# Understanding By Design

Unit Design

For

Statistics and Probability

Developed by

Randa Matyas-Dawood

Cesar Chavez Academy Middle School

Understanding by Design

Unit Design Worksheet

|Unit Title: Statistics and Probability |Subject/Course: Grade 8 Math |

|Topic: Bivariate Data |Grade: 8 |Staff Name: Randa Matyas-Dawood |

|Stage 1 - Desired Results |

|Common Core Standards: |

|8. SP.1 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. SP.2 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. SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a |

|linear model for a biology experiment, interpret a slope of 1.5 cm/hr. as meaning that an additional hour of sunlight each day is associated with an additional 1.5|

|cm in mature plant height. |

|8. SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way |

|table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated |

|for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a|

|curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? |

| |

|Literacy Objectives: |

|RST.8.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context |

|relevant to grades 6–8 texts and topics. |

|RST.8.5 Analyze the structure an author uses to organize a text, including how the major sections contribute to the whole and to an understanding of the topic. |

|RST.8.7 Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, |

|diagram, model, graph, or table). |

|RST.8.9 Compare and contrast the information gained from experiments, simulations, video or multimedia sources with that gained from reading a text on the same |

|topic. |

|WHST.8.7 Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, |

|focused questions that allow for multiple avenues of exploration. |

|WHST.8.8 Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; |

|and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation. |

|WHST.8.9 Draw evidence from informational texts to support analysis reflection, and research. |

|Understandings: |Essential Questions: |

|Students will understand… | |

|written descriptions, tables, graphs, and equations are useful in representing and| |

|investigating relationships between varying quantities. |What relationships can be seen in bivariate data? |

|different representations (written descriptions, tables, graphs, and equations) of|What conclusions can be drawn from data displayed on a graph? |

|the relationships between varying quantities may have different strengths and |How can you recognize patterns using the slope and y-intercept of a line of best|

|weaknesses. |fit on a graph? |

|linear functions may be used to represent and generalize real situations. |How can graphs, tables or equations be used to predict data? |

|slope and y-intercept are key to solving real problems involving linear | |

|relationship models of data. Some data may be misleading based on representation. | |

| | |

| | |

|Students will know... |Students will be able to... |

|what is a scatter plot. Different patterns such as positive and negative linear |construct and interpret scatterplots. Investigate different patterns in |

|associations, clustering and outliers. |scatterplots. Describe different patterns in scatterplots (positive & negative |

|lines can be used to model relationships between two quantitative variables. |association, clustering and outlier). |

|what a linear equation represents. What slope and intercept represent? |create a line of best fit for a set of data on a scatter plot. Assess the |

|what a two-way table is. What is bivariate data? |accuracy of line of best fit by judging the closeness of the data points to the |

| |line. |

| |create a linear equation for a line of best fit. Use a linear equation to |

| |interpret slope and intercept from a linear equation |

| |construct and interpret a two-way table. Describe association between two |

| |variables. |

|Unit Enduring Understanding: |Unit Question: |

|Students will understand how to explore characteristics shared by two populations |How can we model the changes one variable can have on another? |

|or different characteristics within one population by formulating questions, | |

|designing studies, and collecting and analyzing the data. | |

|Common Misconceptions: |

| |

|When plotting data on a scatter plot, students may confuse the independent (y) and the dependent (x) variable and on what axis each should be placed. |

|The language used in questions to help students interpret two-way tables can be very confusing. Be sure to help students break down questions and understand how |

|to determine what information each question is asking for. |

|Stage 2 - Assessment Evidence |

|Performance Tasks: |

| |

|Concert Craze! |

|Goal – To determine if there is a relationship between the fat grams and the total calories in fast food. |

|Role – A student on a diet. |

|Audience – Your best friend. |

|Situation – Your school principal is planning on ordering lunch from McDonald’s fast food menu. On average a person is only allowed to have 22 grams of fat per |

|meal. Your best friend is on a diet and can only have 18 grams of fat. If the sandwich she wants to have a sandwich has 600 calories, will she be able to eat it? |

