Problems and tasks for 6th graders

by Sybilla Beckmann, Department of Mathematics, University of Georgia

The linked problems and tasks are ones I gave (or modifications of ones I gave) to the average class of 6th graders I taught every day during the 2004/2005 academic year at Clarke Middle School, a public school in Athens, Georgia. These problems and tasks address portions of the Georgia Performance Standard M6M, which is shown below. All linked problems and tasks are copyright Sybilla Beckmann, 2004, 2005. Teachers may freely copy and use these problems and tasks with their students. The Georgia Department of Education may use these problems and tasks for the Georgia Performance Standards.

M6M1. Students will convert from one unit to another within one system of measurement (customary or metric) by using proportional relationships.

M6M2. Students will use appropriate units of measure for finding the perimeter, area, and volume and express the answer using the appropriate unit.

Determining area by cutting apart and rearranging:

• activity: shapes to cut out, grid to paste the cut apart and reformed shapes on;
• determining area by cutting apart and rearranging 1,
• determining area by cutting apart and rearranging 2,
• determining the area of a triangle by considering it as half the area of an associated rectangle: by actually cutting and glueing, by thinking about cutting (if necessary) and glueing: example 1, example 2,
• determining the area of a parallelogram by cutting apart and rearranging: by actually cutting and glueing, by thinking about cutting and glueing,

Length and area:

• Units of length and of area,
• units of length and area 2,
• expressions for the total number of objects in a "floor plan" shape, part 2: finding areas and perimeters of floor plans,
• Perimeter and area 1, perimeter and area 2, perimeter and area 3,
• perimeter and area 4, perimeter and area 5, perimeter and area 6,
• creating shapes given the area or given the perimeter,

M6M3. Students will determine the volume of fundamental solid figures (right prisms, cylinders, pyramids and cones).

a. Determine the formula for finding the volume of fundamental solid figures.

b. Compute the volume of fundamental solid figures.

c. Estimate the volume of a simple geometric solid.

d. Solve application problems involving the volume of fundamental solid figures.

Developing the volume formula for prisms:

• Finding the volume of an open top box made from a pattern (net),
• building prisms with blocks and writing expressions using multiplication for their volumes,
• volumes of prisms,
• developing the volume formula for prisms by thinking of prisms as made of layers of cubes,
• perimeter, area, and volume,
• perimeter, area, and volume 2,
• how many bricks are in a stack?,

M6M4. Students will determine the surface area of solid figures (right prisms and cylinders).

a. Find the surface area of a right prism and cylinder using manipulatives and constructing nets.

b. Compute the surface area of a right prism and cylinder using formulae.

c. Estimate the surface area of a simple geometric solid.

d. Solve application problems involving surface area of right prisms and cylinders.

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