Planning to Create a Math-Talk Community
Link for original lesson with answer documents http://maccss.ncdpi.wikispaces.net/file/view/CCSSMathTasks-Grade8.pdf
general outline of lesson activities including homework assignment and formative assessment
Lesson Title: Cookie Calorie Conundrum Grade Level/Course: 8th Math
· Source Credit (if applicable):
Sub-unit: Systems of Equations
Connection to Content Standards (include prior grade level standards if applicable) :
· Primary:
8.EE.8 Analyze and solve pairs of simultaneous linear equations.
· Secondary:
8.EE.7 Solve equations with in one variable
6.RP.2 Understand the concept of a unit rate
Connection to Mathematical Practice Standards:
· Primary:
· Make sense of problems and persevere in solving them.
· Reason abstractly and quantitatively
· Model with mathematics
· Attend to precision
· Look for and make use of structure
What prior knowledge is important for students to understand before starting this lesson?
- Students must know how to compute a unit rate
- Students must know how to solve a multi step equation
- Students must know how to solve a system of equations through substitution, elimination, or graphing
Materials Needed by Students and by Teachers (including worksheets, solution keys, power points, etc):
· Cookie Calorie Conundrum introduction (display for students to see)
· Cookie Calorie Conundrum Handout (one per student)
· Chocolate Sandwich Cookies (optional).
PART 1: SELECTING AND SETTING UP A MATHEMATICAL TASK
(i) What are your mathematical goals for the lesson (i.e., what do you want students to know and understand about mathematics as a result of this lesson)?
Students can solve systems of two linear equations with the model provided.
Students can solve systems of two linear equations algebraically.
Students can reason abstractly and quantitatively.
Students can solve two real-world problems leading to two linear equations in two variables.
(ii) What is the rich task that students will explore?
Students will use nutrition information about regular and double stuffed Oreos to determine the number of calories in only the icing and bottom wafer of the Oreo and white filling.
(iii) In what ways does the task build on students’ previous knowledge, life experiences, and culture? What definitions, concepts, or ideas do students need to know to begin to work on the task? What questions will you ask to help students access their prior knowledge and relevant life and cultural experiences?
Students eat cookies in many different ways. Students need to know there is a difference between regular and double stuffed Oreos.
Prior knowledge activation with unit rate and solving systems of equations.
(iv) What are all the ways the task can be solved?
· Follow the model
· First find the calories of one double stuffed cookie and then divide that number by 2.
· Create two linear equations and solve algebraically.
· Create two linear equations and solve graphically.
(v) Which of these methods do you think your students will use? What misconceptions might students have? What errors might students make?
· Students will follow the model provided on the handout.
· Misconceptions
o They may forget to find the unit rate
o They make think the double stuffed Oreo has doubled the calories.
o Not making a connection between what the variables represent.
(vi) What particular challenges might the task present to struggling students? to students who are English Language Learners (ELL)? How will you address these challenges?
· Translating the words to math.
· Understanding what the question is asking.
· What methods to use to solve the problem.
Addressing the problems by
· Reading the problem
· Group work
· Teacher consultant support
· Underlining key ideas and vocabulary
(vi) What are your expectations for students as they work on and complete this task?
· What resources or tools will students have to use in their work that will give them entry into, and help them reason through, the task? Handout, textbook and Oreos will be provided for resources
· How will the students work—independently, in small groups, or in pairs—to explore this task? How long will they work individually or in small groups or pairs? Will students be partnered in a specific way? If so, in what way? 10 min. discussion, 20 min.to 30 min. exploring the tasks with partners, and 10 min for closure. Pairing of groups is up to the individual teacher.
· How will students record and report their work?
Each students will complete the handout and questions will be posed on the board for extensions to the leson.
(vii) How will you introduce students to the exploration task so as to provide access to all students while maintaining the cognitive demands of the task? How will you ensure that students understand the context of the problem? What will you hear that lets you know students understand what the task is asking them to do?
Whole class introduction of the lesson by reading over the scenario, explain what nutritional facts and discussing questions 1-3 together. Students will be talking about the calories of each of the Oreos.
PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK
(i) As students work independently or in small groups, what questions will you ask to—
· help a group get started or make progress on the task?
o To help them get started teacher will review unit rate.
o Help them define variables x and y
o Assist with algebraically solving two linear equations.
