City University of New York
Section 6.7: Quadratic Equations and Problem Solving
|Teaching point / Objectives: |Length of lesson: |Materials: |
|Zero factor property | |Handout - Students work in groups |
|Factor quadratic equations | |Paper, pencil, quiz questions |
|Problem solving with quadratic equations |45mins-1hour |Markers; white board - Students may display work on board |
|Active learning strategies that this lesson employs: |
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|Break students into groups of 3 or 4 and distribute the handouts. |
|The Handout should consist of review problems, real world problems that is base on today's lesson. |
|Real-world connection / focus / word problem connecting lesson to real-world: (What is the connection between this content and a student’s future study or the “real world”? What is the context of this lesson?|
|What problem will you use to hook students into the lesson to make a real-world connection to content that they are going to learn today?) |
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|The square of a number plus three times the number is 18. Find the number. |
|The A person dive off of 144 feet cliff. Neglecting air resistance, the height h in feet of the object above the ground after t seconds is given by the quadratic equation [pic]. Find how long it takes the |
|person to hit the water. |
|The height of a triangle is 2 meters less than twice the base. If the triangle has an area of 30 square meters, find the length of its base and the height. |
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|How are you using this context to introduce or reinforce the teaching point? |
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|The above problems reinforce concepts that the students already learned such as factoring, adding, and multiplying polynomials. |
|By solving these word problems student will learn the different ways to tackle application problems. |
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|Anticipated time |Stage and aim |Procedure |
|15-20mins |Test- to assess students’ prior |Provide the real-world problems to each student |
| |knowledge, students so task with|Give students 7-10mins to work on this question independently |
| |the target content. T monitors |Remind students of how to factor |
| |to see how well they do. |Actively circulate classroom as students as discussing solutions and jot down notes to help you teach lesson- |
| | |using student input as a starting point |
|10-15mins |Teach- to review/cover content |As the students solve the problem, the teacher either stops them at each step and writes a “rule” for the |
| |that is unclear. After observing|step, or allows them to finish the explanation and then elicits the steps back from the whole class. |
| |Students do task, teacher |The teacher also answers any other questions that came up during the “test” portion monitoring. |
| |presents language that students |The students should write down the steps of the process, or the teacher should keep them visible on the board |
| |had difficulty with or didn’t |for the next step in the process. |
| |know. This stage could be | |
| |teacher fronted presentation. | |
|10-15mins |Test- to assess what students |Give the students a group quiz. This section is mostly word problems and not much concepts to teach. |
| |have understood. Students then |Here are some examples: |
| |do a second activity with math | |
| |vocabulary. After the | |
| |presentation from teacher they |[pic] |
| |should now do task better than | |
| |the first time in stage 1. | |
|5-10mins |Practice Activities- To provide |Solve the following problems: [pic] |
| |students with practice and to | |
| |generate an opportunity for more| |
| |questions | |
|Anticipated problems and potential solutions in this lesson (These can be either problems with logistics / timing, or problems to anticipate with students’ knowledge / grasp of the content. Where will |
|students have difficulties? What would you want a newer teacher to anticipate?) |
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|Students may encounter difficulty translating the word problems to mathematical symbols. Remind students of the mathematical symbols for more than, less than, is, etc. Students may also have difficulty |
|figuring out how many of the solutions solve the problem. For example, if x represents the length, time or distance and the solutions are x = 3 or x = -4, then the students should know to reject x = -4. |
|Differentiation: In what places in the lesson are you differentiating for students in different |Where are these on your lesson plan? |
|ability groups? | |
| |· My lesson plan begins with basic review problems and scaffolds to more difficult problems for students |
|· The fishbowl activity engages all types of learners- auditory, visual, and kinesthetic. |who are more advanced. |
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|· During the “teach” component of lesson, I will be asking varied questions for learners at |· Test, Teach, Test, and Practice activities component of lesson |
|different levels. Giving everyone an opportunity to access this lesson no matter their background | |
|knowledge | |
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|· Practice activity will also have questions for learners who are still grabbling with the | |
|content and more challenging questions for learners who’re ready to take on the more challenging | |
|questions related to the content | |
|Ideas for extensions, notes, considerations, or alternative plans: |
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|It is important to keep in mind that in the test-teach-test approach to this lesson, the professor monitors and listens to the students to see where they are struggling during the opening activity. You will |
|then use this as a teaching point to introduce new vocabulary such as – Zero Factor Property, Factoring, quadratic equation, consecutive integers, and problem solving. |
|Test-teach-test is similar to present, practice, produce, but it’s a bit more active because the lesson begins by figuring out what students know and what needs to be explained. (Source: SACC Active Learning |
|Guidebook) |
|The benefit of this approach is that it allows students to become immediately active and involved in the beginning of the lesson also, shows you what they already know, and it allows you to use students’ |
|existing skills to help you introduce new content. |
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