How To Teach Algebra

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1 Instructional Lesson Plan-1 Subject ALGEBRA 1 Unit/Chapt er Chapter 10-Lesson 1 Lesson Topic Quadratic Patterns of Change Date 1/16/2012 Grade 9 Clas s 25 Size Estimated Time 45 minutes 1 day Materials Needed Data projector, computer, power point file, study guide, worksheets. Teacher Yasemin Gunes School Chesapeake Science Point Public Charter School Program Outcome(s)/ Goal(s)/Expectation(s) Student Outcome(s) CLG The student will describe the graph of a non-linear function and discuss the appearance in terms of the basic concepts of maxima and minima, zeroes (roots) rate of change, domain and range, and continuity. Source: The student will analyze the rate of change in a quadratic representation. Prerequisite Skills Vocabulary Special Ed Section Multiple Intelligence Checklist Students should know how to find slope and they should be able to Quadratics, Vertex, Domain, Range, Rate of Change. During the activity, check on students who have accommodations to make sure they work on the questions and understand what they are supposed to do. Extra study guide will be provided. Work load can be reduced. Extra space can be provided for their scratch work. Extra response time can be provided. Group gifted students with other gifted students or high-level learners, if appropriate. Provide challenging questions as worksheets or on index cards to gifted students. In this lesson, the following (checked) learning abilities are included. Linguistic: Study guide; vocabulary section and definitions Logical Mathematical: Math puzzle, practice questions

2 Musical: N/A Bodily-Kinesthetic: N/A Spatial: Short video & power point presentation Interpersonal: Group Study peer-to-peer teaching Intrapersonal: Individual practice Instructional Delivery Opening Activities/Motivation Warm up question : Have students create a table of values for the function f ( x) 3 4x: x= -1, 0, 1, 2, 3, 4. After creating the table of values ask students what the common difference is for the x-values, for the y-values? Ask students to explain why they believe the common difference is constant. Have students create a table of values for the 2 function gx ( ) 2x: x = -1, 0, 1, 2, 3, 4. After creating the table of values ask students what the common difference is for the x-values, for the y-values? Ask students to explain why they believe the common differences are not constant for the y-values. What about the algebraic representations of the functions would lead them to understand that the common differences will be constant for f ( x ) but not constant for g( x )? Procedure 1. Using: Worksheet Patterns of Change Quadratic Functions have students investigate the patterns of change for a quadratic representation in table form. Have student complete the first part of the worksheet with a partner. 2. Have them check their answers for the first part of the worksheet. Discuss the first and second differences and ask students to recall the Warm-Up to relate findings and to formalize a definition first differences and second differences. 3. Have students complete the part #2-#5 in pairs. When complete ask pairs to regroup with another pair to compare answers. Bring class together to answer any of the groups questions or concerns and to discuss their answers. 4. Finalize their concern by introducing second degree functions-quadratics. 5. Show a short movie which shows a connection of quadratics in real life

3 Exit Ticket Exit ticket question is given as follows. Students write their answer on a paper and turn it in to teacher. Given the table of values determine the first and second differences: x y Does the table represent a quadratic function? Between what two values in the table does the vertex occur? Why? Homework-Traditional Assessment Quadratic Functions: Representations and Patterns of Change 1. For each of the following equations, state whether it represents a quadratic function. Justify your answer. a. y2 x 2 b. y 2 x c. y x x d. y 2 x 2. For each of the following tables of values, state whether it represents a quadratic function. Justify your answer.

4 a. x y b. x y c. x y For each of the following quadratic functions: a. What is the vertex of the graph? b. What is the domain of the function? c. What is the range of the function? 3. 4.

