Differentiated Practice with Number Bonds

Part Part Whole, math facts, fluency, flexibility, application....oh man!  We are working so hard on these skills in our math class.  But (as we all know too well) our students are mastering these must-have skills at their own pace.  And we need to be available to meet them where they are.

Jess (my teammate) and I have tweaked our classroom instruction and routines so many times in the last two years because of our strong belief to support them where they are.  And fine-tuning our routines...well...let's be honest, we will probably never find the best way to do it.  Because our student needs are always changing.  But we will certainly keep trying :)

Recently, we changed up what we call "My Number Time."  This is a 30 minute block of time that we use to differentiate our instruction by providing time for independent work, cooperative groups, and small group interventions.  Some students are working specifically on "their number" that they are trying to master the number bonds for.  Another set of students are playing math games to build their fluency with all number bonds, doubles, making ten, or other +/- strategy.  Then a third group of students is in an intervention group.  Students move between these groups throughout the week.

We just changed up our "My Number Time" with these binders.  The sheets within them are laminated.  The gallon sized bag is filled with all the materials they could need to "play" with their number: chips, cubes, rekenreks, number bracelets, beans, markers, etc.  The binders will work for any number 1-10 that a student may be working on.  They can also use their notebook to record number bonds in a variety of ways.

So far all of our math classes have really enjoyed the new binders.  They are so hands on and allow them to make choices for how they want to "play" with the numbers on that day.  When they feel ready, they are allowed to take an assessment on the number bonds for that number.  It includes many missing addend, subtraction, and addition problems.

One piece that we continued to feel was missing from this "My Number Time" was the ability to go back and "play" with number bonds that have been previously mastered.  Now...they are certainly getting that practice during their game time with all number bonds.  But we wanted more.

I decided to try out a number bond memory game.  Again, I wanted it to be differentiated, just like this block of time is.  What I came up with was this:

There are four different versions and each version is differentiated by the number bonds that the student is current working on.  As soon as they were complete, my daughter and I tested them out (she needs some work in this area, too).

Version 1: Quick Image Memory

This game works on one specific number at a time.  The example above is for the number 5.  Students have to match quick images that have the same number bond.  The two cards flipped over above are not a match because one shows 5 + 0 and the other illustrates 3 + 2.  The quick images included are ten frames, dots, rekenreks, dice, dominoes, and fingers.

Version 2:Number Bond Memory

 Again, this game works on only one number per game.  This time the students must match the number bond to the quick image.  The cards flipped over above do match because they both show 5 + 0 or 0 + 5.

Version 3: Number Bond Memory

This version is played the same way. You must match the number bond and they quick image; however, these game include multiple numbers.  The game above is for the numbers 3-6.  This allows my students to practice all the number bonds that they have learned for 3, 4, 5, and 6.

Version 4: Ways To Make Memory

This version is a little different than the others above.  It includes equations.  Students must match ways to make a particular number.  For example, the cards above do not make a match because they equate to different numbers.  If the cards 3 + 3 and 4 + 2 were flipped over, they would be a match!

After introducing this to my daughter, she just kept asking to play more.  I found that she was really getting to know her bonds 3-6 well.  That made me a happy mom.

The games are all printed, cut, and laminated for our classroom students.  There ended up being 26 DIFFERENT games!  Yikes!  We want to use them during their group game time but we also feel that they could use the individual number games independently during their "play" with number time.

How do you differentiate for math facts and number bonds in your classroom?  Do you have any tips you can pass on to us??!!







If you think you could use these games, as well, you can just click on the image below:

Math Teaching: Reflecting and Changing

Thursday and Friday were both spent at the Ohio I Can Teach Math conference alongside my teacher partner, Jess.  There were four presenters that shared their knowledge on numbers sense, part-part-whole, assessments, and math in the real world.  It matched up pretty well with our math philosophy and we found ourselves nodding to most of the things being said.  And quite honestly, we were already implementing most of the ideas that were presented.  But even with this being true, there is always room to tweak, change, and grow in areas that may already be familiar.

 So, of course, I started connecting, reflecting, and making my list of changes right away. This is great place for me to share and ask for feedback on these new goals.  So I am going to share what we currently do and how we are going to change/tweak it based on our new learning.

First of all, a big theme throughout the conference was that we are working towards conceptual understanding as math teacher because that is what encourages mathematical thinkers.  One quote that really stuck out to me concerning this:

CURRENTLY DO:

Place value was a big topic discussed.  This included place value strips, bean sticks, place value blocks, and discs.  It was recommended that at the first grade level students make the bean sticks themselves so that they can see what a group of ten is composed of.  Many times place value blocks can still be a bit abstract for this age.
I love this!  We do make bean sticks already in our classroom for this exact reason.

CHANGES TO MAKE:

Although our students make these bean sticks and we use them for some +/- tens games, we don't use them enough.  So one of our goals is to use these materials more often.  Here is an example:

Our next story problem theme is "Teddy Bear Store."  We are going to make crates of teddy bears to represent groups of 10.  We will still do this because it is great manipulative and makes it more real life-ish; however, Jess and I have decided to transition over to the bean sticks so that students can make the connection and see a group of ten is a couple of different ways.