· focus students’ thinking on the key mathematical ideas in the task?
o To help them get started teacher will review unit rate.
o Help them define variables x and y
o Assist with algebraically solving two linear equations.
· assess students’ understanding of key mathematical ideas, problem-solving strategies, or the representations?
o Discussions with small groups
o Review handout answers.
· advance students’ understanding of the mathematical ideas?
o Answer extension questions on the board.
o Discussions with small groups.
· encourage all students to share their thinking with others or to assess their understanding of their peers’ ideas?
o All students are required to complete their own handout and will have to ask partner for assistance if needed.
(ii) How will you ensure that students remain engaged in the task?
· What assistance will you give or what questions will you ask a student (or group) who becomes quickly frustrated and requests more direction and guidance in solving the task?
We will use prompting questions like how many calories in one cookie.
We will help them define the visual model using variables and mathematics.
· What will you do if a student (or group) finishes the task almost immediately? How will you extend the task so as to provide additional challenge?
Students will answer extension questions from the board.
1. If you were given the two equations representing both types of cookie, how would you have
approached solving for x and y?: 2x + 2y = 68 and x + 2y = 52
2. How can visuals help to solve a system of equations?
3. Often times we are too quick to use algebra to solve a system without looking for other
representations. What are some ways to represent a system of equations?
· What will you do if a student (or group) focuses on non-mathematical aspects of the activity
(e.g., spends most of his or her (or their) time making a poster of their work)?
o The handout guides students to focus on the mathematical aspect.
o The handout will have to be completed correctly in order to get cookies at the end of the lesson.
PART 3: SHARING AND DISCUSSING THE TASK
(i) How will you orchestrate the class discussion so that you accomplish your mathematical goals?
· Which solution paths do you want to have shared during the class discussion? In what order will the solutions be presented? Why? In what ways will the order in which solutions are presented help develop students’ understanding of the mathematical ideas that are the focus of your lesson?
o Solutions will be presented in the order of the worksheet. The order of the worksheet helps build to the next concept.
· What specific questions will you ask so that students will—
o make sense of the mathematical ideas that you want them to learn?
§ Why do we find the calories per cookie?
§ What values do x and y represent?
§ How many calories would the student consume if she ate 6 cookies with the top wafer removed?
o expand on, debate, and question the solutions being shared?
§ Did anyone else find another method for solving this problem?
§ How do you know your answer is correct?
o make connections among the different strategies that are presented?
§ Are your solutions the same for graphing, substitution, and elimination?
o look for patterns? begin to form generalizations?
§ What pattern do you notice when answering #10, #11, #12
(ii) How will you ensure that, over time, each student has the opportunity to share his or her thinking and reasoning with their peers?
· Students will be working in groups during the lesson and sharing their thinking and reasoning as they work together.
· Each group will present and explain one or two problems from lesson during the closure.
(iii) What will you see or hear that lets you know that all students in the class understand the mathematical ideas that you intended for them to learn?
· The worksheet will be completed and students will participate in the closure.
(iv) What closure will you bring to the lesson? If the lesson is a multi-day lesson, what are some possible stopping points? What closure will you bring at these stopping points?
· Teacher will do whole group discussion of the handout to share any other methods that was used to answer the scenario.
(v) What assignment will you give students to do before the next class?
· Give students a system of equations to solve. Have the students solve using their two favorite methods.
(vi) What will you do tomorrow that will build on this lesson?
· This lesson will lead into translating real life situations into algebraic systems of inequalities.
1. What do the Nutritional Facts tell you?
2. How might this help your classmate figure out how many calories she consumed?
3. How can you make the nutritional facts of the two cookie types easier to compare?
4. How many calories are in just one of each type of cookie?
5. What causes the difference in the amount of calories between the two types of cookies?
6. What is the difference in calories?
7. Why is the difference between the two types of cookies important information?
8. Write an explanation of how the sums below describe the two types of cookies. (Use calorie information from #4 to fill in the blank)
9. Write an equation that models the total amount of calories in each type of cookie.
Let x represent
Let y represent
Equation for cookie with double filling:
Equation for cookie with single filling:
10. Solve for the values of x and y using the substitution method. Show your work.
11. Solve for the values of x and y using the elimination method. Show your work.
12. Use a graphing calculator to graph both equations and
solve for the values of x and y.
(Make sure your equations are in slope intercept form.)
13. How many calories would the student consume if she ate 6 cookies with the top wafer removed?