Math fluency is the ability to perform mathematical operations quickly and accurately. Math automaticity with basic facts is part of fluency. John Munroe (2011) indicates that we as learners have a finite amount of working memory. It is important that student working memory is available to learn new math concepts, solve complex problems and think creatively in mathematics, rather than being used to recall basic math facts.
So, how do we promote automaticity of basic math facts without endless worksheets, mad minutes and text-book assignments? Math games, puzzles and routines related to grade level concepts allow for flexibility in thinking, practice and student engagement and fun. The following documents can help us connect practice with curricula:
- Continuum of Essential Learning Outcomes Grade K – 10
- Grade K – 3 Curriculum Conceptual Through-lines
- Grade 1 – 4 Curriculum Conceptual Through-lines
- Grade 3 – 6 Curriculum Conceptual Through-lines
- Grade 5 – 9 curriculum Conceptual Through-lines
- Grade 7 – 10 Curriculum Conceptual Through-lines
- Grade 9 – 10 Curriculum Conceptual Through-lines Including Modified
- Grade 9 to 12 Workplace and Apprenticeship Conceptual Through-lines
- Grade 9 to 12 PreCalculus Conceptual Through-lines
- Grade 9 to 12 Foundations Conceptual Through-lines
There has been a significant amount of research in the area of mathematics routines to enhance learning, building automaticity and fluency. There are a number of key resources that are helpful to teachers from grades 1 to 10.
Productive Mathematics Discussion
Margaret Smith (2011) has created a structure for planning for and implementing classroom discussion in a mathematics classroom. Discussion and sharing mathematical thinking is the key to most mathematics routines.
This sequence of thinking can be applied to a teaching strategy, Learner Generated Examples (Crawley, 2010), to create a powerful way of sharing student thinking in mathematics.
Learner Generated Examples:
Brian Crawley, a teacher from Saskatchewan, did extensive research on learner-generated examples. Overlaying the Five Practices, you create a cycle that can be applied to many number routines:
Move through this cycle three times. This allows students to push beyond the knowledge that they find easy to access and move to more and more complex ideas.
Examples of Math Routines
There are several powerful math routines gathered from many Math Routine Resources that can be adapted to different concepts over grade levels. The following is a short list:
- Alike and Different
- Counting Circles
- Mystery Number
- Today’s Number
- Number Line
- Number Strings
- Quick Images using Greyson Wheatley’s Best of Quick Draw
- Notice Wonder
- What’s My Rule
- Math 100s Chart
The key to math routines influencing math fluency in your classroom is to choose appropriate concepts and numbers related to your curriculum. For example, in the routine “Today’s Number”, if you are in early primary, you might choose a number between 1 and 10. If you are teaching ideas around skip counting, perhaps choosing the number 6. If you are working on perfect squares, perhaps choosing a number like 36.
Math puzzles allow learners to explore mathematical ideas and practice thinking flexibly. Well-designed puzzles are engaging and logical, with most of the time focussing on solving the puzzle mathematically. As with routines, puzzles can be adapted to the range of numbers and concepts appropriate for a given grade level.
Missing Number Puzzles
- Example Missing Number Puzzle
- These help to build patterns within the 100s chart. More can be found in Melissa Conklin and Stephanie Sheffield’s book “It Makes Sense: Using the Hundreds Chart to Build Number Sense”.
- Extensions can include puzzles that go above the 1-10 line and below the 91-100 line on a hundreds chart. What numbers exist below 0? What numbers exist above 100?
- Examples and explanation are found on Greg Tang’s Kakooma Resources website
- Kakooma helps students build automaticity with addition and multiplication.
- There are a variety of number puzzles, with a diverse range of numbers and volume of questions to solve.
- Created by Dr. Grayson Wheatley, Math Squares can be found at the primary level in his Coming to Know Number resource, and at the middle years’ level in his Developing Mathematical Fluency resource.
- Example: Math Square
- You can also use a blank Math Square sheet to create your own or have students create them for others to practice.
- Also created by Dr. Grayson Wheatley, Math Two-Ways are found in his Developing Mathematical Fluency resource.
- You can also use a blank Two-Ways sheet to create your own or have students create them for others to practice.
- Mazes can be created based on any number type or range.
- Example: Order of Operations Maze
Inaba Place Value Puzzles
- Place value puzzles can help students overcome misconceptions. They were originally created by Naoki Inaba from Japan, and then adapted to decimal numbers on the “Embrace the Challenge” blog.
- Example: Math Inaba Instructions and Whole Number Inaba Sheets
- Example: Decimal Number Inaba Sheets
When choosing and setting up games in your classroom, along with considering the math concepts you are emphasizing, it is also important to consider student grouping and classroom norms.
By creating homogeneous groupings, it is possible that some groups will use tools to help them calculate or identify numbers, such as:
In heterogeneous math game groupings, it potentially frustrating for both the stronger student and student who needs more time to compute or recall math facts.
There are many excellent math games sites that include Math online games. As well, there are many games that require few materials and are engaging for students.
- Back to Back
- Multiplication Toss
- Juniper Green
- Fill the Chutes
- Go Fish with Operations
- Multiplication War
- Roll’n Write with a Place Value Chart, Arrow Cards and Decimal Arrow Cards
- Flyswatter Math
- Multiple Factor
- Condition and Condition Cards
- Battleship for Cartesian Plane
- Decimal War
- Power Yahtzee with Rules
- Capture the Penguins
- Skunk with Rules for SKUNK
Of special note are Alphashapes and Alphashapes Games that can be played to understand mathematics language.
The key to finding and using math games in your classroom is to know the math that you would like to build fluency in, and then search for those concepts. There are literally thousands of great sites that you can access both online and paper copy games.