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 M6G, 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.

M6G1. Students will further develop their understanding of plane figures.

a. Understand the meaning of line and rotational symmetry.

b. Demonstrate understanding of similar plane figures and the scale factor between them.

b. Interpret and sketch simple scale drawings.

c. Solve problems involving scale drawings.

Line symmetry and rotational symmetry:

• completing quilt designs with line symmetry,
• completing quilt designs with rotational symmetry,

Scale drawings:

• treasure map, draw your own treasure map,

Similar shapes:

• Discovering/describing and using scale factors and relative sizes: 1) the scale factor between corresponding lengths of two similar shapes is the same for all corresponding lengths and 2) the relative sizes of different lengths within an object are the same as the relative sizes of corresponding lengths in a similar object,
• Drawing similar rectangles 1, drawing similar rectangles 2,
• describing and using scale factors and relative sizes 2,
• describing and using scale factors and relative sizes 3,
• scale models, scaling up, and scaling down,
• similar shapes, scaling up, scaling down,
• Activity on using similar rectangles and "sighting" to determine heights of tall objects. On cardstock, make rectangles that are 2 times as long as wide and others that are 3 times as long as wide. Children can use a rectangle to "sight" an object -- the child holds the rectangle up to her eye with two sides of the rectangle parallel to the ground, she then positions herself so that she sees the top of the object she is "sighting" aligned with the top far corner of the rectangle and the bottom of the object aligned with the lower far corner of the rectangle (this takes some practice). Go outside and use the recording sheet 1 when "sighting" tall objects such as flag poles or lamp poles.
• Activity on using similar triangles and shadow lengths to determine heights of tall objects. Use recording sheet 2.

M6G2. Students will further develop their understanding of solid figures.

a. Compare and contrast right prisms and pyramids.

b. Compare and contrast cylinders and cones.

c. Interprets and sketch front, back, and side views of solid figures.

d. Create nets for prisms, cylinders, pyramids, and cones.

Sketching rectangular prisms:

• sketching rectangular prisms on isometric dot paper and finding their volumes,
• sketch your own boxes and find their volumes,
• more sketching and volume finding,

Creating nets for cylinders (not including top and bottom):

• Making a label for a can (and other problems about diameter and circumference of circles)
• Graph paper for the label,
• Making a paper label for a small can,

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