Math in Focus: Bar Models with Manipulatives

At my school we use Math in Focus (Singapore Math) program, and with state testing coming up my fourth graders need a lot of review using bar models for problem solving.  This is by far the most challenging chapter (is it just us?).  For those of you who aren't familiar with MIF, one of the earlier fourth grade math word problems might be:

My sister had $8,359, and I had 3,596 less than her.  How much did we have altogether?

Well, my first year I think I was even more scared than they were (at first, since they didn't know better).  Even many adults, at first glance, estimate the answer to nearly $12,000 instead of the actual answer of over $13,000.  Although I'm more familiar with the content now, it's still a struggle for a lot of my students to master the sample problems as they become more complex than this one, and to complete them independently.  Like most programs, Singapore talks about a gradual release of responsibility.  And like most programs, we start with manipulatives before requiring abstract thinking.  Yet there were no manipulatives for bar models; just visuals.  Until now.

All I did was cut strips of paper cut into 2 different sizes.  The yellow paper is a Post It note with the sticky side holding the strips in place.  For my students, "Noun 1" and "Noun 2" were replaced with "Me" and "My sister." 

I told my class to remember these things as we progressed through the chapter:

1.  Bar models are just a tool to make solving math word problems easier; they are not there to make us crazy.  
2.  Bar models are at their most useful in fourth grade problems for helping us keep track of who has the bigger amount, who has the smaller amount, the difference, and the combined total.  

In the above problem, I told my students, "I have some money.  My sister has some more.  Decide where to put the little bar, and where to put the big bar."  Everyone was able to do that, so I told them that in this case, they'd know when it came time to draw the bars and put the bigger number with the right person, they could do it.

Below, I asked them to show me how much we had altogether.  Easy.  Indicate both.  That funny bracket in the book could be indicated with just their fingers.  Again, it totally took away the pressure of "I can't draw that weird mustache thing," (although they love when I draw it because hey, mustaches are cool, haha).

Below, I asked them to cover up all the extra money my sister had so that it looked like we had the same amount.  That covering up was "taking away" the extra. I told them that what I was doing for this sort of question was to subtract.

In the problem below, I told them, "I have some money.  My sister has some more.  Show me how much more."  Those funny brackets they show in the book were indicated with their fingers.  I told them if they were looking for the difference between the two bars, it's a smaller amount than the bigger bar, so they'd know they'd subtract.

The activity was a huge hit.  Notice that no numbers were mentioned today!  It was all about conceptualizing the process using manipulatives.  Kids whose computation is shaky could follow along at the same level as everyone else.  Even those kids who don't like to write were successful.  And an unexpected side effect to using these bars was that when it was time to start drawing them, all but two students had them lined up correctly on the left!  I wanted to go back to do this lesson all over again with my former students from last year who kept drawing the bars right after the words instead of lining them up correctly. next logical step for this lesson is, of course, to use numbers to introduce computation.  I start small (small numbers) and differentiate the numbers used for my class.  There's still minimal writing, and students move the bars around, but this time they also move around the numbers.  We followed up with a fun, free website I describe in this post.  I also created a self correcting bar model activity that you can preview in my store!

Readers, are any of you using Math in Focus/Singapore Math?  Do you have any tips you can share on how to survive chapter 3 with bar models?
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Practicing Long Division with Money

Do you find that the topics that you struggled with the most in school are the ones that you love teaching the most?  That's how I feel about math, and in fourth grade the math topic I remember struggling with the MOST was long division.

I remember when I was a kid, it would take me FOREVER to solve a page of 10 long division problems.  I was one of the last ones done, sitting off to the side to finish up.  I'd stare blankly at 658 divided by 7 and try multiplying every number by 7 in the attempt to get 65.  I felt so frustrated that I had to do all those "extra" math problems and hope that they were right too.

So when it comes time every year to teach my students long division, I've tried lots of ways.  I had them make their own mnemonic devices to remember the steps (similar to the Do My Scissors Cut Bricks type acronym for Divide, Multiply, Subtract, Check, Bring Down).  I've tried partial quotient.  But for me it always comes back to practicing the physical process of dividing.  Base ten blocks are a great way to do it, but my favorite manipulative when it comes to math is money.  There's just something about counting money that makes people happy! 

