Math Coach's Corner

Earth Day Freebie

2015-04-18T07:28:00.002-05:00

It's a big weekend here on my blog! Over the next couple of days, I'm migrating to a redesigned WordPress format. It's exciting, and I think you'll love the new look. There might be a few glitches as the transition takes place, so please give me some grace. Thank you to Christina at Inspired VA Services for handling this process for me and holding my hand every step of the way!

A key component in developing number sense is having the ability to "play" with numbers--take them apart (decompose), put them together (compose), and represent them in many different ways. Today I have a freebie for you that your kiddos can use to explore multiple representations of numbers to 120. It's an Earth Day-themed version of my Number Sense Workout that I published awhile back.

If you're looking for additional Earth Day resources, you might like my Love the Earth, Love Math unit that includes activities for five different 1st grade standards and my free Earth Day Equations, Capture 4 game, also for 1st grade standards.

Grab your multiple representations freebie here.

Developing Fraction Sense

2015-04-12T13:24:00.000-05:00

The Problem

It all started with a question...where should I put 3/4 on the number line? I was starting a unit with my 4th grade RTI kiddos on fractions, and the question was meant to activate prior knowledge and give me a baseline of their understanding. I had passed out fraction tile kits, because I planned to use them in the lesson, so the students had the tiles in front of them when I posed the question. I had also drawn a number line showing 0 and 1 on my white board easel. When I asked the first student, she told me that it wouldn't be on my number line. I asked what she meant, and she said it would be further past the 1. Oh. I erased my number line and drew a new one showing 0 to 5. The student proceeded to tell me that 3/4 would be somewhere between 3 and 4 on the number line. I asked the four other students in the group and the five students in the next group, and I got responses of between 2 and 3, between 4 and 5, between 1 and 2, and more who thought it was between 3 and 4. Not one student told me it would be between 0 and 1. Time to punt.

I asked the students to show me 3/4 using their fraction tiles and, while they did that, I asked if I could borrow their 'whole' pieces. I used the wholes to draw a number line from 0 to 5 on my table and laid the whole pieces under my number line (see picture).

I would like to say that once they saw the concrete pieces together with the number line that the connection was immediate, but it was not. I still had students who thought that 3/4 would be between 3 and 4. We spent the next twenty minutes discussing the meaning of the numerator and denominator and placing different fractions on the number line. I'm confident that my kiddos are on their way to developing strong fraction sense.

What is Fraction Sense?

I've been reading a powerful new resource titled Beyond Pizzas & Pies, by Julie McNamara and Meghan M. Shaughnessy. They describe fraction sense this way:

Fraction sense implies a deep and flexible understanding of fractions that is not dependent on any one context or type of problem. Fraction sense is tied to common sense: Students with fraction sense can reason about fractions and don't apply rules and procedures blindly; nor do they give nonsensical answers to problems involving fractions.

If that sounds a lot like how you might describe number sense, you'd be right, because fractions are numbers. That's the concept that so many of our students lack--the idea that fractions are numbers. Think back to the first student's response about where 3/4 should be placed on the number line. She said between 3 and 4. She saw the 3 and the 4 as two distinct whole numbers, rather than understanding that the 3 and 4, when written as a fraction, imply a relationship between the numerator and denominator (McNamara/Shaugnessy, p xviii).

What Do We Do?

KNOW YOUR STANDARDS Whether your standards are the CCSSM, the Texas TEKS, or some other set of standards, it's essential that you understand the standards for your grade level. The standards for each grade level are perfectly aligned, like interlocking puzzle pieces, to develop deep understanding. If you don't teach your part, it's awfully hard to complete the puzzle. Check out this blog post for an explanation of the 2nd Grade fraction TEKS.

DON'T SKIP THE MANIPULATIVES Fractions are such an abstract concept that without concrete support it is nearly impossible for students to develop conceptual understanding. Manipulaltives and concrete learning are for every grade level, not just the primary grades. In Beyond Invert and Multiply, a companion resource to Beyond Pizzas & Pies, McNamara emphasizes the importance of providing students with visual models for fraction computation.

QUIT TEACHING TRICKS We do our students a huge disservice when we teach them to cross multiply to compare fractions (also known as the "butterfly method") or to "invert and multiply" to divide fractions. This is a short-term solution that does absolutely nothing to develop their fraction sense.

IMPROVE YOUR OWN FRACTION SENSE If you are looking to revamp how you think about and how you teach fractions, the two books I referenced earlier are excellent resources. Not only are both bursting with activities you can try in your classroom tomorrow, but they also come with DVDs that show you what effective instruction looks like in the classroom. The format of the books make them perfect for a book study, a professional development session, or a team planning resource. Check out this video for a glimpse inside Beyond Pizzas & Pies:

Join in this important discussion by leaving a comment below.

What Makes a Teacher Outstanding?

2015-03-25T17:54:00.001-05:00

Tonight I'm asking you to help me write a blog post. We have all read or heard the research that states that teacher quality is the single most important factor in student success. Not class size, not resources, not even socioeconomic factors. Teacher quality.

That has me wondering, how do we define what makes a teacher outstanding? What are the characteristics that an outstanding teacher possesses?

Here's where your part comes in. Please think of a teacher you have worked with who you would consider to be truly outstanding and leave a brief comment describing one or two important characteristics that teacher possessed. You might also think about a teacher that was not outstanding and comment on what they lacked. I will compile all of your wonderful comments into a future blog post, so PLEASE sound off!!

What's My Number? Differentiating in K-1

2015-03-15T10:24:00.002-05:00

In her book How Children Learn Number Concepts, Kathy Richardson devotes an entire chapter to composing and decomposing numbers. It may surprise you that the title of the chapter is Understanding Addition and Subtraction: Parts of Numbers. This quote sums it up beautifully:

"If basic facts are to be foundational, they must be based on an understanding of the composition and decomposition of numbers."

Both the CCSSM and Texas TEKS have a number of standards in Kindergarten and 1st Grade related to composing and decomposing numbers, as shown in this table.

One important feature of the standards that is often overlooked is that they describe the level of concrete or pictorial support a student should receive. Notice that K.OA.3, for example, states that students should use "objects or drawings" and record the decomposition using a "drawing or equation." In that one standard, you hear each phase in the concrete, representational, abstract (CRA) sequence of instruction. Notice how the concrete and pictorial are tied to the abstract (equation) to help students make that important connection. Rushing students to abstract, or purely symbolic, learning is a recipe for disaster, and that is recognized in the standards.

Composing and decomposing numbers is such a critical component of number sense that it should constitute a a major part of the learning that takes place in Kindergarten and 1st Grade. Richardson states, "As children learn the combinations that make up the numbers to 10, they will reach the point where they know the parts so well, they can identify a missing part when they know the total and one part." In other words, students need lots of practice composing numbers, working with the various combinations of each number, before they will be able to decompose numbers, or find a missing part. In your bag of instructional tricks, you will want to have a wide variety of activities to practice composing and decomposing numbers. These blog posts will give you ideas for activities as well as freebies you can use this week!

