composing and decomposing numbers series wrap up

Building kinders with great number sense has really helped us grow in all areas of math this year. Recently, I wrote a 3 part series to illustrate some of how we've worked on it especially in relationship to composing and decomposing numbers using groups of tens and ones. This is the wrap up for those three posts so you've got them all in one go-to location.

decomposing numbers - part 1

In Part 1, I explain the value and long-term picture of breaking and creating numbers using such a format. I also share with you how repeated practice makes a big difference based on the fact that it helps numerals become visual rather than just a written number. Plus, there is a free game in it for you to use with students who are accelerated. {You know I've got your back!}

Decomposing and Composing - Part 1 - Understanding

tips for working on decomposing and composing numbers in kindergarten - part 2

In Part 2, I share my tips and ideas for implementing enough practice through your day and weekly schedule in hopes that you might be able to use one or some of them. This includes practice during calendar, games, small group activities, math journaling and other practice opportunities. I tried to include tons of pictures so you could really see the range of work we do even though most of them are from the spring and show more difficult levels of this skill.

Tips for Practicing Regularly - Part 2

why does 50+7=57? working with accelerated kindergartners - part 3

In Part 3, I was nervous to share with you some of how I work with my accelerated kindergartners. I am not a gifted/talented teacher nor do I want to pretend to be. I want to give my students work that fits them well, not just "more" work since they can do our Common Core standards independently. So I share with you how I check in on my kinders' understanding, give practice to work through any leftover misconceptions and give them larger numbers to manipulate for independent practice.

Working With Accelerated Students - Part 3

I hope this collection of tips, ideas and things I've learned from teaching kinders this skill can be beneficial to you and your class. As always, I like to share from our classroom to yours! Thanks for allowing me into your classroom and for sharing your thoughts and feedback with me.

More on Decomposing Numbers

How to Teach Counting by Tens, Then Adding Ones
A Sample Decomposing LessonWhy Does 10+6=16?
Learning Decomposing with Words
Creating Decomposing/Composing Manipulatives

Phew, it's amazing how far we can come in one year! A little scary to think we get to start all over again soon. {wink}
If you like what I do here on KindergartenWorks, then be sure to subscribe today. I look forward to sharing ideas with you weekly.
- Leslie

*Free downloadable Thank You Gift included when you subscribe via email or RSS.

free measuring booklet and rulers for Kindergarten - K.MD.1, K.MD.2

When I am teaching a skill that doesn't need to be differentiated {really} and that lends itself to exploration I try to accomplish covering it whole group. Most of my math instruction is done in small groups, but today I'd like to share how I teach measurement to my kindergarten class.

When I teach measurement, I do a little bit every day and I use a booklet to give us practical application practice right away. Before we being our guided math zones, we will start out our time together gathered on the carpet. I use hand motions and a chant-like way of explaining "I can measure" and begin to talk about measuring ridiculous things. This captures their attention and they hear the word measuring at least 15 times.

{Free Measuring Booklet}

I use materials each day to practice the measurement concept and teach each attribute with a hand motion to make the vocabulary stick. They complete the first page as we discuss what it means (focusing on the beginning sounds), and the second page of each attribute to draw an example of what we measured and write numbers to match (showing our thinking).

These mini-lessons cover these measurement standards:

• K.MD.1.a Distinguish between measurable and non-measurable attributes of objects. Note: Measurable means quantifiable, such as length, weight, height, distance around.
• K.MD.1.b Name the measurable attributes of a given object.
• K.MD.2 Compare the measurable attributes of two objects using appropriate vocabulary including taller/shorter, heavier/lighter, longer/shorter.

We recall measuring once in a while just for review after this set of mini-lessons as most have it down. They practice comparing weights and heights in the practice zone through a few independent activities.

We also use rulers I made that make measuring length a bit easier on kinders to see that the measurement carries across the depth of the ruler. They are actually inch long segments and feature a caterpillar {that looks very hungry if you ask me} so you can call them inch worms if you want {wink}.

We bring these out later in the quarter to review and explore measuring and documenting measurements in our math journals.

