Transcript The Art of Asking Good Questions

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
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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
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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
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Weight
 Area
 Length and Perimeter
 Volume and Capacity
Weight
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I went shopping and found a one pound box
of Snowflake Sugar Cubes for $1.70. A 1kilogram box of White Cloud Sugar Cubes
offered a better buy. How much might the
White Cloud Sugar Cubes have cost?
Weight
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Give the students the conversion (1 pound =
0.454 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
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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
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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
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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
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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
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A television screen measures 41 inches
along its diagonal. What might the length
and width of the screen be?
Length and Perimeter
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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
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Could $1 million fit into a standard-size
briefcase? Assume the largest denomination
in circulation is $100.
Volume and Capacity
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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
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Using your protractor, can you draw three
adjacent angles that show at least one acute,
one right, one obtuse and on reflex angle?
Geometry
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Find a quadrilateral that can be inscribed in
a circle and one that cannot
Geometry
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It is possible to inscribe only parallelograms
that are also rectangles
Geometry
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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
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This question will help students understand
that all congruent shapes are also similar
Geometry
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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
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Do students understand that the length of
the lateral surface must be the same as the
circumference of the base?