Lookee Here!

"I Have Who Has Cards" spotted at Plains Trading Company!

Input / Output Machines

Input / Output machines always have a way of sneaking into the high stakes tests like the DSTEP. But, as we all know, that is the least of the reasons we should use them. They provide practice in flexible thinking - and are an effective primer for more difficult challenges like the game of 24.

Our Pre-K through second grade students already have access to a very nice input/output machine in their Building Blocks software. But there isn't much for our older students - the same ones who will likely see some of these questions on their standardized tests.

Fortunately, you can find a whole set of more advanced Input/Output Machine activities over at the Mathwire. This activity makes another fine addition to a workshop or menu.

 I'd like to challenge you to send me your own set of cards! Let's see what you can come up with! Here's one I made with third grade in mind: Guess My Rule Grade 3

No offense, language arts teachers - but a great math teacher can bring it!


Having trouble incorporating Marzano's strategies into your math lessons? How about direct vocabulary instruction around math concepts? With some poking from Peggy Diekhoff, and great advice from the "Supporting Student Literacy" strategies of College Preparatory Mathematics, I've put together a guide for embedding solid reasoning and sense-making skills into your mathematics classroom.

While many of the examples are geared toward a high school curriculum, I think teachers of all grade levels can find something valuable here.

Why My Math Teacher is the Most Effective Language Arts Teacher I've Ever Had!

A Menu Structure with Mrs. Hausmann

1st grade menu from (Chris) on Vimeo.

Mrs. Hausmann's students are working in a menu structure. Menu is a way of organizing your workshop around a select number of learning goals. In this video, I also take the opportunity to formatively assess students on their ability to count small groups.

If you are interested in establishing a menu in your classroom, I've put together this overview to get you started.

It's About More Than Numbers

Who says you can't get the warm fuzzies after a good math workshop?

Don't Worry from (Chris) on Vimeo.

Third Grader From North Masters First 100 Facts!

Congratulations to Arvish and her teachers Deb Waln and Pat Eddie!

On Tuesday, October 26th, Arvish became the first 3rd grade student to master all 100 of the addition facts from 0 + 0 to 9 + 9. This means that Arvish was able to solve each of the 100 combinations within 8 tenths of a second! Her achievement required a lot of hard work and perseverance - we LIKE that around here at TCSD Mathematics.

We like that a LOT.

Nice jacket, Arvish. Who's next?

End of Unit Assessment Trackers Now Available!

Please use these trackers to collect your assessment data. Once a unit is complete, just email me your file! For future reference, these trackers will be available on the pacing guide home page.

We are asking you to collect this data for three important reasons. First of all, the district has a vested interest in the achievement of our students as it relates to our day-to-day curriculum. Rather than rely on periodic data from the DACS or the DSTEP, for example, we can track student progress throughout the year on the very learning objectives we strive to teach each day.

Secondly, with data available on each question, we can pinpoint an area of difficulty and then determine whether there is an issue with the question itself, or with our instruction. This will help us refine the assessments from year to year.

Finally, our students are mobile. When a student transfers into a new classroom, a teacher can request previous assessment data and we can supply it.

Grade One Assessment Tracker

Grade Two Assessment Tracker

Grade Three Assessment Tracker

Grade Four Assessment Tracker

Grade Five Assessment Tracker

Grade Six Assessment Tracker

Grade Seven Assessment Tracker

Grade Eight Assessment Tracker

Work Ethic Rubric

Are you using a menu or workshop format in your math block? Working levels are designed to help raise students' awareness of their own behavior, to make expectations more explicit, and to give focus to discussions about what it means to work hard.

Students of all ages must be given opportunities to discuss questions like,

"What does it look like to work hard?"

"What does it look like to be responsible? What will we see? What will we hear?"

"How will we know when we're working hard?"

A working levels rubric gives students more information about what is expected and the information they need to improve.

Work Ethic Rubric

(from Working Levels by Kathy McGrath)

Level 4

• Productive
• Respectful
• Collaborates with Others
• Craftsmanship

Level 3

• Productive
• Respectful

Level 2

• Works when Reminded

Level 1

• Not Working

Level 0

• Interfering with Other's Work

The Cost of "Achievement?"

Making Sense of Division

When solving division problems, students are often able to produce a quotient without realizing what that quotient represents. For example:

The bag has 695 pieces of candy corn, and Alyssa wants to put them into bags of 50. How many bags will she need?

