{"id":263,"date":"2017-05-01T07:22:50","date_gmt":"2017-05-01T11:22:50","guid":{"rendered":"http:\/\/blog.testdesigner.com\/?p=263"},"modified":"2024-09-18T08:14:03","modified_gmt":"2024-09-18T12:14:03","slug":"how-to-write-higher-order-math-questions","status":"publish","type":"post","link":"https:\/\/www.helpteaching.com\/blog\/how-to-write-higher-order-math-questions.html","title":{"rendered":"How to Write Higher-Order Math Questions"},"content":{"rendered":"<p>As educators, we expect our students to learn and apply math concepts using higher-order thinking skills that go beyond rote learning. With the adoption of the Common Core Math Standards, many of us must do just that, by focusing more in-depth on fewer math concepts. However, writing math problems that require higher-order strategies can be almost as difficult as solving them.<\/p>\n<p>To get started, try writing a lower-level math problem then apply one or more of the following techniques:<\/p>\n<p style=\"text-align: center;\" align=\"center\"><strong>Tips for Writing Higher-Order Math Problems<\/strong><\/p>\n<ul>\n<li>&nbsp;Have students determine and extrapolate a mathematical process or pattern and apply it to an unfamiliar problem or scenario<\/li>\n<li>&nbsp;Ask students to identify and evaluate missing or incorrect information<\/li>\n<li>&nbsp;Challenge students to solve one problem using multiple methods<\/li>\n<li>&nbsp;Consider asking, \u201cGiven ____, what would happen if ____ changed?\u201d questions<\/li>\n<li>&nbsp;Give an answer and a mathematical concept, have students write their own questions or equations that produce the given answer<\/li>\n<li>&nbsp;Ask students to justify their solutions or identify and justify the \u201cbest\u201d or \u201cmost correct\u201d solution from a selection of plausible choices<\/li>\n<li>&nbsp;Write problems that ask for connections between more than one set of information, this could include charts, tables, <a href=\"\/help\/math\/index.htm\" target=\"_blank\" rel=\"noopener\">equations<\/a>, <a href=\"\/blog\/using-math-images-on-test-designer-com.html\" target=\"_blank\" rel=\"noopener\">graphics<\/a>, and data sets<\/li>\n<li>&nbsp;Watch that answers for multiple-choice questions are logical and that the correct choice is not structurally different from the incorrect answers<\/li>\n<li>&nbsp;If you are having difficulty writing a problem, start by constructing questions that incorporate these higher-order key words and concepts: <em>analyze, justify, explain, apply, interpret, compare, estimate, predict, prove, formulate, modify<\/em><\/li>\n<\/ul>\n<p>Consider the <a href=\"http:\/\/www.corestandards.org\/assets\/CCSSI_Math%20Standards.pdf\" target=\"_blank\" rel=\"noopener\">Common Core Math Standard 7.G.4<\/a><\/p>\n<p><em>Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.<\/em><\/p>\n<p>A lower-order question for this standard could be:<\/p>\n<p><strong>What is the area of a circle with a radius of 5?<\/strong><br \/>\n<strong>a) 5\u03c0<\/strong><br \/>\n<strong>b) 10\u03c0<\/strong><br \/>\n<strong>c) 25\u03c0<\/strong><br \/>\n<strong>d) 100\u03c0<\/strong><\/p>\n<p>As presented, this question strictly tests student knowledge and application of the required formula. Instead, consider structuring the question using a \u201creal-life\u201d scenario that requires multiple steps to solve:<\/p>\n<p><strong>Official tournament play of Ringer marbles requires a circular game ring with a diameter of 10 feet. Alexis needs to construct multiple rings for a tournament using rope to mark the circumference of each ring. If she has 100 feet of rope, what is the maximum number of rings Alexis can make?<\/strong><br \/>\n<strong>a) 2<\/strong><br \/>\n<strong>b) 3<\/strong><br \/>\n<strong>c) 4<\/strong><br \/>\n<strong>d) 5<\/strong><\/p>\n<p>Finally, try constructing an open-response question that requires students analyze and evaluate the information in a non-routine manner:<\/p>\n<p><strong>Jackson explains to his classmate that doubling the circumference of a circle results in the doubling of the circle\u2019s area. Is Jackson correct? Use the formulas for area and circumference to justify your answer.