Math Connection

NightSeptember 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)

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Understanding versus MemorizationChildren 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 ExpectationsBy 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.

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Common Multiplication StrategiesI 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 StrategiesDoubling: 2 x (3 x 6) = 6 x 6

3 groups of 6 doubled

Common Multiplication StrategiesHalving and doubling: 4 x 3 = 2 x

6

4 groups of 3 2 groups of 6

Common Multiplication StrategiesUsing the distributive property: 6

x 4 = (5 x 4) + (1 x 4) = 20 + 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.

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Part/Whole relationships

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

Common Multiplication StrategiesUsing the distributive property: 6 x 4

= (5 x 4) + (1 x 4) = 20 + 4 = 24 Number bond

Common Multiplication StrategiesUsing the distributive property

with tens: 9 x 4 = (10 x 4) – 4

The “Place” of Place Value

4x 3 12

4 ones x 3 = 12 ones

The “Place” of Place Value

40x 3 120

4 tens x 3 = 12 tens

Multiplying Larger Numbers4 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

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3

5 + 2

15 6+

3 x 7 =3 x (5 + 2) = (3 x 5) + (3 x 2)= 15 + 6 = 21

3 x 7 =__

14 x 25: An Area Model

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20 + 5

10

+

4 80 20

200 50

Open Array or Area Model

Open Array

20 x 10 = 20020 x 3 = 607 x 10 = 707 x 3 = 21

20 7

10 20 x 10 7 x 10

3 20 x 3 7 x 3

Algebra 1: Multiplying Binomials

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x + 5

x

+

4 4x 20

x2 5x

Great Websites for Math Practicesheppardsoftware.com/math.htmtopmarks.co.uk/maths-games/Arcademicskillbuilders.com/

gamesFactMonster.com/math/

flashcards.htmlMultiplication.comIXL.comk-5mathteachingresources.com/