Students may be able to mechanically produce the quotient 13. But do they fully understand the referential meaning of "13"? And let's not even get started about what the remainder represents!

Explicitly teaching students, with a model, that there are two ways to think about division can help them develop powerful mental structures for analyzing their results. I'm going to suggest Cuisenaire Rods as an excellent model for representing division.

Sharing (partitive) division is the situation your students are most comfortable with because it can be solved by dealing out. In sharing division, we know the total and we know the number of groups. The unknown is the number of items in each group. We can solve this by dealing out, or sharing, all of our items one at a time until there are no more to be distributed.

Sarah has 10 puppies and 2 doghouses. How many puppies can be grouped evenly in each doghouse?

The Cuisenaire Rods offer a nonlinguistic representation of the situation. We have a given total divided into 2 groups. We must find the number in each group.

There will be 5 puppies in each doghouse.

In the second division situation, the action to solve the problem is making groups. This is called measurement division, and lends itself well to the idea of repeated subtraction - repeatedly removing groups of a particular quantity until there are no more to be removed.

Climb the Ladder!

Danylle, the 4th grade teacher at Hedog, is concerned about her students' fluency with base-10 concepts. We dug out her Kathy Richardson "Understanding Numbers: Place Value" kit and put together an effective (We hope!) set of activities for Menu.

It was funny, though, because our planning session began with me giving her an impromptu idea that seemed great at first, (Don't they all? Ha!) but looked more and more shabby the deeper we went into Kathy's materials.

Danylle proved her worth as a teacher, though, with unflagging encouragement! "I like your idea, Chris," she said. "I'm going to still use it."

Uh huh.

I left Hedog that afternoon determined to craft this idea into an activity that would produce results, and wouldn't look pitiful next to the other Menu items. I happened across some "Climb the Ladder" activities while browsing Mathwire.

Climb the Ladder was just the touch I needed! So I'm happy to share with you an activity that requires only a deck of digit cards and a work some activity sheets. This should be good for latter year second graders, third graders, and 4th graders who need further support or practice.

Note: The directions ask students to represent their number using squares, lines, and dots. This vocabulary was chosen for simplicity. These representations should be connected with the flats, rods, and cubes of the base-10 blocks, or to the sheets, strips, and singles of the Sticker Station.

Have fun!

Download: Climb the Ladder Base-10 and Place Value Concepts

I Have/Who Has Du Jour!

Do your students need practice with concepts or skills they are working to master? The I Have/Who Has activity is an engaging and motivating way for kids to gain fluency in small groups, with partners, or as a whole class. While they practice, you can check for understanding.

I have x + 1! Who has...

I have 1 ten and 4 ones. Who has...

Follow the break to download card decks and find out more about this activity.

Reporting with Kathy Richardson

Using the AMC software to chronicle your children's thinking is only the first step toward understanding their thinking so that you can provide activities to push them toward a deeper connection with number and quantity.

The next sensible step is to examine the data. Log into amcanywhere.com and look for the "Reports" icon.

From here, you'll be treated to a bevy of options!

The student detail report is extremely handy in getting to the nitty gritty details of an individual student's thinking. This is also a dynamite report for conferring with parents and colleagues about a particular student performance.

Any notes and comments you provide during their assessment will also appear on this report.

How Many?

For every young child, learning to count while simultaneously developing a sense of quantity is challenging work! Our data hints at the complexity hidden within the seemingly simple task of counting cubes.

1st Grade Students Who Can Accurately and Consistently Count a Group of 21 Objects

67% of incoming first graders can accurately and consistently count a group of 21 cubes.

1st Grade Students Who Can Accurately and Consistently Make a Pile of 18 Objects

However, when asked to create a pile of 18 cubes, only 46% of students can successfully complete the task.

Why the discrepancy?

Counting is more than saying a rote sequence and recognizing a numeral. According to Kathy Richardson, "Counting is finding out how many."

I Have... Who Has? Coin Cards!

The Mathwire has an excellent adaptation of the "I Have Who Has" activity using coin cards. Not only will this activity provide plenty of practice in using coin equivalence and coin recognition, but it will also give students some authentic practice in adding small quantities.

Download your own set of coin cards, and read all about the activity here at the Mathwire.

