Planning to Create a Math-Talk Communitygeneral outline of lesson activities including homework assignment and formative assessment

Lesson Title: __7.NS.1-3____________________________________Grade Level/Course: ___7_______ Source Credit (if applicable):

Sub-unit: Apply and extend previous understandings of operations with rational numbers to add, subtract, multiply, and divide rational numbers.

Connection to Content Standards (include prior grade level standards if applicable) :Primary:

7.NS.1a. Describe situations in which opposite quantities combine to make 0.

7.NS.1b. Understand p and q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

7.NS.1d. Apply properties of operations as strategies to add and subtract rational numbers.

Secondary:

7.NS.3. Solve real-world and mathematical problems involving the four operations with rational numbers.

Connection to Mathematical Practice Standards: Primary:

7.NS.3. Solve real-world and mathematical problems involving the four operations with rational numbers.

Secondary:

addition and subtraction & vertical and horizontal number lines

What prior knowledge is important for students to understand before starting this lesson? addition and subtraction

vertical and horizontal number lines

Materials Needed by Students and by Teachers (including worksheets, solution keys, power points, etc):

Chart paper to post the Gallery Walk problems Gallery Walk problems, Student Answer Sheet, and Key Timer Concept Attainment Cards and Key

RATIONAL FLOW CHART document and Key LCD Document Camera Overhead

Electronic polling device (for example: Turning Point)

See attached

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)?

Describe authentic, student-centered situations in which opposite quantities combine to make 0; add and subtract rational numbers.

(ii) What is the rich task that students will explore?

Traveling Around Michigan Gallery Walk (see ten attached questions answer sheet to post around classroom) Make copies of the ten questions about Michigan towns/cities and post the ten problems around the classroom. Direct students to walk around to each of the posted questions in the gallery walk. Use attached answer sheet to compute and

record the answer to each question. Some of the answers will equal 0, others will not. Calculators may be not be used. Check answers from Gallery Walk as a class. Have each group share one response (under the document camera or an

overhead, calling on a student, etc.)

(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?

The sources of information are contextualized to learners’ lives/experiences as Michigan residents.

Why do additive inverses always equal 0?How do operations with integers compare to operations with rational numbers?Understand authentic contexts when opposite quantities of rational numbers are combined.

Rational numbers allow us to make sense of situations that involve numbers that are not whole.

(iv) What are all the ways the task can be solved?

PictorialEstimationNumber LineSimple Arithmetic Guess and CheckWork Backwards

(v) Which of these methods do you think your students will use? What misconceptions might students have? What errors might students make?

Adding instead of subtractingNot knowing where some of the locations areValidating their reasoningAbove and below sea level misconceptions

(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?

Intervention Activity: Additive Inverse Video - http://www.teachertube.com/viewVideo.php?video_id=186908&title=Additive_Inverse_and_Absolute_Value&vpkey=f77dcc4ca3&album_id= Also can be a warm-up, review, or ending activity.

Gifted and Talented Activity: Listen to rap song at http://www.educationalrap.com/song/inversion.html. Instruct students to create their own rap lyrics; combine original lyrics with a song.

ELL: Ask students to draw picture examples of the concept of additive inverse and/or create Frayer model of examples/definitions

(Place Michigan map where all can see with push pins to designate appropriate loacations.)

(vi) What are your expectations for students as they work on and complete this task?

Students will be able to identify and use additive inverses when adding and subtracting rational numbers. Students will be able to work in small groups collaboratively.Students will be able to attend to precision.Students will be able to explain to the whole their reasoning for their outcomes.

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? Chart paper to post the Gallery Walk problems Gallery Walk problems, Student Answer Sheet, and Key Timer Concept Attainment Cards and Key

RATIONAL FLOW CHART document and Key LCD Document Camera Overhead

Electronic polling device (for example: Turning Point)

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?

Small groups. 1 period to gather information. ½ period to explain results. ½ period for exit slip = flow chart which will be completed independently.

How will students record and report their work?They will be provided a student answer sheet to record their data

(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?

