Beyond Basic Facts: Math Fluency for Advanced Students

 

As an enrichment teacher, I work in two different schools. Both of these schools have school-wide fact fluency initiatives in which students in every classroom work toward fluency in addition, subtraction, multiplication, and division facts.

While basic facts are important, there are other aspects of mathematical fluency that I want to address as well. When students have some values committed to memory, higher level problems become faster and more efficient. Understanding number relationships helps students to move quickly between fractions, decimals, and percents. As problems get harder, they can quickly decide when to keep numbers as fractions or when to change them to percents.

I have realized that working toward mathematical fluency has a place in the enrichment classroom. We can go beyond the basic facts to work on topics that have some mathematical richness and room for discussion.

For fourth graders, these topics include:

• addition and subtraction within 100
• extended multiplication and division facts
• simplifying fractions

Fifth graders benefit from fluency practice with:

• multiplication and division by powers of 10
• comparing decimal and fraction values
• fractions to decimals

For sixth graders, fluency practice can explore:

• percents
• exponents and square roots
• integer operations
• using area and perimeter formulas

 Creating fluency practice for students isn't difficult! Choose a topic, then create sets of problems within that topic. Students enjoy competing against themselves week after week, aiming for improvement. With my enrichment students, I made improvement the goal instead of a set number of problems. This makes success within everyone's grasp.

If you would like the sets that I created, they are available below.

Beyond Basic Facts: Fourth Grade

Beyond Basic Facts: Fifth Grade

Beyond Basic Facts: Sixth Grade

Math Jigsaw Problems

 This year, I've been working with math enrichment groups in addition to my regular gifted classes. In math enrichment groups, I pull 10-20 students from a grade level to work on math problems together. It's a lot of fun, but not without some challenges.

One challenge is that the students are often very quiet! I know that some classroom teachers with chatty classes would see this as a very privileged kind of problem. However, when my goals for the enrichment session include getting students to construct and share viable arguments, this silence can be deafening. The students would be quiet for several reasons. Taken from different classes, they often didn't know each other very well. Some of the students would want to work quickly on their own, while others were more tentative. 

A colleague gave me a copy of the book Get it Together: Math Problems for Groups, Grades 4-12. This book has some great problems and worked well for my older students. However, cutting out the problems is a chore! I decided to create some of my own jigsaw problems.

Here's the idea:

• Problems are basic logic matrix problems, with coin amounts and change to add a math component
• Each student only gets one clue, requiring the students to talk together to solve
• A final problem challenges students to create their own clues
  
  
  

You can find a single problem here: Single Problem Jigsaw Problem Solving.

For all four problems and an answer key, click here: Jigsaw Problem Solving for Math Enrichment.