Math Fluency page
What is Math Fluency?
To quote tncore.org: Fluency is not meant to come at the expense of understanding but is an outcome of a progression of learning and sufficient thoughtful practice. It is important to provide the conceptual building blocks that develop understanding in tandem with skill along the way to fluency; the roots of this conceptual understanding often extend one or more grades earlier in the standards than the grade when fluency is finally expected. (PARCC MCF, v3.0, p. 12).
Wherever the word fluently appears in a content standard, the word means quickly and accurately. It means more or less the same as when someone is said to be fluent in a foreign language. To be fluent is to flow: Fluent isn’t halting, stumbling, or reversing oneself. A key aspect of fluency in this sense is that it is not something that happens all at once in a single grade but requires attention to student understanding along the way. It is important to ensure that sufficient practice and extra support are provided at each grade to allow all students to meet the standards that call explicitly for fluency. (PARCC MCF, v3.0, p. 9)
http://tncore.org/sites/www/Uploads/2.25.13Additions/fluency%20documents%20final.pdf
To quote tncore.org: Fluency is not meant to come at the expense of understanding but is an outcome of a progression of learning and sufficient thoughtful practice. It is important to provide the conceptual building blocks that develop understanding in tandem with skill along the way to fluency; the roots of this conceptual understanding often extend one or more grades earlier in the standards than the grade when fluency is finally expected. (PARCC MCF, v3.0, p. 12).
Wherever the word fluently appears in a content standard, the word means quickly and accurately. It means more or less the same as when someone is said to be fluent in a foreign language. To be fluent is to flow: Fluent isn’t halting, stumbling, or reversing oneself. A key aspect of fluency in this sense is that it is not something that happens all at once in a single grade but requires attention to student understanding along the way. It is important to ensure that sufficient practice and extra support are provided at each grade to allow all students to meet the standards that call explicitly for fluency. (PARCC MCF, v3.0, p. 9)
http://tncore.org/sites/www/Uploads/2.25.13Additions/fluency%20documents%20final.pdf
Why is Math Fluency so important? Fact fluency is important for several reasons. The basic facts (multiplications up to 12 x 12 and additions with numbers up to 20) occur so frequently in math problems that total recall and fact fluency make it easier to see connections and complete calculations without the need for calculators or complicated algorithms. With a problem adding mixed numbers such as 1 2/3 + 3 5/8, students using the standard algorithm must find the common denominator of 3 and 8 (24), multiply the numerators (2 x 8 and 5 x 3), add the whole numbers (1 + 3), add the new numerators (16 + 15), then divide 31 by 24 to get 1, and subtract 31 - 24 to get 7, and add 4 + 1 to get 5. Giving the answer of 5 7/24. This involves 8 "basic" operations that, if a student is fluent, can accurately be completed in approximately 10 seconds or less.
When students are not fluent, and need to take time to calculate each step, they can often get lost within the algorithm, forget where they are, become confused and frustrated. Although calculators are helpful, and can allow students to get the correct answer without truly understanding the mechanics being performed, tasks that are required in later courses (such as Algebra) often require students to take apart expressions to see the relationships between them. For example, if a student is asked to factor: a^2 + 16ab + 48b^2, they need to find which factor pair of 48 adds up to 16, which is a problem that most calculators will not be able to solve for them. If they are fluent, then they can list (either mentally or on paper) the factors of 48 and add them together to see if they get 16: 6 + 8 = 14; 16 + 3 = 19; 12 + 4 = 16.
When students are not fluent, and need to take time to calculate each step, they can often get lost within the algorithm, forget where they are, become confused and frustrated. Although calculators are helpful, and can allow students to get the correct answer without truly understanding the mechanics being performed, tasks that are required in later courses (such as Algebra) often require students to take apart expressions to see the relationships between them. For example, if a student is asked to factor: a^2 + 16ab + 48b^2, they need to find which factor pair of 48 adds up to 16, which is a problem that most calculators will not be able to solve for them. If they are fluent, then they can list (either mentally or on paper) the factors of 48 and add them together to see if they get 16: 6 + 8 = 14; 16 + 3 = 19; 12 + 4 = 16.
Improve Math Fluency: The old joke: "A man was walking down the street in New York City, lost. He asked a taxi driver: 'How do you get to Carnegie Hall?' The driver responds: "Practice, practice, practice' " holds true. You can buy or make flashcards, drill-and-practice worksheets, or find video games.
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A related recommendation is to create a modified set of flash cards. A standard set of multiplication flash cards gives a fact question on one side (ex: 3 x 8) and an answer (24) on the other. The modification is to put the question on front, but on the back, put the entire fact family (3 x 8 = 24; 8 x 3 = 24; 24 / 3 = 8; 24 / 8 = 3). Each time through the deck, when you see a question, answer the question, but give the entire family.
Note to parents and teachers: Consider having the students create their own flash cards, however, these cards should be checked for accuracy before the students use them.
Note to parents and teachers: Consider having the students create their own flash cards, however, these cards should be checked for accuracy before the students use them.