M5M1.
Students will extend their understanding of area of fundamental geometric plane figures.
a. Estimate the area of fundamental geometric plane figures.
b. Derive the formula for the area of a parallelogram (e.g., cut the parallelogram apart and rearrange it into a rectangle of the same area).
c. Derive the formula for the area of a triangle (e.g. demonstrate and explain its relationship to the area of a rectangle with the same base and height).
d. Find the areas of triangles and parallelograms using formulae.
e. Estimate the area of a circle through partitioning and tiling and then with formula (let pi = 3.14). (Discuss square units as they apply to circles.)
f. Find the area of a polygon (regular and irregular) by dividing it into squares, rectangles, and/or triangles and find the sum of the areas of those shapes.
b. Derive the formula for the area of a parallelogram (e.g., cut the parallelogram apart and rearrange it into a rectangle of the same area).
c. Derive the formula for the area of a triangle (e.g. demonstrate and explain its relationship to the area of a rectangle with the same base and height).
d. Find the areas of triangles and parallelograms using formulae.
e. Estimate the area of a circle through partitioning and tiling and then with formula (let pi = 3.14). (Discuss square units as they apply to circles.)
f. Find the area of a polygon (regular and irregular) by dividing it into squares, rectangles, and/or triangles and find the sum of the areas of those shapes.
M5M2.
Students will extend their understanding of perimeter to include circumference.
a. Derive the formula for the circumference of a circle.
b. Find the circumference of a circle using the formula and pi ≈ 3.14.
b. Find the circumference of a circle using the formula and pi ≈ 3.14.
M5M3.
Students will measure capacity with appropriately chosen units and tools.
a. Use milliliters, liters, fluid ounces, cups, pints, quarts, and gallons to measure capacity.
b. Compare one unit to another within a single system of measurement (e.g., 1 quart = 2 pints).
b. Compare one unit to another within a single system of measurement (e.g., 1 quart = 2 pints).
M5M4.
Students will understand and compute the volume of a simple geometric solid.
a. Understand a cubic unit (u3) is represented by a cube in which each edge has the length of 1 unit.
b. Identify the units used in computing volume as cubic centimeters (cm3), cubic meters (m3), cubic inches (in3), cubic feet (ft3), and cubic yards (yd3).
c. Derive the formula for finding the volume of a cube and a rectangular prism using manipulatives.
d. Compute the volume of a cube and a rectangular prism using formulae.
e. Estimate the volume of a simple geometric solid.
f. Understand the similarities and differences between volume and capacity.
b. Identify the units used in computing volume as cubic centimeters (cm3), cubic meters (m3), cubic inches (in3), cubic feet (ft3), and cubic yards (yd3).
c. Derive the formula for finding the volume of a cube and a rectangular prism using manipulatives.
d. Compute the volume of a cube and a rectangular prism using formulae.
e. Estimate the volume of a simple geometric solid.
f. Understand the similarities and differences between volume and capacity.