{"id":190,"date":"2017-06-18T10:44:09","date_gmt":"2017-06-18T14:44:09","guid":{"rendered":"http:\/\/sites.miamioh.edu\/edt222-2017\/?p=190"},"modified":"2018-05-24T22:13:29","modified_gmt":"2018-05-25T02:13:29","slug":"bradford-mtv-strategies","status":"publish","type":"post","link":"https:\/\/sites.miamioh.edu\/edt222-2017\/2017\/06\/bradford-mtv-strategies\/","title":{"rendered":"Bradford – MTV Strategies"},"content":{"rendered":"

Rules of Exponents: \u201cUsed to Think\u201d Method<\/u><\/strong><\/h2>\n\n\n\n\n\n\n\n\n\n\n
Lesson Objectives<\/strong><\/td>\nFor this lesson, students are learning to combine rules of exponents to simplify expressions.\u00a0 This activity was created to reveal student misconceptions about exponential expressions, and to cause students to critically think about exponents.\u00a0 This activity encourages students to think about their individual rules for exponents, as well as the \u201cwhy\u201d behind each rule.<\/p>\n

Although students will be problem solving with a partner, at the end of the activity they will reflect upon what they used to think about exponents, and what they now know following the activity.<\/td>\n<\/tr>\n

Lesson Standards<\/strong><\/td>\nCCSS.MATH.CONTENT.8.EE.A.1<\/a> Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32<\/sup>\u00a0\u00d7\u00a03-5<\/sup>\u00a0= 3-3<\/sup>\u00a0= 1\/33<\/sup>\u00a0= 1\/27.<\/p>\n

CCSS.MATH.PRACTICE.MP2<\/a>\u00a0Reason abstractly and quantitatively.<\/p>\n

CCSS.MATH.PRACTICE.MP3<\/a>\u00a0Construct viable arguments and critique the reasoning of others.<\/p>\n

CCSS.MATH.PRACTICE.MP5<\/a>\u00a0Use appropriate tools strategically.<\/p>\n

CCSS.MATH.PRACTICE.MP7<\/a>\u00a0Look for and make use of structure.<\/p>\n

CCSS.MATH.PRACTICE.MP8<\/a>\u00a0Look for and express regularity in repeated reasoning.<\/td>\n<\/tr>\n

Prior Knowledge<\/strong><\/td>\nThis lesson is intended for a 7th<\/sup> or 8th<\/sup> grade classroom in which students are first introduced to exponent rules.<\/p>\n

Prior to this lesson, students have learned order of operations, and the following exponent rules: multiplying powers with the same base, power of a product, and power of a power.<\/td>\n<\/tr>\n

Why Use the \u201cUsed to Think\u201d Method?<\/strong><\/td>\nWhen teaching rules of exponents, many misconceptions can arise. \u00a0The goal of this activity is to cause students to identify some of their misconceptions, learn from their mistakes, and understand the content at a deeper level. \u00a0The “Used to Think” method allows students first to learn from their mistakes, but also become more aware of how their level of understanding changes as they critically think about a topic.<\/td>\n<\/tr>\n
Materials and Set-Up<\/strong><\/td>\nMaterials:<\/strong><\/p>\n
    \n
  • Envelopes with Exponent Cards (See Below)<\/li>\n
  • Pencil and Paper (Students)<\/li>\n
  • White board\/Poster board (Teacher)<\/li>\n<\/ul>\n

    Set-Up:<\/strong><\/p>\n

    In this\u00a0lesson, students will be working with partners to match unsimplified exponential expressions to their corresponding simplified expressions.<\/p>\n

    The teacher should copy and cut the exponential expression cards seen below, and will put the set of cards in an envelope.\u00a0 Each group of students will receive one envelope containing the set of 10 cards.\u00a0 Many of the expressions below\u00a0have similar simplified expressions, which will\u00a0encourage students to think critically about how exponential expressions are simplified.<\/p>\n

    \"\"<\/td>\n<\/tr>\n

Outline<\/strong><\/td>\n(1)\u00a0\u00a0\u00a0 The teacher will pass out a set of cards to each group, and will explain that the students\u2019 goal is to match an unsimplified expression to a simplified expression.<\/p>\n

Note:<\/strong> If students struggle to understand what is meant by simplifying expressions, the teacher can provide some insight by comparing simplifying expressions to simplifying sentences in English class.\u00a0 The following is an example of simplifying sentences:<\/p>\n

\u201cYou and I should both get in the car and go to the grocery store at the end of the street to pick up icecream.\u201d<\/p>\n

\u201cLet\u2019s go get icecream at Kroger.\u201d<\/p>\n

Clearly, the second sentence is much simpler.\u00a0 This example would help students to understand the difference between unsimplified and simplified expressions, as well as the value in simplifying expressions.<\/p>\n

Another example the teacher can use to help students understand the importance of simplifying expressions can be found here.<\/a><\/p>\n

(2)\u00a0\u00a0\u00a0 Students will discuss with their partners and try to match the expressions.<\/p>\n

Note:<\/strong> Many different conversations and misconceptions will arise as students look at the matching cards.\u00a0 For example, some students may struggle to identify the difference between an unsimplified and simplified expression, which could lead to conversations about what makes an expression simplified.\u00a0 Some students may match incorrectly because they mix up when they should add exponents and when they should multiply.\u00a0 This may lead to conversations of how it is important to understand \u201cwhy\u201d the rules work the way they do (exponents are repeated multiplication), and not just what the rules are.<\/p>\n

(3)\u00a0\u00a0\u00a0 After completing the task, students will check in with the teacher, and if they make any mistakes will be asked to correct their matches.<\/p>\n

(4)\u00a0\u00a0\u00a0 Once students complete the assignment, the teacher will lead students into the \u201cUsed to Think\u201d portion of the lesson.\u00a0 A sample script is given below.<\/p>\n

\u201cBefore this activity, you all had some ideas of how to simplify expressions with exponents.\u00a0 I want you to write down a few sentences about what you used to think about expressions with exponents. \u201c<\/p>\n

[The teacher should give students plenty of time to process and write.]<\/p>\n

\u201cNow I want you to think about how your ideas about exponents have changed after this activity. Again, write down a few sentences and what you now think about expressions with exponents.\u201d<\/p>\n

[Again, the teacher should give students plenty of time to process and write.]<\/p>\n

(5)\u00a0\u00a0\u00a0 Once students have written what they used to think and now think, the teacher can ask students to share their change in thinking with the class.\u00a0 The teacher should look for ways to ask questions and push students to think about the content at a more critical level.<\/p>\n

Notes: <\/strong><\/p>\n

Lesson Extension<\/strong><\/td>\nAs an extension for the lesson, students can create their own sets of 5 matching cards.\u00a0 Students should be sure to include examples that address all of the rules they have learned so far (multiplying powers with the same base, power of a product, and power of a power) in their cards.\u00a0 This extension allows for students to synthesize what they have learned, and therefore leads to more reflection and a deeper level of understanding.\u00a0 It also creates a space for students to reflect upon what they have learned throughout the lesson.<\/p>\n

The teacher can also use this video as a reteach and preview of future rules if desired:\u00a0Exponent Song<\/a><\/td>\n<\/tr>\n

Assessment<\/strong><\/td>\nFormative assessments:<\/strong><\/p>\n