In this investigation students explore the concept of ratios and their relationship with factors and multiples. Given an assortment of cogs (gears) with different numbers of teeth, solvers are asked to find which pairs allow for each tooth of one to fit into every gap of the other, and to form conjectures regarding which pairs would work generally. The problem is well-suited for group work. The Teachers' Notes page offers suggestions for implementation, key questions, student sheets, and links to articles, videos, and an interactive Cog Environment (cataloged separately).
4. Find all factor pairs for a whole number in the range 1—100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1—100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1—100 is prime or composite.
Alignment of the Resource to this Standard
IOER Community Rating: Not Rated
1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
Alignment of the Resource to this Standard
IOER Community Rating: Not Rated
Make sense of problems and persevere in solving them.
Alignment of the Resource to this Standard
IOER Community Rating: Not Rated
Reason abstractly and quantitatively.
Alignment of the Resource to this Standard
IOER Community Rating: Not Rated
Construct viable arguments and critique the reasoning of others.
Alignment of the Resource to this Standard
IOER Community Rating: Not Rated
Look for and express regularity in repeated reasoning.
Alignment of the Resource to this Standard
IOER Community Rating: Not Rated