For all of these activities, it's important to understand that students should master the combinations for one number before moving on to the next. It does no good for a child to practice composing and decomposing 6 if he does not know the combinations for 5. That's where differentiation comes in. Richardson describes using the "hiding assessment" to determine a child's fluency with each number. To determine if a child knows all the combinations for 3, ask the child to count out 3 counters or linking cubes. Hide some counters and show some, asking the student to identify how many are hidden. For example, hide 1 counter and show 2. "If I have 3 counters and 2 are showing, how many are hidden?" Continue this routine for each combination for 3 (hide 3, show 0; hide 2, show 1; hide 0, show 3). If the student can name all the missing parts for 3, try the combinations for 4. When the student can no longer easily name the missing parts, that becomes her number. Use a recording sheet to keep track of each student's number so you can differentiate activities, such as those described above, based on each student's needs. For example, all students might be using Shake and Spill in a workstation this week, but each child is using his or her own target number. Every few weeks, "test" your students to determine if they are ready to move on to a new number.

While it might seem daunting to differentiate based on each student's number, the good news is that a few engaging activities go a long way. Constantly rotating the activities keeps engagement high and allows you to meet the needs of each student without a great deal of prep work. For more great activities, check out Building Number Sense: Games and Activities to Practice Combinations for 10 or these other blog posts tagged with the key word "compose."

Rebranding "Show Your Work"

2015-03-01T11:26:00.000-06:00

Marketers know that a product's brand is everything. If a product is not selling to its potential, one solution is often to tweak the brand, or "rebrand" the product. Kentucky Fried Chicken changed their branding to KFC to de-emphasize 'fried chicken" and appear to be a more healthy option. If it works in business, shouldn't it work in education?

In math classrooms across the world, students are told on a regular basis to "show their work". I wish I had a nickel for every time those words came out of my mouth during my educational career. It is certainly done with good intentions--it is critical that students are able to communicate mathematically. Not to mention the valuable feedback teachers receive when they analyze the "work" a student has shown.

My problem is not with the process, it's with the words, so I have been experimenting with rebranding "show your work".

As I see it, there are two major problems with asking students to show their work. First, the words hold a very negative connotation in the minds of students. It's something they have to do. Furthermore, the words are often delivered in a way that is not conducive to cooperation. "John, if I've told you once I've told you a million times, you've GOT to show your work." "Valerie, I'm not taking this paper until you show your work!"

Second, many students don't show their work because they don't know what the heck it means! My favorite is the student who circles the multiple choice answer he thinks is correct and then x's out the other choices. If you ask him, he is "showing his work".

For my suggestions, I will address the second problem first. Students have to be specifically taught what it means to show mathematical thinking (see how I'm rebranding it?). This happens through a great deal of modeling and coaching. I'm blessed to work with small groups exclusively, so I am able to coach my students one-on-one, helping them to understand how to comprehend and make sense of each and every sentence in a math problem.

Now, to overcome the negative connotation of the words "show your work", we have to stop using them. Think about it, when you are solving a problem do you think to yourself, "Hmmm, I've got to show my work." I don't think so. What I DO do, is make notes to myself as I interact with the problem. Those are now my go-to words when working with the students--I document my mathematical thinking by making notes as I interact with the problem.

I have been using this approach with my students for about a month now, and I am very pleased with the results. They seem more open to the process and, through coaching, they are learning how to take notes on their own and determine important information. It's a thinking process, not a rote procedure. In a follow-up blog post, I'll discuss more about how I help them make sense of problems.

I'd love to hear your thoughts!!

Fly on the Math Teacher's Wall: Fractions

2015-02-21T20:02:00.000-06:00

Welcome to the Fly on the Math Teacher's Wall blog hop! In this recurring blog hop series, a great group of mathematics bloggers, covering all grade levels, band together to squash mathematical misconceptions. This time around, we're tackling fractions.

The misconception I am discussing is that a larger denominator means a larger fraction. Ask a handful of third graders (or 4th graders or 5th graders...) which fraction is greater, 1/8 or 1/4, and most are likely to quickly tell you 1/8. With big, proud smiles on their faces. You're nodding your heads out there--I see you! You've been there.

There's a reason this misconception is so widespread. Up to this point in their educational career, bigger numbers always meant bigger values. Eight is greater than four. When students begin to learn about fractions, they erroneously apply whole number reasoning to fractions. One-eighth must be greater than 1/4, because 8 is greater than 4.

So how do we address this misconception? First and foremost, students must have tons of experience with a variety of concrete and pictorial models of fractions. Use fraction tiles, fraction circles, Cuisenaire rods, number lines, and cut paper strips. It's pretty hard to look at models of 1/8 and 1/4 and not see that 1/4 is greater. The idea that fractions should be explored using manipulatives and models is very apparent from the wording of the 3rd grade Texas TEKS, but not so much in the CCSS. I cannot overemphasize, however, do NOT rush to abstract symbols.

The other way we can overcome this faulty reasoning is to help students truly understand the meaning of the denominator. The more parts an object is divided into, whether that object is a pizza or a number line, the smaller the parts.

Both the CCSS and new Texas TEKS address the issue of comparing fractions in a way that will help students deeply understand the denominator. The 3rd grade standards are really well written, once you get past understanding all the 1/b and a/b references, and will definitely result in better fraction number sense for our students.

Here are the standards for comparing fractions for both the CCSS and the TEKS:

Notice a few key points...

Students are only comparing two fractions, not ordering more than two
The denominators are limited to 2, 3, 4, 6, and 8
Students only compare fractions with either the same numerator or the same denominator
The TEKS specifically mention words, objects, and pictorial models along with symbols
Both include verbiage about reasoning about their size and justifying the conclusion
The CCSS states that students must understand that the reasoning only works when referring to the same whole

Let's first consider comparing fractions with the same numerator. When two fractions have the same numerator, it emphasizes that a larger denominator means smaller parts. Look, for example, at the representations below of 1/8 and 1/4. When you look at one piece of each pizza, the idea that eighths are smaller than fourths is pretty clear. It works anytime the numerators are the same. For example 2/6 and 2/4, or 3/8 and 3/6.

Third grade students are also required to compare fractions with the same denominator. This emphasizes that the denominator describes how many parts the whole has been partitioned into (thereby influencing the size of the parts) and the numerator describes the number of those equal parts you have.

That's it! Those are the only two types of comparison 3rd grade students need to do. And if they truly understand and can explain these comparisons, the next generation of students we send up won't leave us scratching our head when they say 1/8 is greater than 1/4.

Do you like the cards pictured above? Well, guess what? They are my gift to you tonight. This freebie includes 16 cards--8 comparing equal numerators and 8 comparing equal denominators--along with a a recording sheet students can use to document their thinking in both words and symbols. Click here to grab your freebie!

