The Art of Asking Good Questions Maria Mitchell Based on Good Questions for Math Teaching Why Ask Them and What to Ask By Lainie Schuster and Nancy Canavan Anderson

Content Strands Measurement questions can be asked in conjunction with: Geometry Collect and analyze data Proportional reasoning Place value and decimal fractions Choosing appropriate measurement use of both customary and metric systems

NCTM Measurement Standard for Grades 6–8 Understand both metric and customary systems of measurement; Understand relationships among units and convert from one unit to another within the same system; Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume. Apply appropriate techniques, tools, and formulas to determine measurements Use common benchmarks to select appropriate methods for estimating measurements; Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision; Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes; Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders; Solve problems involving scale factors, using ratio and proportion; Solve simple problems involving rates and derived measurements for such attributes as velocity and density.

Measurement Weight Area Length and Perimeter Volume and Capacity

Weight I went shopping and found a one pound box of Snowflake Sugar Cubes for $1.70. A 1- kilogram box of White Cloud Sugar Cubes offered a better buy. How much might the White Cloud Sugar Cubes have cost?

Weight Give the students the conversion (1 pound = kilograms) so that they can estimate a possible price. Students should realize that 1 pound is about the same as half of 1 kilogram.

Weight Sheila emptied her piggy bank, wrapped her coins, and put them in a bag to go to the bank. The bag weighed 20 pounds. How much money do you think Sheila had in coins?

Area A ball of dough is rolled out into a circle with a 12 inch diameter. How many cookies with a diameter of 2.5 inches can be made from this dough?

Area I wrapped a rectangular box in a piece of wrapping paper that was 11 inches by 17 inches. I had no paper left over but did have some minor overlaps. What might have been the dimensions of my box?

Length and Perimeter Juana is 5.6 feet tall and Jeremy is 5.8 feet tall. Liza is taller than Juana but shorter than Jeremy. How tall might Liza be in feet and inches?

Length and Perimeter A television screen measures 41 inches along its diagonal. What might the length and width of the screen be?

Length and Perimeter A fifteen foot ladder has a warning that reads “Bottom of ladder should rest between 3 and 4 feet from the wall.” What are some heights that a person standing on the ladder can reach?

Volume and Capacity Could $1 million fit into a standard-size briefcase? Assume the largest denomination in circulation is $100.

Volume and Capacity You write on paper every day in school. If you were to box up all of the pieces of paper you’ve used since entering school, what fraction of the room do you think the boxes would fill?

Geometry Using your protractor, can you draw three adjacent angles that show at least one acute, one right, one obtuse and on reflex angle?

Geometry Find a quadrilateral that can be inscribed in a circle and one that cannot

Geometry It is possible to inscribe only parallelograms that are also rectangles

Geometry I drew a set of seven triangles. Five were similar to one another, three were congruent, and two were neither similar nor congruent to any other. What might these triangles have looked like? Draw the triangles and label their side lengths.

Geometry This question will help students understand that all congruent shapes are also similar

Geometry Draw and label the dimensions of a flat pattern for a cylinder. Label the radius of the base and the length and width of the lateral surface.

Geometry Do students understand that the length of the lateral surface must be the same as the circumference of the base?