Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 71597
Are Corresponding Leaf Veins Proportional to Leaf
Height?
Students will measure the length of different sized leaves and corresponding veins to determine proportionality. Students will graph their results on a
coordinate grid and write about their results.
Subject(s): Mathematics, Science
Grade Level(s): 7
Intended Audience: Educators
Suggested Technology: Interactive Whiteboard,
Basic Calculators
Instructional Time: 1 Hour(s) 30 Minute(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: Proportion, measurement, corresponding
Resource Collection: FCR-STEMLearn Diversity and Ecology
ATTACHMENTS
Leaf Worksheet.docx
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
1. Students will use rulers to accurately measure a length of a leaf, and one vein of that leaf.
2. Students will find the ratio of the vein to leaf length in fraction and decimal form.
3. Students will determine if the ratio of corresponding veins of different sized leaves of the same plant are proportional to the length of the leaf.
4. Students will plot the relationship on a coordinate graph.
5. Students will describe the data and the relationship between vein length and leaf height.
Prior Knowledge: What prior knowledge should students have for this lesson?
1. How to change fractions to decimals
2. How to graph an ordered pair
3. The ability to recognize proportional relationships
4. Measure accurately using a ruler in millimeters
Guiding Questions: What are the guiding questions for this lesson?
1. What is a vein? What are they for? What do they look like?
2. Do leaves have veins?
3. What do veins in a leaf look like?
4. As a leaf grows, do its veins grow proportionally? How can we find out?
5. If they do grow proportionally, how can we demonstrate that mathematically?
6. How can we show proportionality visually?
7. What does corresponding mean in two different things?
page 1 of 5 Teaching Phase: How will the teacher present the concept or skill to students?
Students work in pairs. Write these questions on the board, and give students 5 minutes to read the questions and discuss them with a partner. Then, ask the whole
group each question:
1. What is a vein? What are they for? (Veins support the leaf and transport food and water to the plant, much like our veins transport blood around our body)
2. What do they look like? Can you see them? (They are thin and can look similar to branches on a tree; you can see them sometimes!)
3. Do leaves have veins? (Yes)
4. What do veins in a leaf look like? (They are pale in color and slightly raised above the surface of the leaf)
5. As a leaf grows, do it’s veins grow proportionally (or the same)? How can we find out? (Give students time to plan this)
6. If they do grow proportionally, how can we demonstrate that mathematically? (Making a table and testing for equivalent or similar ratios)
7. How can we show proportionality visually? (Graph it)
8. What does corresponding mean in two different things? What parts match in each leaf?)
9. Are all leaves on the same plant the same? (Some are bigger/smaller)
Give students a brief overview of what they are going to do/learn in class (ID veins in a leaf, measure them, compare them with the leaf length, and then graph the
results). Practice first, and then go outside and pick leaves to measure.
Pass out attached leaf worksheet. (see Guided Practice)
When students are finished with their worksheet move on to the activity under Formative Assessment.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Leaf Worksheet.docx
Have students identify the veins on the leaves on their Leaf Worksheet. Highlight corresponding veins of different leaves in the same color. Circulate and check for
accuracy.
Have students identify and mark where to measure the height on their leaves. Circulate and check for accuracy.
Ask students where to “start” when measuring with a ruler. Make sure they know to start at 0 mark, which is not necessarily the end of the ruler. Have students
locate and point to this part of the ruler.
Ask which unit of measure would be the most accurate (smaller units will give the most accurate measurement). Observe students pointing to this side of their
ruler, and identify the marks as millimeters.
Observe students practice measuring on the leaf worksheet. After they have time to measure and record their answers, give them the accurate measurements and
answer questions to check for understanding.
Observe students making fractions and decimals from the ratio of vein to leaf height. (demonstrate and check for understanding)
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Students will have different answers because they will have different leaves
Take students outside to observe leaves in predetermined areas of your school (scout this out ahead of time to find appropriate trees/leaves). Have each pair of
students choose 5 leaves of varying size from the same tree (different student pairs can choose from different trees, but it's important each group choose their
leaves from the same tree).
Students take the leaves inside, and measure the height and vein length of each leaf, recording the data in the chart outlined below.
Students will use graph paper to record their data, and graph it. Have students use the top half for the data, the bottom for the graph, and answer questions on the
back of their paper. Have students draw this table on the top of their paper to record their data, leaving some space below for notes or observations:
Leaf 1
Leaf 2
Leaf 3
Leaf 4
Leaf 5
Vein height (mm)
Leaf height (mm)
Vein/height ratio
in fraction form
Vein/height ratio
in decimal form
X,Y coordinate
Collect student data from the leaf measurements using the worksheet provided. Check for completion and accuracy turning the ratios into decimals. Look for
correct graphing (the x coordinate and y coordinates are correctly identified), and they have connected the points to make a line.
Have students write a brief summary of their findings and observations. Read the answers to their questions and check for understanding of the concept of
proportional relationships.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Have each group briefly present their findings, and review the questions from the beginning of the lesson (a few sentences per group, or select a few groups as time
allows).
page 2 of 5 Summative Assessment
The Independent Practice is the summative assessment.
