Unit Title: Eco-Friendly
Days 1-10
Algebra
Lesson Plan
Grade: 7th
2013-2014 School Year
Lesson Title:
Invertebrates and their living spaces
STRANDS
Area of Plane and Composite Figures
Volume of prisms, pyramids, cones, cylinders, and spheres
Summary of the task, challenge, investigation, career-related scenario, problem, or community link.
LESSON OVERVIEW
Students will be reviewing area equations for squares, rectangles, triangles, trapezoids, and circles as well as calculating volume for different geometric
solids This should be a review from previous grades and a preview for geometry. Students will also be finding the area of composite figures by
extending area equations. Their project days will allow them to stake off square meter samples and remove the ground cover to a certain
depth(volume). After counting the invertebrates in the one meter square samples, they will convert units and predict the number of invertebrates that
are in an acre of ground cover.
Hook for the week unit or supplemental resources used throughout the week. (PBL scenarios, video clips, websites,
literature)
MOTIVATOR
Students will watch a short video clip about invertebrates and how sometimes small and seemingly insignificant creatures can make a necessary
impact on the eco-system.
DAY
Objectives
Materials &
Resources
Instructional Procedures
Differentiated
Instruction
Assessment
(I can….)
1
I can define
volume and
find the
volume of a
prism and
cylinder.
earthworm
Essential Question:
Paper
How can I define volume and find the volume of a prism and cylinder?
Pencil
iPad
Presentation
Graphing
calculator
Geometric
Solids
Manipulatives
Soup cans
Empty paper
box
Activating Strategy: Tell students that you want to send 20 paper boxes full of a
certain soup can to a needy region somewhere outside the US. What is the most
soup cans possible that they should collect without going over the limit of the 20
boxes.
Teaching Strategy: Define Volume for the students. Lead a demonstration to help
students discover how to find volume of a prism. Start with a plane figure, such as a
square, and then add more squares on top. Lead students to the formula for the
volume of prism: Area of the Base times Height. Use geometric manipulative solids
to help students picture the flat versions of the shapes. Work some example
problems to calculate area as an entire class, then some partner work time, and
finally individual work time. Students will continue to practice this skill with a short
homework assignment.
Intervention and
Enrichment can
be achieved
through varying
the difficulty of
problems during
the individual
work time,
heterogeneous
grouping, and
questioning
during the
activity.
Short homework
assignment
Intervention and
enrichment can
be achieved by
various problems
of pyramid and
cone volumes.
Informal
observation during
the lesson
In-Class work
Exit Ticket
Summarizing Strategy: Discuss how area, if filled up a certain height, creates
volume. Remind students that the capital “B” in the volume formulas causes the
prism and the cylinder formulas to coincide.
2
I can find the
volume of a
pyramid and
cone.
Paper, pencil
Essential Question:
How can I find the volume of a pyramid and cone?
Ipad
Calculator
Geometric
Solids
manipulatives
Activating Strategy: Have a pyramid and a prism and a cone and cylinder that have
the same bases. Ask the students how many pyramids they think can fit in the prism
or cones in the cylinder?
Student
Presentations
Short homework
assignment
Dry rice or
beans or sand
ruler
.
Teaching Strategy: Demonstrate to students how volume of a cone relates to
volume of a cylinder. Fill up the cone with rice, beans or sand. Pour into the cylinder.
You should be able to do this 3 times. Have students discuss the proportional
differences and how this impacts the calculation of the volume of a cylinder. Lead a
brief presentation on volume of pyramids and cones. The volume is one-third the
volume of a cylinder. After placing the cone inside the cylinder, place the pyramid
inside the prism and ask what proportion of the prism that the pyramid is? Practice
finding the volume of pyramids and cones as a whole class, then in small groups, and
finally allow the students some time for individual practice.
Summarizing Strategy: Discuss volume again but in terms of its rapidly decreasing
as it approaches a vertex of no dimension and what effect this has on the
proportional variance of volume from a stated base.
3
I can find the
volume of a
composite
figure.
Paper, pencil
Essential Question:
Ipad
How can I find the volume of a composite figure?
Composite
Figure digital
images
Activating Strategy: Draw a cone on the board with an attached hemisphere. Ask
the class if a can were full and the can had the same radius and height as the cone,
which could contain the most substance? Or same?
Teaching Strategy: Define volume of a sphere for the students. Lead a discussion
that a hemisphere is exactly one half of the sphere volume. Remind students that a
cylinder with the same radius and height as a cone has three times the
capacity(volume).
Summarizing Strategy: Discuss with students other possible composite figures that
might be difficult to compare volume just by their “looks”.
4
Essential Question:
Intervention and
enrichment can
be achieved by
varying the type
of figures for the
area activity as
well as
heterogeneous
grouping and
questioning
during the
activity..
