Mentor Text - Less Than Zero

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Grade 7 Math: Integers  

Differentiated Instruction Teaching/Learning Example 
    1  2  3  4  Subject/Course Code/Title/Curriculum Policy   Duration: Number of X minute periods  Mentor text Less than Zero  Word Study  Puzzle Piece Problem Solving**  Computer Tutorial 

Differentiated Instruction  Teaching/Learning Examples 

**Differentiated Instruction Structure  Differentiated Instruction Details  Knowledge of Students                                                                                            Differentiation based on student:    ;  Readiness   ;  Interests  ˆ Preferences:                                                              ˆ Styles   ˆ  Intelligences   ˆ Other (e.g., environment, gender, culture)  Need to Know  • Student readiness – graphing, numbers less than zero    How to Find Out    • Minds On – mentor text Less than Zero    Differentiated Instruction Response   ; Learning materials (content)  ˆ Ways of learning (process)  ˆ Ways of demonstrating learning (product)   ˆ Learning environment    Curriculum Connections  Catholic Graduate Expectation(s): 
• •

 

• Overall Expectation(s): 


presents information and ideas clearly and honestly and with sensitivity to others; works effectively as an interdependent team member respects the rights, responsibilities and contributions of self and others;  Represent, compare, and order numbers, including integers Make and evaluate convincing arguments, based on the analysis of data;  Identify and compare integers found in real-life contexts (e.g., –10°C is much colder than +5°C); Solve multi-step problems arising from real-life contexts using a variety of tools and strategies Identify and describe trends, based on the distribution of the data presented in tables and graphs, using informal language; Make inferences and convincing arguments that are based on the analysis of charts, tables, and graphs

• Specific Expectation(s):
• • •

• Big Idea(s): • Negative integers are the “opposites” of the whole numbers. Each integer is the reflection of its opposite across a line that is perpendicular to the number line at 0.  Learning Goal(s):
• Identify integers as positive or negative from key language indicators

• Solve problems involving integers    Assessment and Evaluation  Assessment Tools    Assessment/Success Criteria   Thinking  • Checklist  • Reasoning and Proving ≠ Interpret mathematical language charts and graphs  • Problem Solving ≠ Solve problems involving integers  Communication  • Communicating ≠ Use vocabulary of integers in a variety of contexts  • Representing ≠ Translate from one representation to another (ex. numeric → graphical)  Application  • Selecting Tools and Computational Strategies ≠ Select and uses strategies to solve problems  ≠ Mathematical Processes   Prior Learning  Prior to this lesson, students will have an understanding of:  • Reading line graphs  • Working in groups    Materials and Resources   Materials:  Less than Zero, Stuart J. Murphy  Appendix A: Integer Words – Student Anchor Chart  Appendix B: Guidelines for Solving Group Math Problems  Appendix C1‐4: Puzzle Piece Problems (Temperature, Scuba Diving, Football, Golf, Shopping, Hockey, Space, Office Tower)  Appendix D: Assessment Checklist  Appendix E: Problem Solving Answer Key  Internet Resources:  Spy Guys ~ http://www.learnalberta.ca/content/mesg/html/math6web/math6shell.html          Mathematics ‐ Grade 7 ‐ Introduction to Integers   

Differentiated Instruction Teaching/Learning Examples 2009 – Appendix Template                     2009 Differentiated Instruction Summer Program     HANDOUT 4a    Ontario Ministry of Education, Student Success/Learning to 18 Implementation, Training and Evaluation Branch 

1. 

Minds On                                                                                                                               
Š Establishing a positive learning environment                                                                                           Š Connecting to prior learning and/or experiences                                                                                      Š Setting the context for learning        

 
   

 
   

Connections 
L: Literacy  ML: Mathematical Literacy  AfL, AoL:  Assessment for/of  Learning                                               

Whole Class  ⇒ Read Aloud  Read aloud Less than Zero by Stuart J. Murphy. (In the mentor text, Perry the Penguin learns the value of budgeting  money as he attempts reach the goal of owning his own ice scooter. This basic introduction of integers uses  graphical models to extend the number line below zero.)    Pairs  ⇒ Word Study  After reading through the book one time, introduce the Integer Words class anchor chart. For the unit, the anchor  chart will serve as a tool to help students identify terminology that has positive and negative indications.    As the teacher reads through the story a second time, pairs use their student Integer Words chart (Appendix A) to  identify any words that have positive or negative implications.      Whole Class  ⇒ Discussion  Post the class anchor chart Integer Words and facilitate an open discussion of words that could be included under  the Positive or the Negative column. Encourage students to think of words outside the story. 
Action 
Š Introducing new learning or extending/reinforcing prior learning   Š Providing opportunities for practice and application of learning (guided > independent)

 
          AfL: Are pairs correctly  identifying  key words as  positive or negative? 

