LESSON PLAN #1
Name: Noor J. Hoque
Title of lesson: Ratio and Proportion
Length of lesson: 90 minutes
Date of lesson:______
Description of the class:
Name of course: Algebra 1
Grade level: 7 / 8 regular
Source of the lesson:
http://school.discovery.com/lessonplans/programs/architectsinaction/
TEKS addressed:
7.13(A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics.
7.14(A) communicate mathematical ideas using language,
efficient tools, appropriate units, and graphical, numerical, physical, or
algebraic mathematical models.
7.2(B) use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals.
7.2(D) estimate and find solutions to application problems involving proportional relationships such as similarity, scaling, unit costs, and related measurement units.
7.8(C) use geometric concepts and properties to solve problems in fields such as art and architecture.
7.9 The student solves application problems involving estimation and measurement. The student is expected to estimate measurements and solve application problems involving length (including perimeter and circumference), area, and volume.
8.2(D) use multiplication by a constant factor (unit rate) to represent proportional relationships.
8.3(A) compare and contrast proportional and non-proportional relationships.
8.3(B) estimate and find solutions to application problems involving percents and proportional relationships such as similarity and rates.
8.7(B) use geometric concepts and properties to solve problems in fields such as art and architecture.
8.10(A) describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally.
As a result of participating in this lesson, the students will be introduced to the concept of scaling and explore the connections between ratios, and proportions. The students will use estimation to measure and calculate lengths and perimeters of furniture in the classroom by applying the concepts of ratio and scale. They would produce a scaled drawing of the floor plan of the classroom. The skills learnt and concepts explored from this exercise will assist in furthering their final Wonders of the World in My hands project.
Students will be able to:
understand that ratios are used to create scale models of buildings and other structures.
calculate scale using ratios.
observe how representations of objects can be scaled to be bigger or smaller
create a drawing to scale in two dimension and extend it to three dimensions
understand the principles of ratio and apply these principles in the solution of problems.
III. Resources, materials and supplies needed
0.25 inch graph paper
Pencils and erasers
Ruler (metric or inches)
Tape measures
Maps with scales of
IV. Supplementary materials, handouts.
30 copies of activity sheet
Transparency copy of activity sheet
Transparency copies of Skyscrapers of Dallas City
Transparency of Skyscrapers
of A
chemistry model of an atom Transparency of Drawing
1964 for Still Life No. 42 by Tom Wesselmann
(1964) V.
Safety Issues None VI.
Accommodations for learners with special needs (ELLs, Special Ed, 504, G&T)
None
Five-E Organization Teacher Does
Probing Questions
Student Does Engage: Teacher begins by asking students the following
question:
What drawings have you seen that represent something very large in real
life? Teacher puts up a transparency copy of skyscrapers
of famous
If students say bigger, the teacher asks …
How could we find the actual size of the objects in the picture? Teacher asks students to quickly sketch
a rough drawing of the perimeter of the classroom. Teacher asks: Teacher explains that a scale drawing
is an enlarged or reduced drawing of an object. Maps and floor plans are
smaller than the actual size, but they still accurately represent the
larger object. Teacher asks:
Teacher shows class a chemistry model of an atom and asks if the model
is larger or smaller than what it is representing? To understand scale, we have to use what we know about ratios and
proportion. Teacher
gives an example similar to the following: 1 gallon of paint will cover
4 bedroom walls, Teacher asks: Teacher
tells students to look at their rough sketch of the classroom.
Teacher asks… Teacher explains that a scale drawing
uses ratio to ensure that all ratios of lengths in the drawing to their
actual lengths are the same, i.e., that they are a true proportion.
Back to the Critical questions that will
establish prior knowledge and create a need to know
Can anyone tell me exactly how tall and how wide these buildings would
be in real life?
Can anyone tell me if the buildings are at least bigger or smaller than
they are in the painting?
How do you know?