{Free Caterpillar Rulers}

More Math Games

Subtracting 10 Free Bump GameFree Game for Adding 1

Teddy Bear Number Line Addition

Subtraction - Am I the Last One?

free "ways to make 5" bingo - K.OA1, K.OA.4

Bump Games

More Math Tools

Tools for Beginning Number Sense - How to Draw a Ten Frame

creating ten frame manipulatives

subtraction - am I the last one?

free sorting mats

free math songs and chants

Do you have any fun activities to practice naming and comparing the attributes for measurement?

If you like what I do here on KindergartenWorks, then be sure to subscribe today. I look forward to sharing ideas with you weekly.
- Leslie

*Free downloadable Thank You Gift included when you subscribe via email or RSS.

why does 50+7=57? working with accelerated kindergartners

Working on decomposing and composing numbers into their groups of tens and ones is a key standard in kindergarten. Kinders are expected in Common Core standard K.NBT to work within numbers 11-19, but what about students who are ready for an accelerated pace? Here's a glimpse into a portion of a guided math lesson from our classroom to yours. We are focusing on moving into expressing this standard with equations. This is a follow up from the first two posts in this series,

• Decomposing and Composing Numbers- Part 1 and
• Tips for Working on Decomposing and Composing Numbers in Kindergarten - Part 2

Decomposing and Composing With Accelerated Students

Now, I know that we often call this "place value" as teachers, but really it is number sense because they truly have to understand what these numbers are in quantity, number form, numeral and in comparison to their surrounding numbers (like where they fall on the one hundreds chart for example). It's all intertwined. No matter what number or skill you're working on - it can be connected to it's value in tens and ones.

Why does 50+7=57?

The Question
I am about to revisit the lesson in my math groups to ask my students, "Why does 10+6=16?" Just like when I asked earlier this year, "Why do teens have a 1?" I know that I might face blank stares and we might be headed into murky water discussion.

Maybe.

We've worked intentionally to practice understanding teens and other numbers and their value in tens and ones. Yet, that was with pictures and words like "group of tens and ones." I've found that a big misconception comes into place when transitioning to equations because they are used to seeing or representing 16 as 1 group of ten and 6 ones. What if they were to just take what they've always done and put it into an equation?

The "Stuck" Point

Whether we are working on level or numbers to 100... I apply this question... Will writing 1+6=16? Does that make sense?

Well, of course not... because equations don't have words in them, right? So how else can we show 1 group of ten in order to show that it's ten? If we get stuck, this is usually where it happens - the "stuck" point.

Drawing Out Their Thinking

This is where we will be exploring. I usually ask my students to draw or write about their thinking whenever I pose questions like this. Why draw? Because they have a harder time sometimes verbalizing their thinking.

Give 'em a drawing to talk about and they are much more successful.

Pre-Assessing Groups

Last week I began to pre-assess my two highest math groups on this concept to see if we'd need practice or need to address any misconceptions. With these groups of students {and I'll be totally honest that I have an exceptionally high number of students that have these skills this year in comparison to any other year} I know that their number sense is stronger and can apply the same concept, just deeper. So we're exploring, "Why does 50+7=57?"

I simply asked them to "show their thinking" {they must seriously hear that 12 times a day} and handed them a white board.

Their responses gave me great insight as to where we can work next and that making the transition to equations will be a natural next step for them.

Guided Practice - Small Groups

So no blank stares this year when it came time to approaching equations, though I did find that when we practiced it more in our booklets that we had to work through the common misconception with two students. With enough practice and learning to self check by asking like, "Can 8+1=81?" we are figuring it out and moving on!

Follow Up - Independent Practice

As the natural follow up after I've seen we've made good progress in a skill area I'm sure to put materials into our practice zone. For decomposing and composing using equations I'll be adding our equation cards for our magna doodle boards, I SPY tools into our independent practice zone to improve accuracy and fluency (and I have a game in the works).

