Tag / standards for math practice

by Beyond Traditional Math

Raising Rigor for the Smarter Balanced Assessment

In one year, our students will be taking the Smarter Balanced Assessment in place of our current state wide assessment system. You can click the logo below to find out more.

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Our district participated in the pilot test of this assessment, and I was lucky to get a chance to see what we are up against. You can take that first part of the test here (there is not a performance task sample ready yet).

When I peered over the shoulders of my students, my jaw just dropped.  The rigor of this test far exceeds what I’ve been used to for the last 8 years.  There were two parts to the test that I was able to see; a multiple choice/short answer and then a performance task type of test.  The first part was kind of standard, but included a lot of dragging, clicking and typing.

The second part was what really got me.  Nothing in our textbook would ever prepare students for this!  The first section of the problem was a full page of reading that they could go back and refer to over and over.  The second section contained about 20 questions related to that reading passage that built on each other in difficulty.

Notice, this was a MATH test, not a reading test.  If you can’t read you really can’t do well on this test.  If you can’t persevere, you really can’t do well on this test. If you can’t sort through massive amounts of information, or use appropriate strategies and tools, or PERSEVERE when the going gets tough…you will not do well on this test.

In come the Standards for Mathematical Practice. If you aren’t familiar with them, you should get familiar. They are amazing, they are exactly what we’ve needed and wanted students to do since the dawn of time.

I have been thinking about some ways to prepare students. Here are some things I am thinking for the coming school year:

1.  My plan this year is to incorporate deep problem solving DAILY.  I will use mini lessons and structure to help them get started, and then get them working independently. We will do this every day for 15-20 minutes per day, I’ll even set the timer!

2.  I plan to incorporate and embed those Standards for Mathematical Practice. I will explain that they are behaviors that great mathematicians do! I created a systematic way to introduce them to students.

3.  I am going to let them struggle. Sometimes we learn best with our mistakes.  Struggling can help us do our best critical thinking.

4.  I will help them read for understanding, I may even incorporate reading math problems during Readers Workshop. We’ll talk about how math reading can be different than reading for enjoyment. I am going to use these open ended problems that are full of reading, encourage persistence, and are real world.

5.  I’ll blend in reading, writing and math content into my problems so it becomes seamless.

To prepare them for the task coming (which they very well SHOULD be able to do), we’ve all got a lot of work ahead of us! I hope we can join together and re-ignite student’s passion for projects, hands on activities and rigor.

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by Beyond Traditional Math

The Float Challenge

The amount of vocabulary that is embedded in the measurement and geometry Common Core State Standards is staggering. Along with most things in math, I feel that more than ever students need to see it, use it, or touch it in the real world to connect to these words.

This occurred to me halfway through our measurement unit, as I was teaching metric units to measure mass. The day before, we had covered customary units for mass. Adding more vocabulary the next day felt like I was pushing too much information into their brain.

So I tried a little something. A Float Challenge.

I gave the students a 1′x 1′ piece of aluminum foil, and asked them to create a flotation device. This device had to float/carry the amount of mass weights (in grams) as high as they were willing to bet. The person who could successfully float the greatest mass (had to stay afloat for 5 seconds) would be the winner, but if they bet TOO high and their boat sank, they were disqualified. The mass weights that I had came in increments of 1, 2, 5, 10, 20 and 50 grams. They could decide how they wanted to distribute their weight.

The bets came in slow and steady. Some students wanted to see how others would bet. Others worked on their flotation device right away. A few students went for it all, hoping their flotation device would carry 80-100 grams. Every student came to the table at some point in the design process to feel what the weights felt like in their hands. After about 15 minutes of engineering we began the floating. It seemed like every student was hanging on the edge of their seat as the flotation devices came forward. Near the end they were trying to stand on chairs to see the final two. The results as we proceeded were recorded on our easel chart.

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The reflection that followed was powerful and meaningful. Many wished they had bet more weight, others expressed an interest in changing their float design. Some explained that they would have liked the opportunity to test their float ahead of time. Other students felt that they had over-thought their design, and wanted to do it all again.