     

Groups of 4 ⇒ Puzzle Piece Problem Solving  Review Guidelines for Solving Group Math Problems (Appendix B) Create and post a large version of the created  anchor chart in the classroom for student reference.    Differentiate content by problem based on interest:  Place students into homogeneous groups based on interest,  while attempting to vary the readiness levels. (When dealing with insufficient numbers, groups of three may be  created with one student receiving 2 clues)     Groups work on different problems based on their interests. Each student in the group receives one clue for a  problem, based on readiness level that they share with their group members and use in determining the answer to  the problem. (Appendix C1‐4) 

     
AfL: Circulate while observing  group work and listening to  students. Checklist (Appendix D) 

 

           

Consolidation and Connection 
Š Helping students demonstrate what they have learned    Š Providing opportunities for consolidation and reflection

Whole Class ⇒ Discussion  Students post their solutions. As a class, sort the solutions by ways the problem was solved. This provides an  opportunity for students to see the work of their peers and to note similarities and differences in their strategies.  Students ask each other questions about their strategies.    Discuss and summarize the integer vocabulary used in each groups problem solving and add to the class Integer  Words anchor chart.    Individual ⇒ Online Tutorial  Students complete an online tutorial, Spy Guys: Integers, where they will confirm their understanding of the  language of integers. (To access, GOOGLE “Spy Guys”)    Home Activity  ⇒ Math Makes Sense Practice or Journal Entry  Math Makes Sense 7 p. 333 # 8, 11  or  Math Journal Entry: MMS p.333 Reflect‐ When two integers have different signs, how can you tell which is greater?   When two integers have the same sign, how can you tell which is greater?                             

     
AfL : Checklist   (Appendix D) 

                   

Differentiated Instruction Teaching/Learning Examples 2009 – Appendix Template                     2009 Differentiated Instruction Summer Program     HANDOUT 4a    Ontario Ministry of Education, Student Success/Learning to 18 Implementation, Training and Evaluation Branch 

2. 

Appendix A  

 

Introduction to Integers    

Grade 7 Number Sense and Numeration 

Integer Words: Student Anchor Chart  Words that mean “Positive”                                Words that mean “Negative” 

Differentiated Instruction Teaching/Learning Examples 2009 – Appendix Template  Ontario Ministry of Education, Student Success/Learning to 18 Implementation, Training and Evaluation Branch 

 

 

 

 

1. 

Appendix B  

 

Introduction to Integers    

Grade 7 Number Sense and Numeration 

Guidelines for Solving Group Math Problems   

1. Make sure each member of your group has a clue as all clues are specific and needed for the solution of the problem. 2. Read your clue and decide what information is important to the solution of your problem. Determine how your clue might be used in the solution. 3. Share your clue with your group by reading it aloud. 4. Obtain any manipulative that you think might help you understand or solve your problem. 5. Write the important information from each clue down on chart paper. 6. Everyone in your group must participate in solving the problem. 7. Record how you solved the problem. Use pictures, words and/or diagrams. Be prepared to share with the class. You may use manipulative models to support your presentation. ; If your group agrees that it needs help, ask the teacher.
Taken from Differentiated Instruction Educator’s Package: Facilitator’s Guide‐Mathematics (p.23). Adapted from United We Solve by Tim Erikson, eeps media 

 

Differentiated Instruction Teaching/Learning Examples 2009 – Appendix Template  Ontario Ministry of Education, Student Success/Learning to 18 Implementation, Training and Evaluation Branch 

 

 

 

 

1. 

Appendix C1 

 

Introduction to Integers   

Grade 7 Number Sense and Numeration 

Golf Problem
 
CLUE 1: Tiger Woods shot the overall lowest score during the rounds, a 4 under par in the first round, which was two shots better than Mike Weir's first round. Who won the tournament?

