Tag Archives: decimals

Math Warm-Ups April 8-12, 2013

Wow–how has it been a whole month since I last posted math warm-ups?  Oh, yeah, because MARCH was crazy–including a SNOW DAY and SPRING BREAK right next to each other.  And not that April is any less busy, but at least this week could be considered somewhat normal.  Oh, not it wasn’t–I had a sub on Tuesday.  But hey, what’s normal anyway, right?  Regardless, here are some recent math warm-ups I haven’t shared yet.

First of all, a couple from last week:

This one was to help discuss fraction place value, and also to help us talk about writing clear and concise answers to questions like these (in preparation for MAP testing in just over a week).

This one was to help discuss fraction place value, and also to help us talk about writing clear and concise answers to questions like these (in preparation for MAP testing in just over a week).

Can you tell I ran out of paper and didn't have a chance to get more for a couple of days? Sorry. :) This one is another place value one, hoping that students would see the relationship between money and fractions, and how they can just "move" the decimal (by multplying by 10), rather than having to use the algorithm to solve the problem.

Can you tell I ran out of paper and didn’t have a chance to get more for a couple of days? Sorry. 🙂 This one is another place value one, hoping that students would see the relationship between money and fractions, and how they can just “move” the decimal (by multiplying by 10), rather than having to use the algorithm to solve the problem.

This week’s warm-ups:

Wednesday

We needed to reminded (again) about equivalent fractions, as well as their tie to decimals.

We needed to reminded (again) about equivalent fractions, as well as their tie to decimals.

This one came right off of our Edison benchmark practice from this month. We're using the problems on that assessment to help us analyze the "why" of the ones we get wrong. This can help us not make those same mistakes again the next time we encounter them.

This one came right off of our Edison benchmark practice from this month. We’re using the problems on that assessment to help us analyze the “why” of the ones we get wrong. This can help us not make those same mistakes again the next time we encounter them.

This is another Edison problem, but I changed the numbers. Many students are still not remembering to make the denominators the same before they add. This one also elicited great conversations around simplifying answers--both how and why here as well.

This is another Edison problem, but I changed the numbers. Many students are still not remembering to make the denominators the same before they add. This one also elicited great conversations around simplifying answers–both how and why here as well.

 

I’m hoping I’m back in the routine of posting warm-ups.  Sorry if you’ve missed them! 🙂

 

 

Math Warm-Ups March 4-8, 2013

I’m starting to feel like there’s not really such a thing as a “normal” week; every Friday I say something about how this past week hasn’t been.  So–this week was another “unnormal” week.  Here are our warm-ups:

Monday

Screen Shot 2013-03-08 at 8.10.09 PM

I was out Monday with a sick little girl, and somehow forgot to get a picture of that warm-up. This one is practice with both place value and decimals.

 

Tuesday

After reading the note from my Monday sub, I knew we needed to review what to do with the decimal point in this multiplication problem. Then, as in a stroke of genius, we made a connection to our fraction unit where we used fraction bars to help us visualize what the numbers were doing.

After reading the note from my Monday sub, I knew we needed to review what to do with the decimal point in this multiplication problem. Then, as in a stroke of genius, we made a connection to our fraction unit where we used fraction bars to help us visualize what the numbers were doing.

 

Wednesday

After we stumbled upon fraction bars again Tuesday, I gave them a problem where I had them use that strategy again (on purpose!). For many it was the visual they needed to help it click. But, for some others it just made them more confused! :( We had a great discussion about figuring out which strategy or model works for you and making sure you use that one well.

After we stumbled upon fraction bars again Tuesday, I gave them a problem where I had them use that strategy again (on purpose!). For many it was the visual they needed to help it click. But, for some others it just made them more confused! 😦 We had a great discussion about figuring out which strategy or model works for you and making sure you use that one well.

Close-up of the marking on the fraction bar: we took 1/4 out of each one of the 1/10, which made 6/24. Eventually we were able to simplify our answer all the way back to something that we could turn back into a decimal (1.5/10 or .150).

