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Nurturing Mathematicians

Through Conceptual Understanding

Feb. 2019

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Why is Math Important?

Almost 90% of all new jobs

require math beyond high

school level (advanced math)

Preparing students for jobs of

the future- do not exist today

Teaches ways of thinking that

are essential to work and

civic life

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Key Shifts in Math

• Teach less, learn more

• International comparisonsFocus

• Progression across grades

• Foundational skills for the learning of algebra

Coherence

• Conceptual understanding

• Procedural knowledge and fluency

• Problem solvingRigor

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4

Standards of Mathematical Practice

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Fluency- Place Value and Properties of Operations

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x 1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

3 3 6 9 12 15 18 21 24 27 30

4 4 8 12 16 20 24 28 32 36 40

5 5 10 15 20 25 30 35 40 45 50

6 6 12 18 24 30 36 42 48 54 60

7 7 14 21 28 35 42 49 56 63 70

What do you notice about the numbers in each row?

How are they related to the circled number? Why?

Can you find other numbers that are related?

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x 1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

3 3 6 9 12 15 18 21 24 27 30

4 4 8 12 16 20 24 28 32 36 40

5 5 10 15 20 25 30 35 40 45 50

6 6 12 18 24 30 36 42 48 54 60

7 7 14 21 28 35 42 49 56 63 70

2 + 6 = 8

(2 x 1) + ( 2 x 3) = 2 x 4

12 + 24 = 36

( 4 x 3) + (4 x 6) = 4 x 9

Can you find others?

Distributive Property

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16 x 25 = 400

16 20

20 25

20 x 20 = 400

Why?

Does it work for every box of

four numbers?

4 x 4

5 x 5

4 x 5 x 4 x 5

4 x 4 x 5 x 54 x 5

4 x 5

16 x 25 = 20 x 20

(4 x 4) x (5 x 5) = (4 x 5) x (4 x 5)

Commutative and Associative Properties

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Let’s do some thinking:

17 + 39 + 23 + 11

17 + 23 + 39 + 11

40 + 50

90

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Let’s do some thinking:

18 + 18 + 18 + 18 + 18

20 + 20 + 20 + 20 + 20 = 100

2 + 2 + 2 + 2 + 2 =10

100 – 10 = 90

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Let’s do some thinking:

1

2x 8

1

2

1

2x ( 8 +

1

2)

(1

2x 8) + (

1

2x 1

2)

4 + 1

4

41

4

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Let’s do some thinking:

6 1

3÷1

3

How many 1

3s are in 1?

How many 1

3s are in 6?

3 x 6 = 18

18 plus one more third is 19

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zMoney: fourths (25¢), halves (50¢), tenths

(10¢), twentieths (5¢), and hundredths (1¢)

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𝟒-𝟏

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𝟏

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𝟐+ 2

𝟑

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Fractions– Addition/Subtraction

zClock: halves (30 min.), thirds (20 min.),

fourths (15 min.), sixths (10 min.), twelfths (5

min.)

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𝟒-𝟏

𝟐

𝟏

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𝟔

𝟏

𝟏𝟐+

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Fractions– Addition/Subtraction

How Can Parents Support

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Resources for Parents

New Common Core State Standards for Mathematics

www.corestandards.org

National PTA Resources www.pta.org (Parent Guides

to Student Success)

Kahn Academy: www.khanacademy.org

Smarter Balanced: www.smarterbalanced.org