Goliath’s Pencil
Replicas of Goliath’s pencil are around the room. Find out as much as you can about Goliath by knowing
that he uses this pencil. Justify your findings.
Goliath’s Pencil (Teacher Notes)
Modified from NCTM MTMS Vol. 14, No. 7, March 2009
Make large copies of this pencil or one similar.
Purpose: As students are thinking about using this piece of information to find out things about Goliath
the will use what they know about scaling up and proportions to determine different sizes about the
giant. This should also bring out the idea that there is a difference with scaling height and scaling weight
using scale factor.
Core standards: 7.G.1; math practices—Reason abstractly and quantitatively, Construct viable
arguments and critique the reasoning of others, Attend to precision; Related standards: 7.RP.3
Launch: Read the prompt on the student page. You might want to brainstorm some ideas of things you
could find out just by knowing Goliath uses a pencil of that size. Students should suggest things like:
Goliath’s height; weight; size of feet, hands, desk, etc. Have the students brainstorm individually and
then in pairs as they work to find measurements for the giant.
Explore: If students are struggling with a starting point, then go back to a list that you made with the
whole class, or begin making one with the student. While students are working, look for pictorial
representations that would relate Goliath to themselves. Make sure that students that are procedurally
using “cross multiply” can articulate why their method works. Watch for students that use a scale factor
and those that use proportional reasoning (like 4 times as long.) Some misconceptions that may arise
are adding the difference of Goliath’s pencil rather than the multiplicative relationships, measurement
issues between length to weight, and what are the students comparing to Goliath’s pencil.
Discuss: Have a student present that scaled up with proportional reasoning and then move to some one
that used scale factors. During the discussion you might want to have students connect the procedural
method of cross multiplying to the scale factor. Make sure students are justifying their answers and
explaining why Goliath’s measurements might be different from team to team.