|Explain your decision through scientific/mathematical proof. |

|Product – Diagram, charts, and written explanation. |

|Standards – |

|Scatter plot |

|Line of best fit |

|Equation |

|Plugging in equation |

|Written Report |

| |

|Sandwich |

|Total Fat (g) |

|Total Calories |

| |

|Hamburger |

|9 |

|260 |

| |

|Cheeseburger |

|13 |

|320 |

| |

|Quarter Pounder |

|21 |

|420 |

| |

|Quarter Pounder with Cheese |

|30 |

|530 |

| |

|Big Mac |

|31 |

|560 |

| |

|Arch Sandwich Special |

|31 |

|550 |

| |

|Arch Special with Bacon |

|34 |

|590 |

| |

|Crispy Chicken |

|25 |

|500 |

| |

|Fish Fillet |

|28 |

|560 |

| |

|Grilled Chicken |

|20 |

|440 |

| |

|Grilled Chicken Light |

|5 |

|300 |

| |

| |

|Key Criteria: |

| |

| |

|Achieved Honors (4) |

|Exceeded Standards (3) |

|Met Standards (2) |

|Needs More Work (1) |

| |

|Mastery/ |

|Understanding |

| |

| |

| |

| |

| |

|Data and Graphs |

|Table of values is neatly organized & labeled |

|Graph labeled correctly, and has data points plotted correctly |

|A representative best-fit line is drawn |

|Work showing how equation was calculated accurately and explained in detail |

|Graph on Excel is accurate, labeled appropriately with the Best Fit line equation displayed |

|The strength of the correlation is measured and discussed |

|Work shown on Extra credit is accurate and your questions are correctly answered |

|Table of values is labeled and organized |

|Graph is labeled and has data points plotted correctly |

|A representative best-fit line is drawn |

|Work showing how equation was calculated is neat and accurate |

|Graph on Excel is accurate with Best Fit line equation displayed |

|The strength of the correlation is discussed |

|Table is labeled |

|Graph has data points plotted correctly |

|A best-fit line is drawn |

|Work is shown to calculate the linear best fit equation |

|Graph on Excel is accurate |

|Graphs, tables, or equations are missing. |

|Work is not shown |

|Graphs, tables, or the equation of the best fit line are messy or extremely inaccurate |

| |

| |

|Mathematical Analysis |

|Hypothesis is presented and explained in detail. Whether or not it was accurate is also discussed and includes other potential variables |

|The correlation between variables is explained fully and numerical values are given to defend claims |

|The meaning of the equation – and its parts – is presented in context |

|How your best-fit line can be used to predict different outcomes is explained accurately and examples are shown |

|The issue of “causation” is addressed, as well as other possible, conflicting variables |

|Final decision on whether or not she can eat the sandwich is answered with proof using line of best fit and linear equations. |

|Hypothesis is explained well and the accuracy of it is discussed |

|The correlation between variables is explained fully |

|The meaning of the slope & y-intercept is discussed in context |

|How your best-fit line can be used to predict different outcomes is explained accurately |

|The issue of “causation” is addressed and other possible conflicting variables are presented |

|Final decision on whether or not she can eat the sandwich is answered with some proof using line of best fit and linear equations. |

|Hypothesis is explained |

|The correlation between variables is explained |

|How your best-fit line can be used to predict different outcomes is explained |

|The issue of “causation” is discussed |

|Final decision on whether or not she can eat the sandwich is answered without proof using line of best fit and linear equations. |

|Explanations are missing |

|Correlation inaccurate or not discussed |

|Causation unaddressed |

|Uses of best-fit lines not addressed |

|Final decision on whether or not she can eat the sandwich is not answered |

| |

|Work Habits |

| |

| |

| |

| |

| |

|Organization |

|Completed ALL of the steps thoroughly and labeled them accordingly. Organized project and handed all of the steps in on (or ahead of) time and in a legible, |

|clear, neat, and professional fashion. Extra credit included and correct. |

|Completed ALL of the steps thoroughly and labeled them accordingly. Organized the project and handed in all of the steps on time in a clear fashion and included |

|some Extra credit. |

|Completed ALL of the steps. |

|Completed most of the steps on time or late handing in all of the steps. |

| |

|Spelling and Grammar |

|Absolutely no errors. I proofread like a superstar. |

|No errors. Okay, maybe one or two teeny tiny ones. |

|Maybe a few errors but it still flows nicely. |

|Reader has difficulty understanding. |

| |

| |

| |

| |

|Other Evidence: |

|Before |During |After |

| | | |

|Battle Ship: Allow student to |Vocabulary Lessons: Use fryer model (word, definition, picture, sentence). |Content Review Stations: Allow |

|practice plotting points, through | |student to apply knowledge |

|playing battle ship. |Warm-Up: Used as a preview or review of content. |through rotating different |

