Math Connection Night September 24, 2015

Prior Understandings— Grades K-2 Counting numbers in a set (K) Counting by tens (K) Understanding the numbers 10, 20, 30, 40, …, 90 refer to one, two, three, four, …, nine tens (1) Counting by fives (2)

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 2-digit numbers By the end of fifth grade students are expected to be fluent with multi ‐ digit multiplication

Grade 3 Introduction In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; … Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays, and area models; Multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equal-sized group situations, division can require finding the unknown number of groups or the unknown group size. Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By comparing a variety of solution strategies, students learn the relationship between multiplication and division.

Common Multiplication Strategies I can use a multiplication fact I know, to figure out one I don’t… Using the commutative property: 2 x 4 = 4 x 2 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) = = 24 If you don’t know a math fact use what you do know. 6x4--- But I do know 5x4=20 and add one more 4. This uses the 6 groups of 4. Decomposing Numbers leads to number fluency

Commutative Property It is not intuitively obvious that 3 x 8 = 8 x 3. A picture of 3 sets of 8 objects cannot immediately be seen as 8 piles of 3 objects. Eight hops of 3 land at 24, but it is not clear that 3 hops of 8 will land at 24. The array, however, can be quite powerful in illustrating the commutative property.

Part/Whole relationships A guitar has 6 strings. How many strings are there on 3 guitars? Write a multiplication sentence to solve.

Common Multiplication Strategies Using the distributive property: 6 x 4 = (5 x 4) + (1 x 4) = = 24 Number bond

Common Multiplication Strategies Using the distributive property with tens: 9 x 4 = (10 x 4) – 4

The “Place” of Place Value 4 x ones x 3 = 12 ones

The “Place” of Place Value 40 x tens x 3 = 12 tens

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

Distributive Property & Area Models 20www.JennyRay.net x 7 = 3 x (5 + 2) = (3 x 5) + (3 x 2)= = 21 3 x 7 =__

14 x 25: An Area Model *Sketch is not drawn to scale. 21www.JennyRay.net

Open Array or Area Model Open Array 20 x 10 = x 3 = 60 7 x 10 = 70 7 x 3 = x 10 7 x x 37 x 3

Algebra 1: Multiplying Binomials *Sketch is not drawn to scale. 23www.JennyRay.net x + 5 x + 4 4x 20 x2x2 5x

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/