Close-up of the marking on the fraction bar: we took 1/4 out of each one of the 1/10, which made 6/24. Eventually we were able to simplify our answer all the way back to something that we could turn back into a decimal (1.5/10 or .150).

 

Thursday and Friday

Remember that "unnormal" part of this week? On Thursday we were only at school for about 20 minutes before we left to head to the middle school for the dress rehearsal of their Spring production of Guys and Dolls Jr. (which was FABULOUS, by the way!), so we didn't have math this day. We had the discussion over this warm-up today. Because many people got thrown off by both 1) the exponents in this problem and 2) the "backwards" nature of how I did expanded form, we did another example problem first (the number at the bottom). This problem is a great example of how the warm-up is often a response of something that happens in our math rotations: as we were reading the rubric for reading and writing decimals, we realized that we needed more practice with expanded form and so that group requested we do more with it in our morning work. Great idea, friends!

Remember that “unnormal” part of this week? On Thursday we were only at school for about 20 minutes before we left to head to the middle school for the dress rehearsal of their Spring production of Guys and Dolls Jr. (which was FABULOUS, by the way!), so we didn’t have math this day. We had the discussion over this warm-up today. Because many people got thrown off by both 1) the exponents in this problem and 2) the “backwards” nature of how I did expanded form, we did another example problem first (the number at the bottom). This problem is a great example of how the warm-up is often a response of something that happens in our math rotations–as we were studying the rubric for the standard of Reading and Writing Decimals, we realized that we needed more practice with expanded form.  So that group requested we do more with it in our morning work. Great idea, friends!

What are you thinking about our math warm-ups lately?  Do you have a suggestion for a decimal problem we could do?  Feel free to share it and we’ll try it, then leave you the answer!  We’re always ready to try something new!

 

Math Warm-Ups February 11-14, 2013

Another 4-day week for us, but only a 3-day warm-up week because of some very messy cubbies that needed to be attended to on Tuesday morning.  Happy calculating!

Monday

IMG157Can you catch the mistake I made in this warm-up question?  I didn’t catch it until we started discussing how to do it and figured out that you can’t round a decimal to the hundredths place if it’s already a hundredth!  So we changed it to tenths.  Oops.  HATE it when that happens, but LOVE that it continues to teach my kiddos I’m not perfect.  Teachers don’t know everything and they do make mistakes.  And we know how to solve problems like that when they happen.  So I guess in some ways this was a double-whammy warm-up: two lessons in one!  Only wish I’d planned it that way….:)

Tuesday

Oh, yeah, we were cubby cleaning.  There was too much mess to take a picture, so nothing to share here.

Wednesday

IMG158We had been working on place value and rounding with decimals for about a week and were ready to move on to adding and subtracting, which I was figuring would be pretty straightforward, and so relatively easy.  The way this one was worded, though, caught a couple of kiddos because they wouldn’t remember what “sum” and “difference” meant–definitions we reviewed as we went over the problems.

That second problem sparked another one, too, which was a goodie:

IMG159What do you do when you have a whole number and you subtract a decimal?  There isn’t a decimal to line up.  Or is there??

Thursday

IMG160There’s a joke in this warm-up (that’s probably only funny to me and my class).  See, we were noticing on Wednesday that many of the word problems we have in our math book involve running (Sally ran .89 of a mile on Monday, 2.3 miles on Tuesday and .5 miles on Wednesday, etc.).  In our groups we’d been talking about how guilty those references made me feel since I’ve been REALLY lazy about my running the last few months.  So Thursday I made the problem all about my running.  But since I can’t lie about what’s really happening, I made sure to say that we should pretend that I ran all those miles last week.

But aside from making us all laugh at my funny joke, there was another reason I wrote the problem the way I did.  We are going to be moving into multiplication of decimals next week and I wanted to see what they could do with that.  The problem could easily be answered without multiplying, too, for those that weren’t ready yet–and some just used repeated addition to get the answer–but some did try multiplication as a strategy.  Many of those figured out just what to do with the decimal point, and did so in a logical way–which I loved!  Rather than spouting off the rule about having the same number of decimal places in the answer as in the problem, they used what they know about the problem.  They got to the number 2282, and when thinking about what the final answer should be, thought “Well it can’t be 2.282 because that’s not even as far as she ran in one day.  It can’t be 228.2 because number is WAY too big.  22.82 makes sense because 3 miles times 7 days is 21 miles and the answer has to be a little bigger than that.”  THAT is the kind of thinking I look for and was so excited to see as I threw them this new concept.  It makes me excited to hear and see more as we dig in deeper this upcoming week!

