Math 902 Transition to Algebra and Problem Solving Words Pictures.

Math 902Transition to Algebra and Problem Solving

Words Pictures


Using the rectangle below representing an unknown value, x, illustrate the quantity requested.

Illustrate a rectangle that is thirteen units larger than x. (sum)

Problem #1 Words Pictures



Illustrate a rectangle that is five units less than x. (difference)




Illustrate a rectangle that is four times larger than x. (product)




Illustrate a rectangle that is one-third of x. (fractional part)




Illustrate a rectangle that is one less than twice the value of x.




Illustrate a rectangle that is eight more than half the value of x.




Illustrate a rectangle that is six more than one-fifth the value of x.




Illustrate a rectangle that is one-sixth of three more than the value of x.




Illustrate a rectangle that is three times the difference of the value of x and five.




Illustrate a rectangle that is one-quarter of the sum of three times the value of x and two.



Order of Operations Pictures


Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated.

EXAMPLE #1 Order of Operations Pictures

Single Operation

1

Op 1 SUM




2 Operations

Op 1 DIVISION

Op 2 SUBTRACTION

1

2




3 Operations

12

3

Op 1 DIVISION

Op 2 SUM

Op 3 TIMES




4 Operations

2

3

14

Op 1 TIMES

Op 2 DIFFERENCE

Op 3 DIVISION

Op 4 SUM




5 Operations

2

3

1 4

5

Op 1 DIVIDE

Op 2 SUM

Op 3 TIMES

Op 4 SUM

Op 5 DIVIDE



Problem #1 Order of Operations Pictures


Symbols Pictures“FREE RESPONSE with your mind! THINK it out without the Order of Operations.”


Using the rectangle below representing an unknown value, x, illustrate the expression at the right.

Problem #1 Symbols Pictures

Math 902 THIS IS A TOUGH ONE!Transition to Algebra and Problem Solving




At the end of this section, let me know if these tasks are more difficult than the two earlier sets of tasks. you think

Pictures Symbols



Illustration:

Problem #1 Pictures Symbols

What is the Algebraic Expression?



Illustration:



Math 902 You’ve been here beforeTransition to Algebra and Problem Solving

Pictures Solution

We’re going to solve equations made from the expressions in the last two sections for the unknown values of x. Let’s demonstrate your logic and math.



Problem #1 Pictures Solution

The expression has a value of 52; so what is the value of x?

52



x = 45



52



Illustration:





Illustration:



x = 38



Illustration:



45



Illustration:



45

x = 53





55



x = 64



55





75



x = 15



75





12



x = 36



12





15



x = 40



15





90



x = 54



90





52



x = 16



52





73



x = 20



73



Illustration:



14



Illustration:



x = 22

14



Illustration:



35



Illustration:



35

x = 11





25



x = 28



25





13



x = 24



13





30



x = 6



30





5



x = 21



5



Illustration:


20The expression has a value of 20; so what is the value of x?



Illustration:


x = 33

20The expression has a value of 20; so what is the value of x?



Illustration:



22



Illustration:



22

x = 3



Illustration:



26



Illustration:



26

x = 7



Illustration:



10



Illustration:



10

x = 52



Illustration:



9



Illustration:




9

x = 7



Illustration:

Problem #22 Pictures Symbols4 4The expression has a value of 8; so what is the value of x?



Illustration:

x = 27

Problem #22 Pictures Symbols4 4The expression has a value of 8; so what is the value of x?





80



x = 55



80





15



x = 6



15




The expression has a value of 0.75; so what is the value of x?

0.75



x = 15


The expression has a value of 0.75; so what is the value of x?

0.75

Math 902 Recalling the Order of OperationsTransition to Algebra and Problem Solving

Symbols Solution

Math 902 To draw or not to draw, it’s your choice.Transition to Algebra and Problem Solving

As demonstrated in our examples in class, to solve an equation involving:

ADDITION, we do the opposite and SUBTRACT,SUBTRACTION, we do the opposite and ADD,MULTIPLICATION, We do the opposite and DIVIDE,DIVISION, we do the opposite and MULTIPLY.

Examples #1 Symbols Solution

Math 902 To draw or not to draw, it’s your choice.Transition to Algebra

If an equation involves more than one operation, before you solve for x: Suppose a value was assigned for x, number the order in which the expression is evaluated and solve in “reverse” order.



If an equation involves more than one operation, before you solve for x: Suppose a value was assigned for x, number the order in which the expression is evaluated and solve in “reverse” order.


Problem #1 Symbols Solution x =


Solve for x:



Solve for x:

19


Solve for x:



Solve for x:

Problem #2 Symbols Solution x = 68


Solve for x:




Solve for x: (First number the order in which the expression is computed and work backwards.)



21Solve for x: (First number the order in which the expression is computed and work backwards.)




