5th Grade - Solve Problems With Graphs And Equations

 
     
 
     
 
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5th
Graphs
Solve Problems with Graphs and Equations
Use information taken from a graph or equation to answer questions about a problem situation.
When your child begins solving problems he or she must use all information given, including any data shown on graphs. Your child needs to know that an equation has a variable (a letter or symbol that stands for a number) and an equal sign.
 

Sample Problems

(1)

Write an equation and find the value.

Ted had 10 dimes. He gave 4 to Don. How many dimes are left?

(10 – 4=X X=6)



(2)

Use the circle graph to write an equation with a variable. Then solve.



Question: What is the difference between the percent of people who like soccer compared to those who like baseball?

(30% - 16% = X X= 14%)



(3)

Directions: Write an equation with a variable. Solve.


Kindal had 12 CDs and got more for her birthday. Now she has 21 CDs. How many CDs did Kindal get?

(12 + c = 21 C=9 )


(4)

Directions: Use the bar graph to solve.





Question: What meal is liked by 10 more children than hamburgers?

( 60 + 10 = x x=70 ; Pizza )





(5)

Directions: Make an equation and solve.


If Mc Donald’s sells 450 hamburgers during the week, and twice as many hamburgers on the weekends. How many hamburgers are sold during the weekend? (2(450)= X x=900)

Learning Tips

(1)

Math Vocabulary:

Equation- an algebraic or numerical sentence that shows two quantities are equal.

Variable- a letter or symbol that stands for a number

Bar Graph – displays countable data with vertical or horizontal bars; compares facts about groups of data.

Circle Graph- Shows how parts of the data are related to the whole and each other.

(2)

Practice having your child read the word problems at least twice before they begin working. Have them highlight the key word or words that indicate the operation that will be used. For example, more than, in addition too, and in all could indicate addition or multiplication.

Some key words for subtraction could be less than, fewer than, or difference.

(3)

Have your child develop an understanding of variables. Have them read the word problem and distinguish what the question is actually asking them to find. What is missing?

For example:

After John paid $7 for a toy, he had $5. How much money did John have to start with?

KEY WORD :How much money to start with ( - )

Question: asking for the amount of money John had before buying the toy. This is going to be your variable

Missing Info: Amount of money all together (before purchase)


Equation: money to start will be (M)

M – $7 = $5

Solution: M - $7= $5

+7 = +7

M = 12


John had $12 to start.

(4)

Your child should be familiar with Mental Math.

Subtraction problems in which the variable is to be subtracted, such as 10-n=7 may present difficulties with some children.

Remind your child to use mental math with these equations.


Example: Your child should ask themselves, “Ten minus what number equals 7? The answer would be 3 because 10 – 3 = 7.

(5)

When graphs appear in a word problem it is very important that your child realizes the data displayed on graphs can be used to draw conclusions, answer questions, and make predictions.




Extra Help Problems

(1)

Directions: Write an equation. Find the value and explain what the variable represents.


Question:

Javier had 37 tech decks. He gave some away. Now he has 21 tech decks.

( 37-t=21 t=16 )

( t represents the number of tech decks that Javier gave away)

(2)

Directions: Write an equation. Find the value and explain what the variable represents.


Question:

Jenny paid $3 for breakfast and $5 for lunch and then bought dinner. He spent $20 in all. How much did he pay for dinner?

( $3 + $5 + d = $20 d= $12 )

( d represents the price of dinner)


(3)

For Problems 3-4 use the graph to write an equation and solve.


SEE BELOW









For Problems 3-4 use the bar graph to write an equation and solve.





Question:

Mr. Paul surveyed his 5th grade class to find out what type of fund-raiser they want to have. He organized the data in the bar graph above. What is the difference between the numbers of boys that wanted a Jog-A-Thon compared to the girls?



( 39-34=x x=5 more boys preferred the jog-a-thon )







(4)

Directions: Use the bar graph that was used in question 3 to write an equation and solve.




Question:

Which type of fund-raiser was liked by 10 more girls than boys?


(b +10=f b=20 f= Candy Sale)

(b represents boys )

(5)

Directions: Write an equation with a variable. Solve.


