Math Fluency

  • Do Math and You can do ANYTHING!

    Understanding, Accuracy, Fluency

    Fluency in Mathematics 


    Research shows long-term success in mathematics relies on number sense, including fluency with basic facts. SCUC would like to share fluency strategies for families to continue practicing during the summer months. Fluency occurs with efficient and accurate practice using different strategies.

    What are the mathematical progression and understanding?

    Counting Strategies, Structuring Strategies, Transfer of Understanding and Mastery are the phases through which children typically progress in mastering the basic number computations. 

    • The first phase, Counting, is concept learning. The focus here is to understand the meanings of numbers and their relation to others, including joining/combining and separating them.
    • The second phase is Structuring. Where students began to use non-counting strategies to determine quantities.
    • Third is Transfer to other mathematical situations.  There are clusters of addition and subtraction facts that relate to each other. Understanding them is key to fluency.
    • Fourth is Fluency.  This is beyond memorization of basic facts, it is the understanding of them and how to create others . The goal is for students to master sums, differences, multiplication and division, with the ability to recall and apply mathematical thinking.


    Three Steps on the Road to Fluency with Basic Facts

    1.    Provide understanding with concrete models.
    2.    Engender no-counting by one strategies.
    3.    Exposure and Practice


    Positive attitude about math

    This begins with a positive attitude towards math.  Do you like math or does it make you anxious? Your feelings about math can greatly influence your child’s perception of math. Help your child enjoy math by talking about it in a positive way. Think out-loud when you are using math skills so your child will hear your thinking process. Let them know that there are multiple ways to solve problems.  It is critical when you interact with your child about math that you communicate positive messages.  Let them know math is exciting and anyone can learn with the right exposure and effort. Success is not about being “smart”.  After all, math is all around us in the world. Teachers made this video Math Mindset.


    Avoid All Tricks

    Tricks are not reasoning strategies.  Mathematical concepts need to be taught and explained to students through mathematical principles. The use of tricks can stop the progression of learning complex concepts and understandings. All tricks at some point down the road will expire. 

    The best way to do this is through conversations on a daily basis expressing math in the real world coupled with playing games and practicing facts.   We have developed a strategic quick reference chart along with posting other activities and manipulatives to this site.  


    Problem solving with real-world math

    Math has evolved from the computation we most likely experienced in math class to an emphasis on problem solving. Computation is important and is used to solve real-life problems. Rose Garden Students Created this video on Problem Solving  Model the importance of math in the real-world and encourage your child to help when you:

    -    Balance your checkbook

    -    Pay bills

    -    Estimate the cost of the groceries in your cart

    -    Determine how much food to buy or make for a party

    -    Double a recipe or cut a recipe in half

    -    Figure the cost of lunch at a restaurant

    -    Calculate the cost of school lunch for the week or month

    -    Determine how long your child will need to save money to buy a particular item

    -    Determine the number of miles driven in X hours

    -    Determine how long it will take to drive home going X mph

    -    Determine how many gallons of gas you can buy with X dollars


    Other Ways to incorporate Math

    • Games build number sense. Play games with your child to reinforce number sense. Try Racko or Tiny Polka Dots. These games involve numeral order and quanity understanding.  Yahtzee is perfect for working on multiplication facts & reinforcing addition skills. Many fun card & dice games utilize math skills.

    • All math tasks should be written horizontally to promote the development of mental strategies and mathematical fluency.  Limit the facts to be learned at once.  Sort a stack of flashcards into piles; those that are known automatically and those that are not.  Practice one or two unknown facts at a time along with known facts until they become automatic.

    • Math practice should be short and conversational.  They are great for the car ride home or on a walk.  At home, use a timer. Each night, give 1, 2 or 3 minutes to answer as many math facts as possible mentally.  Chart the number right and celebrate/reward increasing automaticity


    Technology and Talk

    • Play oral math games in the car with your child, such as Triangle Math Facts.  Give three numbers from a combination & the child then names the associated facts. Example, Adult says, “Three, nine, six.” Child answers,“3+6=9, 6+3=9, 9-6=3 or 9-3=6.

    • Use the senses in combination to fire neurons & imprint memory. (Say & write, listen & repeat, look & say, trace & say, trace & write, sky write & say, choral recitation, move & say, clap it out,etc.)

    • For multiplication, initially using numbered charts, shade in multiples by skip counting followed  practice of using multiples in games like Quick Draw and Treasure Hunt.  Ask their teachers for games that can be played at home. 

    • There are several Math Apps that can be downloaded to a phone or other device for practice anywhere. Here are some free Apps as recommended by TCEA – Texas Computer Education Association. 

