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Computational Fluency Grades 2 and 3 What is fluency? The NCTM Principle and Standards of School Mathematics (2000) defines computational fluency as having efficient, flexible and accurate methods for computing. The first step in achieving computational fluency with larger numbers is an understanding of numbers, their relationships, and their composition. Understanding versus Memorization Children need to understand what it means to add and subtract before facts can become automatic They need to also understand how they are connected Understanding is necessary but not sufficient When isolated additions and subtractions are practiced, the emphasis is on recalling the answers Teaching facts for automaticity relies on thinking Grade Level Expectations By the end of second grade students are expected to fluently: add and subtract within 20 using mental strategies (know from memory all sums of 2 one-digit numbers) add and subtract within 100 using strategies based on place value, properties of operations, and/or relationship between addition and subtraction Grade Level Expectations By the end of third grade students are expected to fluently: add and subtract within 1000 using strategies based on place value, properties of operations, and/or relationship between addition and subtraction multiply and divide within 100 (know single digit products from memory) Grade 2 Big Ideas Addition and subtraction are used to represent and solve many different kinds of problems. The properties of addition along with place value provide the basis for our understanding of each procedure. Common Counting Strategies Count all 1, 2, 3, 4, 5, 6, 7 Count on from the first number 2, 3, 4, 5, 6, 7 Count on from the larger number 6, 7 5 Common Addition Strategies Counting on 1, 2, 3, and 0 Doubling: 3+3=6 Complements of 10/ Ten Buddies 0 + 10 = 10 2 + 8 = 10 1 + 9 = 10 3 + 7 = 10 Common Addition Strategies Near doubles: 6 + 7 = (6 + 6) + 1 or (7 + 7) – 1 Using the commutative property: 5+3=3+5 Common Addition Strategies Using the associative property: 5 + 6 + 4 = (5 + 6) + 4 = 5 + (6 + 4) From Single to Double Digit Addition (with multiples of 10) Count all (10, 20,30,…) Counting on by tens from 50 (60, 70, 80) *Applying the knowledge of the basic facts. 5 tens + 3 tens = 8 tens 50 + 30 = 80 From Single to Double Digit Subtraction 53 – 20 We start with 53, take 2 tens away and count all that is left. (10, 20, 30, 31, 32, 33) We might begin counting back as we take the rods away. (43, 33) We can apply our basic facts: 5 tens – 2 tens = 3 tens So 53 – 20 = 33 Adding Ones with Regrouping 58 + 6 Counting on: I am going to count from the bigger number. 64 60 62 58 59 61 63 Make Ten: I can make a ten from the 8 in 58 and the 2 from 6. Adding Ones with Regrouping Make Ten using Number Bonds: 58 + 6 = 60 + 4 50 8 2 4 Make Ten using the Number Line: You try it: How would you solve? 197 + 18 Grade 3 Big Ideas Multiplication is a fundamental operation that is used to solve everyday problems. Multiplication has been described as rectangular array, repeated addition, and area. There are patterns and relationships in multiplication facts and multiplication and division are related. Common Multiplication Strategies I can use a multiplication fact I know, to figure out one I don’t… Using the commutative property: 2x4=4x2 4 groups of 2 2 groups of 4 Common Multiplication Strategies Doubling: 2 x (3 x 6) = 6 x 6 3 groups of 6 doubled Common Multiplication Strategies Halving and doubling: 4 x 3 = 2 x 6 4 groups of 3 2 groups of 6 Common Multiplication Strategies Using the distributive property: 6 x 4 = (5 x 4) + (1 x 4) = 20 + 4 = 24 Common Multiplication Strategies Using the distributive property: 6 x 4 = (5 x 4) + (1 x 4) = 20 + 4 = 24 Number bond You try it: Use the distributive property to figure out: 7x3 with an array with a number bond Common Multiplication Strategies Using the distributive property with tens: 9 x 4 = (10 x 4) – 4 Part/Whole relationships A guitar has 6 strings. How many strings are there on 3 guitars? Write a multiplication sentence to solve. Great Websites for Math Practice sheppardsoftware.com/math.htm topmarks.co.uk/maths-games/ Arcademicskillbuilders.com/games FactMonster.com/math/flashcards.html Multiplication.com IXL.com k-5mathteachingresources.com/