Building Mathematical Comprehension Chapter 2

Mathematical Vocabulary, that's the focus of Chapter 2 of Building Mathematical Comprehension.

There are several ideas on graphic organizers and some bulletin board ideas offered in this chapter.  To be honest, I didn't do as well with vocabulary this last year as I had in the past.  As I reflected on the year, vocabulary building and instruction was an area I let slip.  I know how important it is to teach proper vocabulary to students, especially in mathematics.

One thing that I think was very helpful to me was a professional development where we collaborated vertically with the grade level teams below and above us specifically in the area of vocabulary.  We discussed the vocabulary that was currently being used and then suggested vocabulary we'd love for the grade level below us to begin implementing and using.  This was very eye-opening to my team as we spoke with the 6th grade team.  We learned that there were some key vocabulary terms that if we used in 5th grade, would be tremendously helpful to students in 6th grade as they deepen their level of mathematical knowledge.

I would strongly encourage you to get with the grade level teams ahead of, and behind your own and have a vocabulary conversation.  It can be informal and take just a few minutes.  You might be surprised at what you discover either about your own instruction or the instruction that might be happening before your students arrive in your classroom.

I think it's extra important for primary grade teachers to use correct vocabulary.  As a first grade teacher, I was certainly guilty of using "simple" names for math terms because I thought the true vocabulary words would be too difficult.  I soon realized that if taught correctly and used over and over, young students can understand the vocabulary just fine and it sets them up to be more successful in the future.

One of my summer tasks is to create a template/master of a student interactive math notebook to guide me through next year.  Vocabulary will be a strong part of that notebook.

How do you make sure your students get explicit math vocabulary instruction?  Be sure to check out the other posts on Chapter 2 linked up below.


Inlinkz Code:

An InLinkz Link-up

Building Mathematical Comprehension Chapter 1

Now that summer is here, I feel like I can blog again!  Whew, the school year can be busy.  I'm keeping busy through the summer though working on extending my knowledge to be a better teacher for next year.  I love participating in summer professional book clubs.  I plan to join Angela at The Cornerstone for Teachers for her facebook book club of her books beginning in July.  I'll be posting about some of the other books I'm reading as well throughout the summer.

This post, however, is all about the first chapter of Building Mathematical Comprehension.  Abbey at A Teacher Mom is hosting this study.  Be sure to check out the link up to see all the posts from participating bloggers.

To be honest, I've had this book a few years and have skimmed it here and there.  I tweek the structure of my math instruction each year and I'm still looking for a model that will work well for my students and for me.  I'm excited to read the entire book and hope that it will help me get closer to that perfect model this coming year. 

Chapter 1 focuses on comprehension strategies for Mathematics.  Not surprisingly, reading and math comprehension strategies are very closely linked! The biggest take away for me from this chapter is that we need to use a very similar gradual release model that we use in reading with math as well.  

We need to be very explicit in our gradual release: 

1. Explain WHAT the strategy is. 

2. Explain WHY the strategy is important. 

3. Explain WHEN to use the strategy. 

4. Model HOW to use the strategy. 

5. GUIDE STUDENTS how to use the strategy. 

6. Students INDEPENDENTLY use the strategy.  

Think about the "Think Aloud" lessons you often do in reading.  We need to do "Think Aloud" lessons during our math instruction as well.  This model will be great for introducing students to using comprehension strategies in deciphering their math problems. The remainder of the book goes more deeply into each of the comprehension strategies of:

• Making Connections
• Asking Questions
• Visualizing
• Making Inferences and Predictions
• Determining Importance
• Synthesizing
• Monitoring

I'm really trying to move to a more conceptual/exploratory math model to introduce math concepts.  So I wondered if this explanation model would fit into also sharing mathematical solution strategies.  I think that this can certainly happen during the discussion and wrap up phase of those activities.  I also think that we can teach students to model and explain their conclusions using this pattern.  Students can explain to their peers WHAT the strategy is they have determined, WHY it would be helpful or important, WHEN the strategy is useful or if there are circumstances when it fails and model HOW they used the strategy.  From there, they can guide their small group or class to use the strategy and time can be given for students to give the strategy a try.  

This model of students leading the way would need to be carefully constructed and I think the teacher would need to carefully select students who give a full presentation and limit it to 2-3 strategies, depending on the concept. 

