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!