September 07, 2011

Expressionsand VariablesExpressions

and VariablesObjectives:1) To write numerical and algebraic expressions.

2) To evaluate numerical and algebraic expressions.

3) To evaluate area and perimeter

September 07, 2011

1-5 Variables and Expressions

Main Ideas

1) Are numerical expressions the same thing as algebraic expressions? Explain.

 

Key WordsClassification Exercise

Making Connections: We often discover that things we learn about in math are also related to things we learn about in science. How is algebra related to science?

2) Can an algebraic expression be solved?

Brainstorm

1) In your table groups, come up with an agreed upon answer for the following question: "What is algebra?"

Classify the following into the proper categories by writing them in the correct boxes below:

3 + 4 (s)(8) 54 - b

12 ÷ n 9 * 23

Numerical Expressions Algebraic Expressions

Fill in the blanks with the following words: numerical expression , algebraic expression , variable , constant, evaluate, input/output (in & out boxes)

______________ to find the value of a numerical or algebraic expression

______________ a symbol used to represent a quantity that can change

______________ an expression that contains only numbers and operations

______________ a list of numbers that are used to substitute one variable to find the value of the other variable, or missing number

_______________ an expression that contains at least one variable

_______________ a value that does not change

What is an example of a quantity that is a variable? A constant?

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15 + 49 - 7

(9 + 6) - 11

3 x 2

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f - 1513 - n

(9 + w) - 11(3 • 9) - r

These are sometimes referred to as "algebraic expressions"

September 07, 2011

1 Kacie has four flowers. She gave three of them to her mom.

A 4 + 3

B 4 - 3

C 3 - 4

D 3 + 4

4 - 3

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2 Brent had 16 baseball cards. He gave four to Blake. Then he bought three from Gunnar.

A (16 + 4) + 3

B (16 - 4) - 3

C (4 + 3) + 16

D (16 - 4) + 3

(16 - 4) + 3

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3 Corey had a dozen cupcakes. He ate seven. Then he baked some more.

A (12 - 7) + c

B (12 + c) + 7

C (12 - 7) - c

D c - (12 + 7)

(12 - 7) + c

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4 Alex missed one question on his math quiz. He answered all four bonus questions correctly.

A (x - 1) + 4

B (x - 1) - 4

C (x + 1) + 4

D (x + 1) - 4

(x - 1) + 4

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5 Shelby won 5 prizes, and then she won some more.

A p x 5

B p - 5

C 5 - p

D 5 + p

5 + p

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6 Alisha had eleven sharpened pencils, but some broke.

A 11 + n

B n + 11

C 11 - n

D n - 11

11 - n

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7 Joel had some candy. He ate three pieces.

A c + 3

B 3 - c

C 3 + c

D c - 3

c - 3

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8 Mr. Manuel rode the elevator down five flights and rode up two flights.

A 5 + 2

B (x + 5) - 2

C (x - 5) + 2

D (2 + 5) + x

(x - 5) + 2

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9 At 7:00 A.M. the temperature was 58 degrees. By noon it warmed up 10 degrees.

A 58 + 10

B 58 - 10

C 10 - 58

D 58 + 7

58 + 10

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10 14 is subtracted from a number and then 2 is added.

A (14 - w) + 2

B (2 - w) + 14

C (14 + w) - 2

D (w - 14) + 2

(w - 14) + 2

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Expression Value ofthe Variable

Value ofExpression

11

22132

1,800350

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4 3

7 0

2 5

254 9 7 12

2 7

7 - n

1510

n Value ofExpression

(9 + n) - 4n

Value ofExpression

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What is perimeter?

The sum of the lengths of the sides of a polygon.

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Find the perimeter of this shape.

6 miles

6 miles

6 miles 6 miles

6 miles

6 miles

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What is the perimeter of this fence?

20 feet

9 feet

17 feet

15 feet

20 feet

Check your answer by dragging the correct answer into the box

71 feet

91 feet

83 feet

93 feet

81 feet

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The number of square units that covers a shape or figure.

What is Area?

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Determine the area of all the shapes below by dragging them over the grid. Count the total

number of square units.

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Area of Squares and RectanglesHow can you find the area of a figure?

8 ft.

6 ft.

This can covers an area of 40 square feet.

A small can of chalkboard paint covers 40 square feet. Does Mike need more than or less than one small can to paint one wall of his room?

A = b x hArea = base x height

Pull

Pull

8 ft.

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How many square yards are in this fence?

1 square yard =

Each turkey needs one square yard. How many turkeys can fit in the pen?

7 yards

3 yards

squares can moved to fill in shape

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Finding the AREA of different shapes.

rectangle 6 in.

3 in.

Area = L x W Length x Width

Area = 6 x 3Area = 18 sq. in.

in.square

4

4

Area = 4 x 4 Area = 16 sq. in.

in.Area = S x S side x side

triangle

6 in.

3 in.

Area = 1/2B x H 1/2 Base x Height

Area = 1/2(6) x 3Area = 3 x 3Area = 9 sq. in.

circle

r = 3 in.

Area = x r^2Area = x 3^2Area = x 9Area = 9 sq. in.

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Mr. Henry's Garden

Cucumbers

Lettuce

Tomatoes

Unused

1 = 1 square foot

Mr. Henry grows three types of vegetables in his garden. What

is the area of the section he uses to grow cucumbers?

8 square feetAnswer

What is the area in square feet of the garden that is

being used to grow crops?

36 square feetAnswer

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Area of Irregular Shapes

1 sq. foot of carpet

Mr. Fox is covering a miniature golf course hole with artificial grass. How many 1-foot squares of carpet will Mr. Fox need to cover the miniature golf course?

September 07, 2011

Area of Irregular Shapes

1 sq. foot of carpet

Mr. Fox is covering a miniature golf course hole with artificial grass. How many 1-foot squares of carpet will Mr. Fox need to cover the miniature golf course? Why is counting square units not always a good way to find the area of large shapes?Because it would take a lot of time to count all the squares.

Count the square units to find the area.

3 ft. 3 ft.

2 ft.

8 ft.

8 ft.

4 ft. 4 ft.

Answer

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Area of Irregular ShapesDivide the whole into rectangles. Find the area of each rectangle and add them together.

A B

C

Rectangle AA = 3 x 8 - 24

Rectangle BB = 3 x 8 = 24

Rectangle CC = 2 x 4 = 8

Add the areas: 24 + 24 + 8 = 56The area of the golf course hole is 56 square feet.

September 07, 2011

Green:  Part  1• Textbook  pages  31  -­‐33:  problems  1  –  58,  72,  73• Page  49:  problems  57  –  58• Page  51:  problems  11  –  12• Green  Handout

Part  2• Textbook  pages  63-­‐65:  problems  1  –  32,  41,  42• Page  101:  problems  16  –  17• Page  103:  problem  5

Blue:  • Blue  Handout• Blue/Black  Handout

Black:  • Black  Handout• Blue/Black  Handout

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End of Lesson