Expressions and Variables - The Stutz's Home Page · 2011. 9. 19. · Expressions and Variables...
Transcript of Expressions and Variables - The Stutz's Home Page · 2011. 9. 19. · Expressions and Variables...
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Expressionsand VariablesExpressions
and VariablesObjectives:1) To write numerical and algebraic expressions.
2) To evaluate numerical and algebraic expressions.
3) To evaluate area and perimeter
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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"
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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?
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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? 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.
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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