5 The following rubric for the homework above will be given in the next lesson. Quadratic Functions: Representations and Patterns of Change 1. a. quadratic, its graph is a parabola b. not quadratic, its graph is not a parabola c. not quadratic, its graph is not a parabola d. not quadratic, its graph is a not parabola 2. a. yes, since the x values increase by a constant amount, 1, and the second differences in the y values are a constant b. no, since the x values increase by a constant amount, 1, and the first differences in the y values are a constant it is a linear function c. yes, since the x values increase by a constant amount, 1, and the second differences in the y values are a constant 3. a. (2, -1) b. all real numbers c. y 1 4. a. (-1, -2) c. all real numbers c. y 2

6 Lesson Plan Title: The Mystery Footprints Overview What problems occur if information is based only on inferences? Inferences can be very useful. They become the basis for a hypothesis, the next step in the scientific method. However, inferences can cause problems if they are taken as observations because they may be wrong, leading to further wrong ideas. (If you stand inside your nice warm house on that same fall day and look outside to see the trees moving with the wind and leaves blowing around your yard, you might infer that it is cold outside. You re basing this on things you notice the wind, the time of year, perhaps an overcast sky but you are not actually observing the temperature as you stand inside your heated home.) Concept / Topic to Teach: What is observation? What s Inference? Standards Addressed: 1.B.1c.Explain that even though different explanations are given for the same evidence, it is not always possible to tell which one is correct. 1C.1c Give examples of how scientific knowledge is subject to modification as new information challenges prevailing theories and as a new theory leads to looking at old observations in a new way. General Goal(s): Students will learn what an inference is and differentiate between inference and observation. They will examine a series of scenes and then write their observations and make an inference based on what they see at each scene. Specific Objectives: 1. To make observations of pictures, diagrams, samples and specimens in detail. 2. To make inferences based on personal observations 3. To distinguish between observation and inference. 4. To observe qualitatively and quantitatively Required Materials: PPT follow up sheet, practice handout, Dogs and Turnips worksheet and word cards. Anticipatory Set (Lead In): Bell work: Project an image. The students will list their observations and we will create class record of observations. Accept observations and inferences for time being. Step by Step Procedures: 1. I'll start with the power point and have the students write down their observations and inferences as I show one frame at a time.

7 2. At the end of the PPT ask them to write and share what did they learned from this lesson. 3. After the discussion state that scientists develop explanations using observations (evidence) and what they already know about the world. The point is made that scientists change their hypothesis as they gather more information. In addition, scientists who have similar information may not agree on its meaning. Science works this way. 4. (Is this is a block schedule, do this activity after the practice handout, if it s not, use this as bell work in the next class). Show the picture of the day from National Geographic online and ask for 3 qualitative and 2 quantitative observations. Then ask them what their inference would be about the picture based on their observation. Then ask them to make 5 predictions about what will happen next in the scene. 5. Next, have them do the practice worksheet on Qualitative and quantitative observations. 6. Have them do the Dogs and Turnips activity. 7. Procedure for this activity: 1) Pass D & T worksheets and word cards. Have each group spread out its word cards face down on the table. 2) Tell the class that the words form one long sentence that also tells a story. The goal is to figure out the story from the words they turn over. 3) Have each group turn over five cards at random and write what they think the story is on their worksheet (Hypothesis #1). After they have done this, ask them if it would help to have more information. They will, of course, answer yes. 4) Have the groups turn over five more cards and record their new sentence on the worksheet (Hypothesis #2). After they have done this ask them if their idea of the sentence changed with more information. Discuss briefly, but do not have groups share their results, just yet. 5) Have the groups turn over five more cards and record their revised sentence (Hypothesis #3). 6) Allow groups to share with the class what they think the sentence says. Discuss the possible reasons why groups have different answers. Ask them how this might be similar to a paleontologist digging up ancient bones. (Scientists may not have all the information.) Ask why scientists might not agree on explanations of things. (Scientists may have different information or interpret things differently.) 7) Allow all groups to turn over all the cards and to revise their hypotheses (Hypothesis #4). Have groups share out their "final" results. Chances are that the groups will still not have exactly the same sentences. Ask why they didn't. Closure: Ask why scientists may not have the same explanations for things even though they may have exactly the same information. (They may have come with different background information or interpret the same information differently.) Assessment Based on Objectives: Exit ticket: Observation or Inference statements. Adaptations (For Students with Learning Disabilities): Frequent reminder Prompt Questioning Check their work during the PPT

8 Extensions (For Gifted Students): Ask students to make a list of observations and inferences throughout the school day. Challenge students to find inferences in their local newspaper. Highlight observations and inferences with different colors.