| | |stations. |

|KWL Chart: Students will list what |Formative Assessments: Throughout lesson the teacher will use thumbs up/thumbs down and 1-2-3.| |

|they know and what they want to | |KWL Chart: Students will list |

|know about scatter plots. |Notes & Class Discussion: Taking notes and having class discussion what we need to know about |what they know and what they |

| |scatter plots, lines of best fit, etc. |want to know about scatter |

|Pretest: Similar to the post test, | |plots and what they have |

|it will assess what students |Worksheet (Practice Problems): Students will practice how to apply knowledge to solve problems|learned. |

|already know about statistics. |including real world problems. | |

| | |GRASP Performance Task: Student|

|Graphic Organizers: To help |Student Participation: Takes different forms such as answering questions on the board, partner|will apply their knowledge and |

|students organize their |work, group work, small group work, and independent practice. |understanding of this unit to |

|understanding of the different | |apply concepts to a real work |

|types of associations and how they |Quizzes: Short quizzes to determine students’ understanding on different topics before moving |task. |

|look like on graphs. |on to the next topic. Such as a questionnaire as stated in self-reflection section. | |

| | | |

|Quick Write: Describe everything |Vocab Journal: Students will keep a journal of key vocabulary. | |

|you know about this topic. | | |

| |Reflection journal: Students will journal on learning throughout the unit. This may include | |

| |Quick Writes and Reflection questions. | |

| | | |

| |KWL Chart: Students will list what they know and what they want to know about scatter plots. | |

| | | |

| |Exit Ticket: Questions to check students understanding Exit Ticket could also include | |

| |activities such as Quick Write (describe everything you know about this topic). | |

|Describe the assessment/s and state the prompt if applicable. □ F □ | | |

|S | | |

| | | |

|What type of scoring tools will be used for evaluation? | | |

|x Analytic rubric x Checklist | | |

|□ Holistic rubric x Answer Key | | |

|□ Criterion rubric □ Other | | |

| | | |

|Student Self-Assessment and Reflection: |

|Journaling and Quick Write Questions |

|What was the main concept in this unit? |

|Why is it important to learn how to analyze data? How can this skill be used in the real world? |

|Which aspects were the most frustrating to learn in this unit? |

|Which aspects were the most pleasing to learn? |

|What have you discovered about yourself as a learner over the past several weeks? Describe how you will use this newfound insight. |

|What could I have done to be more successful in this unit? |

|Stage 3 - Learning Plan |

|Differentiated Instruction: |

| |

|Level C – 20 points |

|Vocabulary Journal of key terms from the Unit (Choose one the three choices for 5 points) |

|Choice 1: Write definitions of key terms in Vocabulary Journal. |

|Choice 2: Draw a picture to represent key terms in Vocabulary Journal. |

|Choice 3: Creating a matching game to identify different words. |

|Notes for daily lessons (Checklist will be used to grade notebooks) (5 points) |

|Daily assignments (Answer key is used to check work) (Choose one the two choices for 10 points) |

|Choice 1: Complete worksheets provided by the teacher. |

|Choice 2: Create a real world problem, swab with a partner, and solve the questions. |

| |

|Level B – 30 points |

|1. You and a friend would like to determine the relationship between two topics, such as a person’s age and their height. After collecting data, present it in one|

|of the following forms |

|Presenting Data (Choose one of the three choices for 10 points) |

|Choice 1: Present findings in a power point presentation |

|Choice 2: Present findings in a poster |

|Choice 3: Present findings in a written report |

| |

|2. Investigating Scatter Plots: By completing a worksheet of the following topics. (Choose one of the following choices for 20 points) |

|Choice 1: Analyze data on a music artist who receives income based on sales of his music on iTunes. |

|Choice 2: A scientist has been studying the populations of birds in South America. Analyze the data of the population of toucans in Brazil since 1985. |

|Choice 3: Analyze data on a swimmer who has recently joined the swim team. She is keeping track of the number of seconds it takes her to complete one lap during |

|practice. |

| |

|Level A – 50 points |

|Your school principal is planning on ordering lunch from McDonald’s fast food menu. On average a person is only allowed to have 22 grams of fat per meal. Your best|

|friend is on a diet and can only have 18 grams of fat. If the sandwich she wants to have a sandwich has 600 calories, will she be able to eat it? Explain your |

