Download Ballpark Figure

“Ballpark Figure”
Overview
Enduring Understanding:
• (6)ME03: Use systematic procedures to measure, describe, and compare the
area of rectangles and right triangles – identify area as the attribute to be
measured, select and use appropriate unit for area, select and use a tool that
matches the unit chosen, count to determine the number of units, use formulas to
find the perimeter and area of rectangles and right triangles.
• (6)ME04: Identify situations in which estimated measurements are sufficient;
estimate area of rectangles and right triangles.
Essential Questions:
• What is perimeter?
• How do you find perimeter of a rectangle?
• What is the formula for finding perimeter?
• How are formulas used?
• What is area?
• How do you find area of a rectangle?
• How do you find area of a right triangle?
• What is the formula for finding area of a rectangle?
• What is a situation in which an estimate would be sufficient?
• What is a situation in which an exact measurement would be needed?
Prerequisites for Lesson:
• Vocabulary:
• perimeter, area, surface area, rectangle, linear, right triangle, length,
width, unit, square unit, feet/foot, square feet, estimate, formula for
perimeter, formula for area of rectangle, formula for area of triangle, exact
measurement, predictions, dimensions, grid, label, partially, compile, sum,
product, warning track
• Skills :
• Students should be able to identify or describe pictorial representations of
objects or figures illustrating area measurements. (5)ME01
• Students should be able to identify or draw representations of figures to
illustrate the understanding of the difference between area and perimeter.
(5)ME01
• Students should be able to draw, describe, and/or compare perimeter and
area and label measurements to show an understanding that perimeter is
measured Iinear units and area in square units. (5)ME02
• Students should be able to explain or show how the size of a linear unit
affects a square unit. (5)ME02
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•
Concepts:
• Students should be able to solve a problem by doing the following:
• show understanding of the problem by selecting and organizing
relevant information;
• use strategies and procedures appropriately to construct a solution;
• (5)SR02 answer the problem with a viable solution that is
mathematically correct and answers the question(s) asked.
• (5)CU02 Students should be able to clearly explain or describe
mathematical ideas, facts, properties, procedures, or strategies in a way
that is appropriate for a given purpose and/or audience using
mathematical language and notation.
Related GLEs:
EALR 1.2: Understand and apply concepts and procedures from measurement.
GLE 1.2.4 (5) Use a systematic procedure to measure and describe the area
of rectangles or triangles.
GLE 1.2.5 (5) Use formulas to determine perimeter and area of rectangles and
right triangles.
GLE 1.2.6 (5) Understand and apply strategies to obtain reasonable estimates
of angle measurements and areas of rectangles and right
triangles.
GLE 2.2.1 (6) Select and use relevant information to construct solutions.
GLE 2.2.2 (6) Apply mathematical concepts and procedures from number
sense, measurement, geometric sense, and/or probability and
statistics to construct solutions.
GLE 2.2.3 (6) Apply a variety of strategies and approaches to construct
solutions.
GLE 2.2.4 (6) Determine whether a solution is viable, mathematically correct,
and answers the question(s) being asked.
GLE 4.2.3 (6) Use mathematical language to explain or describe numerical,
measurement, geometric, probability, and/or statistical ideas
and information in ways appropriate for audience and purpose.
GLE 5.3.1 (6) Understand that mathematics is used extensively in daily life
outside the classroom.
Test Specs: We suggest you read ME01 (Grade 6), ME03 (Grade 6), ME04 (Grade 6),
SR02 (Grade 6), SR04 (Grade 6), CU01 (Grade 6), CU02 (Grade 6), MC01 (Grade 6)
prior to teaching the lesson, paying specific attention to . . . .
ME01 (Grade 6)
d. Items may ask the student to use area or volume to compare rectangles, right
triangles, or rectangular prisms.
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ME03 (Grade 6)
a. Items may ask students to identify or describe the appropriate units and/or tools
for measuring length, area, or volume.
b. Items may ask students to count or compare the attribute to the units on the
measurement tool to determine the number of units.
c. Items may ask students to use and/or describe procedures for measuring length,
perimeter, and area of a rectangle or right triangle and/or the volume of a
rectangular prism:
• identify the attribute to be measured;
• select and use appropriate unit of measurement;
• select and use a tool that matches the unit chosen;
• count or compare the attribute to the units on the tool to determine the
number of units.
d. Items may ask students to determine whether measurement has been done
correctly in a given situation.
e. Items may ask students to find the perimeter and/or area of a rectangle or right
triangle.