What additional information do we need to know to determine if they are
larger or smaller than their actual size?
Could an architect use your drawing to build an identical room? Why?
How would their drawings be more accurate?
Based on the definition of scale drawing, can anyone tell me what a scaled
model< style='font-weight: normal'> is?
Can you give me examples of scaled models?
Is this chemistry model is a scale model? Teacher asks:
What is ratio?
What is a proportion?
What is the difference between ratio and proportion?
How do we write the ratio?
If 1 gallon covers 4 walls, then show how many gallons cover 8 walls?
Are the ratios of lengths of the walls in your drawing to the actual lengths
of the walls equal?
In other words, are all the ratios a true proportion?
How could we find the actual size of the Frost buildings in
If the buildings in the picture are 1/33rd of the actual size of the real
buildings, what does this ratio tell you about the actual size of the
buildings? Expected Student Responses/Misconceptions Students are listening attentively and answering questions
as follows.
Answers may include maps, floor plans, buildings, blueprints, and manufacturing
ideas.
No.
Students will probably say bigger.
Because the painting is probably not as large as the building.
We need to know the dimensions of the painting.
Responses may vary. (The answer is scale, but the students are not expected
to know this yet.) (Students brainstorm ideas.)
No, the picture is not exactly similar to the room.
A scaled model might be a 3 dimensional model that is smaller
or larger than the real object.
Students’ responses vary.
Smaller.
No. It is not an accurate model of the atom.
A ratio is a comparison between two numbers.
Proportion is a mathematical sentence that states that 2 ratios are equal.
the ratio: 1 to 4 or 1:4
2.
the proportion 1 gallon = 2 gallons. 4
walls 8 walls
No.
Responses may vary.
By using scale.
That the buildings are 33 times bigger in real life. Decision
Point Assessment: The teacher ascertains preexisting knowledge wrt ratio
and proportions and their level of understanding of scale based on their answers
to questions. Some review with more examples on maps and other pictures might
help students relate better.
Explore: Teacher explains to students that they will make a
scale drawing of the furniture in the classroom on graph paper (use as
many sheets as they determine to be necessary). Teacher
divides students into teams of 3. Teacher explains that each team will
measure the surface areas of 3 objects in the classroom (e.g. desks, tables,
closets) The class may choose to use either metric or English measurements. Teacher then explains that once each team has recorded all of their
data, they will decide on the scale of their floor plan. Teacher constructs a class data table on the board with three columns Approx. Time: 30 mins Critical questions (formative) Each team must choose different objects. How do
you think the floor plan would look like? The teacher walks around asking questions and making
sure that all students are on task and participating in the activity. Expected Student Responses/Misconceptions Students form groups of 3 or 4 with access to
tape measures, pencils, graph paper, and paper to record their measurements. Students choose their 3 objects and measure and record and draw their
objects. Our floor plan will show
objects in the classroom from a bird’s eye view. Each group decides on a scale for their
floor plan. Explain: Teacher asks students to come up to the board to fill in the class
data table. Teacher then calls on each group to Teacher
asks: Teacher illustrates how
to draw an object to scale. Using a ruler draw a square on the board with
sides of 10 inches Teacher asks: Teacher
explains that an object is not simply cut in half when it is scaled down.
The whole object is shrunk proportionally, meaning that it doesn’t change
shape but is reduced to a smaller size. Teacher
explains that when an object is scaled down, the length of its sides must
be reduced by the same amount. Teacher asks: Teacher puts up transparency of Drawing 1964 for Still Life and
tells students that the actual height of the Carlsberg bottle in the picture
is 23 cm. Teacher asks:
Teacher asks the class
Teacher tells students to use their scaled measurements, rulers, and
graph paper to draw the objects their respective teams measured on an
8.5 by 11inch paper. For reference on how to draw
a scale, the teacher lays out a few maps with scales on them. Approx. Time: 20 mins Critical questions that will allow you
to help students clarify their understanding and introduce information
related to concepts to be learned Briefly describe to the
rest of the class your floor plan and explain how you chose and used the
scale for the objects you measured. What are
the proportions that would allow us to draw the entire room with its objects
on one sheet of 8.5 by 11 graph paper? How
might you use this square to draw another that is half its size? What are three ways of expressing the ratio of the small square to
the large square? If the height
of the bottle in the painting is 69 cm, what is the scale of the drawing?
