Number Sense Routines #4

I can't believe I have gotten through this book! I highly recommend it for all K-3 teachers! I would say it has been the best math resource I've read yet...and I read a lot :)

So for my last post about this fabulous book...I am going to talk about the data and calendar routines chapter. Now, I am going to admit something that I am a little embarrassed to admit to all of you K-2 teachers.....I do not currently do a whole-class calendar routine.....I hope you don't hate me :) In my defense, in the past I have looked at calendar as something for kindergarten and maybe first grade, but something that was "too easy" for 2nd graders. However, after reading this chapter, I will definitely be doing a calendar routine...different than I had once pictured though.

For any skeptics like me out there - let me tell you why calendar and other data routines are important for building number sense. Shumway says that, "the math is embedded in the discussion -- it is being applied and used authentically within a context." What I love about this is that it brings math to life in a practical way. So often I'm not sure how to make math relevant to my students, but this is so obviously relevant!

Shumway shares 3 basic ways to use data routines are: Calendar, Collecting Data over a Long Period of Time, and Counting the Days of School.

Calendar

Other than the obvious prompts like asking a students to read today's date or asking a student to count the days in a month, Shumway has some great ideas for taking this routine to the next level. 

My favorite idea (that I will be doing this year) is to purchase a 12 month calendar and hang a few months at a time (if not the whole year). This will give students more of an opportunity to see how the numbers and the days work together. It will provide opportunities for discussions on things like, "how many days until ____'s birthday?" or "how long ago was our field trip?"

Some other great questioning prompts she mentions are:

 "Find a number that's made of a 10 and a 2."

"Find a number that's one less than 16."

"If March ends on a Tuesday, what day will April start on?"

Collecting Data Over a Long Period of Time

I am also super excited about this one! I've never done this (other than during a science unit), but I think it will have a huge impact on students if done over the whole year. Some suggestions for collecting data are: weather, temperature, sunrise/sunset. As I was reading this section, even though I was super excited, I was also thinking to myself, "when am I going to have time to do all of these routines everyday?" To my delight Shumway answered my question! She said that even though data is collected everyday (class jobs), the data is not talked about everyday. She said in 3rd grade she did a data mini-lesson once a month, but with Kinder or 1st she did almost daily...which seems more appropriate. I teach 2nd grade, so I think I will find a happy medium between weekly and monthly. Another thing I loved is that Shumway assigns multiple class jobs for the calendar/ data collection (another thing I'll be taking away from this book). She has one person do the actual calendar (days in school), one person do the weather (record the temperature on the graph), one person do the sunrise/sunset times (record on the graph), one person do the moon phases (which I'm not sure I'll do), and one person be the data supervisor to make sure everyone is doing their job correctly or to fill in for someone in case someone is absent. I love it! 

Counting the Days in School

In this section, I again love how Shumway differentiates how this routine looks in K-1 and then in 2-3. One thing that makes sense, but I hadn't considered, is that the use of straws (ones, tens, and hundreds) is not appropriate for K-1. She says it's too abstract of a concept that one 10 = 10 ones, which is called unitizing. That tends to be grasped toward the end of first or in 2nd. I suppose if you have a class of first graders that is solid on unitizing then go for it, but in general, I guess it's best to wait until 2nd grade to use the straws. What do you all think about that? 

Rather than the straws (do you like my technical term?!) in K-1, Shumway suggests using a linear model - on counting tape or an array model on a hundreds chart or pocket chart. She says 2nd and 3rd grade teachers can use these as well, but will need to rachet up the math or change the focus to meet their needs. Some suggestions for that are using colors to make patterns and predict what number will be the next "yellow" number, talk about the patterns on the hundreds chart, and use the calendar to talk about days of school...like what day of school will October 2nd be?  Or what day will it be on our 49th day of school? (So kids have to consider weekends and number of days in each month.)

So that about does it for the number sense routines in this book. The most important idea in this book is being a responsive teacher - constantly assessing what our kids need and then planning routines to help move them to the next landmark in their mathematical thinking. I hope you've enjoyed reading about all the great routines! I'd love to hear more about what works in your classrooms!!

