RE.2 Draw Models
TEACHER: Burning Candle
Summary
Our question: When will the candle burn out?
Students watch a video of a candle burning placed next to a timer and ruler
to determine when the video will burn out. They need to decide what data
to collect. We need them to collect at least 6 data points.
Students make a scatterplot of the data, and use the graph to predict when
the candle will burn out. This data has a very strong correlation, so there
will not be much variation where students draw a line.
Differentiation
Language:
linear function
rate of change
unit rate
scatterplot
linear model
make predicitons
All students
Grouping: Pairs
Formative Assessment:
Can they graph the scatterplot
Scatterplot  scales
 graph points
Can they write the equation of their line?
Line
 slope
 y-intercept
Predict
Can they use math to predict when the candle will burn out?
What to bring out in the Debrief:
o How do you use the data to predict when the candle will burn out?
Algebra 1 by Southwest Washington Common Core Mathematics Consortium is licensed under
a Creative Commons Attribution 4.0 International License 1/20/14
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TEACHER: Burning Candle
RE.2 Draw Models
Resources:
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PowerPoint presentation with video clips linked.
Video without answer - http://vimeo.com/58221490
Video of answer - http://vimeo.com/59029138
Video min-lesson on making predictions from line of best fit.
Regression Equations Learning Targets
Common Core Standards
Regression Equations Learning Targets
Practice 3. Construct viable arguments and critique the reasoning of others.
Practice 5. Use appropriate tools strategically.
Practice 6. Attend to precision.
 S-ID.7 Interpret the slope (rate of
S-IDc I can interpret linear models.
change) and the intercept (initial
 Write a sentence to explain the meaning of slope and y-intercept in
value) of a linear model in the context
terms of the units stated in the data and context of the situation.
of the data.
 S.ID.9 Distinguish between
 Understand and explain that a strong correlation does not mean
correlation and causation.
causation.
 S.ID.6 Represent data on two
S-IDb I can summarize, represent and interpret data on two categorical
quantitative variables on a scatter
and quantitative variables.
plot, and describe how the variables
 Construct a scatterplot on paper and with technology.
are related.
 Identify independent and dependent variables.
 Describe the relationship between both variables.
a. Fit a function to the data; use
 Use a function that model data to solve problems.
functions fitted to data to solve
problems in the context of the data.
c. Fit a linear function for a scatter
 Estimate the equation of the line of best fit without technology.
plot that suggests a linear association.
BIG Idea: Students will be able to graph data, find a function that best fits data, find
and interpret correlation coefficient, graph residual plots to determine if the function is the
best model, and use the model to make predictions.
Algebra 1 by Southwest Washington Common Core Mathematics Consortium is licensed under
a Creative Commons Attribution 4.0 International License 1/20/14
Page 2 of 5
RE.2 Draw Models
TEACHER: Burning Candle
Scaffolding Questions
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How many data points to you need to make a confident prediction?
How might you record your data?
Will everyone have the same data?
Should everyone have the same prediction?
What representation could you use to help you with your prediction?
How can a table help you with your prediction?
What kind of graph would help you with your prediction?
How can a graph help you with your prediction? (If they drew a line) Will everyone have the
same line as you?
What process did you use to make your prediction?
Would someone else reading your poster understand the process you used to make your
prediction?
What else could you add to your poster so that someone else reading your poster understands
the process you used to make your prediction?
Algebra 1 by Southwest Washington Common Core Mathematics Consortium is licensed under
a Creative Commons Attribution 4.0 International License 1/20/14
Page 3 of 5
RE.2 Draw Models
TEACHER: Burning Candle
Watch the video with no set up or prompting.
Ask, “What do you want to know?” “How can math be used here?”
Hopefully someone asks, “How long does it take for a birthday candle to burn out?”
Students watch the video.
Collect data to use to make a revised prediction.
Let x be time in seconds and y be height in centimeters.
Let students decide how many data points to collect and their method for prediction. Expected methods:
draw a line on a scatter plot, or use a table to write an equation.
“What kind of function would model this data”?
You may need to give students the “HOW TO convert sec to min”
How can you use the date to predict when the candle will burn out?
Have students present their solutions.
Make sure everyone understands how to use the equation of the line to make predictions.
Revise Prediction
Use your data the make a revised prediction.
Bring out the concept of using a unit rate to make predictions.
Unit rate -0.0165 means the height of the candle shrinks by 0.0165 cm per second, or 0.99cm per minute.
Southwest Washington Common Core Mathematics Consortium is licensed under a Creative Commons
Attribution 4.0 International License 1/20/14
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TEACHER: Burning Candle
RE.2 Draw Models
Example Solution:
Time (sec)
Height (cm)
3.4
12.5
34.7
12
66
11.5
107
10.5
180
9.5
230
8.7
276
8
324
7.3
360
6.5
0  0.0165x  12.507
0.0165x  12.507
x  758 seconds
x  12.6 minutes
Ask, “Does the length of time the candle burns cause the height of the candle to decrease?”
It does. Causation can be attributed to physical principles.
Southwest Washington Common Core Mathematics Consortium is licensed under a Creative Commons
Attribution 4.0 International License 1/20/14
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