8th Grade Mathematics 4 th Nine Weeks Curriculum Guide Week 1 Suggested Pacing: 5 days 50 min. class period ACOS Standards: ACOS (25): Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [8-SP1] ACOS (26): Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [8-SP2] ACOS (27): Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8-SP3] Mathematical Practice Standards: Special emphasis should be placed on incorporating mathematical practices into daily lessons. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Learning Objectives: Students will: Construct a scatterplot using bivariate data Interpret scatterplots and investigate patterns between two quantities Analyze a scatterplot to determine the type of association
Key Vocabulary: What key terms will students need to know to understand? Scatterplot Bivariate Clustering Outliers Positive Association Negative Association Linear Association Non-linear Association Quantitative Slope Intercept Ordered Pair X and Y-Axes Assessment Plan: How will I assess prior knowledge? How will I know students mastered the standard? (Formative, Summative, Other Evidence): Formative Assessments: o Anticipation guide o 3-2-1 o Journal writing o Cold calling using strategic questioning o Exit ticket Learning Activities: Monday Before: Students will complete an anticipation guide to determine their prior knowledge of scatter plots. During: Students will participate in an inquiry lab. Students will work with a partner (pre-determined by the teacher) to investigate the relationship between each person s height and arm span. The students will measure their partner s height and arm span in centimeters using a tape measure or meter stick. This data will be recorded as an ordered pair (height, arm span). The teacher will compile the class data on large chart paper (or whiteboard if chart paper is not available). Students will graph the ordered pairs on the coordinate plane using their own graph paper. The teacher (or a student volunteer) can graph the class data using the interactive graphing tool http://illuminations.nctm.org/activity.aspx?id=4186 to display the information for the class. The data can also be plotted using the
Promethean board or chart paper if technology is not available. The teacher can question the students to determine what observations they made about the data during this activity. This is an excellent opportunity for mathematical discourse and to gauge students understanding. The teacher should include the appropriate vocabulary, making sure that students understand the meaning of bivariate. The teacher should list examples of bivariate data to assist students in developing a more thorough understanding. Examples could include: Hours studied vs. test grade Height vs. arm span Hours spent involved in physical activity vs. hours spent playing video games Circumference of a circle vs. its diameter This is also an excellent opportunity to discuss the type of association that exists amongst the data. After: Following the class activity, students will complete a 3-2-1. Students will list 3 things they learned during the lesson, 2 things they want to know more about and 1 question they still have. If students already have math journals, this would be an excellent journal entry. Tuesday Before: As an opener for the lesson, the teacher will provide the following prompts: Ask students to give examples (either written or verbal) of relationships between pairs of quantities such that: When one quantity increases, the other also increases (positive correlation). When one quantity increases, the other decreases (negative correlation). A change in one quantity seems to be unrelated to a change in the other quantity (no correlation). After students have identified scenarios/examples, encourage students to discuss the information using the appropriate terminology in order to develop an understanding of the meaning of association. During: For today s activity, students will deepen their understanding of scatter plots by engaging in an activity that compares their heart rate before and after aerobic exercise. This is an excellent opportunity to co-teach with a coach, PE teacher or bring in a guest aerobic instructor. Prior to beginning the lesson, the
teacher should demonstrate how to determine the resting heart rate. The students should then practice recording their resting heart rate (without recording). Students will then record their resting heart rate for 15 seconds (the teacher will keep the time). Remember that this value must be multiplied by four in order to obtain the beats per minute (bpm). After the students have recorded their resting heart rate, they will engage in 10-15 minutes of activity (dancing, exercising, etc.). The type of activity will be determined by the teacher prior to beginning the lesson. Immediately following the activity, students will record their heart rate in beats per minute (bpm). The two heart rates will be recorded as an ordered pair (bpm after exercise, bpm before exercise). Each student will be given a dot sticker to use for recording their ordered pair. Each student will place their sticker on a chart paper graph. The teacher can develop this chart prior to the lesson, or have students discuss how to create it in class as part of the learning process. Each student can also graph the data individually. After: Students will complete a journal entry describing the type of association that they observed in the class data. Students should discuss their opinion of how the scatter plot and correlation would be different if the variables were reversed. Wednesday Before: At the end of the previous lesson, students analyzed the class data to determine if there was a particular type of association or correlation. Based on that discussion, students will be asked to determine if there is a line that can be drawn to best represent the data. They will also be asked to describe the slope of the line (assuming that students have prior knowledge of slope). This can be completed as journal entry. The teacher can call on students to share their entries. During: Students will be given a combination of data sets and scatter plots. Students will determine the line of best fit for each scatter plot. Students will identify ordered pairs on the line of best fit and use the slope formula to determine the slope of the line. Prior to calculating the slope, students should be able to predict the type of slope by analyzing the association and based on prior knowledge of the types of slope. After: Journal entry What mathematical practice standards did you display in class today? Thursday Before: Entrance Ticket As students enter the classroom, the teacher can give each student a sticky note. The teacher will post a reflection question and the students must jot down their responses on the sticky note. Students will post sticky notes on the board as they finish. Responses can be reviewed as a group. A sample reflection could be: How do you determine how well a line of best fit models the data?