Hockey Problem
CLUE 1: The worst plus / minus average on each team (in no particular order) were: -5 , -2 , -4, -4, -9 and -6. Toronto’s worst plus / minus average was less than -5. The difference between Montreal’s best and Vancouver’s worst plus / minus was 7. Calgary’s best player was 9 better than Montreal’s worst player. What were best and worst plus / minus averages on each team? CLUE 2: Edmonton’s best plus / minus was greater than +3. Of the six teams, Calgary had the player with the worst plus / minus. Ottawa and Vancouver had the same worst plus / minus average, while Ottawa and Edmonton tied for the best player average. What were best and worst plus / minus averages on each team? 

 
CLUE 2: Mike Weir shot the same score in each round. Ernie Els had the highest score in round 1, but improved to have the lowest score in round 2. Who won the tournament?

 
CLUE 3: The difference between the highest score and lowest score in the each of the two rounds was 6. Vijay Singh had the highest score in round 2, a three over par score. Who won the tournament?

CLUE 3: Vancouver’s best plus / minus was 12 greater than Calgary’s worst. Toronto’s best plus minus was less than +5. The difference between Ottawa’s best and worst player averages was 9. What were best and worst plus / minus averages on each team? 

 
CLUE 4: Tiger Woods finished with a total score of three under par, five shots better than Vijay Singh's total score. Who won the tournament?

CLUE 4: Montreal’s worst plus / minus was not -2. The difference between Toronto’s best and worst player was 10. Vancouver’s worst player had a plus / minus greater than -5. What were best and worst plus / minus averages on each team? 

   
Differentiated Instruction Teaching/Learning Examples 2009 – Appendix Template  Ontario Ministry of Education, Student Success/Learning to 18 Implementation, Training and Evaluation Branch          1. 

Appendix C2 

 

Introduction to Integers   

Grade 7 Number Sense and Numeration 

Temperature Problem
CLUE 1: A newspaper listed the record low and high temperatures of four Canadian cities since 2001: Vancouver, Iqaluit, Toronto and St. John. The lows were: -42oC, -9oC, -20oC and -23oC. Toronto’s high temperature was 44oC greater than Vancouver’s low temperature. What were the low and high temperatures of each city? CLUE 2: St. John’s low temperature was less than -23oC. The difference between Vancouver’s high temperature and Iqaluit’s low temperature was 78oC. Vancouver’s low temperature was not -20oC. What were the low and high temperatures of each city? CLUE 3: Vancouver’s high temperature was greater than 27oC. Of the four cities, Iqaluit had the lowest temperature. The difference between St. John’s high and low temperature was 50oC. What were the low and high temperatures of each city?

Scuba Diving Problem
 
CLUE 1: Your family is on a dream vacation to the Osprey Beach resort in Turks and Caicos. The resort is located on a cliff overlooking the Atlantic Ocean at 11m above sea level. You have decided to go on a scuba diving adventure as a family and are excited to dive the Grand Turk wall and see the amazing marine life as well as the famous Molasses Reef shipwreck. What is the distance (in metres) from the scuba diving boat to the bow of the shipwreck? CLUE 2: As you approach the scuba site you see a dolphin jump 5m above the surface of the water! Later when you are diving, you see a seahorse swim by 13m above the bow of the shipwreck. The seahorse is swimming 4m below the hawksbill turtle. What is the distance (in metres) from the scuba diving boat to the bow of the shipwreck?  CLUE 3: While you are swimming along the reef, you almost bump into a hawksbill turtle that is gliding along, 6m below the ocean’s surface. Later, you hear that your father saw a whale shark! Lucky for you it was swimming 2m below the bow of the shipwreck – which was too deep for you! What is the distance (in metres) from the scuba diving boat to the bow of the shipwreck?  CLUE 4: You are thrilled when you make it to the bow if the shipwreck. It is amazing how the marine life has taken over the old boat. Later, when you’re safely back in your room you decide to draw a diagram in your journal of what your family saw. The difference between the hotel and the whale shark sighting is 36m. What is the distance (in metres) from the scuba diving boat to the bow of the shipwreck? 

 

 

CLUE 4: Iqaluit’s high temperature was 50oC greater than Toronto’s low temperature. Toronto’s high temperature was less than 36oC. Iqaluit’s low temperature was less than -23oC. What were the low and high temperatures of each city?

 

Differentiated Instruction Teaching/Learning Examples 2009 – Appendix Template  Ontario Ministry of Education, Student Success/Learning to 18 Implementation, Training and Evaluation Branch 

 

 

 

 

1. 

