Teaching to the Next Generation SSS (2007)

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Teaching to the Next Generation SSS (2007). Elementary Pre-School Inservice August 17, 2010. Next Generation Sunshine State Standards . Eliminates: Mile wide, inch deep curriculum Constant repetition Emphasizes: Automatic Recall of basic facts Computational fluency

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Teaching to the Next Generation SSS(2007)

Elementary Pre-School Inservice August 17, 2010

Next Generation Sunshine State Standards
• Eliminates:
• Mile wide, inch deep curriculum
• Constant repetition
• Emphasizes:
• Automatic Recall of basic facts
• Computational fluency
• Knowledge and skills with understanding

Resources with enVisionMATH

Daily Review WB

Problem of the Day

Interactive Learning

Quick Check WB

Center Activities

Reteaching WB

Practice WB

Enrichment

Interactive Stories (K-2)

Letters Home

Interactive Recording Sheets

Vocabulary Cards

Assessments

Four-Part Lesson

Daily Spiral Review: Problem of Day

Interactive Learning: Purpose, Prior Knowledge

Visual Learning: Vocabulary, Instruction, Practice

Close, Assess, Differentiate: Centers, HW

Algebraic Thinking

NGSSS

Participants will explore:
• Students’ progression from arithmetic to algebraic thinking
• Introducing algebraic thinking through patterns
• MA.3.A.4.1Create, analyze, and represent patterns and relationships using words, variables, tables and graphs. (Moderate Complexity)
• MA.4.A.4.1Generate algebraic rules and use all four operations to describe patterns, including non-numeric growing or repeating patterns. (High Complexity)
• MA.5.A.4.1 Use the properties of equality to solve numerical and real world situations.(Moderate Complexity)
ArithmeticAlgebra

7 + 3 = _____ vs. _____ = 7 + 3

The language of arithmetic focuses on

The language of algebra focuses on RELATIONSHIPS

Students begin describing mathematics inpictures, words, variables, equations, charts, and graphs.

k

X

How Does Algebraic Thinking Start?

m

y

Repeating Patterns
• Begins in Kindergarten
• Creating and Extending Patterns
• Naming the Pattern

. . .

A B C …

Repeating Patterns

. . .

• What is the core of the pattern?
• To get at the predictive nature, you need to have terms specified: 1, 2, 3, 4, 5, 6, 7, ….

1 2 3 4 5 6 7 8 9

Repeating Patterns

. . .

• What is the next figure? How do you know?
• What is the 32nd figure? How do you know?
• What is the 58th figure? How do you know?
• Write how you know what numbers are hexagons.
• Write how you know what numbers are squares.
• Write how you know what numbers are triangles.

1 2 3 4 5 6 7 8 9

PATTERNPATTERNPAT…1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
• What’s the core?
• What’s the 70th letter? How do you know?
• What’s the 75th letter? The 76th? The 77th?
• Write how you can determine the letter in position n, where n can be any whole number?
Growing Patterns
• Describe in words, mathematically
• Why is it difficult to describe the nth term?

Dragon Math

Make a series of pattern block dragons

that look like this:

Year 1

Year 2

Year 3

In words, how do you describe the pattern?

Finding the Rule

Let nstand for age, finish the chart.

Finding the Rule

Can you explain each rule above, from the

the dragons? Can you visualize the rule?

What Did We Do?
• Took an “interesting to kids” situation
• Made a chart to organize the data
• Described the data and made a generalization in words
• Described the data and generalization with a variable
• Tied in a visual aspect—justify the rule
Letter Patterns

Objectives

• Describe the growth pattern
• Record data on T-chart
• Describe the rule for growth in words
• Represent the rule with an expression
• Graph the function table
Growing the Letter “T”
• Create the letter “T” using 5 color tiles.

Year 0

Year 1

Year 2

Growing the Letter “T”

# of Years # of Tiles

0 5

1 6

2 7

T - Chart

15

10 ___

n + 5

n ___

Growing the Letter “I”
• Create the letter “I” using 7 color tiles.

Year 0

Year 1

Year 2

Growing the Letter “I”

# of Years # of Tiles

0 7

1 8

2 9

T - Chart

10 ___

17

n ___

n + 7

Making a Chart
• Make the H’s below on your graph paper.
• Make a chart of the term numbers and

number of tiles.

• Predict, before drawing, how many tiles

for the next H. Draw it to check.

Growing the Letter “H”

# of Years # of Tiles

1 7

2 12

3 17

T - Chart

4 22

n ___

5n + 2

How many tiles are needed to make the nth term?
• Can you explain why the nth term has that rule?
• What would this look like if you graphed it?

1st

2nd

3rd

(5n + 2)

What Have We Done?
• Considered a sample of the types of patterns that students will encounter
• Described the patterns in words
• Used charts to see the patterns
• Generalized to a rule with a variable in order to predict

Equality Principles

If you have an equation, you can +, -,

×, or ÷ both sides by the same number

(except dividing by zero), and keep

things “balanced.”

45

Equality Principles

If you have an equation, you can +, -,

×, or ÷ both sides by the same number

(except dividing by zero), and keep

things “balanced.”

If two things are equal, one can be

substituted for the other.

46

Equality Principles

=

Does not mean “find the answer”

Represents a balanced situation

47

Verbal & Algebraic Equations
• Three times a number , increased by 1 is 25.
• If 3 is added to twice a number, the result is 17
• When a number is increased by 8, the result is 13.
• Three times a number, increased by 7, gives the same result as four times the number increased by 5.

FIND THE NUMBER!

What is the value of ?

What is the value of the ?

= 12

+

= 17

+

+

+

7

5

+

=

20

Square + Square = 20

5

=

+

Square − Square + Triangle = 5

What number is the square? The triangle?

How did you know?

Square+Square+Square=21

Square– Triangle – Triangle = 1

What is the square? _______

What is the triangle? _______

7

3

=

A.

B. Cylinder + Square = 3 Cylinders

C. ______ = 6 Spheres

Balance Challenge (B)

Balance Challenge (C)

Shape

Grids (D)

13

12

A

13

15

12

11

Building a Strong Algebra Foundation

With the algebra strand in 3-5,

we’re teaching kids HOW to think,

not WHAT to think.

(Marilyn Vos Savant)

Teaching the Content