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PPS Math Curriculum Grade 7 Unit 1 Performance Task

Performance Task # 1

Goal: Arrange integers in order.

Role: You are a analyzing a Julie Brown Anderson’s dive.

Audience: Reader of article.

Situation: You are interviewing for a job at a sports magazine. You have been asked to comment

on the scuba diving techniques of certain divers.

Product: Brief article describing the dive of Julie Brown Anderson on 5/9/12.

Which standard(s) (priority/supporting) will the task address? 7.NS. 1. Apply and extend previous understandings of addition and subtraction to add and subtract rational

numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has

0 charge because its two constituents are oppositely charged.

b. Understand p + 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.

What essential Question(s) and corresponding Big Idea(s) will this task target?

Why is it useful for me to know the absolute value of a number? Why do we need to agree on a specific order of operations? How does changing the order of operations affect the outcome when simplifying an expression?

Absolute value is useful in ordering and graphing positive and negative numbers. Recognize how addition , subtraction multiplication, division, powers, parentheses and roots of numbers effect the magnitude of the result

Which “unwrapped specific concepts and skills will this task target? Positive and negative numbers Describe Opposite Quantities Understand Addition and Subtraction Show Equivalent forms of rational numbers Interpret Absolute Value Apply Properties of Operations

How will the students apply the concepts and skills? What will they do and/or produce? Construct a number line of the order of the integers.

What resources, instruction, and information will students need in order to complete the task? Teacher model.

What evidence of learning will I look for to show that I know all of my students have


conceptually learned the concepts and skills – the standard(s)? Students will be able to collect data and write a paragraph to compare and contrast. Students have shown proficient on the rubric.

How can I differentiate the application and/or evidence to meet the varying needs of my students? To differentiate the application, small groups of students with learning needs will be given a number line to work with and the ELL students will pair with an English/Spanish speaking student to complete task. Give a personal cue to begin work Give work in smaller units Provide immediate reinforces and feedback Make sure the appropriate books and materials are available Introduce the assignment in sequential steps Check for student understanding of instructions Check on progress often in the first few minutes of work Provide time suggestions for each task Provide a checklist for long detailed tasks Use technological resources


Performance Task # 1 Scoring Guide

Advanced or Exemplary

All “Goal” criteria plus: Correctly identified the intervals, 0-3: Decreasing, going down into water, 3-31: basically level with some increasing, 31-39: increasing, coming out of the dive, going out of the water

Proficient

Goal criteria:

Write four different scenarios for divers

Diagrams correctly depict the addition equations

Created number line and ordered integers

Filled in table of information correctly (estimations accurate)

Progressing

Meets _3__ of the “Goal” criteria

More work is needed

Beginning

Meets fewer than _3_ of the “Goal” criteria

Task to be repeated after re-teaching Comments:


Interdisciplinary Connections and Related Priority Standards

Specific to Task #1

21st Century Learning Skills Specific to Task #1

CCSS.ELA-Literacy.W.7.2b Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples. CCSS.ELA-Literacy.W.7.7 Conduct short research projects to answer a question, drawing on several sources and generating additional related, focused questions for further research and investigation.

Science 5. 4.8 F2 Explain the mechanisms that cause varying daily temperature ranges in a coastal community and in a community located in the interior of the country

those that apply for task:

❑ Teamwork and Collaboration

❑ Initiative and Leadership

❑ Curiosity and Imagination

❑ Innovation and Creativity

❑ Critical thinking and Problem Solving

❑ Flexibility and Adaptability

❑ Effective Oral and Written

Communication

❑ Accessing and Analyzing Information

❑ Other

http://www.corestandards.org/ELA-Literacy/W/7/2/b/

http://www.corestandards.org/ELA-Literacy/W/7/7/


Performance Task # 1 Task 2 Full Description:

You have given the scuba divers a course in how deep they can go below sea level before the pressure becomes dangerous to their lives, they have asked you to help them figure out how fast they can ascend to the surface. Role: You are a scuba diving instructor.

Audience: Students in your class.

Situation: You are a scuba diving instructor and your class needs instruction on how fast they can

return to the surface.

Product : Construct mathematical equations to model scenario

Which standard(s) (priority/supporting) will the task address? 7. NS.2. Apply and extend previous understandings of multiplication and division and of fractions to multiply

and divide rational numbers.

a. Understand that multiplication is extended from fractions to rational numbers by requiring that

operations continue to satisfy the properties of operations, particularly the distributive property, leading

to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of

rational numbers by describing real- world contexts.

b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of

integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–

q). Interpret quotients of rational numbers by describing real-world contexts.

c. Apply properties of operations as strategies to multiply and divide rational numbers.

What essential Question(s) and corresponding Big Idea(s) will this task target? How is the number system used to fit different situations? Why do we need to agree on a specific order of operations? How does changing the order of operations affect the outcome when simplifying an expression? How is the order of operations like a recipe for chocolate cookies? Numbers can represent quantities, relationships, location, and position. Rational numbers have multiple interpretations, and making sense of them depends on identifying the unit. The concept of unit is fundamental to the interpretation of rational numbers. The concept of unit is fundamental to the interpretation of rational numbers.

