Shadows and Data

Grade

6th Grade

Duration

60 Minutes

Standards

• CCSS.MATH.CONTENT.6.SP.B.5: Summarize numerical data sets in relation to their context, such as by identifying patterns in the data or changes over time.
• CCSS.MATH.CONTENT.6.SP.B.4: Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
• CCSS.MATH.PRACTICE.MP4: Model with mathematics.
• CCSS.MATH.PRACTICE.MP5: Use appropriate tools strategically.

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Learning Objectives

By the end of the lesson, students will be able to:

1. Create a line graph from a data set to represent changes over time. (6.SP.B.4)
2. Interpret measurements and analyze data trends from the line graph. (6.SP.B.5)
3. Understand and explain the usefulness of line graphs in real-world data contexts. (MP4)
4. Explore various methods for collecting and representing data.
5. Engage in hands-on activities to deepen understanding of data variability based on real-life phenomena (shadow measurement).

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Materials

• Graph paper
• Rulers
• Pencils and erasers
• Whiteboard and markers
• Printed copies of Mini’s shadow data (times and shadow lengths)
• Blank line graph templates
• Simple shadow measurement props (e.g., small objects, toy bicycles) for extension activity
• Stopwatch or timer (optional for extension activity)

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Lesson Procedure

1. Introduction and Activating Prior Knowledge (10 minutes)

• Engage: Read aloud the Mini’s measurement story outlined above.
• Ask: "Have you ever noticed how shadows change throughout the day?"
• Discuss briefly how shadows come from sunlight and the sun’s position changes during the day, causing shadows to lengthen or shorten.
• Review previous experiences with measurement and charts in math or science classes to connect learning to students’ background.

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2. Data Interpretation and Line Graph Creation (20 minutes)

• Activity 1: Distribute Mini’s shadow measurement data sheet and graph paper.
• Model together on the whiteboard: set up the axes (time vs. shadow length), label them, and plot the given data points.
• Students create their own line graphs using Mini’s data on their graph paper, connecting points with lines to show the trend.
• Teacher circulates to assist students, encouraging neatness and discussion about what the graph is showing.
• Emphasize observing the pattern: shadow length shortens until noon and then lengthens in the afternoon.

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3. Data Analysis and Critical Thinking Questions (15 minutes)

• Pose Mini’s provided questions for pair or small group discussion:
  1. Why do you think Mini used a line graph?
  2. What other methods of collecting data do you know? (Examples: surveys, counting, timing, measuring temperature)
  3. How long do you think the shadow was at 10:30 AM? (Encourage estimating by interpolating between data points on their graph.)
  4. What about at 2:30 PM? (Same interpolation exercise.)
  5. If you measured the shadow of your bicycle, would it be shorter, the same size, or longer than Mini’s dad’s van’s shadow? Explain using reasoning about object size and position of the sun.
• Each group shares their thinking and reasoning with the class. Write key ideas on the board.

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4. Hands-On Extension: Measuring Shadows (10 minutes)

• Students are given small objects or toys (e.g., a toy bike).
• If weather allows, take students outside to measure shadows using rulers or measuring tapes at two different times (or simulate using room lights and timed intervals in class).
• Have students sketch a simple line graph of their shadow measurements over time or imagine how it would change.
• Discuss real-world influences on data collection – time of day, weather, object size, and location.

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5. Closure and Assessment (5 minutes)

• Exit ticket: Students write a sentence answering:
  • "Why is a line graph a good way to show Mini’s shadow measurements?"
  • "What did you learn today about data and shadows?"
• Collect exit tickets for formative assessment.

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Assessment and Evaluation

• Observation during guided graphing and group discussions to check understanding of scale, data plotting, and interpretation.
• Review completed line graphs for accuracy and clarity.
• Evaluate exit tickets for reflection and concept grasp.

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Differentiation Strategies

• For Students Needing Extra Support: Provide a partially completed graph and number lines; allow them to color code data points. Use peer buddies for graphing support.
• For Advanced Learners: Challenge them to predict shadows at additional time points or research factors affecting shadow length such as latitude or seasons.

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Reflection and Extensions

• Consider a follow-up project where students collect their own measurement data on different days or objects and create graphs.
• Integration with science: Study Earth's rotation and how it affects sunlight and shadow length, linking math and science concepts meaningfully.

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This lesson plan not only aligns specifically with Common Core standards for 6th grade mathematics around data and statistics but also engages students with hands-on activities and critical thinking, transforming abstract concepts into tangible learning experiences.