Appendix C3 

 

Introduction to Integers   

Grade 7 Number Sense and Numeration   

Football Problem
CLUE 1: In the final possession of the conference championship game against the Tennessee Titans, the Buffalo Bills need a touchdown to win the game. Luckily during the possession, the star running back ran the ball 41 yards before going out of bounds at Tennessee’s 32 yard line.

Shopping Problem
 
CLUE 1: For your twelfth birthday, your grandparents set up a bank account for you and gave you your first debit card. As an additional gift, they deposited $100 to get you started. Over the month of November you made a variety of purchases and deposited some money that you made babysitting your nextdoor neighbours. At the end of the month, your favourite band released their new album on iTunes for $17.95. Is there enough money in your account to buy the album? CLUE 2: Over the course of the month you babysat for an hour after school 6 times for a total of $42. You treated your best friends to ice cream which came to $18 Is there enough money in your account to buy the album?  CLUE 3: Your favourite store had a HUGE sale on the second week of November and you purchased a new pair of jeans as well as three t-shirts and a pair of sneakers. Your bill came to $73. Is there enough money in your account to buy the album?

Did the Buffalo Bills win the championship? CLUE 2: At the end of one play, the top receiver made a finger tip grab and landed 39 yards from where the ball was released by the quarterback. Did the Buffalo Bills win the championship? CLUE 3: The Bills gained possession of the football at their own 18 yard line. There is a difference of 50 yards from this point and where they would be at the start of their third down. Did the Buffalo Bills win the championship? CLUE 4: The first play of the possession resulted in a near interception, but the ball squeezed through the hands of the Tennessee cornerback and landed firmly in the grips of the Buffalo receiver for 9 yard gain. Did the Buffalo Bills win the championship?

 

 

   
CLUE 4: Before you were able to deposit your babysitting money you spent $12 of it on a movie and popcorn, and leant your sister $12 so she could come - which you are still waiting to get back from her! Is there enough money in your account to buy the album? 

 
     
Appendix C4    Introduction to Integers    Grade 7 Number Sense and Numeration 
        1.  Differentiated Instruction Teaching/Learning Examples 2009 – Appendix Template  Ontario Ministry of Education, Student Success/Learning to 18 Implementation, Training and Evaluation Branch 

 

Space Problem
CLUE 1: If you’ve never watched a NASA shuttle launch – it is a spectacle that you don’t want to miss! In the minutes leading up to the launch are filled with anticipation as the crew gets ready for lift-off. At T-3 hours the astronauts are strapped into their seats in the shuttle. How long after take-off do the astronauts reach the Earth’s orbit? CLUE 2: Astronauts measure time in 2 ways: the time before lift-off (eg. T-10 = ten seconds before liftoff) and the time after liftoff (called mission elapsed time or MET … an MET of 2 minutes means 2 minutes into the mission). At an MET of 2 minutes the two white slender solid rocket boosters (SRBs) are released. How long after take-off do the astronauts reach the Earth’s orbit? CLUE 3: There is 3 hours and 18 minutes between the time the astronauts are strapped into their seats and when they reach orbit. How long after take-off do the astronauts reach the Earth’s orbit? CLUE 4: The dark orange external tank is released to burn up in the Earth’s atmosphere as the shuttle reaches orbit. This happens 6 minutes after the SRBs are released. How long after take-off do the astronauts reach the Earth’s orbit?

Office Tower Problem
 
CLUE 1: Gavin works for the Better than Words Publishing Company in the Glamour Building on Main Street. It is Friday afternoon and he is in a rush to get home and start his weekend. When he reaches his car in Parking Lot B, he realizes that he forgot his cell phone on his desk. Begrudgingly, he makes his way back up to his office, only to realize that he has left his office keys in his car. How many floors apart are the keys and the locked office? CLUE 2: The Glamour Building is known for its Rooftop Restaurant that is 9 floors above the Fitness Centre. Gavin’s office is directly below the Security Firm offices that are 9 floors above Maintenance. The lobby sits at ground level (0), and Parking Lots A, B, and C are the three floors beneath the lobby. How many floors apart are the keys and the locked office? 

