What is the best way to become fluent in math facts?
What is the sum of 7 and 8?
What is the difference between 12 and 6?
What is the product of 5 and 6?
What is the sum of all even numbers from 2 to10?
Math fact fluency is the ability to accurately recall math facts such as multiplication tables, addition, and subtraction. Developing fluency means that kids can quickly recall facts without counting or calculating. Practicing math facts helps kids build a strong foundation for more advanced math skills.
Math Fact Fluency: Developing Automatic Recall of Math Facts
Mastery must focus on Fluency Fluency Develops in Three Phases Foundational Facts Must Precede Derived Facts Timed Tests Do Not Assess Fluency Students need Substantial and Enjoyable Practice
5 Fundamentals of Fact Fluency
Procedural fluency includes accuracy, efficiency, flexibility, and appropriate strategy selection (National Research Council, 2001) We use these general definitions of each component to focus specifically on basic fact fluency: Accuracy: the ability to produce mathematically precise answers Efficiency: the ability to produce answers relatively quickly and easily Appropriate strategy use: the ability to select and apply a strategy that is appropriate for solving the given problem efficiently Flexibility: the ability to think about a problem in more than one way and to adapt or adjust thinking if necessary
Mastery Must Focus on Fluency
As students come to know basic facts in any operation, they progress through three phases (Baroody, 2006): Phase 1: Counting (counts with objects or mentally) Phase 2: Deriving (uses reasoning strategies based on known facts) Phase 3: Mastery (efficiently produces answers)
Fluency Develops in Three Phases
Foundational Facts Must Precede Derived Facts
Tommy is taking his weekly multiplication test. Although he has learned many easier multiplication facts, Tommy still struggles to remember his 7s, and he is very aware of this weakness. Once again, he compensates by skipping around and answering the facts he knows; then he quietly puts his hands under his desk to help him count to answer the remaining, unknown facts. He has learned that he can usually finish the test in time by doing this, and his teacher is therefore convinced he knows his facts.Ellie feels her heart start to race when her teacher announces it is time to start the weekly addition facts timed test. Even though Ellie excels at reading, writing, and solving even the most challenging story problems, as soon as the timer starts, she draws a blank. She struggles to remember the facts she knows well and is so distracted by the timer that she can't apply her favorite strategies to tougher addition facts, like 7 + 8. With tears in her eyes, she once again turns in an incomplete test and tells her friends she's "just so bad at math." Her teacher is puzzled; she has seen Ellie's automaticity with addition facts many times during math games and doesn't understand why that doesn't translate to the test.
Timed Tests DO NOT Assess Fluency
To what extent does the game … Provide an opportunity to practice the subset of facts that the students are learning? Appeal to the age of your students? Employ visuals or tools (such as ten frames, quick looks, or arrays) to support strategy development? Involve selecting from among derived fact strategies (for mastery-level games)? Provide opportunities for discussion among students about their mathematical thinking? Encourage individual accountability? (For example, are students solving their own facts or competing to solve the same fact? The former practice provides more "think time" and avoids opting out.) Remove time pressures? Involve logic or strategic moves, enhancing the "fun factor"? Offer opportunities for adaptation so that all students can experience appropriate challenge? Lend itself to you being able to listen and watch in order to assess progress?
Students Need Substantial and Enjoyable Practice
Math Fact Fluency is an important part of everyday math instruction, as it helps students become more adept with the basic facts that are needed to understand and solve more complex equations. Math Fact Fluency can also help students become more accurate when solving complex math problems, as they will have a better understanding of the basic facts needed to solve the equation. Math Fact Fluency has been found to be important for success in all levels of mathematics, from basic arithmetic to advanced calculus.
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How was the Video and the 5 fundamentals similar and different
Work together in pairs: What strategies can be used to help students improve their math fact fluency?
Work together in pairs: What are the benefits of developing math fact fluency for students?
Brain break: Draw a goofy dinosaur driving a bright red car
What have you learned about the importance of reviewing math facts in your classroom?
Question: What is the sum of the first 10 positive integers? Clues: • The first 10 positive integers are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. • Adding integers means to add the absolute values of the numbers and keep their signs. • The sum of consecutive numbers is found by adding the last number to the sum of the numbers before it. In pairs: Select and solve one of the tasks: A. Solve the mathematical equation. B. Explain your answer and draw a diagram to illustrate it.
Question: What are the two most important math facts everyone should know? Clues: • One math fact is a basic operation, such as addition, subtraction, multiplication or division. • The other math fact is related to fractions and decimals. • Both math facts are essential for everyday life. In pairs: Select and solve one of the tasks: A. Draw a diagram to illustrate how to use the two math facts in everyday life. B. Invent a story and draw a comic strip to explain why these two math facts are important.
Question: What is the sum of 6 + 7? Clues: • Remember to add the numbers together. • Think of it as 6 plus 7 more. • The answer is the same as 7 plus 6. In pairs: Select and solve one of the tasks: A. Work with a partner to draw a picture that shows the answer to the question. B. Explain to your partner how you solved the problem.
Question: What is the sum of 3 and 7? Clues: • The answer is bigger than 3 • The answer is smaller than 10 • The answer is an even number In pairs: Select and solve one of the tasks: A. Write a story about a problem that can be solved using 3 + 7 B. Create a rap about 3 + 7
Question: How can you use math facts to help you solve a problem? Clues: • Math facts are the basic facts that you know about numbers, such as adding, subtracting, multiplying, and dividing. • Think about the math facts you already know, and use them to help you find the answer. • Be sure to use the math facts to check your answer before you move on. In pairs: Select and solve one of the tasks: A. Choose a math problem, and use math facts to solve it. B. Create and solve your own math problem using math facts.
What is the quotient of dividing 20 by 4?