Finally, who doesn't love a giveaway? In the spirit of a fraction blog hop, one lucky winner will receive my Fraction Bundle and five winners will select a fraction product of their choice! But hurry, the giveaway isn't around for long!

a Rafflecopter giveaway
Ready for the next stop along the hop? Head on over to Adventures in Guided Math!

What I'm Reading...Intentional Talk

2015-02-16T14:16:00.000-06:00

"When we press beyond procedural explanations into explanations that include reasoning, we are supporting students in justifying their ideas." Intentional Talk (Kazemi/Hintz)

When you are planning instruction, how often do you consider the sound of your mathematics instruction and the conversations you want your students to engage in? If you answered not often, then Intentional Talk by Elham Kazemi and Allison Hintz might radically change the way you plan.

Math is no longer a spectator sport. We know that to truly develop mathematical thinking, students need to be active participants--they should be doing math and talking about math. This dramatically changes the role of both student and teacher. The teacher becomes a facilitator, rather than a giver of knowledge, while students drive the work and the conversations. Intentional Talk provides a road-map for that change.

If you have tried incorporating accountable talk in your classroom, then you know it is easier said than done. To focus your efforts, the authors outline four guiding principles of classroom discussions in the Introduction and differentiate between Open Strategy Sharing and five targeted structures, each with its own goal and talk moves.

Compare and Connect
Why? Let's Justify
What's Best and Why?
Define and Clarify
Troubleshoot and Revise

Also included in the Introduction is a classroom example of a teacher using Open Strategy Sharing and two targeted follow-up structures with her class. Following the Introduction, each type of talk structure receives its own chapter.

The chapters are thoughtfully organized to provide all the tools you need to implement each structure. Each chapter contains information about the strategy; planning considerations, including completed planning templates (the Appendix contains blank templates); and both primary and intermediate vignettes. The vignettes are the true power of the book, because you feel as if you are actually in the classroom observing a master teacher at work. References to research and the CCSS Mathematical Practices are sprinkled throughout the book, but do not distract or become tedious.

This is a book you will use as well as read. You can't read a chapter and not have a new strategy to try in the classroom tomorrow!

Remediation...Who Needs It?

2015-02-14T12:18:00.000-06:00

I was a classroom teacher for many years, an instructional coach for several more, and I currently serve as a K-5 math interventionist. Each role has allowed me to look at remediation through a different lens. Now that I am intimately involved in the Response to Intervention (RTI) process, I am seeing patterns emerge in how we identify and service students deemed at-risk in math. It can't all be about classroom grades or standardized test scores. We have to look at the underlying reasons for a student's struggles. And if we are identifying large chunks of our student population as Tier II or Tier III, we have to look deeper for systemic reasons.

Students with Behavioral Issues

Let's just take this one off the table. If a child is failing math because of a behavior issue, I can't help. Sure, I can forge a relationship with the student and coax the math out of him, but you can do that as easily as me. It does no good to put a student with behavior issues in a math remediation group with students who truly need remediation.

Students Who Lack Current Grade Level Skills

Face it, students do not all learn at the same pace. Some learn more quickly and some more slowly. If a teacher tries to teach all students at the same pace, some will fail. That doesn't mean those students need to be pulled out for remediation. It probably means that the teacher should reflect on her instructional strategies to determine if they are meeting the needs of all students. A teacher who underutilizes small group instruction will likely have a higher percentage of students not mastering grade level skills, because whole group instruction will not adequately meet the differing needs of students.

Students Who Lack Number Sense

These students are probably good candidates for RTI. If a student does not understand how to compose and decompose numbers, see the relationships between the operations, or lacks a basic understanding of place value concepts, they will undoubtedly fall further and further behind in math until those foundational areas are addressed. That said, this is the primary learning that is going on in K-2, so if a student lacks number sense in K-2, it could be argued that they just lack current grade level skills. So then we go back to the last conversation--is the teacher differentiating instruction and working with students in small groups at their level?

Students Who Can't Apply Mathematics

"They can multiply, but when it's in a word problem they bomb it!" These are often the students who fail standardized tests. Students need to always see mathematics in context. Sure, they need to learn computation skills and how to generate equivalent fractions, but if they learn those skills in isolation, they never see the application of the skills in a real-world setting. Just as we have to teach students mathematical concepts, we have to teach them how to dissect and solve word problems. This should not involve tricks and key words, it must happen through modeling and strategic instruction, including reading comprehension strategies. In Texas, process standards are embedded into 75% of the items on our state assessment. If we don't embed process standards into 75% of our classroom instruction, our students will not be successful.

Students with High Mobility Rates

My heart goes out to these kiddos. Their families can't stay put in one place long enough for them to learn anything! They often come to us with huge gaps, because as they move around they miss big chunks of learning. These students definitely benefit from intervention, which can close the gaps and get them back on track.

Students with Learning Difficulties

There are students who, despite our best instructional practices and efforts, can't seem to overcome their struggles. Additional testing is often required to determine if these students require the specialized talents of a special education teacher.

I hope this list gives you some food for thought. I'd love to hear your comments and personal stories about intervention!

Engaging Games for Composing and Decomposing Numbers

2015-02-07T19:08:00.000-06:00

After spending several weeks exploring number bonds, this week I've been working with my firsties on the combinations for 5. This has been such a fun week as we used three highly engaging activities to practice combinations. On Friday, I asked the kiddos if they'd ever get tired of playing these games, and they said, "No!" Good thing, since once they master the combinations for 5, we'll go on to 6-10.

Shake and Spill

Shake and Spill is such an easy little activity for decomposing numbers, and because it's a concrete activity, it's a great starting point. Notice in the picture that the Shake and Spill mat is inside a plastic workstation box. This helps to contain the spillage. The game involves putting a target number of counters into a cup, shaking them, and spilling them on the mat. Some of the counters will fall on the graphic and some will fall off the graphic. Students verbalize the combination: "Four counters are on the pencil and one is off. Four plus one equals five". This particular Shake and Spill game includes a graphing component, and that was actually what they students enjoyed the most. It was a race to see which combination's bar would win!

In the Cave

Next we played a hiding game called In the Cave. While still concrete, this activity involves identifying a hidden part, so it is a bit higher level. One student hides some of the bears in the cave and the other student must determine how many are hidden. Students verbalize and record their combinations. Check out this blog post to download a free recording sheet.

Make Five Go Fish

Finally, we played Make Five Go Fish. I was shocked to find out that most of my 1st graders had never played Go Fish! I also had to give lessons on holding cards and keeping cards private. That was a hoot! Only later did I figure out there were little card holders that make it easier for small hands to hold the cards. I just ordered mine!