Previous Step: Understanding Composing and Composing Part 1
Previous Step: Tips for Composing and Decomposing Part 2

More on Decomposing Numbers

How to Teach Counting by Tens, Then Adding Ones
A Sample Decomposing LessonWhy Does 10+6=16?
Learning Decomposing with Words
Creating Decomposing/Composing Manipulatives

I hope you enjoyed this series as I enjoyed thinking through what I've learned about working with kinders on this standard. Did I mention that I had nooo clue what it even meant when I first read it? We all learn and grow. {wink}

If you like what I do here on KindergartenWorks, then be sure to subscribe today. I look forward to sharing ideas with you weekly.
- Leslie

*Free downloadable Thank You Gift included when you subscribe via email or RSS.

tips for working on decomposing and composing numbers in kindergarten - Part 2

Decomposing (breaking down) and composing (making) numbers is a multiple part Common Core standard that we work on in Kindergarten. I started out my own exploration with this concept when I shared "why does 10+6=16?," and today I want to give you my tips on ways to work on it during your normal class day. Why is this standard important? Read the last post in this series, Decomposing and Composing Numbers- Part 1.

Now, I know that we often call this "place value" as teachers, but really it is number sense because they truly have to understand what these numbers are in quantity, number form, numeral and in comparison to their surrounding numbers (like where they fall on the one hundreds chart for example). It's all intertwined. No matter what number or skill you're working on - it can be connected to it's value in tens and ones.

Tips for Working on Decomposing and Composing Numbers in Kindergarten

Here are my top ways of integrating decomposing and composing teen numbers 11-19 into your day (and higher numbers):

1. Calendar

Use the repetition that comes during a calendar activity to see it and hear it often. Track the days in school as an example of how to modify a classic calendar activity and then use it to either compose or decompose numbers. You can also use it to figure out how to make 5 and 10.

My students are also working on a variety of composing and decomposing workmats since I change these out every couple of months. They get different kinds of practice that all has a purpose since it comes from the numbers we use in the calendar and they aren't stuck thinking that we can only make or break numbers in one specific way.

Below you see that for a time we were decomposing with words and composing by circling the correct groups of ten and creating the set of ones. Same skill, different format.

2. Games

Finding games to play in small groups, pairs or independently for math centers, stations or zones is crucial. Students often do some of their best work when given the most amount of time to practice. Playing games is one of the best ways to increase the amount of time they are practicing a skill.

Below you can see that we've got our Hurry Up Reindeer Composition game up and ready to be played. Students feed the reindeer glitter ice cubes using tens and ones.

This game is one of my favorites. Playing memory when it is skill specific is a great eye opener. My students work on first finding matches of tens and ones to just the number and are now ready for matching the decomposition equation to the number.

Composing Decomposing Memory

And playing games whenever you can integrate them into your day (computer lab, centers, etc.) is a sure fire way to give them additional practice as long as you can find a skills specific activity like this one below.

Tens and Ones - Online Game

3. Small Group Activities

By far one of my favorite ways to practice since you can work through misconceptions and give students more guided attention. (For example if someone needs practice starting at not 1 when counting, and needs to start at 10.)

Here is an example of when we were learning to create and represent the number in a decomposing statement with words using 10 frame manipulatives.

Decomposing Sheet

When working in small groups, I also try to fit in a warm up or wrap up activity where we get to explore the concept in a different way, like playing I SPY for numbers. As seen below, students find the hidden numbers and then write the decomposed tens and ones equation to match and highlight the number on the hundreds chart.

Place Value Hide and Seek

4. Opportunities to Draw

Students need opportunities to draw out numbers using ten frames and a variety of objects. So give them time to draw in a math journal or during calendar time to express what these numbers look like.

5. Making, Representing and Using Equations

This one seems obvious and it is. Using a variety of tools, let students make equations, draw them out, represent them with objects and also use given equations in order to build their skills is important.

This picture from Mrs. Parker is a great example using our booklet for students to practice using words to make and break teen numbers.

And this is my newest math group recording activity that I am working on with my groups so that they can take the same skill they already have and express it using equations. No matter what range of numbers they have in their comfort zone, they can apply this skill of writing equations with tens and ones.

So there you have it. I find it extremely helpful to incorporate it into calendar time, games, small group work and individual drawing opportunities in addition to finding ways for students to practice making, representing and using equations to show their thinking.

Previous Step: Understanding Composing and Composing Part 1
Next Up: Extending this Standard for Accelerated Students Part 3

More on Decomposing Numbers

How to Teach Counting by Tens, Then Adding Ones
A Sample Decomposing Lesson
Why Does 10+6=16?
Learning Decomposing with Words
Creating Decomposing/Composing Manipulatives

I hope these top tips of mine can help you find ways to incorporate this standard into what you are already doing in your day, just in a variety of ways.