CURRENTLY DO:

Another topic that was discussed is the importance of students representing a number in multiple ways. Yes, yes...we do this.  Our "number of the day" sheet covers this pretty well.  They represent a number with a hundreds chart, ten frames, equations, etc.

CHANGES TO MAKE:

But I quickly learned that representing a number in multiple ways means so much more.  It means to have a deep understanding of how a number can be composed of different parts (part part whole).  For example: a student should understand that 35 is the same as 20 and 15.

Okay...I discuss this with them all the time when we break a number into parts.  But I really believe that I could phrase it differently to support their understanding even more.  In turn, this is going to help them when they begin regrouping when subtracting.

So instead of saying "3 and 5 make 8," I want to add in questions like: Is 3 and 5 the same as 8? or "Are 12 tens the same as 1 hundred and 2 tens?"  Being more purposeful and intentional with my questioning could make a world of difference when it comes to decomposing numbers.

CURRENTLY DO:

Math Talks were discussed in quite a few sessions that I attended.  The book Math Talk by Char Forsten and Torri Richards was displayed and demonstrated.  By displaying the pictures from the book, students are asked to tell what they see.  Through these conversations, different math concepts can be taught, part part whole thinking can be encouraged, and math language can be developed.

We have been using Number Talks to support this language, modeling, and mental math development and we will continue to do so. 

CHANGES TO MAKE:

We do not want to replace our Number Talk routines with Math Talk images; however, we think that using more real world images could be a great tool to support some our guided math routines.

One example that was shown was the use of a family picture.  Students could discuss the members of their family through number bond expressions.  YES!  I love this idea for the beginning of first grade (I want to add this).  Here is my example:

Three people in my family are girls and one is a boy (3 + 1 = 4).  Two people in my family are adults and two are children (2 + 2 = 4).  Four people in my family have blue eyes (4 + 0 = 4).

Another example given was to use pictures of things from our house, places you go, or illustrations from books/magazines.  This got us thinking...we are about to start a unit on missing addend.  Jess and I decided to use this new idea to support missing addend. 

Using this picture above of my girls collecting buckeyes from our tree, I can say: "Gertie is holding 4 buckeyes but she found 11.  How many buckeyes was she not able to fit into her hand?"

It pulls in the real world application of missing addend.

CURRENTLY DO:

Number bracelets. Love them to support part part whole thinking.  We use them each day as students continue to work on learning their number bonds.

CHANGES TO MAKE:

But...I made all of our number bracelets and I used whatever colors I had.  The suggestion was made that students in kindergarten make number bracelets 0-10 and first graders make 11-20.  These bracelets stay with them through second grade.  Then they can be taken apart and reused in kindergarten. 

When making the bracelets certain colors should be used for each number.  This allows the teacher to look out and know immediately that students are using the correct number bracelet. Brilliant!!  Why didn't I think of this organizational tool?

A FEW MORE CHANGES:

As I reflected on my learning, there are a few other minor things I want to work on as a educator.
1. Helping students understand that subtraction is the difference or distance between numbers.
2. When working on story problems (or math stories) I want to ask, "Are we looking for a part or a whole?"
3. When teaching subtraction, I want to turn away from saying "start with the bigger number" to "start with the whole number."

So what are your thoughts?  Is there anything here that you would like to change?  Or any suggestions that you have for me?

Reflection: Math Assessments

We have one week left of school before 2014 comes to a close and 2015 brings on new learning, new challenges, and new successes.  My mind is buzzing with holiday lists, music, and activities.  But reflection, as well.
Jess (my math teammate) and I have been working really hard to improve number sense and math fact recall this year.  And we have tried a lot of new things:
number sense activities
how I see numbers: part-part-whole 
connecting addition and subtraction 
Students have been working on math facts at their own pace and we tried assessing them through flash cards.

That didn't work.

It was a nice try but we just couldn't get to everyone in a timely manner.  We had to change it up.  And I really think it is working out well.  I hope I prove to be right when the end of the school year rolls around.

First change: "My Number Time"
We are giving the students time to "play" with manipulatives for their specific number.  They can decide what materials they would like to use.  Here are some examples:

House with beans

Plate with colored chips

Colored cubes and crayons

Rekenrek

Second change: After each "my number" time students take a quick self-assessment.  This helps them and us to determine if they are ready to take a quick assessment and move on to a new number.

We tell them that if the self assessment is not quick and easy, then they are not quite ready to move on.  Our firsties have really done a great job with this self assessment.  They are honest and I think it is really helping them to realize what they know and don't know (quite yet).
This sheet allows us to determine who we need to meet with the following day.

Third change: When they ARE ready to take an assessment, Jess and I pull over an individual or a small group of students to give them a fact assessment.  They look like this:

Some are mixed sheets and some have facts for only one number.  They all include addition, subtraction, and missing number because we have been teaching all facts as part-part-whole.