To play, you need a deck with four cards each of the numbers 0-5 (keep reading for a link to a freebie!). Partners each get five cards and the rest go in the middle as the Go Fish pile. Players look at their hands to see if they have combinations for 5. If they do, they verbalize them and lay them down. Rather than asking for a matching card, like in the traditional game, players ask their partner for a card that will complete a combination for five. For example, if a player is holding a 3, he would ask his partner for a 2, because 3 + 2 = 5. If the player has the card requested, he must hand it over. If not, he says, "Go Fish", and the requesting player takes a card from the center pile. If a player lays down all of their cards, they take 5 more from the Go Fish pile and play continues. The player with the most combinations at the end of the game wins. Notice that this game is totally abstract (symbols only), so this is definitely the last game they should play.

The game can easily be extended for combinations of larger numbers by adding more cards to the deck. For example, for the combinations for 6, use cards with the numbers 0-6.

Ready to play? Click here to download a set of cards from 0-10. Enjoy!

Freebie for Composing and Decomposing Numbers

2015-02-03T18:53:00.000-06:00

My firsties are working on composing and decomposing the number 5, and today we played a tried and true game, Under a Rock. I had teddy bear counters to use, and I decided right then and there that In the Cave would be a lot more fun than Under a Rock. We used the Under a Rock recording sheet and adapted it, but I came right home, found some cute bear clipart from , and In the Cave was born!

Here's the lowdown. Partners work together on a target number. That's where the differentiation comes in. One pair of students can be working on combinations for 5, while another pair is working on 8 or 10. The students will need an amount of bears equal to their target number. For example, if students are working on the number 5, they use 5 bears. One partner closes his eyes while the other partner puts some of the bears "in the cave". The other partner then opens his eyes and has to tell how many bears are hidden. I make the kiddos says the equation so they are practicing their combinations out loud.

Two bears outside the cave. Three bears inside the cave. 2 plus 3 equals 5.

Ready to play? Grab the recording sheet here.

Setting Goals for Student Achievement

2015-02-01T10:59:00.000-06:00

In my current position as a math interventionist, I work with struggling students in grades K-5. It goes without saying that the students I see in grades 3-5 are at risk for not being successful on the state test they will take in the Spring. I've attended a number of professional development sessions over the past couple of years that stressed the need to have students involved in tracking their own data and setting goals for achievement. This past week, I began the process with my students. This should actually have been done in the fall, but better late than never.

First, let me give you a rundown of the data we used for this activity. I wanted to use the data that would be the best predictor of success on the STAAR test, so we didn't use classroom grades. There are too many factors involved in classroom grades for them to be a strong predictor for STAAR. Over the course of the year, however, our students have the opportunity to take several assessments that mirror the STAAR test, so these are the assessments I decided to use. Some of these assessments are developed at the district level. We call them DLAs, which stands for District Learning Assessments. We also recently gave a STAAR Benchmark test which, in effect, was a practice STAAR test. Because our DLAs are short (15 questions or so), we felt it was important for our students to experience a test that was the same length and rigor of the test they'll take in April (46-50 questions...don't get me started...). In addition, we have previous STAAR results for our 4th and 5th grade students, if they were in Texas and took the tests. I will reference these tests as I discuss our process.

I started with a story about running a marathon. I explained that a marathon is a 26-mile race and that people take up to a year to train for one. I told the students that in order to train for a marathon you have to set goals and make a plan, and that the goals and plan depend on my starting point.

What if I tell you that right now I can only run 1 mile. If I can only run 1 mile right now, what might be a reasonable goal for me to set for the distance I want to be able to run 2 weeks from now? (I got some pretty interesting answers to this question that were definitely a formative assessment for reasonableness!) Two miles? Sure! I think if I can run 1 mile right now, I should be able to reach 2 miles in a couple of weeks.

Now, what if I tell you that I'm already running 5 miles four times a week? If I'm already running 5 miles four times a week, I'm a pretty strong runner. What might be a reasonable goal for me to reach in 2 weeks? Seven or eight miles? I think 7 or 8 miles is pretty reasonable. Because I'm already a pretty strong runner, I might make quicker progress.

The point is that you have to look at where you are right now before you can set goals. That's why we're going to take a look at how you've done on some of the tests you've already taken and then set a goal for what you want to score on the next DLA.

Now remember, if I just set a goal--I want to be able to run 2 miles in two weeks--but I don't actually go out and run, I probably won't reach my goal. So we're also going to decide on three action steps you can take to reach your goal. For example, I might say I'm going to run 4 days a week, I'm going to cut down on fast food and eat healthier, and I'm going to get at least 7 hours of sleep at night. Do you see how doing each of those things might help me reach my goal of being able to run 2 miles two weeks from now? Good! Let's get started!

We used a very plain graph, which you can download here. I worked graphing skills into the activity by having the students add a title to their graph and figure out and add the missing numbers on the graph scale. Then, I told the students their scores for the previous tests, and they graphed them. I have to tell you that seeing the scores came as quite a shock to some of the kiddos. I think we assume our students know their scores and understand them, but seeing them on the graph was very eye-opening for them. I think some students were also surprised at how flat their bars were, or that their scores were actually going down. I'm happy to report there were no tears.

After graphing their scores, I asked each student to consider what they wanted their goal to be for the next DLA they will take. Some of them wanted to set the goals unrealistically high, so I reminded them of my marathon example. I still think some are a little high, but it will be a learning experience. I used a blue highlighter to mark their goal. Here are a couple of the 5th Graders' graphs. You can see that their goals are quite different.

Monday, we will discuss and decide on specific action steps they can take to reach their goals. The action steps should be very specific, such as:

Practice multiplication facts on FASTT Math 5 times a week
Spend more time and effort on my homework
Slow down and read word problems more carefully and draw pictures to help me visualize the math
Ask my teacher to move my desk so I can focus my attention better
Find a math partner to work with who can help me understand math better

These are just some examples I thought of. I'm sure the students will come up with lots more on Monday. The students are going to write their three action steps on the back of their graphs, and we'll review them every couple of weeks to hold the students accountable.

On Monday the students will also take a closer look at their data from the Benchmark to determine the standards they already know well and those they still need to work on. As we work on each standard over the coming months, we'll revisit the data and they'll be able to see growth.

Once the students take their next DLA, they'll add it to the graph and decide if they need to adjust their goal for the STAAR test.

I'd love to hear your thoughts and suggestions on this process! I think holding students accountable for their own data and achievement can be very powerful and is often underutilized.

You can click here to download a copy of the graph,

Reading and Writing Numbers to 20

2015-01-24T19:41:00.000-06:00

I just finished and uploaded a new product and, like many resources I create, it was born of necessity. I'm working with six little Kinders who still can't recognize numbers to 20.

To help with number recognition, I made half-page cards with the number, number name, and a ten-frame representation. The ten-frame representation relates quantity to the number. These cards can serve multiple purposes. Once the kiddos are able to recognize the numbers, we can use the cards to compare numbers.

I made practice sheets for writing the numbers and number names using a traceable dot font. There are sheets for practicing individual numbers, and there are also sheets with number sequences.

Finally, I wanted to help students understand the connection between the single digits and the teen numbers, so I included sheets with ten-frames along withe the numbers and number names.

