Sequência Didática de Equação6

8/9/2019 Sequncia Didtica de Equao6

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Subject:MathUnit:Algebra

Lesson:Three

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Illustrating Equations Worksheet

For this worksheet the tiles represent the following

x -x 1 -1

1. Write the algebraic equation that is represented by this picture belowand solve for x.

2. Write the algebraic equation that is represented by this picture below

and solve for x.

=

3. Fill in the chart below. The first one is done as an example for you.

OriginalQuestion

Isolatex InverseOperationUsed toIsolatex

Solution

x+ 5 = 1 x+ 5 5 = 1 - 5 - 5 x= -4

x 2 = 8

x/6 = 23

9x= 27

=


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4. Illustrate the solution process for this equation using algebra tiles:

4x 3 = 5

=

5.

One half the sum of the sides of a square is 8.2 cm. What is thelength of each side of the square?

6. Jerry has a pocket full of nickels, dimes and quarters. He has 3 fewernickels than dimes and 3 more quarters than dimes. If the coins areworth a total of $4.20, how many of each kind does he have?

7.Illustrate and explain how the algebra tiles can be used to show an

algebraic process for simplifying this equation:-8x+ 6x= 2

8.Illustrate and explain how to solve this equation using algebra tiles:

x/4 = 2


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9.Sarah went shopping for new shoes. When she came home, she set the

new shoes in her room and went to get her mom to show her the greatdeals she got at the shoe sale. Unfortunately, little brother Ben, came intothe room first and tore open the boxes, pulling out all of the shoes andcounting them. He counted 36 shoes in all. How many pairs of shoes didSarah buy today? Draw a diagram to represent this problem and write andsolve an equation.

10. There is a playing field at a park. Andrew is going to train for a school

race, by running around this playing field, but he wants to know whatdistance he will be running. If the area of the playing field is 5640 andthe width of the field is 20, find the distance Andrew will be running if hemakes one lap around this playing field.

A = 5640 m20 m

x


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Illustrating Equations Worksheet Key

For this worksheet the tiles represent the following

x -x 1 -1

1. Write the algebraic equation that is represented by this picture belowand solve for x.

ANSWER:

x+ 7 = 2

x+ 7 7 = 2 7x= -5

CHECK: Check your work by putting the value of xback into the originalequation.

x+ 7 = 2-5 + 7 = 22 = 2

=


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4. Illustrate the solution process for this equation using algebra tiles:

4x 3 = 5ANSWER:

=

4x- 3 + 3 = 5 + 3

=

4x- 3 + 3 = 5 + 3

=

4x= 8

4x/4 = 8/4

x=2

=

=

=


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5. One half the sum of the sides of a square is 8.2 cm. What is the length

of each side of the square?

ANSWER:First we must find the sum of the sides of the square, which is x.1/2x= 8.22(1/2x) = 8.2 2

x= 16.4 cmThe sum of the sides of this square is 16.4 cm.

Now we need to figure out what one side of the square is equalto so we divide 16.4 by 4, since all of the sides of a square areequal in length. 16.4 4 = 0.35 cm. The length of each side ofthe square is 0.35 cm.

6. Jerry has a pocket full of nickels, dimes and quarters. He has 3 fewer

nickels than dimes and 3 more quarters than dimes. If the coins areworth a total of $4.20, how many of each kind does he have?ANSWER:

Coin Number Value

Nickels x 3 5x- 15

Dimes x 10x

Quarters x+ 3 25x+ 75

15x 15 + 10x+ 25x+ 75 = 42040x+ 60 = 42040x= 360

x= 9

x 3 = 6

x+ 3 = 12There are 9 dimes, 6 nickels and 12 quarters.


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7. Illustrate and explain how the algebra tiles can be used to show an

algebraic process for simplifying this equation:-8x+ 6x= 2

ANSWER:

Algebra tiles make it easy to simplify this equation, because a

whitextile cancels out a green xtile so we can just cancel themout to get a single xterm. It helps a lot also if you find negativesconfusing because you can see exactly what you are left with,-2x(two white xtiles. Now our equation is simplified so we

could continue to solve it.-2x= 2

=

-x= 2

x= 2

=


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8. Illustrate and explain how to solve this equation using algebra tiles:

x/4 = 2

=

ANSWER:When we see the xtile is divided into 4 sections, we know wehave to figure out how many one tiles fit in each section of the x

tile to figure out how many one tiles equal 1x.

=

Since we know 1/4 of xequals 2 one tiles, then we know 2xtilesgo in each section of x. So we find that 1 whole xtile equals 8.The algebra tiles show this easily by showing that two tiles go in

each section to equal 8.


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Thank-you to our supporters!- 10

9. Sarah went shopping for new shoes. When she came home, she set

the new shoes in her room and went to get her mom to show her thegreat deals she got at the shoe sale. Unfortunately, little brother Ben,came into the room first and tore open the boxes, pulling out all of theshoes and counting them. He counted 36 shoes in all. How manypairs of shoes did Sarah buy today? Draw a diagram to represent thisproblem and write and solve an equation.


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ANSWER:

2x= 362x/2 = 36/2

x

= 36/2x= 182(18) = 36She bought 18 new pairs of shoes! What a sale!

36 shoes

18 pairs


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10. There is a playing field at a park. Andrew is going to train for a school

race, by running around this playing field, but he wants to know whatdistance he will be running. If the area of the playing field is 5640and the width of the field is 20, find the distance Andrew will berunning if he makes one lap around this playing field.

ANSWER:A = l w

5640 = 20x5640/20 = 20x/20282 = xDistance around the playing fieldP = S1 + S2 + S3 + S4P = 282 + 282 + 20 + 20P = 604 m

Andrew will be running 604 m around the playing field.

A = 5640 m20 m

x

Sequência Didática de Equação6

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