Developing+Math+Fluency

> "According to the National Mathematics Advisory Panel (2008), the ability to recall basic mathematics facts is critical for general success in mathematics" (Stickney, Sharp, & Kenyon, 2012, p. 84)

=Overview= On this wikipage, you will (eventually) find a variety of learning experiences to help students build math fact automaticity using playing cards. You will also find the National Council of Teachers of Mathematics (NCTM) Standards of Learning & Student Expectations, the appropriate connection to the NCTM Curriculum Focal Points & the Common Core Mathematics Standards.

[[image:Screen Shot 2014-03-12 at 4.48.36 PM.png width="360" height="239" align="right"]]1.) Math Fact Automaticity with Playing Cards
>> 1.) Subtraction >> 2.) Addition >> 3.) Multiplication
 * 1) **Headbands** - this learning experience is similar to the popular game Hedbanz
 * 2) **Learning Objective:** develop fluency in adding, subtracting, & multiplying whole numbers
 * 3) **Procedure with the Students**
 * 4) Divide the class into groups of three
 * 5) Give each group a deck of playing cards
 * 6) Each group should shuffle the cards and place the cards in a place where they can be reached like a table or the floor
 * 7) Assign roles to the students
 * 8) **Answer Master (AM)** - this person provides the product of two cards to the other two members of the group
 * 9) **Headband Player #1 (HP#1)** - this person puts a single card on their head. The front of the card should rest on the forward and the numbers (or face card) should be facing the other two members of the group
 * 10) **Headband Player #2 (HP#2)** - same as Headband Player #1
 * 11) Player arrangement
 * 12) The players should be facing each other so that each of them can see the others' faces.
 * 13) The group (or the teacher) decides to practice multiplying, adding or subtracting
 * 14) To start the game, HP#1 and HP#2 put a single card on their foreheads as described above
 * 15) The AM guesses a product, sum or difference depending on what type of math facts they are practicing
 * 16) HP#1 and HP#2 use the AM's guess and the card information on the other player's head to guess the number on their own head
 * 17) The player who guesses the number on their head first gets to keep the cards on both players head
 * 18) Repeat steps 7 - 10 until the entire deck has been used
 * 19) When the deck is depleted, the player with the most cards wins
 * 20) Choose a new AM
 * 21) **Card Values**
 * 22) Ace - can be a 1 or an 11 depending on what the group wants to practice
 * 23) King, Queen & Jack = 10
 * 24) All other cards are the value displayed on the card
 * 25) **Examples**

[[image:Screen Shot 2014-09-04 at 6.56.24 AM.png width="400" height="328" align="right"]]2.) Math Fact Automaticity with Math Magician

 * 1) **Learning Objective:** develop fluency in adding, subtracting, & multiplying whole numbers
 * 2) **Procedure with the Students**
 * 3) Post this link on your classroom web site - @http://oswego.org/ocsd-web/games/mathmagician/cathymath.html
 * 4) Assign students an operation to practice
 * 5) Provide 10 minutes of practice

3.) Math Addition Automaticity with "Make a Ten"

 * 1) **Learning Objective:** develop fluency in adding
 * 2) **Procedure with the Students**
 * 3) Play the game like "go fish" - click here - to learn how
 * 4) Take out the face cards and joker
 * 5) It is helpful to play with 2 decks
 * 6) Instead of matching pairs, students make a pair by matching two cards whose [|sum] is 10. (e.g. 8 & 2; 7 & 3; 9 & 1; 4 & 6; 5 & 5)

4.) Common Core "Sprints"
>>
 * 1) **Learning Objective:** develop fluency in multiplying by 10
 * 2) **Procedure**
 * 3) Pass out sprints to students
 * 4) Provide them with a time to complete the sprint (at this time, I could not find out how long)
 * 5) Example 5th grade module with sprints[[file:math-g5-m1-topic-a-lesson-1.pdf]]
 * 6) Sprint

5.) Fraction Identification Automaticity with PhET (Physics Education Technology)

 * 1) **Learning Objective**: use fractions to represent numbers that are equal to, less than, or greater than 1
 * 2) **Procedure**:
 * 3) Visit the Fraction Matcher
 * 4) Choose Fractions or Mixed Numbers
 * 5) Choose a level
 * 6) - click here - for the link

6.) Composing and Decomposing Tens & Hundreds

 * 1) **Learning Objective:** compose or decompose tens, hundreds & thousands
 * 2) **Procedure:**
 * 3) Use your classroom web site to link to a virtual manipulative
 * 4) - click here - for the link

National Council of Teachers of Mathematics Standards of Learning & Student Expectations
^ Top

Number and Operations Strand
> **1.) Standard: Compute fluently and make reasonable estimates** >> a.) **Pre-K - 2 Expectations** >>> (1). develop fluency with basic number combinations for addition and subtraction; >>> (2). use a variety of methods and tools to compute, including objects

>> b.) **Grades 3 - 5 Expectations** >>> (1). develop fluency in adding, subtracting, multiplying, and dividing whole numbers; >>> (2). use a variety of methods and tools to compute, including objects

Curriculum Focal Points and Connections
^ Top > ===**Grade 1: Number and Operations and Algebra: Developing understandings of addition and subtraction and strategies for basic addition facts and related subtraction facts**=== >> Children use properties of addition (commutativity and associativity) to add whole numbers, and they create and use increasingly sophisticated strategies based on these properties (e.g., “making tens”) to solve addition and subtraction problems involving basic facts. By comparing a variety of solution strategies, children relate addition and subtraction as inverse operations.

> ===**Grade 2: Number and Operations and Algebra: Developing quick recall of addition facts and related subtraction facts ...**=== >> Children use their understanding of addition to develop **quick recall** of basic addition facts and related subtraction facts. They develop fluency with efficient procedures, including standard algorithms, for adding and subtracting whole numbers, understand why the procedures work (on the basis of place value and properties of operations), and use them to solve problems.

> ===**Grade 3: Number and Operations and Algebra: Developing understandings of multiplication and division and strategies for basic multiplication facts and related division facts**=== >> Children use properties of addition and multiplication (e.g., commutativity, associativity, and the distributive property) to multiply whole numbers and apply increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving basic facts.

> ===**Grade 4: Number and Operations and Algebra: Developing quick recall of multiplication facts and related division facts and fluency with whole number multiplication**=== >> Students use understandings of multiplication to develop quick recall of the basic multiplication facts and related division facts.

Common Core Mathematics Standards
^ Top Standard: Operations & Algebraic Thinking > ===Kindergarten: Understand addition, and understand subtraction.=== >> Fluently add and subtract within 5.

> ===Grade 1: Add and subtract within 20.=== >> Add and subtract within 20, demonstrating //**fluency for addition and subtraction within 10**//.

> ===Grade 2: Add and subtract within 20.=== >> Fluently add and subtract within 20 using mental strategies. //**By end of Grade 2, know from memory all sums of two one-digit numbers.**//

> ===Grade 3: Multiply and divide within 100.=== >> Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. //**By the end of Grade 3, know from memory all products of two one-digit numbers.**//

=References= Stickney, E. M., Sharp, L. B., & Kenyon, A. S. (2012). Technology-Enhanced Assessment of Math Fact Automaticity Patterns of Performance for Low-and Typically Achieving Students. //Assessment for Effective Intervention//, //37//(2), 84-94.