ME04 (Grade 6)
a. Items may ask students to determine when or whether estimation is appropriate
in a given situation.
b. Items may ask students to determine if a given angle, area, or volume
measurement is reasonable in a situation.
c. Items may ask students to identify or describe a procedure that would be an
appropriate way to estimate angle measures, area, or volume.
d. Items may ask students to explain why they would use estimation rather than an
exact measurement.
f. Items may ask students to estimate measures of angles or areas of rectangles
and/or triangles.
SR02 (Grade 6)
a. Items may ask students to solve a problem by doing the following:
• show understanding of the problem by selecting and organizing relevant
information;
• use strategies and procedures appropriately to construct a solution;
• answer the problem with a viable solution that is mathematically correct
and answers the question(s) asked.
b. Items may ask students to determine whether a given solution shows the use
and organization of relevant information.
c. Items may ask students to determine whether a given solution shows the use of
strategies and procedures that are appropriate.
d. Items may ask students to determine whether a given answer is a viable solution,
mathematically correct, and/or answers the question(s) asked in a problem
situation.
SR04 (Grade 6)
a. Items may ask students to draw a conclusion and use evidence or information
from a given situation to support the conclusion.
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CU01 (Grade 6)
c. Items may ask students to extract and explain or describe mathematical
information from various sources such as pictures, symbols, text, tables, charts,
graphs, diagrams, and models for a purpose.
CU02 (Grade 6)
c. Items may ask students to clearly explain or describe mathematical ideas, facts,
properties, procedures, or strategies in a way that is appropriate for a given
purpose and/or audience using mathematical language and notation.
MC01 (Grade 6)
a. Items may ask students to use concepts and procedures from two or more
mathematics concept strands - number sense, measurement, geometric sense,
probability and statistics, and algebraic sense.
Materials Needed:
Per student or group based on teacher preference:
• “Ballpark Figure” teachers packet
• “Ballpark Figure” student worksheet packet
• City Park site plan of land to be donated
• Proposed Baseball field site plan printed to scale on 11’ x 17” paper
• 4 acetate grids for each group of two or individual depending on working size
• Transparent tape – 3 or 4 dispensers
• 3 overhead pens for each group (preferred colors; green, brown and red)
• Scratch paper
• Pencil
• Calculators
Suggested Teaching Sequence:
This lesson should be broken into three parts. Part #1, problems #1-10 deal with
the students discussing the formulas for finding area and perimeter, when to estimate
and when to use an exact measurement, and predicting and finding the area of a given
shape, the donated land in this case. Part #2, problems #11-13 has the students
predicting the area of a baseball field. Students are then asked to use grid overlays to
estimate the area of specific parts of the baseball field. Students are also asked to
predict and estimate the perimeter of the baseball field. Part #3, problems #14-27 the
students use the estimated figures for the area of the baseball field, and use given data
to determine what it will cost for the city to construct the new field. Throughout the three
parts of the lesson students are engaged in the scenario of trying to determine if a city
budgeted enough money to build a new baseball field on some donated land.
Modifications for Differentiated Instruction:
• Simplifications
Difficulty level of this lesson can be varied significantly by the amount of
independence expected of students. Students can be grouped so additional
teacher modeling, scaffolding, and monitoring can be provided. The problems for
the cost activity can be divided and shared in the small group.
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Suggested Future Experiences:
GLE 1.2.1 Understand how changes in one linear dimension affect other linear
measurements and area of rectangles, triangles and circles. (7)ME01
GLE 1.2.1 Understand how a change in one linear dimension affects surface area
and volume of rectangular prisms and cylinders and how changes in
two linear dimensions affect perimeter and area of rectangles. (8)ME01
GLE 1.2.5 Use formulas to determine measurements related to circles, triangles,
and rectangular prisms. (7)ME05
Assessments: Incorporated throughout the lesson and additional assessment items
are available as a separate document.
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