Question:

Jayson checked out 12 books from the library. He returned some and now has 5 left.

(12-b=5 b=7 b represents # of books returned )

(6)

Directions: Write an equation with a variable. Solve.

Question:

After 11 people quit the football team, there were 34 players. How many players were originally on the team?

(n-11=34 n=45 n represents the number of players originally on team )


(7)

Directions:

Use the circle graph to write an equation with a variable. Then solve.


Question:

What percent of students chose cheese and pepperoni pizza as their favorite choice?


(30% + 40% = x x=70%)








(8)

Use the circle graph to write an equation with a variable. Then solve.



Question:

10% of the people surveyed chose black olives. Jacob’s favorite pizza topping is twice the amount of black olives. What is Jacob’s favorite pizza topping?

(2 (10%) =j j=40% Since 40% represents pepperoni, Jacob’s favorite topping is pepperoni. )


(9)

Directions: Make an equation and solve.


Dan bought 18 cupcakes for the celebration. Lori bought 4 times as many cupcakes as Dan. How many cupcakes were bought?

( 4( 18)=c c=72)


(10)

Directions: Make an equation and solve.


Sydney ran 12 miles. Keith ran 2 times as many miles as Sydney. How many miles did Keith run?


( 2(12)=m c=24 )

(11)

Use the circle graph for questions 11-13

Use the circle graph to write an equation with a variable. Then solve



Question:


People took a survey about their favorite ice cream flavor. Chocolate chip was chosen 3 times less than what flavor?

( 3(5)= f f stands for flavor f=15 chocolate)



(12)

Use the circle graph from #11 to write an equation with a variable. Then solve


What flavor of ice cream is 5 times a number increased by 12?


( f=5(x)+12 f=flavor x=missing number f=vanilla x=5)


(13)

Use the circle graph from #11 to write an equation with a variable. Then solve


What is the total number of people who took the survey decreased by the number of people who chose strawberry ice cream? ( First step 5+15+13+37= 70 second step: 70-13= x x=57)



(14)

Make an equation and solve.

After the temperature rose 17 degrees, it was 95 degrees outside. What was the temperature to begin with? ( n+17= 95 n=78 )


(15)

Make an equation and solve.

After a number is subtracted from 63 and 5 is added, the result is 60. What number is subtracted? ( (63-n)+5 =55 n=8)


(16)

Make an equation and solve.

Mark and Crystal joined a competition together. To win first place they need to eat a combined amount of 25 hot dogs. Mark ate 13 hot dogs. How many hot dogs does Crystal need to win the competition? (25=13+x x=12)

(17)

Make an equation and solve.

Brian and Tyler were playing basketball. If Brian made 4 baskets and Tyler made 6 times as many baskets as Brian, how many baskets did Tyler make?

( 4(6)=x x=24)

(18)

Make an equation and solve.

Mandy left the airport at 3:oo pm. Her flight will take 4 hours and 15 minutes. What time will she arrive? ( 3+4=x x=7:00pm)

(19)

Make an equation and solve.

Tiffany had 13 apples. She ate some and now has 8 apples left.

(13-x=8 x=5)

(20)

For Problems 20-24 use the bar graph to write an equation and solve.





Question: What vacation spot is two less than the most popular location?

( x= 47-2 x=45 Hawaii )



(21)

For Problems 20-24 use the bar graph to write an equation and solve.


If the same survey was given in one month, and three times as many people voted for Disneyland, How many people would have chosen Disneyland?

( 3(23)=d d=Disneyland = 69)

(22)

For Problems 20-24 use the bar graph to write an equation and solve.

What is the difference between Hawaii and Legoland?

( 45-31=x x=14)

(23)

For Problems 20-24 use the bar graph to write an equation and solve.

How many people answered the survey?

( a+b+c+d=t 47+45+31+23=t t=146)

(24)

For Problems 20-24 use the bar graph to write an equation and solve.

When Disneyland and another vacation spot are totaled the sum is 68. What is the other vacation spot? (23+x=68 x=47)

(25)

Write an equation and solve.

David had 16 baseball cards. He needs 24 to complete his collection. How many more baseball cards does he need?

( 16+b=24 b=8)

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