If you like what I do here on KindergartenWorks, then be sure to subscribe today. I look forward to sharing ideas with you weekly.
- Leslie

*Free downloadable Thank You Gift included when you subscribe via email or RSS.

Decomposing Numbers - Part 1

Decomposing numbers means to break down numbers into their sub-parts. Common Core standards has kindergarten students decomposing numbers in two ways. The first is to decompose numbers into their tens and ones (focus on numbers 11-19) and the second is to show how any number 1-10 can be created using a variety of addends.

I want to focus with you on the NBT.1 Common Core standard which addresses the tens and ones (or place value  aspect of breaking and creating numbers. Let's look at how it develops and how we can practice and extend it for our kinders. I've got three posts in this series for you!

Part 1 - Understanding Decomposing/Composing Numbers as Teachers

There are two main pieces of this standard:

• The first is using objects and words to show that teen numbers have a group of ten and some ones. 
• The second is expressing this break down using equations.

Why Do We Expect Them to Decompose and Compose Numbers?

{And why do I keep writing about it?}

The simple answer is because there is value in students being able to see the groupings, relationships and patterns in numbers. We are laying the foundation for students to be able to do 53+12 and see that they can manipulate it into making 50+15 or 60+5 or 50+10+3+2 or any other variety of ways to see the quantity as it makes sense to them.

Now that's the bigger picture and carries us into older grade level Common Core standards... so lets bring it back down to our kindergarten level and working with slightly accelerated students.

We are working on understanding that numbers 11-19 have a group of ten and then ones. Students in kindergarten are often excited about bigger numbers and want to explore what those other numbers are, look like and "how big" they are.

Seeing numbers broken down into a pattern of their groupings of tens and then the addition of some ones makes numbers palatable and simple. It gives a "visual" {especially if you are representing with ten frames} to what 6, 16 or 67 really looks like and is.

Visualizing Groupings With Accelerated Students

If you have students with good number sense within 100, then you can deepen their skills by playing games like subtract 10 bump. This roll and cover bump game is perfect for visualizing the groups of ten in a given number and then visualizing one group less. Have a 100's chart handy or some pre-filled ten frame cards as a tool if needed, but my goal is to work on visualizing with these kinders.

{Hit or Miss Subtract 10 Bump}

To play this game, students roll two dice to create a number (11-66). They subtract 10 and then cover that space on the two-page game board. It follows the typical "bump" rules to where players can bump or lock their space. First pirate, I mean player, to lay out all of their cannons (linking cubes) wins.

Next Post in this Series:

My Top Activities/Games for Practicing Decomposing 11-19
(Tips for fitting Composing/Decomposing into your day)

More on Decomposing Numbers

How to Teach Counting by Tens, Then Adding Ones
A Sample Decomposing Lesson
Why Does 10+6=16?
Learning Decomposing with Words
Creating Decomposing/Composing Manipulatives

I hope you can use some of these ideas to better understand decomposing numbers. What's your experience with this standard?

If you like what I do here on KindergartenWorks, then be sure to subscribe today. I look forward to sharing ideas with you weekly.
- Leslie

*Free downloadable Thank You Gift included when you subscribe via email or RSS.

guided math - before and after

Creating a guided math schedule that works for you and your daily schedule is important! If you're willing to meet groups of students where they are and give them practice that helps them progress - you're gonna love it. Why? The intrinsic reward as a teacher seeing students succeed is tremendous.

How can someone start? Here are my top tips and ideas on how to put it into practice... as soon as you're willing to start.

What's the first step?
1. Decide to do it. Anyone can complain about lack of time and scheduling. The reality is that if we want to find a way to do something, we will. Make the decision to try it and allow your mind to begin to try and visualize what it might look like in your classroom. If you know why you want to make the change, you're well on your way to making it a success!


What's next?

2. Create a schedule that will work for your time allowance and student needs. You want this to become the main focus of your math time instead of added to your day. None of us have an extra ___ mins or hours in the school day, so it does have to replace something. With some creative thinking I've found that it effectively replaced all of my whole group math time and worksheet practice (we use Saxon in our district). And it allowed me to even add more math time into our day without taking away from anything else we do since it is all so valuable.

Consider how you can s-q-u-e-e-z-e value out of whatever time you determine you can commit.