Students will use graph paper to record their data, and graph it. Have students use the top half for the data, the bottom for the graph, and answer questions on the
back of their paper. Have students draw this table on the top of their paper to record their data, leaving some space below for notes or observation. Label the
columns across the top for the number of leaves you choose to measure. (Recommend 5 leaves)
Leaf 1
Leaf 2
Leaf 3
Leaf 4
Leaf 5
Vein height
Leaf height
Vein/height ratio
in fraction form
Vein/height ratio
in decimal form
X,Y coordinate
Collect student data from the leaf measurements using the worksheet provided. Check for completion and accuracy turning the ratios into decimals. Look for correct
graphing (the x coordinate and y coordinates are correctly identified), and they have connected the points to make a line.
Students will have different answers because they will have different leaves
Read the answers to their questions and check for understanding of the concept of proportional relationships.
Exit ticket: What other examples of proportionality might you find in nature?
Rubric for grading:
Excellent
Chart Complete
All rows filled in
and accurate
Correctly drawn
Graph
Good
Fair
Poor
All rows filled in,
50-75%
50% or less
75% data
completion,
completion,
accuracy
partial accuracy
inaccurate data
Correctly drawn
with labels. X and with labels, but
Partial completion
Y coordinates
or incorrect
coordinates
Data not graphed
correctly graphed wrong.
3 observations
Observations
written in
complete
2 observations
1 observation
Missing
sentences
Example, shows
Example, shows
understanding of understanding of
Exit ticket
Points
the concept, in a
the concept, but
complete
not in a complete
sentence.
sentence
85-100
75-85
Example, but
does not show
understanding of
Missing
concept.
60-75
0-60
Formative Assessment
Assess understanding of knowledge using the Guiding Questions at the beginning of the lesson.
Guided Practice in this lesson is the formative assessment. Circulate and observe student groups and ask questions to determine understanding.
Here are some examples of questions to ask students during their practice:
1. Which vein did you choose and why?
2. Which veins are corresponding?
3. Where on your leaf did you start your measurement?
4. Are your ratios equivalent? Would it change if you round your decimals? How?
5. Do you see any trends, or have a prediction about your outcome?
Feedback to Students
Circulate and give feedback as students are measuring.
Have students work in pairs for support and peer feedback.
Give students the accurate measurements during the guided practice so they can compare answers.
page 3 of 5 ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Peer tutor, work in pairs and mixed ability groups.
Struggling students can measure fewer leaves.
Keep instructions and directions 'chunked'. Provide one step at a time, don't overload the student on too many pieces of information at once.
Give repetition and clarification regularly
Give ongoing feedback.
Provide time extensions as necessary
Provide visual clues, examples. (show practice worksheet on overhead or smart board, hold up examples of leaves and point out length and veins, provide an
example of a completed project, show properly formatted graph paper used in independent practice)
Extensions:
Repeat with leaves from a different plant, compare answers (trade leaves with another team).
Make other observations about the leaves: Is there a pattern on the leaves? Is it the same for all the leaves? Are the leaves symmetrical? If there is a pattern,
does it reflect, rotate, or translate?
Suggested Technology: Interactive Whiteboard, Basic Calculators
Special Materials Needed:
Copies of Leaf Worksheet for each student
Rulers
Calculators
2 different colors of pencils or crayons or markers
5 leaves for each students from the same plant/tree (different students can/should have different types of leaves)
Further Recommendations:
The lesson can be divided into 2 parts/days: The introduction and practice worksheet on day 1, and the independent practice on day 2.
Walk around your school and identify potential sources of leaves. Ensure leaves are taken from appropriate areas. Classes could share leaves if necessary.
Measure the leaves on the worksheet before having students do the activity, so you can be specific about measurements and identify potential questions. After
measuring, fill out a sample worksheet with your answers. Student measurements will vary depending on which vein each group chooses. The teacher may specify
which vein students should use, so their answers will be the same or very close.
Measurements for the independent practice will vary widely based on the species of tree and the specific leaves that the students choose. The teacher should
circulate and carefully check student measurements for accuracy during this time.
Additional Information/Instructions
By Author/Submitter
This lesson address the following mathematical practices:
MAFS.K12.MP.5.1 Use appropriate tools strategically.
Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a
ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently
familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be
gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing
calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that
technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient
students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or
solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
SOURCE AND ACCESS INFORMATION
Name of Author/Source: Anonymously Submitted
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
SC.7.N.1.1:
Description
Define a problem from the seventh grade curriculum, use appropriate reference materials to support scientific
understanding, plan and carry out scientific investigation of various types, such as systematic observations or
experiments, identify variables, collect and organize data, interpret data in charts, tables, and graphics, analyze
information, make predictions, and defend conclusions.
Remarks/Examples:
page 4 of 5 Florida Standards Connections: LAFS.68.RST.1.3. Follow precisely a multistep procedure when carrying out
experiments, taking measurements, or performing technical tasks.
MAFS.7.RP.1.2:
Recognize and represent proportional relationships between quantities.
a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or
graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of
proportional relationships.
c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of
items purchased at a constant price p, the relationship between the total cost and the number of items can be
expressed as t = pn.
d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special
attention to the points (0, 0) and (1, r) where r is the unit rate.
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
Students in grade 7 grow in their ability to recognize, represent, and analyze proportional relationships in various
ways, including by using tables, graphs, and equations.
page 5 of 5