Non Linguistically Speaking

When students struggle to interpret story problems into a mathematical statement they can tackle and solve, a nonlinguistic representation may lead to success. Explicitly engaging students in the creation of lonlinquistic representations increases activity in the brain (Gerlic & Jausovec, 1999)

Language challenged 3rd graders might find this problem difficult to navigate:

Riverside School had 517 students last year. This year, 60 students moved away before school started. How many students does the school have now?

A nonlinguistic representation to help students create a mental picture of, and organize, the essential information.

TOTAL
Part	Part

Substituting the information from the problem, our representation becomes:

517 students (Total)
60 students (Part)	Part

Using this representation, it is perhaps clearer to students that they are looking for the difference between 60 and 517. They could then solve the problem in one of two ways: by counting on from 60, or by subtracting 60 from 517.

Calculation Nation!

Calculation Nation^® uses the power of the Web to let students challenge opponents from anywhere in the world. At the same time, students are able to challenge themselves by investigating significant mathematical content and practicing fundamental skills. The element of competition adds an extra layer of excitement.

“The games on Calculation Nation^® provide an entertaining environment where students can explore rich mathematics,” said Jim Rubillo, Executive Director of the National Council of Teachers of Mathematics (NCTM). “Through these games, students are exposed to the same mathematical topics that they see in class as well as those that are recommended in Curriculum Focal Points.”

The Motorcycle Boy Rules!

Velodrome: A velodrome is an arena for track cycling. Modern velodromes feature steeply banked oval tracks, consisting of two 180-degree circular bends connected by two straights. The straights transition to the circular turn through a moderate easement curve.


I hope that's enough math to justify another motorcycle post. Actually... who cares. The motorcycle boy rules!

What Do Third Graders Know About Addition?

Mr. Birch's third graders have been putting together a list of statements they believe to be true about addition. Here is what they have so far:

What do we know about addition?

1.  Numbers usually get larger.

2.  You are putting things together.

3.  Adding sign is +

4.  Find the total.

5.  How many all together?

6.  What is the sum?

7.  Addends can be added up in any order to the sum.

8.           7   ----addend ------     5
            +5   --- addend ------- + 7
           12  ----  sum     -------  12

What do other third graders think about this list? If you'd care to add something, or have any questions for us, please leave a comment!




I have a question about the first item on their list. Mr. Birch's students suggest that numbers usually get larger with addition. Can you give an example of when the sum gets smaller???

Spring Creek Mathematicians Tell Addition Stories!

8 Sleeping Billy Goats + 2 Billy Goats Playing from (Chris) on Vimeo.

Mathematics is about far more than numbers - and certainly must include more than lists of rules. In her book What's Math Got to Do With It?, Jo Boaler describes math as

a human activity, a social phenomenon, a set of methods used to help illuminate the world

 Second graders at Spring Creek are exploring how mathematics can be used to illustrate simple stories. More specifically, they are crafting stories involving combinations of 10. Perhaps you can tell what time of day these were recorded by all the references to sleep.  /grin

Motorcycles, Math, and Mistakes

First Start from (Chris) on Vimeo.

Some might think that the only math in the minds of bikers heading to Sturgis revolves around miles per hour and motel rates. When things go wrong, though mathematics is often the culprit. And just as reliably - part of the solution.

Two weeks ago, my engine stuck a valve. When I lifted the rocker covers, I found enough evidence to warrant a complete top-end overhaul. There was plenty of good math involved!

Characteristics of an Effective/Ineffective Classroom

During last week's Core Reading class, my table was asked to offer the characteristics of an ineffective classroom. We did ... a serviceable job...  But as I drove home and reflected upon the day, I realized that we had missed a golden opportunity. It is one thing to put together a "horrorshow" list of characteristics. Elements like: "No engagement;" "lack of management," "the teacher doesn't care," and "teacher lacks content knowledge" quickly come to mind. The problem, though, with a list like this is that very few teachers are going to say, "Yep - that's me. I know nothing about the subject I'm teaching." Or "My classroom would be effective if only I could bring myself to care." Typically, we might see that list and think, "Hmmm, they sure aren't talking about me!"

Math Site Crashes and Burns!

Emergency workers unable to save math site. Literacy coach suspected of driving

while texting.

For the 4th time, my website has crashed and burned - all data lost. Being one to persevere and ignore the messages the computer gods are sending me, here goes my 5th attempt! I will do my best to get the most vital information posted over the next couple of weeks.

In the meantime, have a great opening to your new school year! Let's get our AYP on!