Meeting the Goals of an Integrated Mathematics Curriculum · PDF file · 2009-07-12Meeting the Goals of an Integrated Mathematics Curriculum. Ed Thomas Dimension 2000 ... Dimension

Ed ThomasDimension 2000

Meeting the Goals of anIntegrated Mathematics

Curriculum


Meeting the Goals of anIntegrated Mathematics

Curriculum


[email protected]

Integrated Math I and Integrated Math IIAchieve and Succeed Program Order Form

• Mental Math Strings• Function Analysis Activities• Integrated Algebra and Geometry Activities• Weekly Integrated Math Challenges

• Monday- Wednesday- Friday

Daily Problem-Solving Warmups

Program Cost

$ 199.00

SREB Price$ 149.00

Name

School

Street

City - Zip

Phone

Date

PO#

Visa/Master Card

Expiration Date

Math I Integrated Program

Quantity

Math II Integrate Program

Quantity

Total # @ $149 = Shipping and Handling 10%

Total Cost

Fax your order today 770 - 461- 8127

Dimension 20001823 Hwy. 92 South Fayetteville, GA 302151- 888- 461- 9560Dr. Ed Thomas

Word Scramble

1. Find the average of 2, 3, 6, 6, and 8.2. Evaluate 2ab – c where a= 3, b= 4, and c= 12.3. Find the number that is one more than the cube of two.4. Find the square root of 169.5. Find the hypotenuse of a right triangle with leg measures 12 and 16.6. Find f(5.5) when f(x)= 2x + 1.7. Find one more than twice ten.

8. Find the GCF between 16 and 48.

a b c d e 1 - 5f g h i j 6 - 10k l m n o 11 - 15p q r s t 16 - 20u v w x y 21 - 25z 26

Math Concept:Sums and Reasoning

Teaching Strategies:

Five Stages of Learning:Accounting for knowledge,understanding, skill proficiency,applications, and retention

Five Stages

What’s the mathematical term for:

Knowledge

1 + 2 + 3 + 4 + 5 + . . . + n ?

• arithmetic series

What’s the formula for finding the sum?

• n ( n + 1) 2

Five Stages Understanding

For any sum of the form:

1 + 2 + 3 + 4 + 5 + . . . + n ?

Why does the formula work?

n ( n + 1) 2

Sum =

Five Stages

Let’s look deeper.

Understanding

1 + 2 + 3 + . . . + 18 + 19 + 20

21 = (n+1) the sum of each pair

n2

= the number of pairs10 = n ( n + 1) 2

Five Stages Understanding

1 + 2 + 3 + . . . + 18 + 19 + 20

n ( n + 1) 2

20 ( 21) 2

= 10 • 21 = 210

Five Stages

1 + 2 + 3 + . . . + 200

Find the following sum:

Proficiency

200 • 201 / 2 = 100 • 201 = 20,100

Five Stages

• Make 2 summation problems of the form 1 + 2 + 3 + . . . + n

Peer Problem Solving Challenge

Proficiency

• On separate paper, solve the two problems you made• Exchange problems with a partner and solve your partner’s problems• Swap back and evaluate each other’s work

Five Stages

If ten people are in a room, how manyhandshakes would take place if eachperson shook hands with every otherperson exactly once?

Application

9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 11 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9

Connecting the HandshakeProblem to Geometry

1 2

3

4

5

67

8

9

10


1 2

3

4

5

67

8

9

10

Sides + Diagonals

n + n(n–3)2

n + n(n–3)2

2n + n(n–3)22

n2 – n2

=

=


1+2+3 + … + (n–1) + n

(n–1)n2

= n2–n

2

Teaching Integrated Math

Monday - Wednesday - FridayWarmups

The following samples are part of Dimension 2000’s Integrated Iand Integrated II Achieve and Succeed Programs.

Algebra and Number Sense Level 1

Which value represents the square of five lessthan twice the value of x if x=10?

A) 5

B) 125

C) 150

D) 225

Prob

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Mental Challenge: Find 250% of 40.

Dimension 2000's Integrated Math Challenge #1

Line m is parallel to line n. Find the equation of line n.

m

A) y = 2x + 4

B) y = (1/2) x - 4

C) y = (1/8) x – 4

D) y = (–1/2) x + 4

B( 8 , 4.5 )

A( 4 , 2.5 )n

S( 4 , –2 )

Geometry and Measurement

Multiply 43 • 7.Mental Challenge:


Level I

Prob

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Algebra and Number Sense

Use algebraic notation to represent the square offour less than three times a number.

A) 4 – 3x2

B) (3x – 4)2

C) 42 < 3x

D) (3x – 42)

Find 250% of 60.Mental Challenge:


Level I

Prob

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s fro

m D

r. Th

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lleng

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sion

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©20

09

Isosceles trapezoid ABCD with median EF is given.Find the measure of angle CEF.