Grab this new product by clicking here. I'm looking forward to seeing big improvements with my Kinder babies. Please share any ideas you have for helping children recognize their numbers.

Using "I Can" Charts to Make Learning Visible

2015-01-20T19:20:00.000-06:00

I have a confession to make. I have never been the teacher who posted the objective I was teaching on the board. I know that it's a requirement at many schools, but I have never taught in one of those schools. But recently, with my focus on encouraging students to take more ownership of their own learning, I came to the realization all by myself how powerful the practice can be.

Tonight I want to talk about "I Can" anchor charts. I know that "I Can" statements for standards are plentiful. I'm sure a Google search would turn up a ton of hits. But I think it's more powerful to develop "I Can" anchor charts together with the students, rather than posting a preprinted chart on the wall. Here's how it looked in my classroom today.

As my 4th graders came in the Math Lab, I had the "I Can" statement shown in the picture above written on my whiteboard easel. The red notations were not on the original statement--I added them as we discussed the statement. Since this was the first time I had used "I Can" statements with my students, I explained to them that the purpose of the statement was to tell them exactly what they needed to be able to do master the standard. We talked about each part of the chart, because I wanted to make sure they understood what all the parts meant. As I taught the lesson, I continually referred back to the chart. Since we will work on this standard all week, I wanted to transcribe the chart onto chart paper after the class, so I took a picture of what I had written on the easel. You can see that when I recreated the chart, I added some additional information. The chart will hang on the board in my small group area throughout the week.

Here are some additional pictures of my 3rd and 5th grade before and after charts.

And here's my small group teaching area with the final charts posted so the students can refer to them throughout the week.

How do you use "I Can" statements in your classroom?

Who Owns the Learning?

2015-01-17T08:15:00.000-06:00

We are inundated with data is today's world. It can, at times, be overwhelming. But used correctly, data can be an important component of student success.

In their book, Small Steps, Big Changes, authors Confer and Ramirez state that, "Part of the teacher's task is to help students become intentional learners." To support that task, they outline four steps educators should take:

convey the message over and over again that "Smart is not something you are; smart is something you get": "It's possible."

explicitly help students become personally invested in their own learning until they understand that success will have a positive effect on their choices today, next year, and throughout their lives: "I want"

help students set achievable goals and track their own movement toward success: "I can."

share examples and stories from this class that illustrate the payoff of effort: "I will."

Today I want to share an example of how one teacher at my school is putting this in action in her 3rd grade classroom.

A lack of fact fluency can be crippling for emerging mathematicians. Students who don't understand number relationships struggle to use mathematics to solve problems, because they are using all of their mental energy on basic facts. A strategy-based approach for learning facts leads to automaticity while at the same time it helps students understand how numbers are related. But instruction needs to go hand-in-hand with practice to build speed and fluency.

Our district uses Scholastic's FASTT Math program to provide engaging fact practice. Students can use the program in school and at home. Scholastic's data shows that students need to use FASTT Math three or more times per week to show the biggest gains. At our school, we have set a campus goal that each of our students in Grades 2-5 will use FASTT Math three or more times per week, and students can do two lessons per day. The FASTT Math system provides teachers several reports to track student progress and activity.

Linda Vasquez, 3rd grade teacher at Morton Ranch Elementary in Katy, TX, has been sharing the FASTT Math data with her students in an effort to show them that practice pays off. She came to me and asked if I could create some graphing sheets her students could use to track their data. Working together, we designed a graph that students could use to graph both their usage and their mastery.

Each Monday, Linda projects student data from the previous seven days (students are encouraged to use the FASTT Math program on the weekend at home) for whole class viewing. Students copy their data onto a recording sheet:

Time period: The prior seven day period (eg., 1/4/2015-1/10/2015)
Average Lessons per Week: Students can do two lessons per day, so the highest number possible is 14. We designed the graph with a scale from 0 to 10+.
Fast Facts: A fact is considered a Fast Fact when the student can consistently solve it in 0.8 seconds or less. The number students record tells how many of the total facts are Fast Facts. For example, the Addition 0-9 module includes 100 possible facts. The students records the number out of 100 that are Fast Facts.

After recording their data, students then graph the data on two different bar graphs. For each week, the bar for Average Lessons Per Week is right above the bar for Fast Facts, with the idea being that students can see the relationship between lessons per week and fact mastery. The students get so excited when they see their bars move! They are truly taking ownership of the data and their learning. The FASTT Math graph is only one part of Linda's overall own-the-learning plan. We are now working together to develop student-friendly graphs for common assessments and learning standards.

Linda says it best: "Graphing their own progress has enabled my students to internalize their growth. They willingly want to get on FASTT Math. They are self-driven to reach or surpass the number of lessons they had the prior week, and they are extremely excited to see the report each Monday. They now understand that practice results in growth. The ones who didn't see growth realize they must try harder."

If you use FASTT Math in your classroom, you can download the graphing and recording sheets here.

How do you help students own their learning? Please join in the conversation and share in the comments!

Developing Part/Whole Thinking

2015-01-12T20:02:00.000-06:00

I've been working with my firsties on composing and decomposing the numbers 3, 4, and 5. Last week, I used number bond cards and manipulatives--linking cubes and ten-frames--to introduce the idea of number bonds. Read more about that here. Over the weekend, I finished up a set of cards showing pictorial representations for numbers bonds, and this week we're using those cards to further develop the idea of the relationships between the numbers in number bonds. I wanted to give you an idea of how I plan to develop the concept throughout the week.

Monday

I showed the students a number bond card and we went over the meaning of the whole and parts. I reminded them they had built number bonds using ten-frames and linking cubes last week. I then showed the students a picture card that matched the number bond card and asked them to explain why the picture card matched the number bond card (There are 4 cubes. Three are purple and one is red.). I handed out the mats we will be using the rest of the week. I have them laminated, and the students use wipe-off markers to show their work.

Working together, I modeled how they will use the mat to describe the picture cards. It took a LOT of modeling, and word choice is very important. I constantly repeated, and had the kiddos repeat, the meaning of each part of the number bond. My whole is four, because I have four cubes. Part of the cubes are purple and part of the cubes are red. The purple part is 3 cubes and the red part is 1 cube. Together, the parts make 4 cubes.

Then we wrote the equations. We wrote equations last week, but I can tell this is something the students will need lots of practice with. We discussed that for the addition equations, we are joining the parts together to make the whole (One red cube plus 3 purple cubes equals 4 cubes). As we wrote the subtraction equations, I referred to the picture card, covering the part we were taking away (If I have 4 cubes and I take away the red cube, I have 3 purple cubes left...4 minus 1 equals 3). We practiced several of these together.

Tuesday

We're going back to concrete learning on Tuesday, but this time the students will use cards that show the parts, but not the whole, and they will use teddy bear counters to find the whole. They will still use the mats to show the equations.

Wednesday

Today's activity will be similar to Tuesday's, but students will use ten-frames and counters instead of teddy bear counters. It's good for them to see a variety of representations.

