What Can I Make with 30 Centimeters?
Connections to the mathematics TEKS
(3.11)
Measurement. The student selects and uses appropriate units and
procedures to measure length and area.
The student is expected to:
(A)
estimate and measure lengths using standard units such as inch,
foot, yard, centimeter, decimeter, and meter
(B)
use linear measure to find the perimeter of a shape
(C)
use concrete models of square units to determine the area of
shapes
(3.13) Measurement. The student applies measurement concepts.
The student is expected to:
measure to solve problems involving length, area, temperature, and time
(3.15) Underlying processes and mathematical tools. The student applies Grade
3 mathematics to solve problems connected to everyday experiences and
activities in and outside of school.
The student is expected to:
(B)
use a problem-solving model that incorporates understanding the
problem, making a plan, carrying out the plan, and evaluating the
solution for reasonableness
(D)
use tools such as real objects, manipulatives, and technology to
solve problems
(3.17) Underlying processes and mathematical tools. The student uses logical
reasoning to make sense of his or her world.
The student is expected to:
(A)
make generalizations from patterns or sets of examples and non
examples
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Mathematics overview
Students create polygons with perimeters of 30 centimeters, use the centimeter
grid paper to determine the area of each shape, and organize the shapes to make
generalizations from the patterns they see.
Lesson Overview
Students compare shapes with perimeters of 30 centimeters by categorizing them and
looking for patterns.
Materials
centimeter grid paper
scissors
square tiles
markers
Set-up (to set the stage and motivate the students to participate)
1.
Give students square tiles and have them build a flat shape. Have students discuss the perimeter and area of their shapes. (3.11A, B, C)
2.
Challenge students to build a flat shape with a perimeter of 16 units
(where a unit is equal to the length of the side of one of the square
tiles). Discuss the areas of the different shapes made. Bring students to
the conclusions that different shapes can have the same perimeter, and
shapes with the same perimeters can have different areas. (3.11A, B, C;
3.17A)
3.
Pass out centimeter grid paper and ask students to find as many shapes
as possible that have perimeters of 30 units. Discuss the need to follow
the lines on the grid paper in making the figures in order to be able to
measure the perimeter easily. (3.11B, 3.13, 3.15D)
4.
Have students post their shapes in a display area. (3.15B, D)
5.
Have the class organize the displayed shapes in various ways, such as
from least area to greatest area, and discuss patterns they see. (3.11A,
B, C; 3.15B, D; 3.17A)
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Teacher notes (to personalize the lesson for your classroom)
Guiding Questions
(to engage students in mathematical thinking during the lesson)
•
How do you know the perimeter of this shape is 30 units? (3.11A, B)
•
Are you using the same number of squares (same area) each time to make a
shape with a perimeter of 30 units? (3.11C)
•
What strategies are you using to find your shapes? (3.13; 3.15B, D)
•
What patterns have you found in the shapes? (3.17A)
Teacher notes (to personalize the lesson for your classroom)
Summary Questions
(to direct students’ attention to the key mathematics in the lesson)
•
How is perimeter measured? (3.11A, B)
•
How is area measured? (3.11C)
•
What techniques could you use to change a shape to increase its area while
keeping the perimeter the same? (3.13; 3.15B, D)
•
What techniques could you use to decrease a shape’s area while keeping the
perimeter the same? (3.13; 3.15B, D)
•
Do all the shapes with perimeters of 30 centimeters have the same area? (3.11A,
B, C; 3.13; 3.17A)
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•
Do some of them have the same area? (3.11A, B, C; 3.13; 3.17A)
•
What is similar about the shapes with the smallest area compared to the shapes
with the largest area? (3.13, 3.17A)
•
What statements could you make about using a certain perimeter to enclose the
smallest area? The largest area? (3.13, 3.17A)
•
What strategies did you use to find shapes with perimeters of 30 centimeters?
(3.13; 3.15B, D)
•
Did looking for patterns help you solve the problem? If so, how? (3.17)
Teacher notes (to personalize the lesson for your classroom)
Assessment Tasks
(to identify the mathematics students have learned in the lesson)
•
Have students record their summary statements in a journal.
•
Have students write a description of the activity and what they learned from it.
•
Have students make a shape on the grid paper that has a perimeter of 42
centimeters and encloses the most (or least) area. Students should justify their
choice of shape.
Teacher notes (to personalize the lesson for your classroom)
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Extensions (to lead students to connect the mathematics
learned to other situations, both within and outside the classroom)
Students can investigate questions such as: Can you make your initials with a 30-centimeter perimeter? On the grid paper? What if you had a piece of string 30 centimeters
long? If you had a piece of string 30 centimeters long, how could you use it to find
shapes with 30-centimeter perimeters? Would you still have to follow the lines on the
grid paper? Find some other shapes using the string.
Teacher notes (to personalize the lesson for your classroom)
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