How do you facilitate comprehension in your classroom?  Do you consciously use a think aloud method for teaching comprehension or solution strategies to your students?  

I'm excited to learn more explicitly about using each of these comprehension strategies in teaching mathematics. Come back each Tuesday for the next 2 months for ideas on the rest of the book.  Join in the conversation by leaving comments on the posts. 

An

InLinkz Link-up

Guided Math Conferences Chapter 1

This really is a summer of professional reading for me, and I'm loving it!  I'm excited to join Brenda for this study of Guided Math Conferences by Laney Sammons. Don't have a copy? Click on the link to get in on Amazon.  

I attempted some guided math last year with a little success and am looking forward to doing it a bit better this year.  My grade level team decided last year to ability group our students across the grade in math.  I spent most of the year with the students that needed the most support and adding guided math was very helpful.  

I did conferring with my students at least at the end of every unit.  Part of our assessment of students included an interview on the concepts.  It was incredibly helpful to see what students were thinking and understood as I watched them work through the problem or heard them orally respond.  I haven't done that since moving to fifth grade, and it would be so valuable to understand what they really understand.  

The first chapter of Guided Math Conferences is "Conferring with Young Mathematicians".  This chapter explains the differences between many types of conferring you might do.  What I described above was more of an interview.  Last year, I tried to do some small-group instruction and sometimes did a bit of conferences.  Conferences is the area I want to really improve on next year. This involves taking a look at the student's current work and taking them where there currently are in understanding to the next step.  To help me do this, I'm going to keep a list of student names in a checklist on a clipboard.  Each time I conference with a student, I'll write the date in the box next to their name.  When everyone has a date in the first column, I'll start marking the next column.  This will be a good start for me.  Once I get good at that, I'll add notes to my system, hopefully by November.  I think adding notes right away will overwhelm me, so I'm going to start out with forming the habit first.  

Be sure to check out the posts on this chapter from the hosts, Thinking of Teaching and Primary Inspired.  Clicking on their names will take you to their Chapter 1 posts.  Several bloggers have also linked up with them, like I have, so be sure to read those posts as well.  You're welcome to link up too or add your comments or questions in any of our comment sections.  

Do you confer with your students?  What type of conferring do you do or plan to do?

Review Ordering and Operations with Decimals

We've been reviewing everything over the last few weeks.  We started testing writing in February, and it seems like we've been testing ever since.  That's made for a very long end of year...

I can't take credit for this idea, it comes from my teammate.  This is how it happened in my classroom though.   It's a super idea and my students were engaged and loved it.  To review decimal numbers, she made a tented cards with a decimal number on each; one for every student.  I strung a piece of yarn across the front of the room from a 3M command hook I have on the side of a shelf to the cart my document camera is on.  Here's how the lesson played out:

1. I handed out a card to each student.  This worked really well as I could easily differentiate for each child as I passed them out.  I passed them out randomly to mix them up and as I did so, I could give more difficult numbers to students who better understand decimals and I gave the whole numbers to my students very below grade level in mathematics.  
2. I called a table at a time to bring their cards to the front of the room and place the tent over the string in the general area they thought the card should go.  
3. Only the table whose turn it was could adjust the tents.  That was very difficult for my high students who wanted to jump in and fix everything. 
   
   
   
   


4. After every student had placed his/her card, I asked the students to examine the number line carefully and see if anything needed to be fixed.  We had 3 mistakes and they became very good discussion pieces to clarify misconceptions that a few students had.  
5. Once our number line was in order, we did some decimal operations with the cards.  I would choose two cards and post them on the white board with magnets and write in an operation between the numbers.  Students then figured out the solution.  Students solved on their whiteboards (or desks as I let them write with Expo markers on their desks) or in their math notebooks.  I just wanted to see the work, wherever it was done.  I was surprised how engaged the students stayed with the challenge of just solving each problem.  I didn't have to incorporate any kind of competitive incentive at all.  After giving time for students to solve each problem, we did it together on the board.  Mostly I just quickly demonstrated the solution, but I had a few students show their solution as well.  We also had some good discussions during this time about where decimals should go moving decimals in division, etc. 

This was a great review of decimals with my students.  In incorporated so much, allowed us to discuss understanding and got the students moving.  

