6th Grade - Graph And Solve For Unknowns

 
     
 
     
 
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6th
Reasoning
Graph and Solve for Unknowns
Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.
Use or create different types of graphs to obtain information. Use logical reasoning, math calculations and/or algebraic equations or expression to estimate unknown quantities from a graph.
 

Sample Problems

(1)

Using the line graph, what is a good estimate of the probable cellular phone usage in 2005?

(about 20 million people)


(2)

According to the bar graph, what is a probable estimate for the Sunday before the graph begins?

(67 degrees)

(3)

The line plot shows the scores of all the students in John’s math class on the last test. Use the line plot to determine John’s probable test score, if he is an average student.





X

X

X X X

X X X X X X

X X X X X X X X X X

___________________________________________________

45 50 55 60 65 70 75 80 85 90 95 100


(John mostly likely got a score between 75 and 85.)

(4)

Use the data from the table to make a line graph. Then, use your line graph to estimate the height of the plant at the end of day10.

Day 1

Day 2

Day 3

Day 4

Day 5

0.5 cm

0.75 cm

1 cm

1.25 cm

1.5 cm



(3 cm)

(5)

Use the ordered pairs graph the data. Then, write an algebraic equation that shows the data pattern and use it to find the next ordered pair.

Ordered pairs: (0,0) (1,1) (2,2) (3,3)

y-axis

x-axis


(Answer:

x + 1 =y + 1, (4,4))


Learning Tips

(1)

Graphs are helpful because they allow children to access data visually. They can help children understand complicated information by showing relationships between pieces of data. Different graphs are better at revealing different information. Bar graphs display countable data using horizontal or vertical bars. The graphs are useful in comparing different categories of information. Line graphs are usually used to show change over time (hours, days, months, years, etc…). Line graphs are often used to make future predictions. A circle graph shows how parts compare to a whole. By showing each part as a fraction of a circle, it is easy to relate the sizes of the parts to one another.

(2)

Review different graph types with your child. Be sure that when looking at a line graph, that your child understands that when a line is moving up and to the right that it is showing an increase. However, if the line is moving down and to the right, it is showing a decrease. When the line is moving horizontally across the graph, it is unchanged.

(3)

Research shows that the majority of sixth grade students can read data displays, but have difficulty constructing graphs from given data. Make sure your child has plenty or practice using data to create different types of graphs.

(4)

If the data in a graph follows a general pattern or directions, it can show a trend. For example, if the line on a line graph is moving up 5 points each minute, the trend would be 5 points per minute. This trend could be used to predict future events. So if a line graphs showed a game player earning 5 points for each minute the game was played, we would use this data to write an algebraic expression to find an estimate of points for n minutes. The expression 5n could be used to show this trend. Now, the player could estimate the number of points for any number of minute, he/she would like to know by inserting the number of minutes in where the n is. For example, if the player played for 40 minutes, 5 x 40 = 200, so it could be estimated that the player would earn 200 points.

(5)

In 5th grade, your child learned how to plot ordered pairs on a coordinate grid. Remind your child that a coordinate grid has an x-axis (horizontal line) that is intersected by a y-axis (vertical line). Ordered pairs are pairs of numbers that can be plotted on a grid. Ordered pairs are shown in parenthesis, separated by a comma ex. (3,4). The first number in the ordered pair tells you the direction to move across the x-axis, so in the ordered pair sample, you would move to the positive 3 on the x-axis. The second number in the ordered pair tells you how to move up or down the y-axis. Sixth graders will need to use the ordered pairs plotted to find trends and write and expression or equation to show a trend, when applicable.

Sample Problem – Finding a Trend for Ordered Pairs

(2,4), (3, 6), (4, 8)

The equation 2x=y can be used to show the trend, because y is always two times the amount of x. This equation could be used to find any new set of ordered pairs, when either x or y is known.

Extra Help Problems

(1)

The line plot shows the scores of all the students in Adrian’s math class on the last test. Use the line plot to determine Adrian’s probable test score, if he is an average student.


X

X

X

X

X

X X X

X X X X X

X X X X X X X X X

___________________________________________________

45 50 55 60 65 70 75 80 85 90 95 100

(Adrian probably got an 80.)

(2)

The line plot shows the scores of ten new bowlers. If Diego has never bowled before, how can she use this data to estimate the score she can expect to get?


X

X

X

X

X X

X X X X

___________________________

40 60 80 100 120


(He could estimate a score of about 60, because most new bowlers received this score.)

(3)

Use the bar graph to estimate the temperature on Saturday, if the trend continues.


(74 degrees)


(4)

Use the bar graph to estimate the temperature on Sunday, if the trend continues. Explain.


(It will be 76 degrees, the pattern is up one for two days, then up 2 degrees on the third day.)


(5)

If the trend from week 3 to 4 continues for 6 more weeks, how tall will the plant be on the 10th week?

(12 inches, 1 foot tall)

(6)

If after the 10th week, the plant from extra help problem 5 begins to grow 1 ½ inches per week. What is the best estimate for how long it will take the plant to grow to 2 feet?

(18 weeks)

(7)

The graph below shows student data fundraising data for 5th and 6th grade. The red line represents the 6th grade and blue is 5th. Looking at the line graph, what is the best estimate for what 6th grade will fundraise in January?



($50.00)

(8)

How could the double line graph in extra help practice 7 be used to determine the total estimated funds for sixth grade for the school year (10 months), assuming the trend will continue? What is the estimated amount the 6th grade earn altogether?

($375.00)

(9)

Using the line graph from extra help practice 7, what can 5th grade be expected to fundraise in January?

($50.00)

(10)

If the fundraising trend for 5th grade continues, how long will it take them to fundraise at least $200.00?

(They should have over $200 by February.)

(11)

If the trends continue for both grade levels, which will fundraise more for this school year?

(5th grade)

(12)

Use the data from the table to make a line graph. Then, use your line graph to estimate the height of the plant at the end of day 7.

Day 1

Day 2

Day 3

Day 4

Day 5

2 cm

4 cm

6 cm

8 cm

10 cm



(14 cm)

(13)

Use the data from the table to make a line graph. Then, use your line graph to estimate the height Justin’s block tower at the end of day 5.

Day 1

Day 2

Day 3

Day 4

1 cm

2 cm

4 cm

8 cm



(16 cm)

(14)

Use the ordered pairs graph the data. Then, write an algebraic equation that shows the data pattern and use it to find the ordered pair when x = 10.

Ordered pairs: (4,2) (8,4) (2,1)

y-axis

x-axis


(x/2=y, (10,5))


(15)

Use the ordered pairs graph the data. Then, write an algebraic equation that shows the data pattern and use it to find the ordered pair when y = 2.

Ordered pairs: (6,3) (7,4) (8,5)

y-axis

x-axis


(x-3=y, (5,2))


 

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