Thursday

Thursday I will introduce the missing part number bond cards. After discussing the card, I will show students three pictorial cards, only one of which matches the number bond card. Their job will be to decide which picture card matches the number bond card and explain why. They will also find the missing part.

Friday

To finish out the week, I want to do a little assessment to see what direction I need to take next week. I'm going to use the recording sheet shown below and have the students work independently to describe four different pictorial cards.

You can grab the number bond cards here and the pictorial cards here.

I'd love to read your comments about how you develop part/whole thinking in your classroom!

Modeling Mathematical Thinking

2015-01-06T19:41:00.001-06:00

Problem solving has been defined as knowing what to do when you don't know what to do. I love that definition, although I don't know who to credit it to. Last summer, I was privileged to hear Yeap Ban Har speak about Singapore math at the SDE National Conference on Singapore Math. One fact about the Singapore system that stuck with me is that 20% of their standardized tests are items of a kind that students have never seen or worked before. That's true problem solving.

Students need to opportunity to work non-routine problems, but they also need to be taught what it sounds like for a mathematician to work through a tough problem.

Consider this item from the 2013 Texas 4th Grade STAAR test:

This item was coded as a perimeter problem, but because it has process skills embedded, a child could totally know how to find the perimeter of a figure and still miss the problem. Stop for a minute and consider the skills needed to solve this problem.

Here's where modeling comes in. Students need to hear your thinking about how to work this problem. That's the way to develop true problem solving/critical thinking skills. It might sound something like this...

[teacher reads the problem, which is projected on an overhead, document camera, or interactive white board]

Wow! That's a pretty complicated problem! I heard several math vocabulary words as I read, so I'd better think carefully about the meaning of each word. Let me break this down and see if I understand each part.

[re-reading] Use the ruler provided to measure the side lengths of the figures below to the nearest centimeter. Okay, I need to measure the sides, and I'm using centimeters, not inches. Let me make sure I'm using the correct side of my ruler. [measuring the first side] I'd better be sure I line my ruler up carefully. I know that's important when I'm measuring length. As I measure, I should write my measurements on each side. That way, I'll have the information I need to work with. [measures all sides and record the measurements] Hmmm, I notice that all the sides on this hexagon, because it has six sides, are congruent. They're all the same length.

I'm done with the measuring. I'll read more and see if I can figure out what to do next. [re-reading] What is the difference between the perimeters of these figures? Okay, it mentions the perimeters of the figures. I know that perimeter is the distance around a figure. I'll find the perimeter of each figure by adding up the side lengths. Oh! The sides on the hexagon are equal, so I can multiply those. [finds perimeter of each figure, recording the calculations].

Hmmm, now I've got the perimeters, but is that my answer? I'd better re-read the question again. [re-reading] What is the difference between the perimeters of these figures? Oh!! I need to find the difference between the perimeters. I remember that difference is like subtraction. I'm comparing the perimeters of the two shapes, so I'll subtract the smaller perimeter from the larger perimeter. Oh! I already know that 29 can't be the answer, because that number is too big. I'll bet that's adding the perimeters. The perimeter of the triangle is 17 cm and the perimeter of the hexagon is only 12 cm, so 17 - 12 equals 5.

Wow! That wasn't really so hard after all. It had a lot of steps, but each of the steps was pretty easy once I read it and broke it down.

Notice a couple of things:

The teacher does all the talking. This is not the time to have students help you solve the problem--that can come later.
It really doesn't take all that long! Model one problem like this a day, and you're sure to see your students' problem solving abilities grow.
Pack as much math into the problem as possible. This was not a geometry problem, but I took the opportunity to use the names of the geometric figures as well as the word congruent.
Be sure to model the habits you want your students to develop. By recording all of your work when you model the problem, and commenting on why it's important to do so, you are showing the students that mathematicians communicate their thinking using words, numbers, and pictures. That's better than just telling your students, don't forget to show your work.

Bottom line, our students don't come to us knowing how to think critically. It's part of our job to help students develop analytical skills right along with the math content.

P is for Pirate

2015-01-03T11:58:00.001-06:00

Author Dave Burgess is at it again with a delightful new book for educators. Last spring, I did an online book study series on his bestselling first book, Teach Like a Pirate, and since then I've had the privilege to meet and hang out with him several times. Phenomenally creative and inspirational guy, not to mention highly entertaining. :)

For his newest book, P is for Pirate: Inspirational ABC's for Educators, Dave collaborates with his wife, educator Shelley Burgess, to create a gorgeous picture book for adults. What? A picture book? Yes, a picture book. Each letter of the alphabet features a word or phrase with easy ideas that you can use to transform your classroom into a high-energy, engaging learning playground. If that's not enough, the back of the book includes additional ABC's from more than 70 educators.

This is a book that will make you smile and make you think. It also has the ability to transform your teaching. If you are trying to think of your One Word for 2015, this book is full of them.

What are you waiting for? Go get it!!

Introducing Number Bonds with Hands-On Experiences

2015-01-02T13:56:00.000-06:00

Last week I blogged about number bonds and part/whole thinking, something I'll be working with my Firsties on after the break. I've been thinking through how I want the lessons to go in my head. This is going to be my introductory lesson the first day back.

Put linking cubes of two colors into a bag. There's nothing magic, of course, about using linking cubes. You could use teddy bear counters or other manipulatives. What's important is that you have two different colors. I will probably repeat this activity on several different days using different manipulatives each time. You might want to put more of one color in the bag, so you increase the chance that you'll pull out only one color.

Display the number bond cards for the number three--there are only two as shown in the picture above. You want cards showing the whole and both parts. I'm starting with the number three just to introduce the idea of a number bond, explain how the cards represent the number bond, and show how to write the equations associated with a number bond. Ask students to look at the cards and make observations about what they see. Some ideas they might verbalize include:

There are numbers in boxes
There are three boxes on each card
Some boxes are bigger than others
Once card shows 1, 2, and 3, and 1 + 2 =3
The boxes have words in them--part and whole

Show the students the bag containing the linking cubes. Let them look inside and explain that there are cubes of two different colors. Have one student draw out 3 cubes without looking (or choose 3 students to each draw out one cube), and place the cubes on the table with the cards. Ask the students how they would describe the cubes that were chosen (all green, two greens and one yellow, etc.). Have students turn and talk to a partner about which of the number bond cards they think matches the cubes that were drawn and why.

The conversation can now go something like this:

Which card do you think matches the cubes? The one that has 3 as the whole and 1 and 2 as parts

Why do you think that one matches? Because there is one yellow cube and two green cubes and it has a 1 and a 2

So the parts are the colors? Yes

How about the 3 that's on the card? How does that match the cubes? Because we pulled three cubes out of the bag...there are three cubes total

Oh, so the whole is the three cubes...one part of the whole is yellow and the other part is green! Yes

Next I would connect the cubes to the equations without, however, writing them yet.

