Math with Ms. Routt- Problem Solving

The fourth component of my math block is problem solving. This component of "Math with Ms. Routt" generally takes about 15 - 20 minutes. While I am a big proponent of authentic problem solving, that which arises naturally through the content that we teach, I also realize that those opportunities do not always arise at the time they are needed. Therefore, I use this time to both model and reinforce how to solve problem solving tasks and the strategies we use to attain this goal. In addition, I also hold a word problem workshop throughout the week to model/ reinforce how to analyze and successfully attack word problems. 

During this time, I either model how to address the task with a think-aloud or I ask the

Solution Strategy Poster

students to work individually, in pairs, or small groups, depending on the difficulty of the task, to complete the work. If the students complete the task without my help, we debrief the task before moving on. I have students share their work by creating a solution strategy poster (see picture to the right), review their work with the document camera, or talk through the steps they used to solve the problem. A copy of my "Open-Ended Questions Poster" can be found here. 

I use a variety of resources to find problems. Great problem solving tasks can be found via the web, in supplemental materials, or in your textbook series. For word problems, the best tasks are the ones that include extra information or include a lot of information that could be used to answer multiple questions. 

I have posted a few resources to share with you in the the "Problem Solving" section of my "File Cabinet." There is a problem solving strategies pack to expand your students' problem solving toolboxes, two packs which include a structure for analyzing word problems, and a problem solving task from one of my holiday packs (Note: you can make this an everyday task by changing the holiday words to everyday words). Click here to check out my file cabinet!

Math with Ms. Routt- Computational Fluency

The third component of my math block is computational fluency. According to Robert Ashlock (2010), author of Error Patterns in Computation: Using Error Patterns to Help Each Student Learn, today's mathematicians "need to be able to use efficient and accurate methods for computing." To meet this goal, I include this five minute segment to encourage fact fluency and flexibility with composing and decomposing numbers. 

Over the years, I have done this many different ways depending on the grade level and ability level of my students. Here are a few ways I have structured this time over the years:  

1. Counting and Grouping Methods: With younger students, I begin the year using Greg Tang's math picture books to support the development of this skill. 

"Snail Parade" from The Grapes of
Math written by Greg Tang and
illustrated by Harry Briggs.
Picture from:
http://eduscapes.com/nonfiction/10.htm

The "Snail Parade" picture above is from Greg Tang's book titled, The Grapes of Math. I put this page under the document camera for about 5 seconds. Students are then expected to determine how many snails are on the page. In the beginning, students attempt to count them one by one, but they quickly realize there is not enough time to count them all. They then move to other grouping techniques, such as "I see two rows of five and three rows of four, or 10 + 12, so there are 22 snails." Another student may say, "I see five rows of five with three snails missing, or 25 - 3, so 22 snails." In both cases, these methods provide a very rich opportunity for me to extend the students' thinking to numerical equations, such as (2 x 5) + (3 x 4) = 22 or (5 x 5) - 3 = 22. This provides a good foundation for the work with order of operations that will come later. 

At some point, I switch to making dot pictures with transparent chips or dot stickers. This allows me to create larger array-like pictures that are easier for the students to decompose quickly. For example, in the picture to the left, students may notice four rows of four plus the four corners, six rows of four minus four, or two rows of six plus two rows of four. In all of the cases, the students have identified 20 dots. After hearing the verbal descriptions, I connect them to numerical expressions. 

Over time, I noticed my students' fluidity with numbers and their ability to compose and decompose numbers quickly improves. 


2. Fact Fluency: With middle grades students, the primary focus for fact fluency is learning multiplication and division facts. To help the students meet this goal, I use mini-lessons and frequent practice to increase fact fluency. Check out my Engaging Mathematics: Learning Multiplication Facts here. 

3. Using Mental Math: With my upper grades students, I use this time to practice using mental math to solve simpler multiplication and division problems. For example, for 52 x 7, it can be decomposed into 50 x 7 and 2 x 7 for a final product of 364. Practicing mental math computations increases computation speed and supports fluidity with numbers. 

References

Ashlock, R. (2010). Error patterns in computation: Using error patterns to help each student learn. Boston, MA: Allyn & Bacon.

Math with Ms. Routt- Warm-ups

  
The second component of my math block is a warm-up. Warm-ups are a great way to review recent material and to spiral required content and skills. Warm-ups should be short and require minimal time to review. There are many ways to format your warm-up. You just have to find the best one for you!

The picture below shows the warm-up program that I have frequently used in the classroom. It is modeled after the Mountain Math program and the Lone Star Learning TEKSas Target Practice program. It includes all of the grade-level content and skills my students were required to learn. I created 30 different questions. Each question is broad enough that I could change the numbers every other week to create a new problem. The students completed 3 of the numbered problems each day for two weeks. I then put up a new set of numbers to create 30 new questions and the process repeated. 