Questions to Consider:

1. How long can your guided math time be? {Actual, physical time...}
2. How long would you ideally like to meet with a group of 5-6 students to cover a warm up, main activity and wrap up?
3. What kind of transition method(s) would you apply? Would you do a rotation in a day?
4. What would other students be doing to be learning independently allowing you time to work with your group?
5. Will you be able to meet your standards and student needs if you adopt this new style? Will you need to add anything, or can it be integrated into this time somehow?

I know that my answers won't fit your classroom, but perhaps some of the way I came to my decisions will help you determine yours {under the green banners}. I'll also link to my answers now that I am on the other side of the fence {under the red banners}.

How long can your guided math time be?

Previously my math lesson and worksheet time worked out to be about 40 minutes. If I can use 40 minutes, that won't be long enough with transitions to meet two groups in a day. Yet, if I can figure out an additional 20, then I think an hour would make it possible. What can I tweak a few minutes or get better at to gain 20 mins., four times a week? An hour should be enough time... I think.

How long would you ideally like to meet with a group of 5-6 students to cover a warm up, main activity and wrap up?

I know that it wouldn't be beneficial to meet every group, every day with the current time I have allotted. Groups would be ridiculously short with very little time to dig deeper and explore. However, I could meet half of the class each day and schedule in sharing time so that I can check in with everyone, every day. Plus, if I have some accountability from the other half of the class it'll be super close to this goal.

allow enough time to explore and dig deeper

> Read about changes in timing

> Read about a lesson plan flow that works

What kind of transition method(s) would you apply? Would you do a rotation in a day?

I should keep the same transition method of turning on the clean up song and use an icon chart just like during literacy centers. Why change something that is working and they know how to use independently? The only thing will be bigger groupings of students so I'll need to spread them out around the classroom to keep voice levels lower and help keep them on task. I could do two rotations to meet with half of the class each day of guided math.

math zone rotation

> Read about our expectations, schedule and rotation

What would other students be doing to be learning independently allowing you time to work with your group?

This one requires some planning and begs more questions. How can I break them up so that they are spread out across the room and on task? How can I give them enough practice with everything we need to cover if they are only meeting me twice a week?

I don't want to make myself a "zone" or center, but I can't think of a way to make that happen as I have only come up with 3 independent zones. I feel good about them showing their thinking in math journals, this will greatly replace their worksheets and then some! I am excited about them practicing math using technology... I hope that really reaches some that are not as high and can extend those that are getting it. I know that giving games and activities that are practicing the same concepts we do in a group will be the right thing for independent practice.

utilizing the recording zone for students to show thinking

> Read about our technology zone

> Read about our recording zone directions, sample and benefits

> Read about our practice zone full of standards based games, activities and how it allows me to differentiate

> Read about the teacher zone, questioning and what they teach me

Will you be able to meet your standards and student needs if you adopt this new style? Will you need to add anything, or can it be integrated into this time somehow?

To be honest, I don't know. I figure that decreasing the time I spend with all students could have an impact, but how self-aggrandizing is that to think that I am the secret to their learning? If I structure things correctly, they should be able to practice, make mistakes and learn without me. Plus, the time they have with me will be more valuable since it is hitting exactly what they need versus having to do what everyone else is doing regardless of their skill level.

meeting a group's needs

Truth be told, that I have found that I generally want to add in a mini-lesson some days before or after our math time as a way to make the management of it all smoother or to hit something that doesn't need the intensity of being hashed out in the teacher zone. I find ways to fit it in and learned that I can still create some whole group math time that is more fruitful using our calendar binders as a way to unify what we are all learning and working towards. The planning and flexibility make it happen.

I know this list won't be the end all be all, and I'm still learning how to improve all the time. But I hope it helps as you plan to move towards differentiated instruction. Our classroom motto is, "The more we practice... the better we get."

More On Math

> Read about calendar binders

> Read about planning/aligning to Common Core

> Read about creating a planning binder

> Read about adapting in the moment

Based on what I've learned, tried and continue to see in my kinders... Now that I'm here, there's no turning back! If you like what I do here on KindergartenWorks, then be sure to subscribe today. I look forward to sharing ideas with you weekly.
- Leslie

*Free downloadable Thank You Gift included when you subscribe via email or RSS.