Math Warm-Ups February 4-8, 2013

We had a pretty much normal week with warm-ups, so I have five to share!  This week we started working on decimals, and our warm-ups were related.

Monday

IMG133

 

Tuesday

IMG134There are two notes to make about this warm-up: 1) that should say “expanded form” rather than “extended form”, and 2) I realized after I’d written it that they weren’t ready to talk about that yet.  Sometimes I’ll do a warm-up about a brand new concept, especially if we’re going to talk about it that day in rotations, but that just didn’t make sense for this one.  I was out with a sick baby, and we weren’t going to talk about it for another couple of days, so we skipped that part until later.

 

Wednesday

IMG135

 

Thursday

IMG136So this was the day when we came back to expanded form.  I was glad that we waited, because I could tell from their responses that they didn’t have a clear idea about what it meant.  Many wrote the number in words–which is word form instead of expanded form.  Once I showed them what it was, many remembered, and so after the whole number we tried it with a decimal (the part at the bottom).  The whole idea of expanded from with decimals is new (both to my students and to me!) and was added in because of changes we’re making to align closer with Common Core standards.  Once you start talking about how it works, though, it’s really the same idea as with a whole number.  Most picked up on it pretty quickly.

 

Friday

IMG138

1/8 is 12 1/2%

At our school we use Investigations for math.  One thing I love about the program is that it usually digs into the why of each math concept instead of just the how.   It encourages students to create their own strategies for solving problems, emphasizing that there is not just one way to come to a solution. In the case of our fraction/decimal unit that we’re in now, we are doing more than just learning the rote definition of a fraction and coloring in fractional parts of pictures or just adding or subtracting them using the method I directly taught them–like I know I did in 5th grade.  Instead, we are investigating and creating and figuring out and–most importantly in my opinion–using what we already know to discover something we don’t.

Here’s an example of what I’m talking about:

We are at the beginning of a unit called What’s the Portion?, which includes experiences with fractions, decimals and percents. Yesterday and Thursday we were working on figuring out the percent that is equivalent to a fraction.  We started by making drawings on a 10X10 grid (which helped us “see” what was going on) since we know that percent means “out of a 100.”

We used this visual, and what we knew about fractions and percents already to figure out that 1/8 is equivalent to 12 1/2%, because 1/4 is 25% and an eighth is half of a fourth. Our music teacher, Mrs. Kesler, will be tickled to know that I even had one kiddo make the connection between this and what he knows about music notes to help him figure it out.

So after the initial idea of fraction and percent equivalents was presented, they were to dig in a little deeper.  I gave them a chart to fill in, that had lots of other fractions to work with.  I told them to fill in all that they could with the directions to NOT do thirds and sixths, that we’d do them the next day.  But what they did instead, was make it their goal TO DO the thirds and sixths.  In this case I didn’t really care that they did the opposite of what I said, because it meant that they were going to try something that might be a challenge, might stretch them a little, might give them questions to ask when we worked on it together.

And for the most part, they all totally rocked it.  They made it look really easy.  Like they’d been figuring out fraction and percent equivalents for years. (Ok, 5th grade readers—which character from one of our favorite read-alouds did that sound like?  Comment on this post with your answer if you know!!)

Here’s what our chart looked like when we were done:

The thing that I think is really remarkable about the thinking behind this is that they are already getting comfortable with going back and forth between fractions and percentages, and can tell you how that relates to a group of things, like how getting 10 out of 20 of your spelling words right is 50% or that 3/4 of a class of 24 is 18.  There is understanding being created that goes far beyond just memorizing definitions.  I like that.  And they like it, too.