        • Arithmetic Invaders Express: Grade K-2 Math Facts Defend the solar system by solving counting, addition, subtraction, and multiplication problems.
        • Cloud Math Free - With animation and great sound effects, Cloud Math presents a set of problems to the player. For each of the problems, several "avatars" with possible answers bounce into view. The player's goal is, of course, to choose a correct answer. Difficulty level is easily controlled by a choice of operations, number ranges, number of answers to choose from, the number of problems in a set, and an option for a Fail-Safe mode. In this free version, there are problems with addition and subtraction operations on numbers up to 50.
        • Counting Bills & Coins - Count, match, and make change with coins up to quarters and bills up to $20. Practice money skills in five unique activities.
        • Counting Money - In practice mode, the user must answer the question correctly in order to proceed to the next question. The user presses the check button after each attempt to check the answer. In quiz mode, the user has one opportunity to answer the question correctly. There are two difficulty types, beginner and normal.
        • Dial-a-Fraction - As you move the two dials, denominator and numerator, the picture adjusts instantly to show the fraction you have created.
        • Dominoes Easy Match - The player simply matches numerals to corresponding sets of dots. Built-in instructional audio supports the learner with both identification of numerals and counting.
        • Fill the Cup - Four math games allow children to experience math concepts through manipulation.
        • Interactive Telling Time Lite - Learn to set the time via Interactive clocks with movable hour and minute hand! Learn the concept of day and night. Learn how to use AM/PM, 12-hour, and 24-hour clock notation.
        • Kids Learning – My First Numbers Counting Game – An introduction to numbers 1 to 20. Add your own voice and photos.
        • Lobster Diver HD This app, designed for grades 3-8, is great for reading numbers, understanding fractions, reading a number line, and comparing and ordering fractions.
        • Math Flash Cards * - This app allows the user to practice simple basic multiplication facts or extend the user’s ability to work out complex multiplication problems up to three digit numbers. Users can control the number of digits used to generate the problems. Users can also control the number of questions given during one session. If a wrong answer is given by the user, the correct answer is shown before the next problem is given. Sound feedback is provided to the user for correct and incorrect answer
        • Mathical - Mathical was developed by teachers for practice of addition, subtraction, multiplication and division facts; fractions of shapes and place value. The games within the app have adjustable difficulty to suit differing abilities for ages 5 - 10.
        • Math Puppy This app features both Bingo and Challenge modes. Its animated math calculator and subtraction module are included in the free app; other modules may be purchased.
        • A Montessori Approach to Math – Hundred Board Lite Students must drag numbers from 1 to 100 into their correct order on the board. Even numbers and odd numbers are also available.
        • Multiplication Genius x19 Free - Encourage your students to master 9, 12, and 19 Times Tables!
        • Number Frames – This app helps students structure numbers to five, ten, twenty, and one hundred. Students use the frames to count, represent, compare, and compute with numbers in a particular range.
        • Pick-a-Path - Help Okta the octopus reach the target (maximum, minimum, or a specific value) by choosing a path from the top of the maze to the bottom. Seven levels with seven puzzles will test your skills with powers of ten, negative numbers, fractions, decimals, and more. How many starfish can you earn?
        • Pizza Fractions 1 - In a chef's pizzeria, your child masters the concept of naming simple fractions using pizza picture examples. Designed for grade levels 2-6, Pizza Fractions provides introductory practice with fractions in an approachable, game-like environment.
        • Teaching Number Lines - Little Monkey Apps Number Lines aims to students to visualize numbers for rote counting and ordering and to see the physical position of a number linking patterns and relationships. Unlike counters, which model counting, a number line also models measurement, which is why the number line begins with zero as you would see on a ruler. Students are also exposed to different vocabulary for addition and subtraction, such as step forward or jump back to physically suggest the movement of the frog along the number line. This free version includes ads.
        • Telling Time Free - Instead of giving the user multiple choices, Telling Time Free lets the user input the time by the hour, ten minute, and minute. The user inputs the digital time based on the analog time. There are two game modes, Practice and Quiz.
        • Tell Time – Little Matchups Game - Little Matchups is an exciting interactive matching game that helps your child rapidly learn how to tell time by matching analog and digital clocks.
        • Virtual Manipulatives! – Excellent app for introducing fractions.

    Some websites and apps support the development of fluency.  However, nothing is as powerful as face-to-face in the thick of math activities.  Here is a link to games that you can play with a deck of cards. ACING Math with Cards

    Do Math and You can do ANYTHING!

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