Previously I described how I introduce the concept of dividing hundred dollar bills, ten dollar bills, and one dollar bills into "wallets" over in this post.  This activity helps get the kids used to the manipulatives involved and has a high success rate; with numbers that are carefully chosen to be evenly divisible (such as 486 divided by 2) the kids are able to compute in their heads before long.  So to up the ante the next day, I give the kids numbers that are not as simple to divide.

In the TOP PHOTO, you can see that the child knew he couldn't divide a hundred dollar bill 4 ways, so he had to regroup it for ten tens.  He was then able to put 2 ten dollar bills in each wallet, and he had 2 ten dollar bills left as a remainder.

Of course this does not complete the problem, but he is learning that 20 is a reasonable answer to 100 divided by 4, which is pretty powerful!  I'm much happier with him knowing this than memorizing DMSCB and not understanding what numbers to compute at each step. 

The child in the MIDDLE PHOTO is working on the same problem.  She also knows that the answer to 100 divided by 4 will be about $20.  However she is developing her understanding of the regrouping process.  She is trading in those 2 ten dollar bills for one dollar bills.  Although she has written a bunch of zeroes in the ones place on her place value mat, she will soon be able to refine her answer to include the ones place. child who completed the problem on the BOTTOM PHOTO has completed the process of dividing 100 by 4.  She is also able to accurately record the steps she has taken to arrive at an answer.  She regrouped the one hundred to become ten tens (although she forgot to erase the hundred).  She also knew she could tally up the 4 twos in the tens place when writing out the long division algorithm.  She used the difference (10 - 8 = 2) to find how many tens to regroup into ones, and she divided the twenty ones by 4 to get 5.  Although the photo does not show her paper, she transferred the process she used with the manipulatives to the traditional long division algorithm. 

I love this activity because pretty much everyone has play money they can use in their own classroom.  But just in case you don't, you can get play money here (affiliate link). And if you need more examples of numbers that increase in difficulty when it comes to long division, I have 3 different levels of long division task cards with numbers similar to these two examples available as a bundle.  I use the cards as review throughout the year because long division is one of those concepts that kids need to see many times before they can master it.  I never feel guilty leaving these in my sub plans because the kids know what to do and actually enjoy long division when they get to use the money.

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Teaching Poetry with CCSS in Mind

National Poetry Month is coming, although now with the emphasis that the Common Core State Standards puts on nonfiction it's become more like poetry fortnight.  And technically I had to teach it at the beginning of March, but nevermind!  There has always been a poem on the fourth grade MCAS test, from 2004 onward.  So because our reading program has very little poetry in it, I made an executive decision and decided to teach my poetry unit, but with a few "tweaks."

Of course the first step is to help kids understand what a poem is, and I do that by getting them thinking about how poems differ from paragraphs.  We looked at a poem and a paragraph side by side a that I engineered to have nearly the same content and most of the same words.  The kids came up with the following list mostly on the first day, although we added to it as the week went on.

During our immersion phase, kids read TONS of different types of poems with different styles and themes.  I asked them to pay attention to:
*How they look
*How they sound
*Why they think the poem was written
*Their favorites and why they like them

Once students understood more about what poetry is and started to get an appreciation for some (not necessarily all) types, I got into the meat and potatoes of the unit:  poetic devices.  Over the years, there seems to be the same 6 terms asked again and again.  So this year I created an anchor chart with those 6 poetry terms (if you like the anchor chart, I've created a student handout and added it to the PREVIEW of my poetry mini unit.  The unit itself is a priced item, but the preview is free to download).

Now, as I told my students, the word "onomatopoeia" has never, to my knowledge, made its way onto our fourth grade standardized tests, but the concept is almost always there.  I told my students, "You don't need to be able to spell it, or even say it, but you do need to be thinking about how the poems would sound if you were reading them out loud, and why the poet chose to make that sound at that moment."

