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).


  • Mathematics > General
  • Education > General

Education Levels:

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Grade 3,Grade 6,NSDL,Grade 4,Factors,Critical thinking,oai:nsdl.org:2200/20140728161033244T,Express regularity,Representation,Number concepts,Social Sciences,Arithmetic,Analyze and persevere,Concept formation,Process skills,Number and operations,Visual representation,Mathematical language,Word problems,Grade 5,Ratio and proportion,Multiplication,Real world applications,Informal Education,Whole numbers,Middle School,Problem solving,NSDL_SetSpec_ncs-NSDL-COLLECTION-000-003-112-027,Reason abstractly,Practice Standards,Elementary School,Reason quantitatively,Operations,Mental calculation,Upper Elementary,Communication,Mathematics,Connections,Engineering,Engineering mathematics,Critique reasoning,Education,Construct arguments,Reasoning



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