|decision through scientific/mathematical proof. (50 points) |

|Learning Activities: |

|Where are we going? – To a deeper understanding of statistical operations. |

|Why? Because it allows students to apply their knowledge of scatter plots, and lines of best fit to analyze data from real world problems. |

|What is expected? Go over rubric and course overview. |

|Hook – Teacher will hook students’ interest by asking them by introducing the grasp activity and asking them if they think she will be able to eat the sandwich or |

|not. Students will hypothesize if she will be able to eat it or not, and they will be told they’ll be able to answer the question by the end of the unit. |

|Equip – Teacher will equip students to do well on this unit through journaling, a variety of lessons and assignments, quizzes, and class discussions. |

|Rethink/Revise – Students will be asked to rethink and revise their work through their K-W-L charts at different times during the unit to rethink the use and |

|understanding of scatter plots and lines of best fits. Students will also have an opportunity to share their thinking during class discussions. |

|Evaluate – Students will self-evaluate through Quick Write and Exit Tickets and through journaling. |

|Tailor – Learning will be tailored by using the differentiated instruction above. |

|Organize – The unit will be organized so that key concepts build upon one another. See calendar below for day-by-day schedule. |

|Essential Vocabulary |

|Bivariate Data – Data for two variables (usually two types of related data). Example: Ice cream sales versus the temperature on that day. The two variables are Ice|

|Cream Sales and Temperature. |

|Categorical data – When the values of the variables are distinct groups or categories (no measurements). |

|Cluster – When data seems to be "gathered" around a particular value. |

|Linear association – When the pattern of points in a scatter plot resembles a line. |

|Line of best fit – A line on a graph showing the general direction that a group of points seem to be heading. |

|Negative association – A correlation where a relationship between two variables in which one variable increases as the other decreases, and vice versa. |

|Outlier – A value that "lies outside" (is much smaller or larger than) most of the other values in a set of data. |

|Positive association – A correlation where a relationship between two variables such that their values increase or decrease together. |

|Relative frequency – The fraction or percent of a total that has particular characteristic, rather than an actual number with that characteristic. |

|Scatter plot – A graph of plotted points that show the relationship between two sets of data. |

|Two-way table – A table that shows two-variable categorical data. |

|Sequencing the Learning |

|Monday |Tuesday |Wednesday |Thursday |Friday |

| | | | | |

|Pretest |Hook |Warm up |Warm up |Warm up |

| | | | | |

|KWL |Class discussion |“What is a relationship ” |“What is a relationship ” |“What is a relationship ” |

| | |(8.sp.1) |(8.sp.1) |(8.sp.1) |

|Battle Ship activity |Level C: Vocabulary | | | |

| | |Thumbs up/Thumbs down or 1-2-3 |Graphic Organizer |Level B: Determine relationship |

| | | | |between two topics |

| | |Level C: Notes & worksheet |Level B: Determine relationship | |

| | | |between two topics |Exit Ticket |

| | | | | |

| | | |Exit Ticket | |

|Monday |Tuesday |Wednesday |Thursday |Friday |

| | | | | |

|Quiz |Warm up |Warm up |Quiz |Warm up |

| | | | | |

|“Line of Best Fit – drawing |“Line of Best Fit – finding |“Line of Best Fit” (8.sp.2) |“Using and Interpreting Linear |“Using and Interpreting Linear |

|line” (8.sp.2) |equation of the line” (8.sp.2) | |models – creating the models” |models – analyzing data from |

| | |Level B: Analyze given data and |(8.sp.3) |models” (8.sp.3) |

|Level C: Notes & worksheet |Level C: Notes & worksheet |determine the line of best fit. | | |

| | | |Level C: Notes & Worksheet |Level C: Notes & Worksheet |

|Exit Ticket |Exit Ticket |Exit Ticket | | |

| | | |Exit Ticket |Exit Ticket |

|Monday |Tuesday |Wednesday |Thursday |Friday |

| | | | | |

|Warm up |Warm up | | |Share GRASP |

| | |Work on GRASP |Wrap up GRASP | |

|“Two way tables” (8.sp.4) |Content Review Stations | | | |

| | |Level A: Apply knowledge from |Level A: Apply knowledge from | |

|Level C: Notes & Worksheet |Introduce GRASP & give rubric |first 4 lessons here |first 4 lessons here | |

| | | | | |

|Exit Ticket |Level A: Apply knowledge from | |KWL chart | |

| |first 4 lessons here. | | | |

| | | | | |

| |Exit Ticket | | | |

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