This idea of tented cards on a yarn string could certainly be adapted to many topics.  I'd love to hear what your ideas are on using this idea.  Please share in the comments section below this post.

Thanks to Meg of The Teacher Studio for hosting this linky!

Click the button above, or here, to see all the other great lessons that are linked up. 

Organizing Task Cards with Folders and Bags

I have been loving all the task cards that I have collected from many great sellers.  Task cards have become a staple to my math instruction, especially the last couple of weeks as I have been trying to figure out how to make guided math / math workshop work for me.  One of the difficulties becomes how to best store all of the cards.  For me, the best way I have found to store them is in 9x12 zippered bags which I then place in file folders in my file drawers according to the concept they match.  The 9" x 12" 4 Mil Clear Zip Lock Bags are a bit heavier than the standard zipper bags you use in your kitchen and even the gallon size bags are just a bit too small to fit a full sized page.  You can get 100 bags on Amazon for under $15, click the picture to be taken directly there.

I like that I can keep the full page cover, instructions, answer sheets and blacklines in the same bag together with the cards.  I simply grab the bag from the file and it is ready to use.  I place them in the center and students have the directions, cards and answers all there at their fingertips.  When it's time to replace with a new concepts, I just file the bag back in the correct folder.
Here they are in the bags and the drawers.

These are regular zip gallon bags because I ran out of the 9x12 bags and needed to get these cards done.  You can see that the bags don't close.  I didn't think to grab some cards in the bigger bags to show you.

I often put the cards on a shower ring.  I find them in the shower curtain section at Walmart.  There are 12 in a bag for less than $3 and they stay together much better than the binder ringers.  The smaller end at the top also makes them easy to grab and carry.

Some of my favorite shops for task cards and projects are:

If you have some great task cards for math to share, be sure to add the link to your blog or TpT store to the linky at the bottom of this post. 

In addition to the great bags I have found to store my task cards in, some other office supplies from Smead have been very helpful. Smead's new file folders and hanging file folders make the organization even easier.  They now have larger tabs so that finding the topic behind located on the folder tab behind all of the bags is so much easier now.  The Smead file folder tabs are a bit taller and longer, you can see the difference in my photos of my file drawer between my older folders and the new Smead ones.  The hanging files now come with tabs attached.  I no longer have to worry about those plastic insertable tabs the I would have to fuss with.  Now the same large tabs are already attached to the hanging folders so they are ready to use right away. Additionally, there's a new Smead expanding pocket I love to use at home.  It's perfect for thowing the bills into so I know where they are when it comes time to pay them.  The new expanding pocket has a "no slip" surface added to the top making it easier to grab and take to my computer.  With the bags and folders, you'll be all set to organize your task cards for easy use in your classroom year after year. 

You can see the light green tabs in this picture as well that are the new tabbed hanging folders.  Soo nice to have them already tabbed!!

Do you have some math task cards or task projects that you love or created and would like to share the link to them, feel free to add it to the linky below.  If you have a post about how you use or organize your task cards, please link those posts as well. 

Note: I was sent the above described promotional products by Smead at no cost in exchange for a blog post review. The use and opinions described above are true and accurate and in no way coerced by Smead or Shoplet / Shoplet UK.

Free Math Games Online

Bob at the Garfield Learning Portal sent me a message to inform me of his great game that uses a Rekenrek.  It's a great game focused on Kindergarten through Second grade students.  Bob said there will be an app soon.  Check out this fun game at http://www.professorgarfield.org/yourfuture/math.html  The first two activities use the rekenrek and the second two are great extensions to equations.  The Garfield Portal includes games on other subject areas too, check out the menu at the top of the page.

Magnificent Math Tool - Rekenrek

Student using Rekenrek to answer a
3 number addition problem

The Rekenreck, also called a Math Rack or Counting Frame, is a wonderful math manipulative tool that I have been using for three years.  My students love it and it is the tool they use the most for just about every kind of math.  Most recently, we used them to aide us in adding 3 numbers and in finding missing numbers in an equation: missing addend and missing subtrahend / minuend problems.  We have used them throughout the year for all types of addition and subtraction and counting.  The best things about the Rekenrek tool are:

Pair of students working together
to answer a 3 number addition problem. 

• It is contained.  There will be no beans, blocks, cubes, counters or bears to pick up around the room for weeks after using them. 