Girls (+) line up across from boys (-). Each pair of girls and boys will sit down until there are no more opposite pairs left. Students will then have to determine what just took place, why there are some students left standing, or maybe why there are no students left standing. Teacher should hear canceling out, negative positive, opposites, left overs, no leftovers.

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?

Do you understand the question? Do you know what I am asking you to find?Where is the location of…?What does above and below sea level mean?What is a coast line?Etc……

focus students’ thinking on the key mathematical ideas in the task? Is this a 0 out situation or a leftover situation? Is it a positive or negative outcome?

assess students’ understanding of key mathematical ideas, problem-solving strategies, or the representations?What mathematical operation are we asking you to apply to the situation?

advance students’ understanding of the mathematical ideas?

What generalizations can you make about your answers?

What was your answer for U of M? What were the steps that you used to arrive at your answer? If all students had the answer $4.85, is there a way that you could only have $3.60 left?

How are your answers for the cities similar? How are they different? Explain.

What would the sum be of Houghton Lake and Sioux Locks? Let’s analyze this: 90 + (-90). What does the symbol in the middle tell you about what you’re going to do with these numbers? What is the relationship between negative 90 and positive 90? Example

answer: they are the opposite. What’s another word for opposite? Example answer: inverse. Therefore, with these numbers we are working with the additive inverse, just like in the concept attainment activity. (A number line may be used to model these numbers for a visual representation).

encourage all students to share their thinking with others or to assess their understanding of their peers’ ideas?

After students explain their reasoning to the class, ask individual students to paraphrase their peer’s explanations. Can you say this in a different way or give an additional example?If student do not comprehend, go back to the warm-up as a reference.

(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?Proximity control!!! Tell students to re-read their answers and to make sure they have answered the questions correctly.

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?

Have them go back and check their answers. Have them re-write their answers so they are legible. Have them create their own problems that could be used as an assessment.

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)?

Assign everyone in the group a job title. If they complete their job, they should assist with one of the other job’s not finished.

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?

Students will be picked at random to present one of their findings to the class. They will explain and show their work via ELMO to help present their materials.

With the students knowing they will be picked at random to discuss their information, the students will then better prepare themselves and put more thought into the comprehension of the task.

What specific questions will you ask so that students will—o make sense of the mathematical ideas that you want them to learn? o expand on, debate, and question the solutions being shared? o make connections among the different strategies that are presented?o look for patterns? begin to form generalizations?

Teacher will ask questions to clarify students’ explanations so that the group as a whole can comprehend and remain focus. Teacher may call on other group member s if the presenter stumbles on his/her approach. Students will have confidence knowing that team members are there for support.

(ii) How will you ensure that, over time, each student has the opportunity to share his or her thinking and reasoning with their peers? Since everyone has a job in the group, they will all have to collaborate with one another throughout the entire task. If teacher notices non-participants, the teacher can create an anonymous evaluation where each group member grades their peer.

(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?

Teacher will see and hear from the groups presentation. Key words: Additive inverse, rational, opposite quantities, negative, positive, etc….

(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?

After Group Presentation, discuss that opposite quantities combine to make 0, just like we did in the warm-up activity including other possibilities. Discuss with the class that the context of these problems were real-world problems that could occur in everyday life.

(v) What assignment will you give students to do before the next class?Rational Flow Chart (Formative Assessment Exit Slip)

(vi) What will you do tomorrow that will build on this lesson?

Multiplication:

To assess prior knowledge, display the problems and have students answer:

Janine earns $15 per hour and works for 6 hours. What are her total earned wages?

Kyle is cutting a 16 foot 2x4 piece of wood and needs 6 equal sections. What length will each of the sections be?

Discuss how the “product” and “quotient” compare to the “factors” and “divisors” and “dividends.” Will the answers be larger or smaller? Why is that?

Resource for Modeling Multiplication and Division: http://www.teachfind.com/national-strategies/models-and-images-multiplication-and-division

To review operation sign rules, have students think through a solution as well as a picture (number line, etc.) to represent each of these scenarios:

iTunes sells 4 iPhone apps at the cost of $2 per app (4 x 2 = 8).

You spend $3 each on 4 bottles of Gatorade. (4 x -3 = -12).