While the students take the assessment, we watch them and time them.  Jess and I decided not to set an exact time that each student needed to finish the sheet by but we really hope for it to be under 1 or 2 minutes (depending on the student).  We are trying to make sure that they don't use their fingers or another strategy. We want them to KNOW these parts.  And for some students they just need to be reminded (they need the confidence) that they do KNOW the parts.

But some students do not know the parts automatically.

I created these intervention sheets and they have really, REALLY helped.  These half-sheets help to illustrate how the parts of a number are connected.  I think they help because it is pretty explicit and concrete for them.  There are two different types of sheets, depending on what the individual student needs.

This routine has been working so well for our first graders.  They are feeling successful and enjoy this individual time.  For Jess and I, it is a time that we can provide differentiated, individual instruction.

We plan to continue this routine in 2015 but will continue to add components as we see the need for individual students.

If you would like to try this out with your students in 2015, it is half off right now.

 

What do you think? Is there anything we could add to this instructional time?

A Bright Idea For A Part-Part-Whole Manipulative

I have been on a part-part-whole kick.  So let's just continue that with one more bright idea (well, for now!)

I love using number bracelets, divider plates, and shake and spill to work on part-part-whole.  But I wanted a manipulative that tied directly to the number bond graphic:

I started with chenille sticks (or pipe cleaners).

Then I created a number bond manipulative.  The two parts are one color and the whole is a different color.

Once it is made, students can use any kind of manipulatives to break apart numbers (buttons, beans, or beads.)  We used beads.

Students can move the beads around to create different combinations of a specific number.

The great thing...this number bond manipulative can be used over and over with different numbers.

If you would like to hear some more ideas, please join me on TPT and Pinterest.

Please check out the links below for a variety of bright ideas from many, many other bloggers!

An InLinkz Link-up

How I SEE Numbers: Part-Part-Whole

I think that it is a pretty good sign that our Number Talks are working when my firsties just start to EXPLAIN how they see a number before I can even ask the question.
They touch their little noses (our sign that they are ready) and are so eager to talk about how they see the dot cards, tens frames, or rekenreks.
I touched on skill this last year but after reading Number Talks and being more intentional about the cards I show, I see a BIG difference. 

I love having the conversation about how they see a dot card in different ways.  We even have a bulletin board right behind my table where I display the different ways that they see the same exact dot image.

This led to an idea...

I stated in one of my previous math posts about our routine of each student working with "their" number.  They are doing lots of different activities to help them see the different number bonds for a given number.  They are moving at their own pace and do not move on to the next number until they know the different parts of the number they are on.  You can check out that post HERE:)
I wanted to give them the freedom to visualize these numbers in their own way.  

I quickly went home and created something like this and tried it out on some of my firsties.

They really seemed to enjoy it, the activity tied to our daily discussions, and best of all...they were working on "their" number.  But, of course, I was not satisfied with just these sheets.  I needed more.

I made sheets for the numbers 3-10 that look like this (These are four different sheets).  I need differentiated materials for my groups because everyone is working at different levels.  This gives me some different options because some students can handle three problems and some can handle more.  Some kids need the whole number filled in right now and some do not.

But still...I wanted more because we are also working on to help them see the connection between addition and subtraction. 

What do you think?  I hope that it will be helpful to my firsties and your students!!  If you want to try it out...I put a sample up for FREE.  It is for the number five.  Otherwise, the full pack includes numbers 3-10!

 Are there any routines you are using to help with fact fluency?

Number Sense....Trying Something New

I've said it before and I will continue to say it....I love that our career allows us to try new ideas.  And if they fail, we try something else.  And if they don't fail, we try it again, but make it even better!

One problem we have found at my school...our kids don't know their facts.  Like really KNOW them.  So we are really trying to build their number sense understanding.
Number sense...I am learning.

My teammates Jess, Carrie, and I have been reading:

 The Right Brained Addition and Subtraction suggests to set up the facts as a neighborhood. Here is what Jess made:

Our overall goal is to help the kids visual the facts.  Jess really builds the foundation for these "streets" during her number of the day routine.  Then we expand on it in guided math goups.

We start each of our guided math groups with some math talks.  I found all the "number talk" strings on TPT from the Number Sense Guy.  Um...thank you!! This saved me a lot of creating.  Here is the pack I bought:

Now times this stack by 2 because I bought the first grade and kindergarten set.  Needless to say...my hand hurt from cutting!

 Once we complete our discussion, each student gets to work on their "number." (A little something I learned from the Math Coach.)  We are trying to give each student some time to work with their particular number.  and once they master the facts for that number, they move on.
Our firsties get to use number bracelets, rekenreks, and houses to practice their facts.

 I really like the house manipulative because I think it makes our "fact neighborhood" more concrete.  They get to drop the beans in the house and find out how many people live upstairs and downstairs.  Sometimes they record this on the sheet that I made up and sometimes they just make a simple T-chart.

During this time, Jess, Carrie, and I are able to work individually with students.  We are completing quick assessments to determine what "number" each student is on.  It looks like this:

We are hoping, hoping, hoping that these little changes will make a big impact on our students and help them to KNOW their facts.

Any suggestions...we will take them!

Up next...connecting addition and subtraction.