2

1




21

34




21

3




21

3 4

Math 902 THIS IS WHAT IT IS ALL ABOUT!Transition to Algebra and Problem Solving

Words Solution

Applications(some from your text)

TV Watching. On average, people age 12 or older spent 1704 hours watching TV in 2008. This is 202 more than in 2000.

Determine the number of hours people in this age group spent watching TV in 2000.


Problem #1 Words Solution FROM YOUR TEXT on page 65 problem # 9

PROBLEM FROM TEXTBOOK

Longest Rivers. The longest river in the world is the Amazon in South America at about 4225 miles. The longest river in the United States is the Missouri-Mississippi at about 3860 miles.How much longer is the Amazon?




Motorcycle Sales. Motorcycle sales totaled 521,000 in the United States in 2008. Sales in 2006 exceeded this total by 669,000. How many motorcycles were sold in 2006?




Yard-Sale Profit. Ruth made $312 at her yard sale and divided the money equally among her four grandchildren.How much did each child receive?




Refrigerator Purchase. Gourmet Deli has a chain of 24 restaurants. It buys commercial refrigerator for each store at a cost of $1019 each.Determine the total cost of the purchase.




Elena buys 5 video games at $64 each and pays them with $10 bills.How many $10 bills does it take?




The balance in Dylan’s bank account is $749. He uses his debit card for purchases of $34 and $65. Then me makes a deposit of $123 from his paycheck.What is his new balance?




A mining company estimates that a crew must tunnel 2000 feet into a mountain to reach a deposit of copper ore. Each day, the crew tunnels about 500 feet. Each night, about 200 feet of lose rocks rolls back into the tunnel. How many days will it take the mining company to reach the copper deposit?




Laura has a charge of $477 on her credit card, but she then returns a sweater that costs $129. How much does she now owe on her credit card?




Surface Temperature on Mercury. Surface temperatures on Mercury vary from 840°F on the equator when the planet is closest to the sun to -290°F at night.Find the difference between these temperatures.




Peter had $4.00 while Mary had $7.oo. How much did they have altogether?


Problem #1 Words Solution

Jim took $23.00 with him to go shopping. His sister, Loretta took $13.00 more than he did.

How much did Loretta take shopping?



Barbara fills a container with 9 cartons of maple syrup. Each carton contains 2 quarts of maple syrup.What is the capacity of the container (in quarts)?



Bonnie spent a total of $140 on her car. Jim spent 5 times the amount that Bonnie spent.

What was the total spent by Bonnie and Jim?



Jerry weighed himself. His weight was 175 lbs.He was 5 times heavier than his brother, Sam.What was the difference in their weight?



Mary had a box of mangos. After giving 3 mangos each to 7 children, she had 20 left.How many mangos were there in the box at first?



Dylan bought 4 boxes of cookies. There were 12 chocolate and 8 sugar cookies in each box. He put together a platter of 40 chocolate and 25 sugar cookies for church.How many of each kind of cookies did he have left?



Mary had 1240 picture cards. She kept 80 cards for herself and gave the rest to a group of children. Each child received 8 cards.How many children were in the group?



Each pen cost 85 cents while a package of 3 pencils costs 65 cents. Kyle purchased 8 pens and 12 pencils.How much did Kyle spend on his purchase?



For the past 4 months, Grace’s salary was $1895 per month. She saved $3032 during the 4 months and spent the rest.How much did she spend?



Bob had a total of $825 to spend on Christmas shopping. He spent 2/3 of it on his wife’s present.How much did he spend on his wife’s present?



Simi withdrew $1224 from his savings. He spent half of it on fixing his car. One-third of what he had remaining was used for school. How much did he have left?



Sally took three-eight of a cake to her office to share with her office mates, and her sister ate one-fifth of the remaining portion.What fraction of the cake was left?



Judy bought some eggs. She used 2/5 of the eggs to bake cakes. She had 18 eggs left.How many eggs did she did she buy?



Fred could not divide the amount of money in his pocket equally among his 4 kids. His wife gave him an additional $3 after which each of his 4 kids received $8.How much money did Fred have at the beginning?



Cindy received 2/5 of her grandfather’s estate which totaled $220,000. How much did she receive?



Marian’s portion of lottery ticket winnings was $1,575,000 which was 3/8 of the total. How much was the total winnings?



Jimmy shops at the farmer’s market each weekend and buys twice as many bananas compared to the total amount of all the other fruits he purchases. he purchased 7 apples, 4 pears, and 3 oranges.

How many bananas did he buy?



Tristan divided a certain amount of money into 3 equal shares. He gave the first share to Betty, the second share to Veronica, and then divide the remainder into 3 equal shares and gave one share to Archie. He kept the rest totaling $24.How much money did Tristan have at the beginning?



Tom spent three-quarters of his money on a dictionary. He spent one-half of the remainder on a calculator. The dictionary cost $30 more than the calculator. How much does the dictionary cost?



Math 902 Transition to Algebra and Problem Solving Words Pictures.

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Transcript of Math 902 Transition to Algebra and Problem Solving Words Pictures.