Informal
observation during
the lesson
Student
Presentations
Short homework
assignment
Project – Refer to Unit Plan
Watershed Health
Essential Question:
5
Project – Refer to Unit Plan
Watershed Health
6
I can define
area and find
the area of a
Paper
Essential Questions: EQ: How can I define area and find the area of a square, rectangle,
Enrichment:
Formative:
Pencil
and triangle. How can I derive the formula through visual proof for the area of a
parallelogram.
Short
Exit ticket
square,
rectangle, and
triangle.
iPad
I can derive the
formula
through visual
proof for the
area of a
parallelogram.
Graphing
calculator
Presentation
Area of triangles
discovery
activity.
Activating Strategy: Tell the students they can suggest to paint the room any color
they’d like. The group that can find the area of the room to the closest square foot
gets to have their color suggested for painting during summer break..
Teaching Strategy: How did you find the area of the wall? Have a short teacher led
discussion over the definition of area and common units used to express area. Also
review the equations for finding the area of a square and rectangle. Try some
examples as a whole class, some small group work, and finally some individual work.
This should lead into the parallelogram area formula discovery activity. Give all
students some Parallelograms. Then, have them create a rectangle out of the
parallelogram by cutting a triangle from one end and moving it to the other. Lead
students to the formula that the area of a parallelogram is the same as the area of a
rectangle. Finish with a short presentation on the area of a parallelogram. Include
parallelograms that are not “right side up” and introduce the concept of height in a
parallelogram.
Summarizing Strategy: Exit Ticket - Put a parallelogram, rectangle, and square on the
board. Have the students find the area of each, they should be close, and have them
put them in order from smallest to largest.
7
Essential Question:
homework
assignment
Remediation:
Have students
write out steps
for finding area
of triangle and
rectangle
Summative:
Survey student
classwork
IEE
Project Day: Refer to Unit Plan
8
I can find the
area of a
trapezoid and
triangle.
I can derive the
area formulas
for a trapezoid
and triangle
through a
visual proof.
I can find the
area of a circle.
Paper, pencil
Essential Question: EQ: How can I find the area of a trapezoid and parallelogram? How
Ipad
can I derive the area formulas for a trapezoid and triangle through a visual proof? How can
I find the area of a circle?
Ruler
Grid sheets
Activating Strategy: Put a big triangle on the board and have students discuss at
table groups how to find the area of a triangle. Also, draw a large square and
rectangle with a diagonal in each. Have students share the results of the discussion.
Teaching Strategy: Lead a quick review over the homework on the area of a
parallelogram, square, and rectangle from the previous day. Have students write
examples on the board or have them share through airplay. Pass out the grid sheets.
Give students a picture of a triangle or trapezoid. Ask them to use another shape of
equal size to construct a parallelogram or rectangle. Then ask them to find the area
of the larger shape and describe how the two are related. At the end of the activity
have students share results and then introduce the area formulas for trapezoids and
triangles. Have students practice a few examples.
End the lesson with a short presentation on the area of a circle. Introduce the basic
vocabulary of diameter, radius, and pi. Work some examples as an entire class. Some
should have radius given and some diameter. Have students practice some
examples.
Enrichment:
Formative:
Short
homework
assignment
Exit ticket
Remediation:
Have students
write out steps
for finding area
of trapezoid and
parallelogram
Summative:
Survey student
classwork
Summarizing Strategy: Exit Ticket - Put a parallelogram, rectangle, square, triangle,
and trapezoid on the board. Have the students find the area of each, they should be
close, and have them put them in order from largest to smallest.
9
I can find the
area of a
composite
figure.
Paper, pencil
Essential Question: EQ: How can I find the area of a composite figure.
Ipad
Grid paper
Activating Strategy: Draw a picture of a football field with two semi-circles attached
on each end whose diameters are the same as the width of the field. Ask the
students to find the area and also as simple as possible or is it that simple? Let them
argue for a minute then tell them to show you on paper or Ipad.
Teaching Strategy: Finish the field problem with presentations of students or with
instruction. Work one example of a composite area problem as an entire class. Show
the students how to break the image into shapes that are known. Next, pass out
challenge problems that ask students to find the area of a composite figure. Each
group will get a different problem. After each group has had time to complete the
problem, they will the present how to find the area to the entire class.
Summarizing Strategy: Present students with the composite area problem they will
face during the project day to find the cross sectional area of a planter. Lead the
students through one example problem.
10
Essential Question:
Enrichment:
Formative:
Short
homework
assignment
Exit ticket
Remediation:
Unit squares
Different unit
squares
Summative:
Give test on areas
and volume on next
regular scheduled
class
Project Day: Refer to Unit Plan
STANDARDS
Identify what you want to teach. Reference State, Common Core, ACT
College Readiness Standards and/or State Competencies.
7.G.6 - Solve real world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of
triangles, quadrilaterals, polygons, cubes, and right prisms.
G-MG1 - Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
G-MG.2 - Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot)
G-GMD.3 - Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems