Curriki

Counting Cogs

Website Address:https://www.curriki.org/oer/Counting-Cogs-140746
member-name
Learning RegistryLearning RegistryDistrict of Columbia, District of Columbia, US,
November 11, 2016
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Type:

Other

Description:

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).

Subjects:

  • Mathematics > General
  • Education > General

Education Levels:

  • Grade 1
  • Grade 2
  • Grade 3
  • Grade 4
  • Grade 5
  • Grade 6
  • Grade 7
  • Grade 8
  • Grade 9
  • Grade 10
  • Grade 11
  • Grade 12

Keywords:

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

Language:

English

Access Privileges:

Public - Available to anyone

License Deed:

Creative Commons Attribution Non-Commercial Share Alike

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None
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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).
↓http://nrich.maths.org/6966

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