So 1 (touching the yellow cube) plus 2 (pushing the two green cubes together with the yellow cube) equals 3. Or 2 plus 1 equals 3. If I have 3 cubes, and I take away the yellow cube (push it away), how many cubes are left (2)? If I have 3 cubes and take away the 2 green cubes (push them away), how many cubes are left (1)?I

Finally, I would use the mat and ten frame to represent the same number bonds and write the equations. So I'd put one of the cards in the space and have the students tell me how to represent the number bond on the ten frame. I'd ask them to tell me the addition and subtraction equations while I model how to write them.

We will repeat this activity numerous times using different numbers for the whole. Once the students are comfortable with the process, the activity can be used in a workstation. Differentiate the activity by having students use the number they are working on. See this blog post for more information about identifying a student's number using a hiding assessment.

The ten frame/equation mat is part of my Using Number Bonds to Develop Part/Whole Thinking unit, which you can grab here.

Check out this post for some next steps in teaching number bonds.

My One Word for 2015

2015-01-01T09:44:00.000-06:00

January 1. Blank slate. I love the start of the new year. It's a time to reflect on what worked well during the past year and to retool for the new one. Last year, I stumbled on the idea of replacing the standard New Year's resolution with one word that would shape and define the coming year. There have been several books published on the idea, and there are many websites as well. Just Google "one word for new year" and you can read all about it.

Last year, my word was fit. I had purchased myself a Fitbit Flex for Christmas, and fit seemed like a good choice. I had a milestone birthday in 2014 (think AARP...), and I wanted to be more healthy to end the year than when it started. But beyond the physical aspect of the word, I wanted to find people and activities that were a better fit for me. I think I achieved that goal. The physical goal...not so much.

Having not entirely met my goal, of course I had to reflect on why. Otherwise, what's the point? I concluded that I broke the cardinal rule of goal setting. While the word was a great word, I didn't have actionable milestones. That's a change I intend to make this year with my new word...

I thought hard, and I really like my new word. It implies that you're going to take everything you do to the next level. So let's talk about those actionable milestones. I have been faithful wearing my Fitbit Flex every single day of 2014. What I have not been faithful about is meeting my 10,000 step goal each day. That's my first actionable milestone. My son bought me an adorable dachshund calendar for Christmas and I hung it on the wall right next to where I work. I'm going to use it as a kind of BOOST diary. I'm going to put a sticker on each day I reach my 10,000 step goal. I'm also going to jot down other ways I have boosted my teaching, my social life, my business, my LIFE!

I am VERY excited about what 2015 will bring! If you had to choose your one word, what would it be? Share it in the comments below.

One more thing...today is the last day of my giveaway and sale. Be sure to check out this blog post to enter!

New Year Sale and a GIVEAWAY!

2014-12-30T08:31:00.001-06:00

I hope you are enjoying your holiday break! What better way to start back after the new year than with new products for your classroom? Check out my 2015 Happy New Year sale where most of my products are discounted 20%. This is a great time to pick up those bundles you've been eyeing!

After the break, I'll be using my Number Bond Cards and Missing Part Cards to help my firsties develop an understanding of composing and decomposing numbers. My 2nd graders will be exploring addition and subtraction using To 100 and Beyond: Hundreds Charts to 1000. They'll also be creating and using their own personal 1200 charts. Check out this blog post for more information and to grab a free download.

A great sale deserves a great giveaway! Enter now to win a $25 TpT gift certificate. The mandatory entry is easy--just leave a comment on this blog post telling your favorite Math Coach's Corner product. After that, you can also visit my Facebook page and tweet about the giveaway for additional entries. Please note that I do check to make sure the chosen winner fulfilled the requirements of the entry. :)

a Rafflecopter giveaway

Number Bonds and Part/Whole Thinking

2014-12-29T09:55:00.000-06:00

I've been working on place value with my firsties, but when we get back after the winter break, I want to do some work on composing and decomposing numbers to 10. This is technically a Kindergarten skill, but remember that I work with RTI kiddos. Understanding how to compose and decompose numbers to 10 is the basis for developing addition fact fluency, so it's super important.

A great way to start with number bonds is with a little activity called Shake and Spill. Working with a target number, students can explore the different combinations that make that number. This is a very concrete way to see that numbers can be decomposed into different parts. Remember, however, that we want to overlap concrete learning with abstract representation. Enter the number bond. It's a graphical representation of the combinations for a number. So, after students have had a chance to explore Shake and Spill without recording the combinations, introduce how to record the combinations using a number bond. The next step would be to have students write the four corresponding equations. But remember, baby steps...not all at one time!

After students have worked with Shake and Spill and have had practice recording the number bonds and equations, you can move to a different representation--ten frames. Students can now work with number bond cards and represent the number bonds using a ten frame.

I recently updated my number bond flashcard product and renamed it Using Number Bonds to Develop Part/Whole Thinking. It's already a best-seller, but I love the changes I made to it. The cards all used to be missing part, but that's really difficult for kiddos (especially my struggling babies). I wanted to change the cards to allow the students to truly develop an understanding of number bonds over time, so I created three different sets of cards.

Both parts and the whole known This will allow the students to work with the relationship among the numbers in a number bond at the simplest level. They can build the number bond and write the equations without having to find an unknown.
Both parts known, the whole unknown At the next level, students will combine the two parts to find the unknown whole.
Whole known, one part missing This is the most difficult skill. Students need to have had lots of practice with the other structures or they will try to simply add the two numbers they see on the cards.

Finally, I've got a couple of freebies for you (and me! ha ha). Click here to grab the Winter Owl Shake and Spill and here for the Number Bond Recording Sheet.

Happy holidays!! :)

Update: Check out this blog post for more on introducing number bonds.

Another Look at 2-Digit Numbers

2014-12-28T09:52:00.000-06:00

A couple of weeks ago, I blogged about working with my firsties on 2-digit numbers. This is a follow-up to that post.

Let me reiterate that the idea of tens and ones is not an easy one for young children to understand. It is incredibly abstract. As I said in my previous post, students need lots of experience with 2-digit numbers before they can fully understand the concept of tens and ones. And as with any new experience, students need concrete and representational experiences to support the abstract understanding. My students had previously worked with linking cubes (building trains of ten) and ten frames and counters. These are both concrete methods of instruction. With both, however, I recorded equations corresponding to their models to connect the concrete experience with the abstract (symbolic) representation. That connection between concrete and abstract is often left out of instruction, but it's so very important.

Since the students had had a variety of concrete experiences, I decided to move on to representational instruction, so we used our individual student ten frame kits. I love these!! They are small plastic tiles that students can use to build numbers. Each student gets his own little 'wallet' with tiles. It's a little faster than ten frames and counters. Now, you might think this is concrete instruction because students are manipulating the tiles, but it's not, it's representational. The dots on the tiles represent real counters on ten frames. You definitely don't want to start your instruction with the tiles.