Some of the poetic devices can be related to understanding fictional prose as well, such as mood, comparison, and inferring the author's meaning.  So those terms have already been reintroduced and spiraled throughout the year, but during our unit on poetry they become magnified! 

Usually the kids can see and verbalize on their own that a poet is a writer who tried to make a point with fewer words than a writer of stories.  So I tell them that figuring out what a poem means is like solving a puzzle.  Each line has a clue that's hidden inside a poetic device.  After thinking about each line from the text, you can figure out what the mysterious poem is really about!  Two column notes (a tool we use all year across the content areas) can help us record evidence from the text as well as our reactions to it.

 Finally, to round out the unit, I do have the kids write their own poems.  However, I don't focus so much on the form, but if they are able to use poetic devices that we've discussed.  To take the pressure off of them to start out with, first I ask them to think about their favorite color, objects that are that color, how those objects move, and how their favorite color makes us feel.

This year I also projected cool images onto the computer screen to get them talking even more (it's as simple as google image searching "green picture," just screen them before showing them to the kids).  We wrote the nouns (objects) on yellow paper, the verbs (movements) on blue paper, and the emotions (usually adjectives) on orange paper.  Identifying the parts of speech is the best way I know how to incorporate grammar into a poetry unit!

The results are short pieces that have so much going on so quickly that they can make the reader feel like they are dreaming!

Finally, we spent time talking about comparisons.  They could all relate to those Geiko ads that promise, "Our customers are happier than..."  I asked them to underline them in poems they read.  For some kids, we stuck with using color in their writing (as green as grass) and for my deeper thinkers, we used emotion (as angry as a scalded cat). miss teaching the different forms, like diamante and cinquain, but at the same time I feel like a focus on theme and making meaning is a worthwhile one.  The kids were still enthusiastic about poetry by the third day because we still embraced the playfulness and diversity of poetry. 

Are you feeling pressure to limit the amount of poetry you teach?  You can preview my 4th grade poetry unit to see if it works for your time frame. 

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This article was reposted from All Things Upper Elementary.


Response to Reading ANSWER Method

In Massachusetts, our standardized test is the MCAS, and in 4th grade, one of the challenges our students face on their reading test is the Open Response question. We've been gearing up for the test because it starts in mid-March this year, so test taking strategies have been at the forefront of my mind. 

We spend time every week pouring over past MCAS selections to help our fourth graders become more familiar with test taking language, as well as the stamina for an independent writing task for a topic they are probably seeing for the first time in printed form.  The kids have weekly homework practice, and I have an MCAS Practice Tips letter to parents that I posted previously.  Teaching the kids to use a graphic organizer for pre-writing, and analyzing the question (such as with the QAR method) is something we've done for years.  But this year is the first full year that we've implemented the ANSWER method.  And I think it's been working VERY well for this specific purpose.

The acronym is from the Keys to Literacy, who have provided a number of professional development trainings for my district, and if you ever see one offered in your area, I HIGHLY recommend you check it out (the vocabulary one was another fantastic experience).  I only tweaked it slightly by adding a bit to the "E" (originally the acronym read: "Analyze, Notes, Scan, Write, End by Rereading") and of course the explanations are my own rewording according to what's been working for my class over time.  Because as my students would tell you, I do my anchor charts in pencil, and that's only after I've written them on the white board with them first, until I'm feel that I've answered all of their clarifying questions and I'm happy with the exact wording.  They actually tease me, "You really ARE a rough draft kind of gal!"  I like to think this helps to instill a sense of importance of the revision process for them!

Each component of the ANSWER method is a lesson (or two) in and of itself, but by this point in the year, nearly every kid (as of last week, every kid, yay!) in my class knows what is expected of them when it comes to preparing and composing a written response to writing.  Along with a goal setting sheet each week, they know that when it comes to formal assessments, they don't just write about the story; they have to ANSWER the question!

How do you prepare your students for standardized test reading responses?

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This article was reposted from All Things Upper Elementary.
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