One interpretation of a rational number is as a part-whole relationship.

One interpretation of a rational number is as a quotient.

Recognize how addition , subtraction multiplication, division, powers, parentheses and roots of numbers effect the magnitude of the result


Which “unwrapped specific concepts and skills will this task target? Skill : Concepts: Add and Subtract Positive and negative numbers Describe Equivalent forms of rational Understand Opposite Quantities show interpret Absolute Value Apply Properties of Operations

How will the students apply the concepts and skills? What will they do and/or produce? Students will write four addition equations and draw a diagram of the zones to depict the equations.

What resources, instruction, and information will students need in order to complete the task? Students will need to know the dangerous pressure point to dive and the zones below sea level.

What evidence of learning will I look for to show that I know all of my students have conceptually learned the concepts and skills – the standard(s)? The evidence will be the equations with correct solutions and the diagram.

How can I differentiate the application and/or evidence to meet the varying needs of my students? Give a personal cue to begin work Give work in smaller units Provide immediate reinforces and feedback Make sure the appropriate books and materials are available Introduce the assignment in sequential steps Check for student understanding of instructions Check on progress often in the first few minutes of work Provide time suggestions for each task Provide a checklist for long detailed tasks Use technological resources

Interdisciplinary Connections and Related Priority Standards Specific to Task #1

CCSS.ELA-Literacy.W.7.2b Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples. CCSS.ELA-Literacy.W.7.7 Conduct short research projects to answer a question, drawing on several sources and generating additional related, focused questions for further research and investigation.

Science 5. 4.8 F2 Explain the mechanisms that cause varying daily temperature ranges in a coastal community and in a community located in the interior of the country

http://www.corestandards.org/ELA-Literacy/W/7/2/b/

http://www.corestandards.org/ELA-Literacy/W/7/7/



Advanced or Exemplary

All “Goal” criteria plus: has ALL of parts 2 and 3 correct WITH correct labeling of units.

Proficient

Goal criteria:

Write four equations for the scenarios for dives (First) Has 3 of the correct answers for the 4 scenarios (Second) Has 2 of the correct answers for the Third part Has correctly labeled 5 of the 7 questions

Progressing

Meets _2__ of the “Goal” criteria More work is needed

Beginning

Meets fewer than _2_ of the “Goal” criteria Task to be repeated after re-teaching

Comments:

Research-Based Effective Teaching Strategies

21st Century Learning Skills

Task /Activities that solidifies mathematical concepts

Use questioning techniques to facilitate learning

Reinforcing Effort, Providing Recognition

Practice , reinforce and connect to other ideas within mathematics

Promotes linguistic and nonlinguistic representations Cooperative Learning

Setting Objectives, Providing Feedback Varied opportunities for students to communicate mathematically

Use technological and /or physical tools

those that apply to the unit:

❑ Teamwork and Collaboration

❑ Initiative and Leadership

❑ Curiosity and Imagination

❑ Innovation and Creativity

❑ Critical thinking and Problem Solving

❑ Flexibility and Adaptability

❑ Effective Oral and Written

Communication

❑ Accessing and Analyzing Information

❑ Other


Grade 7 – Unit 1

Task 1: Scuba Diving Down

Goal: Arrange integers in order.

Role: You are a analyzing a Julie Brown Anderson’s dive.

Audience: Reader of article.

Situation: You are interviewing for a job at a sports magazine. You have been asked to

comment on the scuba diving techniques of certain divers.

Product: Brief article describing the dive of Julie Brown Anderson on 5/9/12.

Standard: CCSSM 7.NS.1 & 3

Assessment: You will be assessed using the attached rubric.

Cold Water Diving: It’s all relative … how cold is “cold”?!?

By Julie Brown Anderson On June 4, 2012 Posted in: Scuba Diving

Below is a graph of one dive by diver Julie Brown Anderson. She has charted her depth and temperature of the water she was in and compared them to time. The x-axis is the time she is underwater. For example, 3’00 means she was under water for 3 minutes and 27’00 means she was under water for 27 minutes. The y-axis on the left shows the number of feet below the surface (be careful: the lines going horizontal do not match up with these!!). The y-axis on the right shows the temperature of the water she was diving in at that time.

