Tag / rigor

by Beyond Traditional Math

Crank It Up a Notch: Add Something They Can Touch When Problem Solving

One of my favorite ways to amp up problem solving is to throw something into the mix that they can touch.  This makes the project or problem so much more interesting to students in one instant.  We are working on the Design a Dream Bedroom project, so I picked up some free samples from the hardware store:

Hans On Real World Math

Give them stuff to touch when they are working on real world math activities.

Of course you can be sneaky about introducing the materials.  Before I even went over the problem during math, I spent the morning organizing the materials on a common table when they were arriving for the day. I got about a million questions, and hands were reaching out to touch the carpet and flooring samples before I could even get them in the bucket.

That is all I needed to do to get them interested in the problem.  After I read through the introduction with them during math problem solving time, the students literally leaped out of their carpet spots to run up and grab the problem from me.

That is what we want problem solving to be like…exciting, engaging, rigorous and motivating! Putting things in their hands to make it real world has worked every time.

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by Beyond Traditional Math

Open Ended Math Problems Promote Reading, Writing AND Math

Last spring I had the opportunity to take a practice version of our new state assessment (the Smarter Balanced Assessment). In some states in the U.S. the PARCC is the new assessment which is similar in nature.

Talk about a jaw dropping, sweat on my forehead, instant anxiety through my whole body moment.

What the students are being asked to do is way more than a few math problems. They are expected to read, write and use appropriate grade level math in VERY complex ways. I realized that I needed to add some deep problem solving to my math instruction.  So I began to make open ended problem solving problems to introduce regularly into the classroom.

I decided to create Doggy Dilemma, a free problem for anyone to try out.  It is a highly motivating, real world problem in which students must read through information to decide what dog they must adopt. They draw a diagram of the dog pen, calculate the cost of the fencing, and write a letter to their parents explaining why they made the choices they did.

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My third graders have gone crazy over it.  They love it!  There are two full pages of reading involved which mimics the new assessments.  I have enjoyed creating it and want to make it available to anyone who teaches elementary math so that you can give your students the experience they need before the real assessments begin. You can get it by clicking on the picture below:

Open Ended Problem: Rigorous Problem Solving for Elementary Students

I’d love to hear how other teachers are encouraging this type of thinking in their classrooms. Please feel free to share in the comments!

I am happy to link up here:

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by Beyond Traditional Math

Inquiry Learning: YES!

A little while back I wrote about letting students discover math patterns and connections on their own.  Inquiry learning truly does help students do the majority of the learning.

Well, check out this blogger from The Research Based Classroom. I love her post this morning citing Piaget:

The Research Based Classroom

“Each time one prematurely teaches a child something he could have discovered himself, that child is kept from inventing it and consequently from understanding it completely.”   Piaget

Right on Brandi!

How do you all help your students discover concepts on their own?

by Beyond Traditional Math

Transform Problem Solving: Push Them to Explain Their Thinking in One Simple Step

A few weeks ago it was time for our daily problem solving block in math class, and I looked over a few shoulders to find the most aggravating thing. The answers written (sometimes incorrectly) with nothing else.

So here was the problem (from Practice Problems for Multiplication and Division):

Jessie bakes cupcakes for her local business.  Six orders were called in on the phone. Each order included a half dozen cupcakes. How many cupcakes should she make?

Young learners are notorious for answering math problems like this:

Problem Solving Answer

That’s it. Granted it is the correct answer, but no explanation of their thinking or their strategy. SO aggravating for a teacher who is constantly pushing for students to explain their reasoning.  SO not in line with the math practice standards and what they are pushing students to do.

So I implemented a little game to help transform problem solving, specifically targeting how they are explaining their thinking. This poster is up hanging on my chalkboard:

Problem Solving Explanation

Here is how the “game” works:

1.  A student rolls the dice.

2.  Whatever we land on is the preferred method of communication for the day. The students must try to explain their strategy on their papers using:

  • words to describe the steps taken to solve the problem, including how you arrived at the answer.
  • a picture or a model of the problem.
  • a number sentence to show how the problem was solved.
  • tools (manipulatives) to act out the problem. We typically gather around a desk (each student has their own bag of tools) to see how they solved it.
  • FREE choice means just that, they can use their favorite way to solve the problem (maybe some other creative strategy beyond any of these four).
  • Teacher’s choice. This is kind of awesome because I can ask them to use number lines, graphs, skip counting or some other type of strategy that is appropriate to the problem type.

3.  The same student reads the problem out loud to the class (twice).

4.  The students solve the problem on their paper as many ways as they can (choosing their best way first), but when they explain it they should try to use the method of communication that was rolled.

5.  Two students are asked to come up to the board to show how they solved the problem, and explain their thinking. At least one of the students must have used the method of communication that was rolled.

Since I’ve started to use this, students have gotten better at showing their work, which in turn has made them better at explaining their thinking verbally. It also leads to awesome questions asked of the students who come up to explain their strategy.

Here is what that same problem looked like after we rolled the dice and asked that same student to use the strategy of a model/picture:

Problem Solving Explanation

Additionally, the other student who came up used a number sentence.

Problem Solving Explanation

Both great strategies!  I love that it encourages the use of different ways to explain, especially when some students get in a rut by only one strategy or one way to explain.  It has also been a big help to students who have trouble putting their picture into number sentences.

The best part? The kids think it’s like they are playing the lottery every day.