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

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

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

Data Collection

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

Scatter Plot

_____________________Label

_______Units

_____________________Label

_______Units

Scale

Scale

_________________Title

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

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

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

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

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

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

Non-linear Model

• Balloon activity – breaths vs circumference.

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Questions