There are three parts to fluency. Students need to be able to show that they are efficient, flexible in their thinking and accurate. When students are efficient, they are solving a procedure in a reasonable amount of time by selecting an appropriate strategy. When students are flexible, they demonstrate the ability to know multiple procedures and apply one to problem solve. When students are accurate they are correctly solving a procedure. (SanGiovanni, Bay-Williams, Serrano, 2022 as cited in Figuring out Fluency) Students spend years developing their conceptual understanding which allows them to become fluent. Students develop automaticity with basic facts (addition, subtraction, multiplication and division) through implementing strategies.
Games provide an enjoyable and purposeful way to practice both addition/subtraction and multiplication facts. Please see the Math Games page for games that strengthen fact fluency.
Encourage students to use the strategies explained here rather than simple memorization. Practice will still lead to fluent recall and more quickly. Once a strategy is mastered, use the suggested ways to practice through games, activities, online practice or flashcards.
Some good online practice options are listed on our general K-5 Math math site. Scroll down to 1-2 Addition Facts.
sites.google.com/westonps.org/mathk5/links
Strategies for Division (SanGiovanni, Bay-Williams, Serrano, 2022 as cited in Figuring out Fluency)
Strategies for Multiplication (SanGiovanni, Bay-Williams, Serrano, 2022 as cited in Figuring out Fluency)
Strategies for Single Digit Multiplication
Doubling - Student sees an even factor, finds the product of half of that factor, and double their answer. EX: 6x7 - I know 3x7 is 21 and I double 21 to get 42. 6x7=42
Add-A-Group - Student thinks of a known fact where one of the factors is one less, multiplies, then adds a group back on. EX: 6x7- I know 5x7 is 35 and 7 more is 42. 6x7=42
Subtract-A-Group - Student thinks of a known fact where one of the factors is one more, multiplies, then subtracts a group. EX: 6x7 - I know 7x7 is 49, so I subtract 7 to get 42. 6x7=42
Near Squares - Student uses a square fact they know and then adds or subtracts a group. EX: I know 6x6 is 36, and I add 6 more. 6x7=42.
Click the link below to see many options from our general K-5 Math math site.
sites.google.com/westonps.org/mathk5/multiplication
Other good online practice options are listed on our general K-5 Math math site. Scroll down to 3-5 Multiplication Facts.
Having students make their own flashcards for the facts they need is ideal. If you would prefer to print some out, here are some links:
The 2 sets below allow you to print the ones the child needs. They are made to fold and have the answer on the back.
www.k5learning.com/free-flashcards/math/addition
www.k5learning.com/free-flashcards/math/multiplication
This set is smaller and complete. It must be printed on a back to back setting.
www.masterschool.org/pdf/SummerPDFs/Addition_Flash_Cards.pdf
This site has several printable options for multiplication.
www.multiplication.com/resources/free-multiplication-flash-cards