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OverviewIn this activity students use a line of best fit to model data with a linear trend and then use the line of best fit to interpolate and extrapolate information about the relationship shown by the linear trend.Important Mathematical Ideas A relationship with a linear trend can be modeled with a line of best fit.A line of best fit is useful to interpolate between given values and extrapolate beyond given values.Prior KnowledgeCharacteristics of a good graph (appropriate title, labeled axes with units, uniform scale, points plotted correctly, independent variable on the horizontal axes, and dependent variable on the vertical axes).Plotting and interpreting points on a scatter mon MisconceptionsReversing dependent and independent variables.Lines of best fit go through (0, 0).Lines of best fit always go through the first and last points on a scatter plot.Distinguishing between interpolation and extrapolation.Steeper trend lines indicate stronger correlations.Interpolating between points is appropriate for discrete data.Extrapolating data that is unrealistic for the contextCurriculum Notesy = mx + b notation is NOT an expectation for this courseInformation to support/ enhance/ extend learningStudents are asked to keep a journal for each unit in the course. It should contain notes of important mathematical ideas with examples and new vocabulary.ePortfolio may be used for these journal entries.Students can make individual choices whether this is a paper or digital personal resource.Consider a variety of formats as alternatives to journal entries (e.g., student note, pair/share, group discussion, exit card, poster, electronic posting).Develop a Word Wall and continue it throughout the unit as new vocabulary and terms arise that require clarification (e.g., interpolate, extrapolate, line of best fit, trend line).Consider a variety of formats as an alternative to journal entries (e.g., student notes, pair/share, group discussion, exit card, poster, electronic posting).Minds OnTask 1: Estimating Data – Journal Prompts and Sample ResponsesExamine the graph and make predictions based on the data.How tall do you think Julie was when she was 6 years old? I think Julie was about 120 cm tall when she was 6 years old.How old was Julie when she was 90 cm tall?I think Julie was almost 3 years old when she was 90 cm tall.How tall do you think Julie will be when she is 10 years old?I think Julie will be 150 cm tall when she is 10 years old.How tall was Julie when she was born?I think Julie was 60 cm tall when she was mon misconception:students will answer question iv. based on the graph and not think about the context of new born babiesConsider organizing this task as a Think/Pair/ShareActionTask 2: Line of Best Fit videoStudents will:examine pictures of scatter plotsdetermine if there is a trend, and if so, visualize a Line or Curve of Best Fit.check their prediction with a possible line or curve of best fituse the criteria for drawing a line of best fit to compare their line of best fit on Julie's Height vs. Age graph to the samplecriteria for drawing a line of best fit:the line must follow the trendthe line should go through as many points as possiblethere should be approximately as many points above and below the lineWatch the video either in small groups or as a whole plete the rest of the assignment in small groups or in pairs.To provide a visual clue for Criteria for Drawing a Line of Best Fit, consider co-developing an Anchor Chart to be posted in the classroom for student referral.Journal Prompts and Sample ResponsesUse your line of best fit to make new predictions to the following questions. Compare these to your earlier predictions.How tall do you think Julie was when she was 6 years old? I think Julie was about 117 cm tall when she was 6 years old.How old was Julie when she was 90 cm tall?I think Julie was almost 3 years old when she was 90 cm tall.How tall do you think Julie will be when she is 10 years old?I think Julie will be 153 cm tall when she is 10 years old.How tall was Julie when she was bornI think Julie was 65 cm tall when she was born. My original predictions were close to these answers. Most were off by a few cm.Task 3: Interpolation and Extrapolation Journal Prompts and Sample Responses?Compare your predictions to the given diagram. Make notes in your journal about interpolation and extrapolation.Interpolation is estimating data points that fall within the range of the data you have (i.e., between your existing data points)use grid lines (marked in red) that guide your eye from the axis to the trend line, to estimate the answerExtrapolation is estimating data points beyond the range of your data setyou will have to extend your line of best fit beyond the given range of data to extrapolate.Extrapolating Data Cautionpredictions made from extrapolating may not be accurate or realistic since they are beyond the given dataWhat do you notice about your prediction for Julie's height at birth? This prediction was made by extrapolating data.answers will vary.feedback is providedConsolidate the difference between interpolation and extrapolation and add to the Word WallTask 4: Line of Best Fit - Trends in Scatter Plots GizmoStudents will:use this Gizmo to place a line of best fit for a random data set with either negative or positive correlationvary the type of correlationexplore how correlation is reflected in the scatter plot and the trend line;check their line of best fit with the actual trend lineThis Gizmo uses y = mx + b notation, which is NOT an expectation for Grade 9 Applied Mathematics To use the ministry- licensed Gizmos teachers will need to set up a Class Code to create an account and give students a password.The teacher can do a class demonstration with an interactive whiteboard of the Gizmo Activity, or allow students to take turns using the Gizmo, and discuss the placement of trend linesThe Gizmo activity may also be used for students who require additional reviewJournal Prompt and Sample ResponsesAdd new information about the line of best fit in your journal.I noticed for strong positive or negative trends, the points are either on or very close to the line of best fit (trend line).When there is no trend, there is no possibility of a line of best fit (trend line). The points are scattered.ConsolidationTask 5: Lines and Curves of Best Fit Practice Exercise Students will:draw a trend line or a curve of best fit for a variety of relationships on a given worksheetcheck solutions with the sample solutions providedConsider a Think/Pair/Share before students check their answers.Consider a Coach and Be Coached strategy to complete the task.Task 6: Forensic Analysis Practice Exercise Students will:investigate the relationship between the length of the humerus bone and the length of the radius bonecreate a graphical model of the relationshipdraw a trend lineinterpolate and extrapolate information from the graphical modelcheck their answer with the sample solutions providedAnswers for question 6 will vary depending on the line of best fit. Generally, the line should follow the trend, have approximately the same number of points above and below it and go through as many of the data points as possible. Extrapolated and interpolated answers should be approximately the same as those on the answer sheet. Differences are likely due to the scales on the graph being large and values being estimated.Task 7: Assignment 1 Data CostPosted with the unit.See sample solution in the Teacher Notes posted on the vLE.Task 8: Student ReflectionStudents are asked to reflect on their understanding of this topic.These reflections can be used as assessment for learning to help determine next steps for individual students. ................
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