During: Students will work with a partner to complete a NMSI lesson Fitting a Line to Data that involves analyzing scatterplots and determining the best line of fit. *See attachment for instructional activities/procedures* After: The teacher will cold call students immediately following the lesson to discuss concepts covered in the activity. Cold calling is a method of randomly calling students to respond to questions. Students never know when the teacher will call on them to respond; therefore it requires them to remain actively engaged in the lesson. Friday Before: Journal entry List three real-life scenarios in which data collected can be represented using a scatter plot. Teachers should discuss these scenarios with the class. During: Students will work with a partner to complete a NMSI lesson Fitting a Line to Data that involves analyzing scatterplots and determining the line of best fit. The second portion of this lesson will focus on developing an equation for the line of best fit. *See attachment for instructional activities/procedures* After: Students will revisit the anticipation guide that was completed at the beginning of the week. Students should complete the after section of the guide. Students will engage in a Think-Pair-Share activity to compare their before and after responses. During the activity, students will think individually about their responses, share with a shoulder partner and then discuss with the whole group. Materials: Day 1: Monday Anticipation Guide Tape measure, ruler or meter stick Chart paper Markers Graph paper Day 2: Tuesday Teacher Notes to accompany the In a Heartbeat lesson from http://www.pbs.org/mathline Chart Paper and markers
Timer (if a handheld timer is not available, use the timer function in ActivInspire on the Promethean board) Dot stickers Day 3: Wednesday Chart paper from the previous lesson showing the scatter plot of the class data Day 4: Thursday NMSI lesson Fitting a Line to Data student activity sheet and teacher notes Sticky notes Day 5: Friday NMSI lesson Fitting a Line to Data student activity sheet and teacher notes Anticipation Guide ** The teacher can also include any additional resources that may assist with instruction (i.e. textbook and related materials). Differentiation/Accommodations: Varying presentation of material to accommodate all learning styles. Interactive lessons will also address students individual learning styles. Students will work individually and collaboratively. Additional accommodations can be made by the teacher based on the demographics of each class. Technology Integration: Use of the Promethean board http://illuminations.nctm.org/activity.aspx?id=4186 - This interactive activity allows the user to enter a set of data, plot the data on a coordinate grid, and determine the equation for a line of best fit As an extension graphing calculators can be used, if available, to create scatterplots. o YouTube video tutorial on creating a scatterplot using a graphing calculator if the teacher is unfamiliar with the process: http://www.youtube.com/watch?v=bqent6orwho
Teacher Notes: Students should be familiar with constructing a graph prior to introducing scatter plots. Students should know how to construct and label the axes and develop an appropriate scale. As an extension, graphing calculators can be used, if available, to create scatterplots. o YouTube video tutorial on creating a scatterplot using a graphing calculator if the teacher is unfamiliar with the process: http://www.youtube.com/watch?v=bqent6orwho Resources used in developing this guide include: Glencoe Mathematics Course 3, Volume 2 NMSI resources from www.nms.org YouTube http://www.pbs.org/mathline Other websites previously mentioned in this guide for interactive tools