non certain just why, just a lot of my spider web log readers appear to acquire the impression that I'm super-organized.  I'm nearly definitely not.  (Though, I am trying to give-up the ghost to a greater extent than organized!)  

Here's a prime number representative of my disorganization.  Behold, my desk drawer!  


And, this moving-picture present was taken alone a span of weeks later I had done a consummate overhaul/re-organization of this drawer.

I don't know if you lot tin say or not, just at that spot are desk organizers inwards this drawer.  Obviously, they weren't working.  I had to a greater extent than materials than would correspond inwards the organizer.  Thus, the organizer was alone taking upwards space.


One of the things I learned from reading The House that Cleans Itself by Mindy Starns Clark (affiliate link) is that I demand to create systems that function for me instead of systems that are equally good difficult for me to maintain.  I honey that I tin apply these same principles to assistance me give-up the ghost along both my identify as well as my classroom clean!

I ended upwards ordering roughly render baskets from the Achieva brand (affiliate link).


Here are (affiliate) links to the baskets I used for my desk drawer make-over.


I honey that these baskets are withal height.  This allowed me to construct a modular pattern of organizers to accept upwards equally much of my drawer infinite equally possible.

And, here's the finished product:


Now when I opened upwards my drawer, it's super slow to position materials dorsum where it belongs.  This agency my desk stays corking as well as tidy.

Another perk of this system?  I tin describe out my handbasket of pretty pens as well as railroad train it on my desk when working on my interactive notebook pages.  Then, when I'm done, the handbasket slides correct dorsum into my desk drawer.




Step-by-Step Directions for Factoring Polynomials Using the Box Method

When I posted my interactive notebook pages for our Algebra 1 unit of measurement on Polynomials, I said that I was going to post service step-by-step photographs of how to role the box method to constituent polynomials.  Here's that post.  

Begin past times drawing a box.  Quadratic trinomials require a 2 x 2 box for factoring.  This box volition besides run for divergence of squares factoring.  


ALWAYS cheque to come across if y'all tin constituent out a GCF from the polynomial first.  If y'all can, this goes inwards forepart of the parentheses inwards your answer.  This year, I added a infinite betwixt the equal sign together with the foremost parenthesis to compass students a house to write the GCF.

There isn't a number that divides evenly into 2, 11, together with 5, together with therefore nosotros tin skip this step!


The x squared term is written inwards the overstep left mitt box.  The constant term is written inwards the bottom right mitt box.  Students should live on used to this equally a upshot of lots of multiplying polynomial problems using the box method!


This takes aid of the 2x^2 together with the five from 2x^2 + 11x + 5.  The 11x term tells me that my 2 missing boxes add together to 11x.  I possess got my students depict an arrow together with write this fact adjacent to the arrow.


We know from examining patterns amongst multiplying polynomials that are 2 missing boxes multiply to the exact same value equally the 2 boxes nosotros possess got filled in.

This agency nosotros are looking for 2 price that add together to 11x together with multiply to 10x^2.


Those 2 price are 10x together with 1x.  Write those price inwards the missing boxes.


Now, we're almost done.  We quest to figure out what to lay on the exterior of our boxes to compass us these multiplication results.  I possess got my students get past times picking 2 boxes together with finding the GCF of those 2 boxes.

For example, the GCF of 2x^2 together with 10x is 2x.  So, I tin write 2x on the exterior of those 2 boxes.


Similarly, x is the GCF of 2x^2 together with 1x.


five is the GCF of 10x together with 5.


And, 1 is the GCF of 1x together with 5.


At this point, I instruct my students to ever terminate together with double cheque that their multiplication is correct.  Every i time inwards a while, at that spot volition live on an number amongst positives together with negatives that needs to live on cleared up.

Once everything is double-checked, it's fourth dimension to write the answer.  Since nosotros didn't possess got a GCF to constituent out at the beginning, nosotros don't quest to worry almost putting a value inwards forepart of the parentheses.  The price from the side of the box (2x together with +1) learn inwards i laid of parentheses.  The price from the overstep of the box (x and +5) learn inwards the other laid of parentheses.  We possess got successfully factored a quadratic trinomial!


Let's get unopen to other one!


First, nosotros quest to cheque together with come across if nosotros tin constituent out a GCF.  10, 80, together with seventy are all divisible past times 10.


When I separate all 3 price past times 10, I am left amongst x^2 + 8x + vii to factor.


I'm going to learn ahead together with possess got the 10 I factored out together with lay it inwards forepart of the parentheses for my end answer.


My x^2 term goes inwards the overstep left square.  My constant of vii goes inwards the bottom right square.


My 2 empty boxes must add together upwards to 8x.


Lots of price add together upwards to 8x, together with therefore I quest to a greater extent than information.  I know that my 2 missing price multiply to the same value equally the 2 given terms.  So, I'm looking for 2 price that add together to 8x together with multiply to 7x^2.


Those 2 price would possess got to live on 7x together with 1x.  So, I write those inwards the missing boxes.


Now, I start looking for the values that learn on the exterior of the boxes.  The GCF of x^2 together with 1x is x.


Similarly, the GCF of x^2 together with 7x is x.


The GCF of 1x together with vii is 1.


And, the GCF of 7x together with vii is 7.


Now, I quest to terminate together with double cheque that all of my multiplication industrial plant out correctly.  If it does, I'm hit to write my end answer.  The 10 is already written exterior my parentheses.  The x and +1 from the overstep of the box learn inwards i laid of parentheses.  The x and +7 from the side of the box learn inwards the other laid of parentheses.


We've finished unopen to other problem!  I possess got i to a greater extent than instance I desire to exhibit you.  I don't learn factoring divergence of squares equally a separate topic.  I brand my students role the exact same box method.  This keeps factoring the divergence of squares from seeming similar a "trick" to memorize.

x^2 - xvi tin live on rewritten equally x^2 + 0x - 16.


There is no GCF to constituent out.  So, I tin write x^2 inwards the overstep left box together with -16 inwards the bottom right box.


The middle 0x term tells me that my 2 missing boxes add together to 0x.  At first, students ALWAYS yell back this is impossible.


The 2 boxes that are given multiply to the same value equally the 2 boxes that are missing.  So, I know I am looking for 2 price that add together to 0x together with multiply to -16x^2.


Those 2 price would live on -4x and +4x.  So, I quest to write those inwards my empty boxes.


x^2 together with -4x possess got a GCF of x.


x^2 together with 4x besides possess got a GCF of x.


The GCF of -4x together with -16 is -4.


Meanwhile, the GCF of x^2 together with 4x is 4.


So, I tin write my respond using the x +4 from the side together with the x -4 from the top.  x^2 - xvi is the same equally (x+4)(x-4).


And, that's the beautiful box method.  I promise this step-by-step explanation has helped clear upwards whatsoever questions y'all mightiness possess got had almost how the box method works.  If y'all withal possess got questions, delight move out them inwards the comments!

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.