Your brother owes $6 to each of 4 friends, (-6 x 4 = -24).

You tell 3 of your friends not to worry about paying you the $6 each that they owe you. (-3 x -6 = 18).

How to use this lesson:

Step 1: Warm-up activity from above where you pair up girls with boys.

Step 2: Have students make observations based on the warm-up activity. Ask engaging questions.

Step 3: Explain and have the students complete the Gallery Walk. Number students off to create 10 groups.

Step 4: Using popsicle sticks, have students, with the support of their group members, explain the reasoning behind their answers.

Step 5: Pass out the Flow Chart as their exit slip

LANSINGIn Lansing, the local government owns a total of 5,300 acres. Of this land, 950 acres are public parks, 3,780 acres are lakes, and 530 acres are ponds. The Symphony Woods comprise 40 acres. How many acres of government-owned land are unaccounted for?

TRAVERSE CITYLast year, the Cherry Festival hosted 15,000 visitors. This year, the festival hosted 2,078 senior citizens, 8,766 adults, and 4,156 children ages 12 and under. What is the difference in attendance between the two years?

UPPER PENINSULAOf the 52 bridges in Michigan, Northern Michigan originally was home to eight of them. Of those eight bridges, two were destroyed by fire; one was destroyed by storms; and five have been deemed unsafe due to neglect. How many bridges in Northern Michigan are still useable?

DETROITThe Detroit Lions started a play on their 45 yard line. They rushed for 15 yards. The New York Jets pushed them back 22 yards on the next play. Then the Lions completed a pass for 7 yards. Where on the field are the Lions now?

U of MA student at University of Michigan (Go Blue!) has $12 in her food plan account. She bought pizza for $3.75, two cookies for $1.25, and a sports drink for $2.15. Now, the student wants to lend her friend $4.85 for lunch. Will the student have enough money on her account to lend her friend $4.85? Why or why not?

HOUGHTON LAKEIn July, the early morning temperature of sand on the beach is usually about 50ºF. By 3 p.m., the sand temperature can go up to 140 ºF. What is the difference in temperatures?

SIOUX LOCKSA submarine on its way to Lake George is cruising at a depth of 161 feet in Lake Superior. The submarine rises 80.5 feet every ten minutes. What is the new depth of the submarine in twenty minutes?

MAPLE RAPIDS Kris shot a 630-pound deer while Rick caught fifteen, 42-pound wild turkeys. Which scale below represents the weight comparison of Kris’ deer versus Rick’s total wild turkey catch, if Kris’ deer is in the left pan and Rick’s catch is in the right pan?

a. b. c.

Explain your reasoning.

LAKE MICHIGANThe distance from the Lake Huron coastline to Las Vegas is 2,560 miles. The distance from the Lake Huron coastline to Frankenmuth (in between the coastline and Las Vegas) is 107 miles. What is the distance from Frankenmuth, MI to Las Vegas, NV?

INDIAN HEAD

Ironwood, Michigan is at an elevation of 627 feet. The Indian Head Ski Resort, 45 miles away, has a maximum elevation of 3,080 feet. What is the difference in elevation?

Student Answer Sheet: Traveling Around Michigan Gallery Walk*please show all of your work in the space provided below* circle your answers!

LANSING: TRAVERSE CITY:

UPPER PENINSULA: DETROIT:

U of M: HOUGHTON LAKE:

SIOUX LOCKS: LAKE MICHIGAN:

INDIAN HEAD: MAPLE RAPIDS:

ANSWER KEY:

LANSING = 0 TRAVERSE CITY = 0

UPPER PENINSULA = 0 DETROIT = 45

U of M = Yes, she will have $4.85 left over. HOUGHTON LAKE = 90

SIOUX LOCKS = -90 LAKE MICHIGAN = 2,453

INDIAN HEAD = 2,453 MAPLE RAPIDS = Scale is equal, B

RATIONAL FLOW CHART

‾6 __ __ __ 0 __

‾9.75 1.7 ‾17.3

+‾ 102 −‾221

−3.25 −‾108

−121.6

+0.5

+‾ 8.7

KEY

KEY

KEY: RATIONAL FLOW CHART

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