 

 

CLUE 3: Marla Malkinson, the infamous model lives in the Penthouse suit, which is convenient considering it is only a 6 floor ride down the elevator to the Photography Studio offices. The fitness centre is located on the first floor of the building, which is 5 floors above Maintenance. How many floors apart are the key and the locked office?  CLUE 4: Parking Lot A is one floor below the lobby and 3 floors below the Insurance offices. There are three condo levels between the Security firm offices and the Penthouse Suite. The higher up in the building, the more expensive the condo becomes – so the 8th floor condos are the most expensive in the building. How many floors apart are the key and the locked office? 

 

Differentiated Instruction Teaching/Learning Examples 2009 – Appendix Template  Ontario Ministry of Education, Student Success/Learning to 18 Implementation, Training and Evaluation Branch 

 

 

 

 

1. 

Appendix  D 
 

 

Introduction to Integers   

Grade 7 Number Sense and Numeration 

Puzzle Piece Problem Solving – Observation Checklist (AfL) Name: ____________________
Categories / Mathematical Processes

Thinking

Reasoning and Proving Problem Solving

Communication
Communicating Representing

Application
Selecting Tools and Computational Strategies
 

Criteria and Indicators The student: Interprets mathematical language, charts and graphs Solves problems involving integers The student: Uses vocabulary of integers in a variety of contexts Translates from one representation to another (i.e. numeric Æ graphical) The student: Selects and uses strategies to solve problems

9

Name: ____________________
Categories / Mathematical Processes

Thinking

Reasoning and Proving Problem Solving

Communication
Communicating Representing

Application
Selecting Tools and Computational Strategies

Criteria and Indicators The student: Interprets mathematical language, charts and graphs Solves problems involving integers The student: Uses vocabulary of integers in a variety of contexts Translates from one representation to another (i.e. numeric Æ graphical) The student: Selects and uses strategies to solve problems

9

Differentiated Instruction Teaching/Learning Examples 2009 – Appendix Template  Ontario Ministry of Education, Student Success/Learning to 18 Implementation, Training and Evaluation Branch 

 

 

 

 

1. 

Appendix  E – Problem Solving Answer Key  

Introduction to Integers  Grade 7 Number Sense and Numeration   

Golf Problem
Mike Weir won the tournament.
TW MW EE VS   Round 1 -4 -2 +2 -1 Round 2 +1 -2 -3 +3 Overall -3 -4 -1 +2

 

Hockey Problem
The best plus/minus averages were as follows:
CiTY Toronto Ottawa Montreal Vancouver Calgary Edmonton BeST +4 +5 +3 +3 +4 +5 WoRST -6 -4 -5 -4 -9 -2

 

Shopping Problem
There is enough money in your account to by the cd. Total earnings $100.00 (gift) + $42.00 (babysitting) $142.00 Total spending $ 18.00 (ice cream) $ 73.00 (clothes) $ 12.00 (movies) + $ 12.00 (lent to sister) $115.00 Earnings – Spending $142.00 - $115.00 = $27.00 There is $27.00 left in the account, which is more than enough to buy the cd for $17.95

 

Office Tower Problem
The keys are six floors away from the locked office.

Rooftop Restaurant Penthouse Condo Level 3 Condo Level 2 Condo Level 1 Security Firm Offices Better than Words Offices Photography Studio Insurance Offices Fitness Centre Lobby Parking Lot A Parking Lot B Parking Lot C Maintenance
+10 +9 +8 +7 +6 +5 +4 +3 +2 +1 0 -1

Temperature Problem
The low and high temperature of each city is as follows: CiTY HiGH LoW Vancouver 36 -9 Iqaluit 27 -42 Toronto 35 -23 St. John’s 30 -20

Space Problem
The astronauts reach the Earth’s orbit 18 minutes after liftoff. MET-18min MET-8min MET-2min 0 T-3 hours
(reach orbit) (orange tank released) (SRBS released) (liftoff)
(astronauts strapped in)

-2

-3 -4

     

 
Hockey Problem
CiTY Toronto Ottawa Montreal Vancouver Calgary Edmonton

The best plus/minus averages were as follows:
BeST +4 +5 +3 +3 +4 +5 WoRST -6 -4 -5 -4 -9 -2

   

 

 

 
Football Problem

Scuba Diving Problem

The distance from the scuba diving boat to the bow if the shipwreck is 23 meters.

The Buffalo Bills get the touchdown and win the game.

     
 

 
Differentiated Instruction Teaching/Learning Examples 2009 – Appendix Template  Ontario Ministry of Education, Student Success/Learning to 18 Implementation, Training and Evaluation Branch          1. 

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