Friday, February 20, 2015

Fly On The Math Teacher's Wall: Fractions!

Thanks for joining in on the Fly on the Math Teacher's Wall Blog Hop. This is definitely one of my favorite blog hops out there because it is CONTENT focused! Just a bunch of math nerds talking about instruction :)

If you look at the CCLS, fraction standards don't start until 3rd grade.

... or do they?

Primary learners are studying the foundations of fractions and the K,1,2 standards support this learning. If you are a primary teacher or an intermediate teacher struggling with how to reach students who are having difficulty with fractions take a walk back into primary math standards.

If you stick with me to the end of this post, you will be rewarded with an activity that can be used with either second grade students or as an intervention for older students who are struggling with the idea of understanding the meaning of a denominator and how denominators can be used to compare.

If you would like to explore unit size through measurement with your second graders OR if you have intermediate students who still struggle to compare fractions with like denominators who need more instruction on the relationship between unit sizes, click HERE to grab a free activity.

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Next stop on the blog hop is The Recovering Traditionalist. Head on over! 

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Tuesday, January 27, 2015

Addition with Regrouping... The Place Value Way!

A few months ago, I wrote a post on using place value strategies to add two 2-digit numbers.  If you remember, students were decomposing numbers into tens and ones and combining like units. By using base ten blocks, students were able to easily make the connection between the digits in a number and their values.

 <<Here>> if you would like to take a look in more detail. 

I also promised in that post that students WOULD eventually get to the traditional algorithm. You'll also remember that I said that the traditional algorithm was a 4th grade standard so we are still eeking out as much place value understanding as possible as taught through addition.

If you want to skip to the addition strategy jump below to the large letters that say "STRATEGIES START HERE". Otherwise, keep reading to see how we have bridged the gap between these basic skills and larger sums.

Our second graders have been working towards this goal over the past few months. They have done extensive work in the world of place value and also in mental addition strategies. I am condensing here <in a big way> but one aspect of place value work they have studied is grouping and renaming units. 25 is 25 ones but is also 2 tens 5 ones. 345 is 345 ones, 34 tens and 5 ones or 3 hundreds, 4 tens and 5 ones. Etc.

Additionally, they are thinking of addition and subtraction in terms of place value. For example, if you have 46 and want to add 10 more, a student well grounded in place value knows that 46 is also 4 tens and 6 ones. "+10" is really just adding another ten. The result is 5 tens and 6 ones or 56.

Here is a look at some of the place value work we have been doing. 
Students are also able to add numbers such as 59 + 12 using mental strategies. If you were to add 59 + 12 in your head, you likely wouldn't line up the digits in your mind and think  "9+2, put down a 1 and carry a 1 and 5 + 1 + 1 = 7 so 71!"

You would likely solve the problem by thinking something like "59 + 10 is 69. Two more is 71." Or, 50 + 10 = 60. 9 + 2 = 11. 60 + 11 is 71." Students have learned ways to note this mental strategies and, as they have, their mental math has really grown.

Strategies Start Here
*If you are REALLY in a hurry, scroll down to the bold conversation below*

I walked into a 2nd grade class last week ready to show them a new way to organize 2-digit numbers vertically **read: leading to the standard algorithm*. Students would be using place value disks to show addition. If you aren't familiar with place value disks, they are foam disks about the size of a quarter that say "1" "10" "100" etc. They are a non-proportional model that students who already understand the magnitude of 1s, 10s, and 100s can use to organize their learning when working with place value.

To add 59 + 12, students would build 59 with 5 tens disks and 9 ones disks horizontally. Below this number they would build 12 by showing 1 ten and 2 ones. Students would then look at the ones and determine how many there were:
S: 11
T: What is another way to say 11.
S: 1 ten 1 ones.
T: How could we regroup our ones to show 1 ten 1 ones.
S: Trade 10 ones in for a 10 disk

Easy as pie.

So we did. We traded in ones for tens. We found the total number of tens and ones and were pleased to find the answer.

This was the first day of this new instruction on NON-mental addition strategies. We weren't doing any writing or algorithm to accompany the number disks. And something funny happened.

T: Can we build 23 + 72?
S: Do I have to? It's 95. I did it in my head.
T: Alright, I'll give you a harder one. How about 34 + 57.
S: I can do that in my head too!