While I will admit that this program took some time to create, once it was created, it was done and lasted the entire school year. There are, however, many ways to create your own warm-ups. Here are a few ideas: 

• Use a basic template of 4-6 boxes and add one problem to each box.
• Use the spiraled review questions in your textbook series.
• Create a few basic questions for important skills and change the numbers each day.  
• Create a slideshow of 4-6 questions and display it for students to complete. 

In addition, I created a Pinterest board with more ideas. Click here to check it out!

Math with Ms. Routt- Starters

The first component of my math program is what I call a starter. I first learned about the idea of a starter at a workshop presented by Marcy Cook. A starter is designed to get the students thinking about math. Starters include critical thinking activities incorporating grade-level content and skills, vocabulary, and strategic thinking.

Starters are designed to take no more than five minutes of instructional time. Therefore, in order to accomplish this goal, the activities are short but full of opportunities to review and extend the required content and skills at your grade level.

I typically choose starters that are fun and challenging for students in order to hold their interest. For variety, each day of the week features a different starter. This allows me to stretch the available resources I have a bit further since each activity is only used once a week. For example, with my last group of fifth graders, I used the following schedule:

• Monday: Number of the Day- This activity challenges the students to show ways to compose and decompose a number. I featured this activity in my Engaging Mathematics series. Click the links above to learn more.
• Tuesday: Critical Thinking Activity- This task builds critical thinking and strategic thinking skills. It includes a wide variety of activities and challenges. I generally use the same activity for 4-6 weeks before changing to another activity. Click the link above to download a free resource to support this goal. (See the picture to the right.) 
• Wednesday: Today’s Number- This activity is similar to calendar math in the younger grades but has been adapted to suit the skill level of older students. It reviews important number sense-related vocabulary. Generally, I choose a number (1-100) for the students to use as "Today's Number". (You can also use the current day of the month as your number.) Students complete the half-sheet using this number. (If the arrays are large, students can just write the factor pair instead of drawing the array.) Click the link above to download a free resource to support this goal. Please Note: The top portion of the sheet includes even/ odd vocabulary. The bottom portion of the sheet includes prime/ composite vocabulary. Choose the portion of the page that is most appropriate for your students. 
• Thursday: Word Wall Activity- This activity emphasizes important math terms and vocabulary displayed on your math word wall. I featured this activity in my Engaging Mathematics series. Click the link above to learn more.
• Friday: There is no starter due to our weekly homework review.

Additional Resources for Starters:

• The Routty Math Teacher Critical Thinking File Cabinet- FREE!
• Marcy Cook Math- Resources are generally around $15 each.

Math with Ms. Routt

One of the biggest challenges that teachers face in the classroom is time. There just never seems to be enough of it. This series will offer practical tips and strategies for getting the most from your math time. Below, you will find a poster of the way I structure my math block throughout the week. I have used this model with a variety of grade levels, including middle school, and various student demographics. It has been successful with almost all of my students! Each post in this series will spotlight a different segment and detail how I use the time to provide a variety of focused and purposeful learning opportunities for my students. 

Here's a quick overview of "Math with Ms. Routt": 

• Starters- critical thinking activities incorporating grade-level content and skills, vocabulary, and strategic thinking
• Warm-up- spiraled review of previously taught grade-level content and skills
• Computational Fluency- quick games and activities to increase fact fluency
• Problem Solving- dedicated time to emphasize the thinking skills needed to be successful problem solvers
• Math Lesson- 5-E model focused lesson emphasizing student-constructed knowledge
• Assessment/ Journal- informal assessments and journal tasks designed to reveal both student understandings and misunderstandings 

Over the next two weeks, I will highlight these six math block components and provide ideas and strategies to help you implement them in your classroom. 

Second Semester Recharge!

Welcome back! I hope you had a fabulous winter break and enjoyed holiday time with your family and friends. It's a new semester-- an opportunity to start fresh and refocus our minds. I always love returning to the classroom during the second semester to implement new programs and try out some new ideas and strategies. With that in mind, here are some of the exciting things that I have planned for the next few months:

• January Series- Math with Ms. Routt- Tips and Strategies for Fitting It All In
• February Series- Math Picture Books I Love
• March Series- "13 Rules that Have Expired" Revisited

I am so excited about these upcoming series and hope that you will be able to join me for some great learning opportunities. If you'd like to stay up-to-date with the series but do not want to have to visit the blog each day to see new posts, enter your email address in the box on the right side of the page. Happy Reading!