A) 120 degrees

B) 110 degrees

C) 105 degrees

D) 205 degrees

A B

CD

60

E F


Add 46 + 12 + 14.Mental Challenge:


Level I

Prob

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09


The width of rectangle ABCD is five more thanhalf its length. The length is 42cm. Find theperimeter of the rectangle.

A) 63 cm.

B) 136 cm.

C) 110 cm.

D) 120 sq. cm.

A

CD

B42

Simplify 4 ½ + 2 + 3 ¼.Mental Challenge:


Level I

Prob

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m D

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sion

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Level II

Find the midpoint of the points shown.

A) 10 + 3i

B) 10 – 2i

C) –10 + 3i

D) 1 + 3i

Prob

lem

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r. Th

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Mental Challenge: Find the sum 1 + 2 + 3 + . . . + 20.

i

R-5 5

5

Complex Numbers and Geometry

Polynomials, Quadratic Expressions, and Geometry


Level II

Find the area of the figure below.

Check your answer using x= 6.

Prob

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Mental Challenge: Multiply 20 • 44

L= (3x + 1)

W= (2x – 1)

Arithmetic Series and Algebra


Level II

Use the formula to solve the problembelow.

Prob

lem

s fro

m D

r. Th

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09

Mental Challenge: Subtract: 24 – 18.75 + 12.25

n(n + 1)

2

Twenty people in a room shake hands witheach other once and only once. How manytotal handshakes take place?

Algebra and Geometry


Level II

The circle below is divided into 60 and 30 degreesectors. Find the area of the blue portion of thecircle. Note, r= 9.

A) 9π sq. units

B) 27π sq. units

C) 18π sq. units

D) 81π sq. units

Prob

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Mental Challenge: Solve for x: 8x – 32 = 128

Algebra and Geometry


Level II

The diameter of a typical billiard ball is 2.25 inches.Find the surface area of a sphere with diameter 2.25inches to approximate the surface area of a billiardball.

A) (81/16)π sq. in.

B) (9/4)π sq. in.

C) (3/2)π sq. in.

D) 4π sq. in.

Prob

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Mental Challenge: Find the sum of the even numbers between10 and 20.


Function Analysis Activities


Dimension 2000 Function Analysis Activity

Function rule:

Base Graph

Modified Graph

Domain

Range

X-intercepts

Y-intercepts

Interval of increase

Interval of decrease

Maximum value

Minimum value

Lines of symmetry

Even, odd, neither

Dr. Thomas’s Math Challenges • Dimension 2000 ©20098

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

10

9

8

7

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

Dimension 2000 Function Analysis Activity

Function? yes or no

Piecewise Graph

Piecewise Equation

Domain

Range

X-intercepts

Y-intercepts

Interval of increase

Interval of decrease

Maximum value

Minimum value

Lines of symmetry

Dr. Thomas’s Math Challenges • Dimension 2000 ©20092

5

10

-5

5

-5

10-10

-10


Integrated Algebra and GeometryActivities

A Sample was provided at the workshop.


Integrated Math Challenges


Dr ThomasDr Thomas’s’s

Integrated Math I Challenge

Extra for experts: Use the definition of a circle to argue that ‘no portion of the edge of a circle can contain a line segment, even if it is infinitesimally small.’

Extra for experts: Given ! 1 + 2 + 3 + . . . n =

n(n+1)/2, find ! 2 + 4 + 6 + . . . + 200.

1. Find the value of x if 2(x - 6) - 10 = 5(x -2).

a) 4 b) - 4 c) 2 d) 3 e) 6

2. Using the given

measures, find the value of

the area of triangle ABC .

a) 84 b) 94 c) 86 d) 36 e) 96

3. The Wilsons have a rectangular vegetable

garden which is 25 feet longer than it is wide. They used exactly 222 feet of fence to enclose the garden. Find the width of the garden.

a) 43ft b) 50ft c) 68ft d) 33ft e) 107 ft

1. If 4x + 2y - 6 = 4, find the value of 6x + 3y - 9.

a) 4 b) 8 c) 5 d) 6 e) 9

2. An isosceles triangle is

inscribed in a square with side length = 1. Find the area of the isosceles triangle.

a) b) c) 1 d) 2 e) 4 1 4

1 2

1

3. If a = 2b, find the value of (7a - 2b)(8b - 4a)

a) 0 b) 1 c) 4 d) 8 e) 12

10

618

A

B

C

Dr ThomasDr Thomas’s’sIntegrated Math II Challenge

#5: Equations, Area, Perimeter

Dr ThomasDr Thomas’s’sIntegrated Math II Challenge

#6: Equations, Area, Exponents


Mental Math Strings


Start with the number of lines of symmetryassociated with a square

Cube your answer

Add the digits of your answer together

Cube your answer

Multiply by the number of sides on a hexagon

Add the digits of your answer together

Documents

Meeting the Goals of an Integrated Mathematics Curriculum · PDF file · 2009-07-12Meeting the Goals of an Integrated Mathematics Curriculum. Ed Thomas Dimension 2000 ... Dimension