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Water In A Bucket Activity
A data collection, organization, and linear modeling activity for multiple
grade levels.
Algebra For All13 May, 2011Presented by
Michelle Edlbeck, Gail Everhart, Lesley Hicks, Scott Martin, Brenda Quaak, Douglas Quaak, Jamie Tuch
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Areas of Focus for each level
• Data collection at all levels• 6th grade
– Proper presentation table & scatter plot• 7th grade
– Statistics mean median mode– Line of best fit– Slope – Data into words
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Areas of Focus for each level
• Algebra 1– Equation to model of best fit– Interpolation or extrapolation– Domain & range
• Algebra 2– Non-linear relationships– Balloon - # of breaths vs diameter activity
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Data Collection
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Data Table
Trial # Depth of water inches
Weight of bucket and water
lb. / oz.
Weight of bucket and water
oz.
1 1.5 1 lb. 12 oz. 28
2 2.5 2 lb. 14 oz 46
3 3.75 4 lb. 5 oz. 69
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Scatter Plot
_____________________Label
_______Units
_____________________Label
_______Units
Scale
Scale
_________________Title
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Scatter Plot
10
20
30
40
50
60
70
80
Depth_of_w ater_inches
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Depth vs w eight of w ater and bucket Scatter Plot
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Statistics
• Depth of water– Mean – Median
• Weight of bucket with water– Mean – Median
• No mode for either data set
1.5 2.5 3.752.383
3
in in inmean in
2.51.5, , 3.75
28 46 6947.6
3
oz oz ozmean oz
28, 46 , 69
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The best fit line and the meaning and nature of slope
• Positive slope– As the water rises the weight increases
80
70
60
50
40
30
20
10
-10
1 2 3 4
Best fit line
Run
Rise
Weight of bucketand water in oz
Depth of water in inches
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Linear model80
70
60
50
40
30
20
10
-10
1 2 3 4
D: (3.00, 55.33)
C: (1.06, 20.00)
AB: y = 18.22x+0.67
Best fit line
Weight of bucketand water in oz
Depth of water in inches
D
C
B
A
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Linear model
• Equation of the line– Slope 18.22 ounces of water per inch– Y-intercept 0.67 ounces (weight of the empty
bucket• 3 in. of water would weigh 55.33 oz• 20 oz of water would have a depth of 1.06 in.• 10 inches of water would weigh 182.87 oz
18.22 0.67y x
18.22 0.67
18.22 10 0.67
182.87
y x
oz
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Domain and range
• The mathematical model is only valid within the confines of the bucket.
• Domain- the bucket is 7.5 inches deep so
• Range is limited by the domain and the original weight of the bucket thus.
18.22 0.67y x
0 7.5domain x
0.67 137.32range y
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Non-linear Model
• Balloon activity – breaths vs circumference.
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Questions