Report

Computational Fluency Grade 4 and 5 Understanding versus Memorization Children need to understand what it means to multiply and divide before facts can become automatic Understanding is necessary but not sufficient When isolated multiplications and divisions are practiced, the emphasis is on recalling the answers Teaching facts for automaticity relies on thinking Grade Level Expectations By the end of third grade students are expected to have mastered all the facts for multiplication and division within 100 By the end of fourth grade students are expected to multiply a whole number up to 4 digits by a 1-digit whole number and two 2digit numbers By the end of fifth grade students are expected to be fluent with multi‐digit multiplication 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 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. Grade 4 Big Idea To find the products for multi-digit multiplication, I can break apart the numbers using place value. The “Place” of Place Value 4 x3 12 4 ones x 3 = 12 ones The “Place” of Place Value 40 x 3 120 4 tens x 3 = 12 tens The “Place” of Place Value 400 x 3 1200 4 hundreds x 3 = 12 hundreds The “Place” of Place Value 4000 x 3 12,000 4 thousands x 3 = 12 thousands Multiplying Larger Numbers 4 x 13 = 4 groups of 13 or 13 groups of 4? How would you model this problem? I am retiling my hallway. The dimensions are 4 feet by 13 feet. Each tile is one square foot. How many tiles do I need? My 4’ x 13’ hallway The Open Array Now let’s try bigger numbers 1,423 x 3 Show 1,423 chart with the disks Area Model 3 1,000 400 3 x 1,000 3 x 400 3,000 1,200 20 3 3 x 20 3 x 3 60 9 Understanding the Standard Algorithm starting with Partial Products 1423 x 3 9 60 1200 3000 4269 3 x 3 ones 3 x 2 tens 3 x 4 hundreds 3 x 1 thousand Understanding the Standard Algorithm 1 1423 x 3 4269 Two-digit x 2-digit Area Model with Base Ten Blocks Leads to the… Open Array or Area Model Open Array 20 10 3 7 20 x 10 7 x 10 20 x 3 7x3 20 x 10 = 200 20 x 3 = 60 7 x 10 = 70 7x3= 21 Multiplying Decimals Multiplying Decimals by rounding 2 x 2.4 “2.4 is closer to 2. My answer should be more than 4.” * Now I know where to put the decimal. Multiplying Decimals Multiplying Decimals by renaming 2 x 2.4 = 2 x 24 tenths = 48 tenths = 4.8 * What are you actually doing to the numbers? With Blocks Build 2 groups of 2 and 4 tenths (2.4) = 1 whole Area Model Division with Disks Model this problem using the disks. 396 ÷ 3 How do the disks support understanding of division with large numbers? 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