By the end of the lesson, every student in the room could tell me what 1 gram felt like. A week and a half later, they could STILL tell me what 1 gram feels like, AND they are connecting it to other things in the world around them. Seeing the success of something that was so simple, and that truly took only 25-30 minutes makes me see that I need to do this more. I need to connect it more to their lives, allow them to see it, touch it, (maybe even taste it!) to make it meaningful.

You can check out my Float Challenge in the Resources for Educators section, or just click here! In it is the lesson in GANAG format (Jane Pollock’s amazing lesson planning format) and includes goal setting, the guidelines for the contest, and formative assessment at the end. Happy Floating!

by Beyond Traditional Math

The Trouble With Learning Math Facts

The benchmarks for learning math facts in the Common Core State Standards are clear:

By the end of Kindergarten know all sums and differences to 5.
By the end of First Grade know all sums and differences to 10.
By the end of Second Grade know all sums and differences to 20.
By the end of Third Grade know all products and quotients to 100.

That is a tall order!

Last spring as I sat with a student who was painfully trying to learn his x8 and x9 facts, I had a bit of an epiphany about math facts and the difficulty of learning them.

When math facts are taught using only 1 method (such as flashcards or time tests), they aren’t connected to anything in the student’s real life.  We rely on basic repetition and the ability to recall this isolated thing.  We would never do that with spelling words.

Think about word study, reading and spelling.  Words are EVERYWHERE.  They are in front of us every waking moment of the day. Our brains connect letter patterns, word clusters and we read them constantly. Where do you ever see math facts? I mean truly, where do you ever see a math fact out in public?

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Words are everywhere. Math facts, not so much.

I am not entirely sure what the answer is, but I think we need to recognize this so that we are more sympathetic to students when they find difficulty in learning them.  I think we need to connect them to their lives as much as possible, present them with multiple ways of learning them and give them strategies so that they can see the awesome patterns that are present in math facts.

by Beyond Traditional Math

REAL Problem Solving at the Elementary Level

One of the things that I struggle with as an educator, is how to incorporate real problem solving in mathematics instruction.  As an adult, I don’t sit down and think about how if Johnny gave me 3 apples and Julie took 1, how many I would have left.  That type of simple math is probably useful for K-1, but not for 2nd grade and beyond. The intermediate grades are READY for multi-step, complex problems that require creativity and critical thinking.  The problems that are part of our math series are not deep, nor are they relevant to student’s lives. They don’t differentiate for gifted and talented students, and they definitely aren’t always appropriate for students with special needs.

Last year when I handed out the Problem of the Day book, supplied by our math series, I cringed a little.  Students didn’t open up these books the same way they open up a book like Harry Potter. There was no excitement, the general feeling was very “blah” in the room.  I know that there has to be a better way.

So, like any teacher, I turned to Google to solve my problems.

“elementary problem solving”

“project based problem solving”

“motivating elementary problems”

There is really not a lot out there.  There are suggested ideas and a few projects here and there, but the majority of the problems are for middle school and higher.  With the new Common Core State Standards and the up and coming Smarter Balance Assessment, I knew that what we currently have isn’t enough.

I have introduced some problems each year, and each year they get better and better.  I will keep on searching for more, as well as continue to tweak what I have.  The best place I have found ideas has been on Twitter, where someone’s language arts lesson prompts me to think of how I could do a similar project in math. Here are some of the problems I currently do, and I am slowly uploading them to share in Resources for Educators:

Book Order Analysis
The Float Challenge
Housing Market Analysis
Mini Golf Course Geometry
Wind Powered Car
Classroom Economy
The Great Air and Water Craft Extravaganza
Desert Hike
Elementary Architect
The Last Summer Picnic
Restaurant Dreams
Family Reunions
Desert Island Playlist

We’re getting there but it’s coming slowly. Join me by posting any of your ideas and products in the comments area!