Can you suggest a scale
to use such that the classroom floor plan with its objects would fit on
an 8.5 by 11inch paper? Do you all agree with
the suggestions? Remember to include a title,
labels, and scale. Expected Student Responses/Misconceptions
Students come up to the board to fill
in their data, listen attentively and answer questions. ·
Students’ answers vary.
Students’ answers vary.
·
Student’s answers vary.
5:10, 5 to 10, or 5/10,
69/23 or 3/1 or 3:1 or
3 to 1.
Students respond with suggestions for the class to use.
Students are all converting their measurements and drawing
their objects using the scale agreed upon by the class.
Each team will turn in one paper. Evaluation(Decision Point Assessment)
The
teacher walks around and listens to the student’s presentations of their
floor plans to evaluate their ability to apply the concepts of scale
and ratio to their calculations. Each group converts their measurements into
scaled equivalents and creates their floor plans. Extend / Elaborate: Learning
Experience(s) As students complete their drawings, teacher encourages
them to calculate the perimeter of the objects and to
When all the groups
are finished teacher asks the following: Teacher explains
about objects that have been scaled down proportionally… Approx.
Time: 15 mins Critical questions that will allow you
to decide whether students can extend conceptual connections in new situations
Think about the relationship between the perimeter of the
objects in your drawing and the actual perimeter of the objects.
If we know that each side of an object has been scaled
down by a third, how would we find the scaled down perimeter?
If an object has been scaled down proportionally, how will
the perimeter of the object have scaled down
Expected Student Responses/Misconceptions Students
are calculating the perimeters of their objects and thinking about how
the concepts they have learned apply to perimeter and apply to their project.
Students’ responses vary.
Students say that it is by the same ratio.
Evaluate: Lesson
Objective(s) Learned (WRAP
–UP at end) -> Summarize Teacher tries to make students draw connections
between new concepts learnt and overall goals Based on the students’ verbal
responses, the teacher will evaluate the students’ ability to apply what
they learned to the concept of perimeter and their ability to apply the
concepts to their final project.
Approx. Time: 5 mins Critical questions that will allow you
to decide whether students understood main lesson objectives
How does what we have learned today have to do with your design and construction
project?
What are some examples of where scales are found and what do they measure?
What are some more examples of how money can be turned
into scale?
Why is it important to maintain the same scale for each
measurement you record when making your monument model? Expected Student Responses/Misconceptions Answers might include the following:
Scale will help us design our design model on a smaller
scale.
It will help us with the blueprints
of our models.
It will help us figure out the lengths,
perimeters, areas and volumes of the world wonder that we are researching.
So that your model will be an accurate representation of
the real monument. As a final
assessment, have students write a minute paper on:
1) What they thought was the most important thing/concept of the lesson?
2) How will that help them in their final project?
3) What they were still unsure about?
Take-Home Activity Sheet: Architects in Action Home Measurements Name:______________________ Directions: Create a floor plan of
your classroom. Your floor plan should represent all the major objects in
the room. Use the data table below to record your information. Then draw your room on
graph paper. Room: ______________________ OBJECT MEASUREMENT SCALE
RATIO SCALED
MEASUREMENT EXAMPLE WALL 12
X 12 1
INCH : 1 FOOT 12
INCHES
Learning Experience(s)
Approx. Time: 20 mins
Why not?
Learning Experience(s)
Learning Experience(s)
which is a fraction that reduces to 1/2.