- \r\n \t
- Module 3: Measurement<\/strong> can be combined with Module 5: Fractals<\/strong>, completed together in a week's time.<\/li>\r\n \t
- If you want to go into more depth with fractal dimension, teach Module 5: Fractals<\/strong> after\u00a0Module 8: Growth Models<\/strong>\u00a0and\u00a0Module 9: Finance<\/strong>, where logarithms are introduced and practiced in applications. Computations of fractal dimension in\u00a0Module 5: Fractals<\/strong> are presented as a calculator exercise, and therefore do not require knowledge of properties of logarithms.<\/li>\r\n \t
- Module 7: Voting Theory<\/strong> can be taught any time after Module 2: General Problem Solving<\/strong>. Computation in this module is minimal, where the focus is on the use of logic and following a set of prescribed practices for tallying ballots.<\/li>\r\n<\/ul>\r\nWe recommend NOT doubling up the following modules, as they are more dense than other modules, or provide important foundational concepts:\r\n
- \r\n \t
- Module 2: General Problem Solving:<\/strong>\u00a0foundational<\/li>\r\n \t
- Module 4: Graph Theory:<\/strong>\u00a0dense<\/li>\r\n \t
- Module 6: Set Theory and Logic:<\/strong>\u00a0dense<\/li>\r\n \t
- Module 12: Probability:<\/strong>\u00a0dense<\/li>\r\n<\/ul>","rendered":"
![\"icon](\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2025\/2017\/07\/10205220\/stopwatch.png\")
The Math for Liberal Arts textbook contains twelve modules\u2014roughly one module per week for a 12-week semester.<\/p>\nIf you plan to modify the pace of the course or rearrange the order of the modules, please keep the following notes in mind to ensure your students are well prepared for new concepts:<\/p>\n
- \n
- Module 1: Historical Counting Systems<\/strong> can be skipped without affecting future modules.<\/li>\n
- Module 2: General Problem Solving<\/strong> should be taught either first or second.<\/li>\n
- Module 3: Measurement<\/strong>\u00a0is best taught immediately after\u00a0Module 2: General Problem Solving<\/strong>.<\/li>\n
- Module 4: Graph Theory<\/strong> can be skipped without affecting future modules.<\/li>\n
- Module 5: Fractals<\/strong> can be skipped without affecting future modules.<\/li>\n
- Module 7: Voting Theory<\/strong> can be skipped without affecting future modules.<\/li>\n
- Module 8: Growth Models<\/strong> should be taught before Module 9: Finance<\/strong>.<\/li>\n
- Module 10: Statistics – Collecting Data<\/strong>\u00a0should be taught before Module 11: Statistics – Describing Data<\/strong>.<\/li>\n
- Module 12: Probability<\/strong> should be taught after\u00a0Module 10: Statistics – Collecting Data<\/strong>\u00a0and\u00a0Module 11: Statistics – Describing Data<\/strong>.<\/li>\n<\/ul>\n
A few additional notes involving possible adjustments:<\/p>\n
- \n
- Module 3: Measurement<\/strong> can be combined with Module 5: Fractals<\/strong>, completed together in a week’s time.<\/li>\n
- If you want to go into more depth with fractal dimension, teach Module 5: Fractals<\/strong> after\u00a0Module 8: Growth Models<\/strong>\u00a0and\u00a0Module 9: Finance<\/strong>, where logarithms are introduced and practiced in applications. Computations of fractal dimension in\u00a0Module 5: Fractals<\/strong> are presented as a calculator exercise, and therefore do not require knowledge of properties of logarithms.<\/li>\n
- Module 7: Voting Theory<\/strong> can be taught any time after Module 2: General Problem Solving<\/strong>. Computation in this module is minimal, where the focus is on the use of logic and following a set of prescribed practices for tallying ballots.<\/li>\n<\/ul>\n
We recommend NOT doubling up the following modules, as they are more dense than other modules, or provide important foundational concepts:<\/p>\n
- \n
- Module 2: General Problem Solving:<\/strong>\u00a0foundational<\/li>\n
- Module 4: Graph Theory:<\/strong>\u00a0dense<\/li>\n
- Module 6: Set Theory and Logic:<\/strong>\u00a0dense<\/li>\n
- Module 12: Probability:<\/strong>\u00a0dense<\/li>\n<\/ul>\n\n\t\t\t
\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t
\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCC licensed content, Original<\/div>- Pacing. Provided by<\/strong>: Lumen Learning. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul>CC licensed content, Shared previously<\/div>
- Stopwatch. Authored by<\/strong>: Adrien Coquet, FR. Provided by<\/strong>: Noun Project. Located at<\/strong>: https:\/\/thenounproject.com\/term\/stopwatch\/1094680\/<\/a>. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Stopwatch\",\"author\":\"Adrien Coquet, FR\",\"organization\":\"Noun Project\",\"url\":\"https:\/\/thenounproject.com\/term\/stopwatch\/1094680\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Pacing\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2912","chapter","type-chapter","status-publish","hentry"],"part":2906,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/2912","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":15,"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/2912\/revisions"}],"predecessor-version":[{"id":3059,"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/2912\/revisions\/3059"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/pressbooks\/v2\/parts\/2906"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/2912\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/wp\/v2\/media?parent=2912"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapter-type?post=2912"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/wp\/v2\/contributor?post=2912"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/wp\/v2\/license?post=2912"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- Module 4: Graph Theory:<\/strong>\u00a0dense<\/li>\n
- If you want to go into more depth with fractal dimension, teach Module 5: Fractals<\/strong> after\u00a0Module 8: Growth Models<\/strong>\u00a0and\u00a0Module 9: Finance<\/strong>, where logarithms are introduced and practiced in applications. Computations of fractal dimension in\u00a0Module 5: Fractals<\/strong> are presented as a calculator exercise, and therefore do not require knowledge of properties of logarithms.<\/li>\n
- Module 2: General Problem Solving<\/strong> should be taught either first or second.<\/li>\n
- Module 4: Graph Theory:<\/strong>\u00a0dense<\/li>\r\n \t
- If you want to go into more depth with fractal dimension, teach Module 5: Fractals<\/strong> after\u00a0Module 8: Growth Models<\/strong>\u00a0and\u00a0Module 9: Finance<\/strong>, where logarithms are introduced and practiced in applications. Computations of fractal dimension in\u00a0Module 5: Fractals<\/strong> are presented as a calculator exercise, and therefore do not require knowledge of properties of logarithms.<\/li>\r\n \t