• It is coded for easy recognition of working in the base 10 system.  The beads are color coded in groups of 5 which enable students to see numbers quickly.  Each row contains 10 beads which also lends to quick number identification and manipulation. 

• It is kinesthetic and visual.  Students physically manipulate the beads and see the numbers.  This is an added help that is not given to students when using a number line. 

• It is available in three sizes: a single 10 row for preK-K students or for students who may need extra support, a double row containing 20 beads for K-2 students easily facilitates working with all problems within sums/differences within 20, and the final option is a ten row board containing 100 beads for use with all students allows many options for number work.  

There is information available on how to use and instruct with the Rekenrek all over the internet.  I really like this PDF book available online that gives step by step lessons you can teach your students to introduce them to the tool.  

Another resource includes the book Number Sense Routines: Building Numerical Literacy Every Day in Grades K-3  in which Chapter 3, Visual Routines, includes several pages about the Rekenreck.  Author Jessica Shumway also includes questions to ask to get students thinking about the tool and ideas for problems and numbers to try.  One of her ideas also includes reading books by Greg Tang (read one of the problems a day) and working them with the Rekenrek.

If you already teach using ten frames or dot cards, the Rekenrek is a perfect companion and extends the same concepts kinestheticly.

There are also virtual versions of the Rekenrek and an App.
Here's the link to an online version.  
Here's the link to the free app. 

    

Commercial Rekenreks can be very costly.  Of course, I have a solution for you! The Dilly Dabble Rekenreks are made to be of quality between the major commercially available Rekenreks and the personally made ones.  They are durable enough to last through several years of classroom use and much more affordable than the metal or wood ones available.  You can see pricing and details at the Dilly Dabbles Store here.

   

Of course, this post wouldn't be complete without some Freebies!  Here's a link to a recording page on which students can record ways they make numbers or solve problems using the Rekenrek and prompts you can use when working generally with the Rekenrek.

Would you be interested in Counting Frame flash cards or problem cards?  I'd love to hear your requests in the comments below.  Also, please share if you've used this tool before and how.

Addition Cootie Catcher - Freebie

I'm so excited!  I just got news today that I have been invited to be a contributor to Classroom Freebies!  I have been contributing to Classroom Freebies Too, and now get the opportunity to share on the original blog.  In celebration, here's the freebie I'll be sharing there first. This freebie is the beginning to a larger pack I'm working on.  I'd love to hear your ideas for using cootie catchers in your classroom and other themes / subjects you'd like to see them in.  You can get the freebie here and you can see a tutorial video on how to fold them below.

Number Formation Posters

Last week I posted about using the left hand to check for correct number formation and I offered student "book marks" for students' reference.  If you missed that post, you can read it here.  I promised posters for your wall, so here they are.

Trick to Solving Backward Number Formation

Here's a little tip about how to help your students form their numbers the correct direction.  Students can check the numbers with their left hand: 2 and 3 hang off the thumb, 4 sits on the thumb, 5 curves around the thumb, 6 leans against the first finger and sits on the thumb, 7  and 9 hang off the thumb.  How "handy" is that?  Here's a printable page of "bookmarks" that you can give to each student to reference as they write their numbers.  Think about sending these home at your math night or back to school night for parents to have at home as a helper.  Look for posters that you can post in your room on this blog next week.  Tip for you:  As I've taught this to my students, I've learned that I need to make sure that I take my lefties aside and remind them that they need to set their pencil down to check their numbers.  Otherwise, my lefties start writing backward numbers. ;)

Storing and Organizing Math Manipulatives

Using and storing math manipulatives can be cumbersome and chaotic.  I wanted my students to have access to the math tools any time they needed them and to be able to choose the tools that they related to and used the best.  I used this storage unit from IKEA for my children and had the thought that it would make the perfect storage for math manipulatives.  Well, it is perfect.  You can get the unit on Amazon, here's the unit I have:
or if you're lucky enough to have an Ikea within driving distance, you can get it a little cheaper and buy directly. Bins in medium and large sizes are also available along with other variations of the shelf unit.  Students can access the tools easily and they can be put away right back where they belong.  Here are some labels you can print out for whatever storage solution you have or come up with.  I just printed them on regular paper and put them on the drawers with clear packing tape.  How do you store your math manipulatives?