Wednesday, June 27, 2012

Number Sense Routines #2

Hi Everyone! Before I begin talking about more number sense routines, I just wanted to share with you a great giveaway being hosted by Sweet Seconds! I just found her blog - and because she has 200 followers, she is giving away not 1, but 2 $25 gift cards to tpt!!! Amazing! So head on over to enter!

Ok - back to number sense :)

For those of you who missed my previous post, I am reading this book and posting about my new learning :) Hope you enjoy!!


The next section I'm going to talk about it on Counting Routines. Of all the sections, this is the one I feel I have done the best in my own classroom. Maybe you feel the same - but for some reason, the counting routines come easier to me.

So - why use counting routines? 

Have you ever had a student who (whether it be in kindergarten or in 3rd grade) wants to count by ones  rather than using any number of the more sophisticated strategies you and other students have modeled? I know I have. This past year, I can think of a couple! Shumway says students like this are not fully comfortable with the idea of skip counting and they probably don't SEE the patterns of ten on the number grid. The word "see" has come up over and over again in this book. I never knew how important it is for kids to SEE the math in their minds. I don't know that I rely on a visual strategy, so I didn't know that most people actually do...especially our K-3 kids! Shumway says the two objectives for counting routines are: 1) to understand counting sequences, 2) solidify fluency with counting sequences through recognizing and using counting patterns, 3) practice estimation, and 4) use additive and multiplicative ideas.

What are the counting routines?


Count Around the Circle


If you have not heard of this activity before, it is exactly what it sounds like. All students sit in a large circle (possibly at the carpet) so that everyone can see each other. The teacher explains the counting sequence (by 1s, 2s, 3s, 5s, 10s, forward, backward...), what number to start with, and who will start. From there, the kids go one-by-one saying what number comes next in the sequence. For example, I might tell my second graders that we are going to count by 2s starting at 131. The purpose for this particular count around the circle is to notice that all of the numbers will be odd and to continue getting comfortable with numbers, decades, and centuries after 100. As Shumway notes, it is important to set expectations when introducing this routine. The ones Shumway talks about are: everyone needs to listen to each person and count in their heads as each person says his or her number and give everyone the thinking time they need. The first expectation is important because in larger classes (like mine - 30 kids) it is easy for kids to get distracted and lose out on learning opportunities. The second is equally important, as we want our kids to feel comfortable making mistakes and needing more time without worrying about being rushed or embarrassed. One of the questions I had while doing this routine in my class was: What happens when we get to _____ and she has no clue and won't have a clue no matter how long we wait because her instructional level is so much lower than the rest of my class. I still don't have a perfect answer to this, but what I did was give her the same amount of wait time as I would have with anyone else so that she didn't think I didn't think she could do it - and then I would ask her if she wanted help and depending on how out of her range we were - I would either tell her to call on someone to help her (give her the answer) or call on someone to give you a clue. If anyone has better ideas, I'd love to hear what you do!

One thing I love about count around the circle, is how many ways it can be differentiated. For third graders (or maybe end of year 2nd graders) - counting around by halves or other fractional parts could be a stretch. I also think counting backwards by 3s starting at 5679 would be challenging for 3rd graders at first, but if they start to SEE the pattern, it will get more fluent.

Another way to change the routine a bit is to add in estimation. This year I did a lot of estimating with counts of 1 and counts of 10. For example, I might say, "We are going to count around the circle by 1s starting at 560. Who do you think will say 600?" OR "We are going to count around the circle by 1s starting at 560. What number do you think Darrius will say?" The important thing with estimation is that you praise the kids who actually use estimation strategies. I had some kids who knew how to count around the circle quickly to determine the exact right answer, but it was the kids who knew how to give a reasonable guess who were really estimating.

Something I had never thought to do with counting around the circle, is attaching number stories or word problems to the counting sequence. This is probably obvious to all of you, but it never really occured to me before. I can introduce a number story right after our count around the circle and ask, "how would we use what we just did/ just learned in this problem?" So simple! Of course when kids are problem solving and either using or not using a strategy from the count around the circle, it's a great opportunity to bring it up in a conference.

One last way to do count around the circle is to write the numbers as the kids say them. There are of course different formats to writing numbers in a sequence: list, number grid, or number line format. Shumway says all can be useful for different purposes. If you want kids to notice the pattern of the number in the tens place changing when you count by 10s - the list format might be the best. One of the objectives to writing the numbers down is for kids to really look for patterns and relationships between the numbers. As I'm thinking about when I would do this in my own class - I might write down the numbers maybe the first few times with a particular number pattern to help kids really SEE the patterns and relationships and really get it imprinted in their minds so they can begin to SEE it without actually seeing it :)

Choral Counting


Choral counting is exactly what it sounds like too - counting aloud a number sequence as a whole class.  Shumway says it's best to use this routine when the whole class is learning a new counting sequence. Because of this, I'm thinking this routine would show up more in K-1 than in 2-3, but correct me if I'm wrong! A couple tips Shumway noted that I loved are:
- "When choral counting by tens, have students show all ten fingers as you say each number. They clench their fists, and then when you say each number they stretch the fingers our to show all ten at once. This reinforces the idea that they are adding another ten with each number."
- "When choral counting by ones, emphasize different groupings by doing different whole-body movements. Count one through ten doing jumping jacks, then count eleven through twenty doing squats, then count twenty-one through thirty doing twist, and so on."
I think both of these tips are great kinesthetic ways to help kids internalize counting sequences. I can see in 2nd grade using this with some of my tier 3 students. I'm trying to think of a counting sequence I introduce to my whole class...I'm drawing a blank. 2nd grade teachers? What am I forgetting?

One last thing, Shumway makes a point to say that choral counting needs to be used in conjunction with count around the circle so that students who are struggling don't continue to count incorrectly!


Start and Stop Counting


This routine can be done as a count around the circle, as choral counting, or by individual students. The idea here is that students will be getting more familiar with the difference between two landmark numbers. For example, I might say, "We are going to count by 5s starting at 31 and stopping at 101." OR "We are going to count backwards by 1s starting at 78 and stopping at 26." This second one is getting them reading for problems like 78-___=26.

As with all of the routines in this book, it is important to think about the objective of the routine when choosing numbers/ counting sequences. Possible objectives for start and stop counting might be: keeping students flexible with counting on and counting back, helping students to gain an understanding of fractions and decimals and larger numbers, finding patterns (even/odd), and helping students think about magnitude and the difference between numbers. I love how the routine can change for whatever the students need!!

Organic Number Line


This was a new concept for me, and I LOVE it!! The idea is that you start with a rope, cord, strip of paper, whatever - and place "0" at the end of the left side. Then you pose the question where to put "1." Place it where the kids tell you. Then...hold up "1/2" and ask where it goes. Hopefully they will tell you to put it halfway between the 0 and wherever the 1 is. Not done yet....then move the 1 to somewhere else on the number line and then ask students where the "1/2" goes now. Hopefully this will start a discussion about the concept of the whole. As students learn about fractions and different visual  and pictorial representations of fractions, they can be added to the number line. I don't think I would go past "2" on the number line in 2nd grade. I'm just sorry I don't have a picture to show you what this looks like! Google images didn't help me either!

I hope this helps to add something to your math workshop or your math block! I saw a big difference in my students number sense after using these routines consistently! What do you all do? I'm sure there are more routines out there!! 

2 comments:

Sandra said...

I love the circle counting!! :)
I need to get this book!
❤ Sandra
Sweet Times in First
sweettimesinfirst@gmail.com

Mrs. Sheehan said...

This sounds like a good book to read! Thanks for sharing!

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