Enduring Understanding: Develop a better understanding of how to use data from a table to create a graph and make a prediction of values not included in the data set.
Essential Questions:
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What is an informative/meaningful title for a graph?
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What are appropriate intervals for the x- and y-axes?
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How is a fitted line determined?
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How is a fitted line represented as an equation?
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How is a fitted line used to make a prediction?
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When reading a graph, where are the x- and y-intercepts? What is meant by vertical intercept? What is the relationship between the intercepts and the context of any problem?
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What does it mean to have negative values when you are working with years?
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What is meant by domain and range?
Lesson Overview:
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Before allowing the students the opportunity to start the activity: access their prior knowledge with regards to experiences on the Columbia River—fishing, camping, windsurfing, boating, visited the Coulee Dam, gone to a concert at the Gorge.
 Discuss a “fitted line”—What is it? How would a person use a fitted line? How would you show an understanding of a fitted line?
Why do you think a fitted line is used? What would happen if a person inaccurately used a fitted line? What operations are necessary to create a fitted line?
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In this activity, the independent variable is river depth (in feet) and the dependent variable is river velocity (in feet/second).
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How are the intervals on a graph determined?
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How can you support a conclusion that you make? What evidence from graphs can be used to support/justify your conclusion?
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Use resources from your building.
EALRs/GLEs
1.4.4
1.5.2
1.5.4
3.1.1
4.2.2
5.1.1
Item Specifications: PS03; AS02; SR03; CU02; MC01
Assessment:
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Use WASL format items that link to what is being covered by the classroom activity
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Include multiple choice questions

In order to understand how velocity varies within a channel, current velocities were measured on a number of transects across the Columbia River in Washington State. The velocity at any point in a river is controlled by a number of factors, including the river’s slope or gradient, roughness of the channel bed, turbulence of the flow, depth of the river, etc. Typically, water moves faster away from the bed of the river, where obstacles create drag and turbulence. The highest velocity overall is usually in the deepest part of the channel, just below the surface. Knowing the average velocity in a channel is extremely important when calculating river discharge, the volume of water flowing past in a given amount of time.
The data on velocity versus depth in the channel were acquired at a station below Grand Coulee Dam at a distance of 13 feet from the edge of the river. The depth of the Columbia River at this spot was about 12 feet at the time of measurement. Velocities were measured at various heights in the water column.
Columbia River Below Grand Coulee Dam
Current Velocities and River Depth
Savini and Bodhaine (1971)
USGS WSP 1869-F depth (ft)
0.66
1.98
2.64
3.3
4.62
5.94 vel (ft/sec)
1.55
1.11
1.42
1.39
1.39
1.14
7.26
8.58
0.91
0.59
9.9
10.56
0.59
0.41
11.22 0.22
Reference: Savini, J. and Bodhaine, G.L. (1971), Analysis of current meter data at Columbia River gaging stations,
Washington and Oregon; USGS Water Supply Paper 1869-F .

1. Graph the data.
2. Draw a line (fitted line) for the data.
3. Write an equation that describes a line that fits the data displaced.
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4. Explain what the vertical-intercept of the fitted line means for this scenario.
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5. Explain what the horizontal-intercept of the fitted line means for this scenario.
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6. Explain any limitations on the Domain and Range of the graph. (Remember that Domain is the collection of all allowable values for the control/independent variable and that Range is the collection of all achievable values for the dependent variable.)
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7. Predict the velocity of the river at a depth of 8 feet. __________________________
Support your answer using words, numbers and/or diagrams.

8. Predict at what depth the river has a velocity of 1 ft/sec. _______________________
Support your answer using words, numbers and/or diagrams.
9. Every December, Mary’s Sweet Shop has a $1.00-off sale. The table shows the prices for selected pies.
Pie
Apple
Original Price
$6.00
Sale Price
$5.00
Which graph represents the relation between the original price and the sale price?
Pumpkin
Mince
Pecan
$7.00
$9.00
$10.00
$6.00
$8.00
$9.00

10. David walked up a hill. His position changed vertically one foot and horizontally four feet as he moved forward up the hill.
Which graph best represents David’s position as he walked up the hill?