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Subject Area: 7th grade algebra
Lesson Design
Mathematics
Grade Level: 7
Benchmark Period: CST
Duration of Lesson: 1-2 hours
Standard(s): 7th Grade: MG 2.2 Estimate and compute the area of more complex or irregular two-and three-
dimensional figures by breaking the figures down into more basic geometric objects.
Learning Objective: Students will determine the area of complex geometric shapes.
Big Ideas involved in the lesson: Break down irregular or complex two-or three-dimensional figures to
estimate and compute their areas.
As a result of this lesson students will:
Know:
 Vocabulary:
 Surface area – An area obtained by adding the area of all the faces of a solid (the amount of gift paper you
need to wrap a gift).
 Area – The measure of the amount of plane occupied by a two-dimensional object.
 Complex or irregular figures – A figure composed of more than one geometric shape.
Understand:
 How to break down a complex figure into more basic figures. They can use the area formulas to find the area
of each basic object and add these areas to find the area of the complex object.
Be Able To Do:
 How to compute the areas of two or three-dimensional geometric figures that are irregular.
Assessments:
Formative: ABWA,
CFU Questions:
What will be evidence Quiz and homework.  Break up the figure into component geometric shapes. Show on
of student knowledge,
white boards.
understanding &
Summative: CST
 Determine the area of each component shape.
ability?
 Determine the area of the whole shape.
Lesson Plan
Anticipatory Set:
Given the diagram below, (also on a transparency) have students identify the
a. T. focuses students
shapes.
b. T. states objectives
CFU:
c. T. establishes purpose of the
How would you find the area of each shape?
lesson
We have formulas that help us to calculate the
d. T. activates prior knowledge
area of basic plane or solid objects. We will use
them to find the area of a more complex figure
that is composed of these basic figures.
How would you find the area of the total shape?
What would you need to know.
Instruction:
a. Provide information
 Explain concepts
 State definitions
 Provide exs.
 Model
b. Check for Understanding
1
Why – This is a great application of geometry in everyday life, such as calculating
flooring needs. Most building do not have pure rectangular floors.
Teacher will give the students pictures of complex objects and show them how they
can break them down to find their areas. Teacher will CFU (check for
understanding) randomly.
This is a rectangle + a semi-circle
d
1
2
Area = base ( height) +  ( r )
2
b
where r = half the diameter
Lesson Design
Mathematics
 Pose key questions
 Ask students to explain
concepts, definitions,
attributes in their own words
 Have students
discriminate between
examples and non-examples
 Encourage students
generate their own examples
 Use participation
h1
This is a rectangle + a triangle
1
h2
Area = base ( height2) + base ( height1)
2
The surface area = 4 faces of the pyramid + 4 walls of the prism + base of the
prism
Surface area = 2(0.5)(bh1) + 2(0.5)(ah3) + 2(bh2) + 2(ah2) + ab
h1
h3
h2
a
b
Check for understanding on the white boards. Put the picture of each object on the
over-head projector and ask the students to write down the formulas for the volume
and the S.A. on their white boards.
Check for understanding by asking students to demonstrate how they would break
apart each problem with the correct formulas, etc. using their white boards.
Find Area:
1.
Label as follows: Rectangle Length= 6 m
Triangle Height = 3 m, Rectangle Width = 4m
1
A  bh  lw
2
A = 0.5 (6m)(3m) + (6m)(4m)
A  33m 2
2. Find Area:
Draw a picture of a rectangle with two semi-circles on each end. Label the radius
(or half of the width) of one of the circles as 50 yards and the length as 200 yards.
1
A  2(  r 2 )  lw or
2
2
A   r  lw
A  3.14(50yd)2  (100yd)(200yd)
A  3.14(2500yd 2 )  2000yd 2 A  9850yd 2
Remaining problems are in Problems for M&G 2.2 file.
For 3-D rectangular prism related problems, students can build the figures using
multilink cubes
CFU – Have students use their whiteboards to break apart complex shapes into
component parts. Discuss how to find the area of each part.
CFU – Students randomly selected to answer questions about the process of
dividing the figure into its components and finding the area of each component.
2
Guided Practice:
a. Initiate practice activities
under direct teacher
supervision – T. works
problem step-by-step along
w/students at the same time
b. Elicit overt responses from
students that demonstrate
behavior in objectives
c. T. slowly releases student to
do more work on their own
(semi-independent)
d. Check for understanding that
students were correct at
each step
e. Provide specific knowledge
of results
f. Provide close monitoring
What opportunities will students
have to read, write, listen &
speak about mathematics?
Closure:
a. Students prove that they
know how to do the work
b. T. verifies that students can
describe the what and why
of the work
c. Have each student perform
behavior
Lesson Design
Mathematics
CFU – Students work with a partner to discuss each problem as they work through
it with the teacher. The first 6 problems are done with partners and teacher, the
next 2 problems students should work alone with guidance from the teacher.
Teacher checks each student’s work on whiteboards and through questioning.
Problems are on guided practice worksheet in Problems for M&G 2.2 file
They read the learning objective in their pair share. They listen to instruction and
write on their white boards. They work as partners on the guided practice problems
and on problem in Closure.
Allow students to work together to create their own 2- and 3- D shape that can be
broken apart to find the area or the volume. Students demonstrate which formulas
they will use. These are done on whiteboards that teacher checks.
Independent Practice:
a. Have students continue to
practice on their own
b. Students do work by
themselves with 80%
accuracy
c. Provide effective, timely
feedback
See Independent Practice problems in Problems for M&G 2.2 file
Resources
Problems for M&G 2.2 file
Man for M&G 2.2 file
Multi-link cubes
3
Lesson Design
Mathematics
4