Number Sense Routines #3

For those of you who have missed my previous posts on visual routines and counting routines, I am doing a series of posts on number sense routines from this fabulous book:

This post is on Playing with Quantities: Making Sense of Numbers and Relationships

The sentence in this section that stood out to me the most was: "The base ten numeration system and the concept of place value are crucial components of students' number sense development. Therefore, it is essential that students understand the number ten and play with grouping of ten." (page 80)

Why do playing with quantities routines? 

The purpose of these routines is to encourage students to play with quaitities, decomposing and composing them, as well as think about how the base 10 place-value system works. In some ways, this seems to be the most important (I don't want to devalue the other routines though) category of routine - only because I see time and time again students struggling with place value. 

The Ten Wand

This is by far the cutest routine in the book! The ten wand is made up of unifix cubes (2 different colors). Shumway talks about how she introduced it in her school by dressing up as the Queen of Ten on the 10th day of school (and again on the 20th and 30th). The Queen of Ten was very clumsy and her wand would always break. The students were given the job of figuring out how to put the wand back together by finding sums of 10. This routine is great for students getting comfortable with: combinations of 10, part-part-whole relationships, commutative property, and using the 5 and 20 structure. 

I was sort of wondering if this could be used at a math work station? I'll be working on that!

Ways to Make a Number

This routine is very much like "Name Collection Boxes" from Everyday Math. What I love though about the way she explained it, is she breaks down how we as teachers should be looking at our students' work. We want to look for the math in what they are doing so we can push them to think about numbers in increasingly more sophisticated ways. Here are some of the big ideas she says to look for:

- Decomposing a number into expanded notation (If the number is 470, a students may write 400+70+0 with lines drawn from each addend to each digit).

- Various groupings of ones, tens, hundreds, and thousands (If the number is 124 - a student could draw: 1 flat, 2 longs, 4 cubes; 12 longs and 4 cubes; 1 flat, 1 long, and 14 cubes)

- Using a pattern (if the number is 50: 49+1, 48+2, 47+3, 46+4...)

- Interesting ways of thinking about numbers using coins, pictures, subtraction, tallies, multiplication, etc.

- Showing a variety of ways to think about a number

Today's Number

This may sound no different than "ways to make a number," but it is! The idea behind this routine is to help students expand their thinking about a given number in relation to different situations and scenarios. 

For example, let's say the number is 50. Some questions Shumway suggests that we as teachers pose to are students are:

When is 50 big? 

When is 50 small?

When is 50 a lot?

When is 50 very little?

Make 50 using three addends.

Make 50 by subtracting two numbers.

Divide 50 in half.

Double 50.

Divide 50 into four equal parts.

What other ways do you think about 50?

**What is 50's relationship to 10? to 100? (Shumway makes a point to discuss how valuable it is to relate numbers to 10 and 100 as it will facilitate a deeper understanding of magnitude, the number line, and seeing differences.)

What is 50's relationship to the age of your mom? to your age?

**How much is ten groups of 50? (Shumway talks about how talking about groups of numbers is a great way to establish understanding of the base 10 system....ten groups of 22 is 220 and one hundred groups of 22 is 2200...) 

To extend this routine, Shumway talks about having students come up with number stories to match equations to match the equations students came up with in response to things like "make 50 using three addends." If a student came up with 20+20+10, a number story could be: I had 20 red beads on my necklace, 20 blue beads on my necklace, and 10 green beads on my necklace. How many beads in all? I also wonder if this extension could be turned into a math work station?? Ideas?

Mental Math Routines 

I am so glad Shumway included a section about mental math routines. I am always looking for ways to get my students away from relying on things like the number grid and their trusty fingers :) So, mental math routines aren't anything other than just posing a problem to students (at the carpet - preferably in a circle, but doesn't have to be) and telling them to give a thumbs up when they have found the answer. The most important part of this routine is helping students to verbally and symbolically represent the strategy or strategies they used to find the answer. Process over Answer!!! This is where things like turn and talk, active listening, and think alouds are so important! Shumway gives a great progression of possible mental math problems to use. Side note - she says it's important to give a context to problems (number story) in k-1 and even for much of 2nd grade, but by the end of 2nd and for sure in 3rd - they shouldn't need a context anymore. 

- Making Ten (6+4 or 16+4)

- Counting on or Counting back (58-4 or 99+3 or 78-10)

- Decomposing Numbers into Tens and Ones (10+17, 36+20) - this would also be a good time to try a number string (36+10, 36+20, 36+22...)

- Using Ten or Compensation Strategies (9+11...changing the 9 to a 10 by adding 1 and changing the 11 to a 10 by subtracting 1)

Aren't these great routines? I loved this chapter!

That's it for now! Let me know any questions or comments or suggestions!!!

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!! 

Number Sense Routines #1

Hi Everyone! I have been a very bad blogger and blog stalker! I opened my google reader and guess how many unread posts I had.........655!!! I can't believe it. I don't know how I'm going to get through it all and not miss anything! 

Well, school is out - YAY! But, this week the K-3 teachers at my school have been attending PD at Erikson Institute, with whom we have a 4 year partnership to improve our math instruction and understanding of early childhood math development. We just finished our first year of the partnership and I have learned so much already! This year was also the first year I attempted math workshop - so the professional development and coaching from Erikson was perfect timing! I am reading a couple books to further my learning this summer. The one I am reading now is called Number Sense Routines, by Jessica Shumway. 

I am going to try something I've never done before - and that's post about something I am reading as I am reading it. There are four types of number sense routines, so I think I will try to do four posts. So here goes #1!

Before I begin, I want to back-up and talk about what number sense is. Have you ever had a student say the difference between 17 and 9 is 2 because they subtracted 9-7? If the student had any number sense, they would be able to see that 2 doesn't make any sense for the answer to 17-9 because 9 is much further away from 17 than just 2 jumps.....but plenty of students make that mistake over and over again because they lack number sense and rely on the algorithm. Before Erikson, I thought I knew what number sense meant, but I didn't really know how to assess if kids had "it" or to what extent they had "it" and I didn't really know how to help students effectively when they didn't have "it." Here are some of the big ideas your students will have mastered if they have number sense (not necessarily in this order):

Subitizing

Magnitude

Counting

One-to-one correspondence 

Cardinality

Hierarchical Inclusion

Part/whole relationships

Compensation

Unitizing

Now, if you're like me, many of these terms are new. I had never heard of subitizing or compensation when it comes to math before. After going to Erikson for these PDs and reading this book, I feel like I have a whole new framework to looking at my students math knowledge. I now feel equipped to assess their number sense skills and strategies and make an appropriate instructional plan to target specific needs. 

Shumway believes that spending 10 minutes a day on number sense routines (as the beginning to math workshop or during a morning meeting) will greatly improve our students' number sense. If your students are anything like mine, this is the area in math that they are lacking in most....and it's probably the most important, as it's the foundation for everything else! Shumway makes a great point in saying it's important that these routines are responsive - that we plan them based on student need. 

Shumway talks about 4 different types of number sense routines: visual routines, counting routines, playing with quantities, and calendar and data routines. I am going to talk about the visual routines today. I have tried all of these out in the classroom, so I can give some real feedback :) 

Visual Routines:

In this chapter, Shumway talks about how important it is to give our students a picture of numbers and quantities. We want our kids to "see" a given number. My favorite quote from the chapter was, "Counting does not mean much to young children if they do not have the visual images to go with the number words or written numerals. Also, many children seem to lack a visual framework for quantities. They have a difficult time organizing amounts in their head, and later that leads to difficulties with computation, mental calculation, using efficient strategies, and having clear understandings of number properties and the base ten number system." When I read that - I was like - ding, ding, ding...that is all of my struggling math students! I need to go back to the basics with them and build up their number sense! So, here are the three visual routines Shumway explains in her book. I have tried all three with my students, and they have really improved my students' number sense, their abilities to mentally calculate using a 5 and 10 structure, and their ability to compose and decompse numbers. I am looking forward to hearing the 3rd grade teachers' opinions about this because this is the first year I've implemented these routines and I'll be curious to see if they notice a difference!

Ten Frame

If you use Everyday Math, I know you've seen these before. I never paid much attention to them, but after learning more about them, they are really an amazing tool. Some of the benefits to using them are:

- students have a mental picture of what a number looks like 

- students have a mental picture of combinations of 10

- students become familiar with composing and decomposing numbers - which means that they begin to see groupings within numbers and use those groups to find the whole

- commutative property 

- learning the teen numbers when using a whole ten card and another card

- part and whole relationship

I've only used these with small groups, but next year, I'd like to try using them as a math routine more. 

Quick Images Using Dot Cards

These dot cards are awesome! I've used these as a warm-up to math workshop and in small groups. They work well for both situations. I wish I had a picture of the ones in my classroom - they are packed away - so I had to find a pic online. These will work fine though. You can make dot cards in so many various ways and use them in so many ways. At the very beginning, you may make cards that look like the dots on dice (or other familiar patterns), but as children get older and more advanced in their number sense, making all sorts of combinations, holding up 2 cards at a time, and using different colored dots are great ways to keep building number sense. The cards are meant to be held up only for a few seconds so that students have to find an efficient strategy to find out how many dots in all. Using the above picture, a more advanced example that I might use in my 2nd grade class might be the middle two in the top row. After holding them up for a couple seconds, I would ask students to tell me how many they saw and how they saw that number. Some students may say they saw 4 blue and 5 green dots to make 9 dots altogether. Other students may say they saw 3 and 2 on the first card and 4 on the second card. There is no "right" way of getting to 9 dots total, but there are more efficient ways. We want our students to become flexible and strategic in their mental math thinking. 

Rekenrek

This is my favorite!!! Again, I wish I had a picture of all of the rekenreks in my class - we have a large one similar to this one, about 10 mini ones, and one made out of pockets (for students to put popsicle sticks into) stuck to the white board for our "question of the day," but this one will have to do. If you are like me, this may be new for you. I had never heard of a rekenrek before this year. All rekenreks have 10 beads on each row - 5 white and 5 red. This rekenrek has 20 in all, but others have just 10, and some go up to 100 (for older and more advanced students). The rekenreks in my classroom have 20 beads, except the one on my white board has 30 because I needed enough for all of my students to be able to answer the question of the day. 

The rekenrek is an amazing, kinesthetic tool that helps students develop a strong sense of quantity (up to 20) and mental math strategies that can be used for two-digit addition and subtraction. I use the rekenrek daily as a whole class to answer the question of the day as well as at a math work station (there are many variations of games and activities to use with rekenreks). For the question of the day, I have a question written on the board when my students come in in the morning. The question is always a yes/no question. If their answer is yes, then they may place a stick into any of the 30 pockets (they are in rows of 10 with 5 white and 5 red - just like the picture above). The idea is that students then have to add up different combinations of numbers everyday. My hope is that students get away from counting by 1s and get more comfortable using doubles, sums of 5 and 10, and the base 10 system to add efficiently. 

So that's about it for the first post. I'd love to hear some feedback, questions, comments, or how you are using any of these routines in the classroom!!! I know you all have some great ideas!

I'm Obsessed...

Hi All! Im linking up with Living a Wonderful Life to share my obsessions! I love this idea!

1. Dessert - I loooooove dessert! I am really trying to quit, but it's hard for me. They are just too good! Here are a few pics of some of my faves!

2. Shoes!

Wish I had an occasion to wear these!!

3. Organizers

source

How cool is this? If I ever have a walk-in closet, maybe I'll get to do something cute like this!

And of course I love organizing in the classroom!

4. Books! I can't stop ordering from Amazon and Scholastic!!

5. Football! I look forward to the fall for the sole reason I know exactly what I am doing on Sundays and Monday nights! Go BEARS! BEAR DOWN! :)