&nbsp;&nbsp;<\/strong><\/p>\n<p>This problem still satisfies skills posed in standard 7.G.4, however it now requires students not only demonstrate knowledge and application of the formulas, but also analyze the relationship between them.<\/p>\n<p>Writing higher-order problems takes time, but ideally, the additional time will help students further develop the critical-thinking skills we strive to nurture as educators.<\/p>\n<p>For more examples of higher-order math questions, view these questions created by HelpTeaching.com members:<\/p>\n<p><em>Example 1:&nbsp;<\/em> <a href=\"\/questions\/67943\/deandrea-raven-jessica-and-skye-all-got-different-flavors-of\" target=\"_blank\" rel=\"noopener\">Problem Solving Strategies<\/a><br \/>\n<em>Example 2:<\/em>&nbsp; <a href=\"\/questions\/17429\/evander-does-not-know-how-many-tadpoles-will-hatch-from-the-\" target=\"_blank\" rel=\"noopener\">Fractions<\/a><br \/>\n<em>Example 3:<\/em> &nbsp;<a href=\"\/questions\/17428\/it-is-summertime-and-the-polk-family-wants-to-fill-their-poo\" target=\"_blank\" rel=\"noopener\">Logical Thinking<\/a><br \/>\n<em>Example 4:<\/em>&nbsp; <a href=\"\/questions\/129753\/parker-makes-the-pattern-below-with-square-tiles-he-wants-to\" target=\"_blank\" rel=\"noopener\">Area<\/a><br \/>\n<em>Example 5:<\/em>&nbsp;&nbsp;<a href=\"\/questions\/92303\/think-about-the-pattern103--1000102--100101--10100--1what-do\" target=\"_blank\" rel=\"noopener\">Exponents<\/a><br \/>\n<em>Example 6:<\/em>&nbsp; <a href=\"\/questions\/271816\/the-table-shows-the-number-of-minutes-by-subject-that-julia-\" target=\"_blank\" rel=\"noopener\">Ratios<\/a><\/p>\n<p>Visit HelpTeaching.com to browse&nbsp;our collections of <a href=\"\/free-math-worksheets.htm\" target=\"_blank\" rel=\"noopener\">math worksheets<\/a> and <a href=\"\/self-paced-math-lessons.htm\" target=\"_blank\" rel=\"noopener\">math lessons <\/a>or <a href=\"\/create.htm\" target=\"_blank\" rel=\"noopener\">create questions and worksheets<\/a> that meet your teaching needs.<\/p>\n<blockquote><p><strong>Related Topics:<\/strong><br \/>\n<a href=\"\/blog\/using-math-images-on-test-designer-com.html\" target=\"_blank\" rel=\"noopener\">Using Math Images on HelpTeaching.com<\/a><br \/>\n<a href=\"\/blog\/how-to-use-questions-with-images.html\" target=\"_blank\" rel=\"noopener\">How To Use Questions with Images<\/a><br \/>\n<a href=\"\/blog\/how-to-math-equations.html\" target=\"_blank\" rel=\"noopener\">How to Format Math Equations<\/a><br \/>\n<a href=\"\/blog\/how-to-customize-your-tests.html\" target=\"_blank\" rel=\"noopener\">How to Customize Your Tests Created on HelpTeaching.com<\/a><br \/>\n<a href=\"\/blog\/how-to-find-questions-for-a-test.html\" target=\"_blank\" rel=\"noopener\">How to Find Questions on HelpTeaching.com<\/a><br \/>\n<a href=\"\/about\/how_to_write_good_test_questions\/\" target=\"_blank\" rel=\"noopener\">How to Write Good Test Questions<\/a><\/p><\/blockquote>\n<!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content --><!-- AddThis Related Posts generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"<p>As educators, we expect our students to learn and apply math concepts using higher-order thinking skills that go beyond rote learning. With the adoption of the Common Core Math Standards, many of us must do just that, by focusing more [&hellip;]<!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt --><!-- AddThis Related Posts generic via filter on get_the_excerpt --><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[19,15,23],"class_list":["post-263","post","type-post","status-publish","format-standard","hentry","category-how-to","tag-math","tag-stem","tag-teaching-tips"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>How to Write Higher-Order Math Questions - HelpTeaching.com<\/title>\n<meta name=\"description\" content=\"On HelpTeaching, it&#039;s possible to write higher-order math questions. 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