Source: http://scubadivergirls.com/scuba-diving-2/cold-water-diving-its-all-relativehow-cold-is-cold/ Grade 7 – Unit 1

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http://scubadivergirls.com/author/juliebrownanderson/

http://scubadivergirls.com/category/scuba-diving-2/

http://scubadivergirls.com/scuba-diving-2/cold-water-diving-its-all-relativehow-cold-is-cold/


Task 1: Scuba Diving Down

Student Name: _____________________________________Date: _______________ Teacher: ___________________________________________Section: ____________ You are interviewing for a job at a sports magazine. As part of your initial interview you have been asked to analyze Julie’s dive. You will need to collect the data from the graph above. :

1. Complete the table of the 3 types of data. a. Estimate the depth to the nearest foot b. Estimate the temperature to the nearest tenth of a degree

2. Construct a number line to graph the integers in correct order from the depth column.

Time (mins) Depth (ft) Temperature (°F)

0

3

6

9


3. You have decided to give some scuba divers a crash course in how deep they can go below sea level before the pressure becomes dangerous to their lives, approximately 40m. Since you are the expert, the scuba divers present various scenarios for you to explain. For example, if a diver is 7 feet below sea level and descends 85 feet, where is the diver relative to sea level? Is she safe? You are to use your number line and table to write addition and subtraction equations, write and draw a diagram for four different situations depicting how far a scuba diver can go below sea level to study marine life, and explain your solutions. Write 2 addition equations and 2 subtraction equations. (Hint: you must convert to find the maximum depth in feet. 1m is approximately 3.3 feet)

4.Describe what happened during the interval of 0 minutes to 3 minutes, the interval of 3 minutes to 31 minutes, and the interval of 31 minutes to 39 minutes.


Grade 7 – Unit 1

Task 2: Scuba Diving: How Fast UP? & What about the air?

Goal: Create 4 number sentences showing multiplication and division of positive and negative numbers. Role: You are a scuba diving instructor. Audience: Students in your class. Situation: You are a scuba diving instructor and your class needs instruction on how fast they can return to the surface. Product: 4 number sentences as examples for your students. Standard: CCSSM 7.NS.2 & 3 Assessment: You will be assessed using the attached rubric. Description:

Since you have given the scuba divers a course in how deep they can go below sea

level before the pressure becomes dangerous to their lives, they have asked you to help

them figure out how fast they can ascend to the surface. Since you are the expert, the

scuba divers present various scenarios for you to explain.

First, you must lead them to find the maximum speed at which they can ascend. We

know from the last class that the maximum depth of a dive for recreational divers is

approximately 130 feet. At a safe speed it should take you at least 4 minutes and 20

seconds to get to the surface. What is the safe ascending speed? (Round to the

nearest foot.)

Second, Now the group presents you with scenarios.

1. How long will it take for a diver to return to the surface from a depth of 98ft?

2. A diver decided to ascend going slower than the maximum return rate. She goes

at 20ft/min from a depth of 123 feet below surface. How long will it take her to

return to the surface?

3. A Navy SEAL is returning to the surface from a depth of 165 feet. The Navy uses

an ascent rate of 60ft/ minute, how many minutes will it take for the SEAL to

return safe to the surface?

4. A diver off the shore of Malibu, California is 112 feet below and realized she

needs to meet her friend in 13 minutes. The boat is 9 minutes from the dock.

Can she make it?

You now have to show them the solution to each scenario.


Third, your class is now concerned about diving time. You now instruct the class on

using an air tank. The standard size tank is 100 cubic feet and lasts about 50 minutes.

So you present the class a scenario.

A. Peter filled up only ¼ of the 100-cubic feet air tank because he was short on

money. He used ½ of the air in a quick dive with some friends. How long was

he under water?

B. He decides to get air at this point to fill his tank, how many gallons will he be

adding to fill the tank?

C. If air cost $0.50 a cubic foot how much did he pay for the air?

You now have to show them the solution to each scenario.


Grade 7 – Unit 1

Task 2: Scuba Diving: How Fast UP? & What about the air?

Student Name: _________________________________Date: _______

Teacher: ______________________________________Section: ____________

Answer form: Present each scenario in an equation. Show you work here and place the

answer on the blank provided.

First: What is the safe ascending speed? (Round to the nearest foot.)

Equation: ____________________________________________

Answer: ____________________________________________

Second: Diving Scenarios

1. How long will it take for a diver to return to the surface from a depth of 98ft?

Equation: ____________________________________________

Answer: ____________________________________________

2. A diver decided to ascend going slower than the maximum return rate. She goes

at 20ft/min from a depth of 123 feet below surface. How long will it take her to

return to the surface?

Equation: ____________________________________________

Answer: ____________________________________________


3. A Navy SEAL is returning to the surface from a depth of 165 feet. The Navy uses

an ascent rate of 60ft/ minute, how many minutes will it take for the SEAL to

return safe to the surface?

Equation: ____________________________________________

Answer: ____________________________________________

4. A diver off the shore of Malibu, California is 112 feet below and realized she

needs to meet her friend in 13 minutes. The boat is 9 minutes from the dock.

Can she make it?

Equation: ____________________________________________

Answer: ____________________________________________

Third: Air Tank Scenarios - 100 cubic feet and lasts about 50 minutes

A. Peter filled up only ¼ of the 100-cubic feet air tank because he was short on

money. He used ½ of the air in a quick dive with some friends. How long was

he under water?

Answer: ____________________________________________

B. He decides to get air at this point to fill his tank, how many gallons will he be

adding to fill the tank?

Answer: ____________________________________________

C. If air cost $0.50 a cubic foot how much did he pay for the air?

Answer: ____________________________________________

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