## Achieving Fact Fluency

The resources in this collection help students develop fluency with number facts. These resources strive to deepen mathematical thinking, develop problem solving, and encourage reasoning and strategic thinking. They take advantage of patterns and number sense. By employing a variety of strategies and representations, they help students make connections, thereby improving retention and transferability. Additional resources for educators can be found in a companion Professional Development collection, "Developing Fact Fluency."

## Collection Discussion

Replies: 6
Created:06-07-2012 by bethb
Last Post09-07-2014by BobbiGomez

With this interactive Flash applet students make use of complements of 10 to develop fluency with addition within 100. Users "repair" a water slide by selecting pairs of numbers that add to 20 in the first round, and then to 100. In successive rounds they may choose to practice with any multiple of 10 from 30 to 90.
1, 2, 3, 4, 5

This interactive applet contains four puzzles which develop fluency with addition facts and foster logical reasoning. Each puzzle provides a shape with blanks along its sides and diagonals. The user must fill in the blanks with the numbers provided to reach the same target sum along each side/diagonal.
K, 1, 2, 3, 4, 5, 6+

This flexible, interactive Flash applet allows students to explore number patterns and to develop number sense and fluency with addition, subtraction, and multiplication. The student or teacher enters a starting number and a step increment. Both values may be up to 4 digits and either positive or negative. The user then mentally carries out the sequence and enters the resulting 10th and 11th terms. The first 9 terms are color-coded in groups of 3 and may be shown or hidden one group at a time. Users have the option of hiding or showing the starting number and/or the increment.
1, 2, 3, 4, 5

This game for two players provides students with practice in whole number addition and subtraction while developing strategic thinking. It is played on paper on a 0-20 number line. Player 1 crosses off two numbers and circles either their sum or difference. In each successive turn players cross off the last circled number and one of their choice, and then circle the sum or difference. The player who makes the last possible move wins. The game also may be played co-operatively. The Teachers' Notes page offers suggestions for introducing the game, discussion questions, and extension ideas.
2, 3, 4, 5

This problem provides an opportunity for students to form and test conjectures, and make generalizations, while exploring the effect of parity on simple whole number sums. Solvers are asked to arrange given sets of numbers in a V formation so that the sums of the numbers in each "arm" are equal. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, a printable record sheet (pdf) and links to two YouTube videos demonstrating use of the problem in a professional development setting (videos cataloged separately).
1, 2, 3, 4, 5

This interactive Java applet provides students with practice in subtraction and pattern recognition. Starting with four numbers in the corners of an outside square, students find the differences (larger minus the smaller) between the pair of numbers on each side of the square. After correctly completing each square, they repeat the process for the next inner square, until all squares are complete. Students can explore the patterns that emerge as they work toward the center square. Users can choose to work with whole numbers, integers, fractions, decimals, or money. They may also create their own problems by selecting the four starting numbers for the outside square.

This interactive online game helps students develop fluency with multiplication facts as well as strategic thinking. The goal is to claim four numbers in a row (vertically, horizontally, or diagonally) on a 6 by 6 game board displaying the products of one-digit numbers. Players take turns moving one of the two factor markers to claim a product on the board before time runs out. This game is part of NCTM's Calculation Nation project. Users may login as a guest and play against the computer, or register (free) to challenge other players online.
3, 4, 5

This interactive applet helps students develop mental arithmetic skills and strategies for learning multiplication facts. Frog asks the user to type in a known multiplication fact and then asks the user to complete a related fact by using one of several strategies, including commutativity, doubling a factor, halving a factor, multiplying one factor by 10. The student's fact and Frog's related one are recorded in a window to help students discover relationships and internalize the strategies.

This interactive Flash game gives students practice in identifying multiples of given numbers. Users choose two multiplication tables (from 2 to 9) and the number of examples/bees they want to try (from 4 to 34). The game displays the chosen number of bees with numbers on them; users identify whether each is a multiple of one factor or the other, both factors, or neither factor. At the end of a round players may check their answers. ["e" = "and" in Italian]

This 7-minute video highlights patterns in the multiplication table and offers strategies for learning multiplication facts. The presenter makes effective use of color on a multiplication grid.

This interactive Flash game helps students understand remainders while developing reasoning skills and facility with multiplication and division facts. Playing against the computer, the student creates division equations from 3 randomly-generated numbers (1-6) with the goal of making the largest remainders.

KenKen is a puzzle game that helps students develop whole number calculation skills, logical thinking and perseverance. Users complete the interactive grid with the digits 1-4 (or 1-6) so that each digit appears exactly once in each row or column, while also forming a target number using a specific operation. This page provides four new KenKen puzzles daily with a range of difficulty. Each puzzle includes instructions, rules, and a print option.
1, 2, 3, 4, 5

This interactive online game for one or two players provides practice with number facts and builds strategic thinking and pattern discovery. Players choose an operation (addition, subtraction or multiplication) and 100 problems appear in a 10 by 10 grid. They then select problems that match given target numbers while attempting to get 5 in a row in the grid. Users have the option of working for 3 in a row on a 5 by 5 board, and of turning the sound off. This game is a good balance of skill and luck.

This interactive Flash applet helps students develop fluency with addition, subtraction, doubling and halving. The applet presents a starting number, a target number, and four choices of operations (double, halve, add 7, subtract 3). The goal is to arrive at the target in as few steps as possible. [This is similar to The Near Doubles Machine but with different parameters.]