I gave students a place value mat labeled tens and ones so they could more clearly see that the filled ten frames represent tens, while the partially filled ten frame represents the ones. You can download your own copy of the mat here. Once again I gave students 2-digit numbers to build. As we discussed what they had built, I recorded each number in two different ways, again trying to promote the idea that two tens equals 20.

If the ten frame kits are cost prohibitive, you can create your own students kits using this file. I also uploaded a B&W version, in case you want your kiddos to color their own.

Stay tuned after the winter break for more adventures in place value!

Early Place Value Experiences

2014-12-15T19:28:00.000-06:00

I've been working with my firsties on understanding numbers to 50. We've practiced counting forwards and backwards, writing and reading the numbers, as well as comparing numbers. By far our biggest challenge, however, has been understanding the meaning of the digits in a 2-digit number. Children can count out 26 counters and relate the counters to the number 26 long before they understand that the digits represent 2 tens and 6 ones. We have been using linking cubes and ten-frames to try to make meaning of these early place value understandings.

Here's what we were up to today. I gave each pair of students four empty ten-frames and a pile of counters. I asked them to talk to their partner and decide what the biggest number would be that they could show with their ten-frames. This turned out to be a great question! It was an awesome formative assessment. As I listened to the conversations, I heard that some students immediately said 40, while other responses were all over the board (20, 100, 50, etc.). I reminded students that they needed to explain their answers, even when talking with a partner ("I think it's 40 because..."). My Tier III kiddos were not even in the ballpark, so I scaffolded...

[Putting out one ten-frame] If I have one ten-frame, what's the biggest number I could show? (10)

[Adding a second ten-frame] Okay, if I have two ten-frames, what's the biggest number I could show? (20)

At this point, I thought they would make the connection, so I asked them to look at their ten-frames, talk with their partner, and decide the biggest number they could show with four ten-frames. They still did not come up with 40. This was fascinating to me! Once again I repeated my questions about one and two ten-frames. I added a third empty ten-frame and asked what the largest number I could show would be (30). I then asked them the original question again ("What is the largest number you could show with your four ten-frames?"). They finally decided 40, but this just shows how much support our Tier III kiddos need!

Back to the planned lesson...I wrote the number 26 on my whiteboard and chose a student to read the number. I have learned not to assume students can read 2-digit numbers when they see them in isolation. Then I asked the students to work with their partner to build the number. While all the students successfully built the number, it was fascinating to see that most students were counting by ones as they put their counters on the ten-frames. After they had built the number, I asked them if they had to count by ones and reminded them that if the ten-frame was full, it was ten. We continued practicing this throughout the lesson ("If it's 26, how many filled ten-frames will you have? Which digit shows you how many filled ten-frames you will have?").

On my whiteboard, where I had written 26, I wrote the equation 26 = 20 + 6. I asked the students to talk to their partners about what this equation meant. They were able to tell me that the 20 was the two filled ten-frames and the 6 was the counters on the ten-frame that wasn't full. It is not obvious to children that a filled ten-frame can be called a ten, and that when we have two filled ten-frames it is two tens but represents 20 counters. HUGE concept and hurdle in understanding.

Next, I wrote 32 on the whiteboard and asked them to build the number. It was interesting to see that some students knew to fill another ten-frame automatically, while others were counting by ones. After building the number, I again asked how many filled ten-frames they had (3) and asked a student to help me finish the equation.

Finally, I thought I'd throw a little problem solving into the mix, so I wrote 45 on the board and asked them to build it (remember they only had four ten-frames). My Tier II kids just added 5 counters below the fourth filled ten-frame, but my Tier III students were lost without another ten-frame to hold the five counters. So interesting. I gently led them through questioning and they figured it out.

As a final activity with my Tier II students, I wrote 20 + 4 on the board and asked them to build it. I just wanted to see if they could look at it from the other perspective, and I thought it would help them better understand that the 20 is represented by 2 tens in the number.

We will practice this a LOT more! It is so important that they really understand these early place value concepts.

iHeart Math Holiday Hop

2014-12-08T19:12:00.000-06:00

I am so excited to be linking up with a group of wonderful math bloggers to bring you nearly a month of holiday surprises! Each day, a different blogger's post will go live. Be sure to check out each and every one. You can click on the images in the picture above to go directly to each blogger's post.

Stocking Stuffer #1--Giving Back Idea

Who are the hardest working people in a school building? If you said the custodians and cafeteria workers, I'd probably agree! Last year, we started a wonderful tradition at our school. Each staff member picked up a few extra holiday groceries during our weekly shopping trip, and we assembled baskets of food for our custodians and cafeteria staff. The administration chipped in a ham for each basket, and we presented the baskets at our holiday luncheon. They were overwhelmed! Try this on a small scale. I work breakfast duty in the cafeteria, and every year I like to bake the ladies in the cafeteria a treat!

Stocking Stuffer #2--Holiday Math Tip

Face it, there is almost no way to keep a normal schedule during the last couple of weeks before the Christmas break. Be prepared for those crazy schedules with a few easy go-to math games that you can pull out in a moment's notice. I like these games for practicing addition and multiplication facts. Laminate them, and all you need is a wipe off marker for 10 minutes of engaging math fun! Click here to grab yours.

My special gift to you this holiday season is a special version of my themed number cards. This set ranges from 1-20 and includes cards showing numerals, number words, and a ten-frame representation. Here are some idea for using them:

Have students choose a number word or ten-frame card and write the corresponding numeral
Students can play War with the cards
Students play a Memory game either matching different representations or matching cards that make a 10
Have students randomly choose 4 numeral cards and put them in order
Students choose a numeral card and use counters to show the number
Students draw two numeral cards and write an addition or subtraction story using the numbers

I'm sure you can think of lots more uses for these cards! Click here to grab your set.

The next stop on this festive hop is over at Lessons With Coffee. You can check out her post by clicking on the image below!

Winter Freebie Ebooks...A Holiday Gift!

2014-12-05T11:20:00.000-06:00

Again this year, Teachers Pay Teachers has sponsored their Winter Holidays Tips & Freebies ebooks! This annual Christmas present has grown from one book with 50 pages (and freebies!) to FIVE books for separate grade bands containing over 200 pages.

For those of you not familiar with the format of the ebooks, each page contains a holiday tip and a link to a freebie. The books include pages from some of your favorite sellers as well as some talented new sellers. I am honored to have been included in this year's Grades 1-2 book. You will find the links to the other ebooks (PreK-K, 3-5, 6-12 ELA/SS, and 6-12 Science/Math) from the Grades 1-2 book page.

My freebie is a winter-themed Capture 4 game for the meaning of the equal sign. Such a hard concept for kiddos to grasp, so lots of practice is important. The strategy component of Capture 4 games adds a problem solving element to the activity. Consider putting ten-frames and counters in the workstation with the game for students who need concrete support.

Click here to go directly to the freebie or here for the link to the Grades 1-2 ebook. Happy holidays!!