... thank you place value and mental strategies... No worries, they built them all "because when numbers get larger you will be glad you learned to organize your work!"

So the next day, students were tasked with writing numbers that match their number disks. *Read: The traditional algorithm". Their work in place value again supported this work. Here's what a problem might sound like:

T: Let's build 75 + 18. 
S: [Build 7 tens and 5 ones horizontally. Below, they build 1 ten and 8 ones.]
T: How may ones are there in the two numbers together? 
S: 13 ones. 
T: What is another way to say 13? 
S: 1 ten 3 ones. 
T: Can you regroup your disks to show 1 ten and 3 ones? 
S: [Students trade in 10 ones disks for 1 ten disk] 
T: On our paper we can show 13 ones as "1 ten and 3 ones". Let's put the 1 ten in the tens column above [or below, on the line if you are doing "New groups below"] the 7 and the 1. We'll put the 3 ones below to show the total. 
T: How many tens do we have in all now? 
S: 7 tens plus 1 ten is 8 tens. Add in the new 10 and we have 9 tens. 
T: What is the total? 
S: 93. 

By thinking explicitly about teen numbers as tens and ones, students give meaning to the traditional "carry the 1". Fewer students are making errors like carrying the 1 where no new 10 exists, not carrying a ten when there ARE more than 10 ones and other errors that demonstrate a lack of understanding.

Even better? When a student does make an error, you know that there is a breakdown in place value and addition understanding rather than an error in a procedure. When the algorithm is built on place value and understanding the results will be more consistently successful!

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Monday, December 8, 2014

iHeart Math Holiday Hop

Welcome to day #9 of the iHeart Math Holiday Hop! I am so excited to join 22 other math bloggers to bring you holiday tips and treats through the month of December! If you have never been to my blog before, I am a math interventionist in NYS. I work with students in grades K-5 and have a background in intermediate special education. Image Map
Holiday Tip #1: Giving Back
It is easy to get caught up in the stress of the holiday season. I love the idea of committing to 1 act of kindness towards someone else and 1 act of kindness towards yourself each day of the month to keep yourself and others sane! This may be as simple as committing to leaving within 45 minutes of the end of the school day to get home and spend time with family, treating yourself to a special drink in the morning (Starbucks!), or putting down your pile of grading so that you can go to the gym. Work will always be there, it will NEVER truly be "done" so take time for yourself. An act of kindness towards others could be as easy as leaving a copy of that great lesson you are doing on a colleague's desk, bringing in a muffin for the teacher who comes flying in having already readied their 3 kids and dropped them off at their own respective schools. You know how exciting it is to have an anonymous treat dropped off in the morning- commit to giving someone else a great start! 
Holiday Tip #2: Math Tip
Picture this, it's the day before the holiday break, the kids are excited and bouncing off of the walls and you just want everyone to be safe until dismissal. Learning would be a MAJOR victory but it seems like a far fetched dream... 

Or is it? 

I save my best trick for the day before breaks. Math scavenger hunts :) Ahead of time, I prepare, essentially, task cards and tape them up around the school. Students are broken into teams and they go off and do math review. But because they are in a team and walking around the school it seems super novel and they have no problem at all doing a set of math problems quickly and accurately! 

I would recommend making the tracking sheet novel in some way. At Thanksgiving, I have students collect a turkey feather at each station, when their turkey is complete with all 8 feathers, they are done. At Christmas, they are collecting ornaments as they go. When their tree is fully decorated the hunt is over. Before April break? Easter egg hunt with fake money inside. Get counting kiddos :) 

Also, if your students tend to bring in a CRAZY amount of snacks on the day leading up to a break, it is fun to set up a snack in the classroom and allow students to come back at the 1/2 way point for a special treat. 

I am telling you, I have used this strategy for years and it works. every. time. 
Holiday Gift for YOU!
Want to try the scavenger hunt? I put together a scavenger hunt for you! I have included one set of task cards appropriate for grades 1 and another appropriate for grade 2. Both use the same game board. Click the collage below to grab it. Enjoy! 

Thank you so much for stopping by today! Tomorrow, head over to Math Coach's Corner for the next day of the iHeart Math Holiday Hop!

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