Bell Work Booklet Rationale:

Bell work is meaningful work meant for the beginning of class time which gives both students and teachers a chance to settle into class and be prepared for learning. It gives a chance for late students to proceed to class without missing instructional time. It provides teachers with an opportunity to complete tasks such as attendance, one-on-one conversations, and catch-up to take place without delaying the instructional process. Bell work can be focused on any area of curriculum with it tending to be cross-curricular in elementary and subject focused in higher grades. It is a great place to focus new, on-going, or big picture ideas that are being initiated into your classroom.

The bell work booklet for my project is individualized per the unit, so will deal with problems pertaining to the unit, Equations, as well as other logic and critical thinking problems. This bell work would be continued throughout the year, taking what is learned in the last unit and continuing to learn and develop knowledge pertaining to critical thinking through each individual unit. It is a stable continuum of learning that connects the units together creating a flow from one unit to the next; a routine students will come to expect. The bell work will help to encourage students to open their minds to view problems from different sides both mathematically and socially. Throughout the booklet students will develop critical thinking skills that will follow them through their lives. Specifically, I will focus student’s learning on professional discussion and how to defend/dispute opinions in a logical and evidence-based way. Some skills include:

How to professionally have a discussion/argument Open mindedness Valid/Strong reasoned arguments Attitudes pertaining to critical thinking Strategies to start a problem/issue

Over-arching Question:What does critical thinking look like in the math classroom?

Through this question we will begin our journey to discovering and analyzing what it means to be a critical thinker. We will look at how to implement and use it in our math classes, other subject classes and how we can take this skill out of the classroom and use it in our everyday lives.

Bell Work BookletUnit : Fractions

Name:

Page 1: Discuss questions with your elbow partner quietly.

What does it mean to think critically?

What does critical thinking have to do with this unit, Fractions?

Page 2: Individually answer the following questions.

1. What can a fraction tell you?

2. Which fractions are the same?

a) ½

b) 7/14

c) 1/3

d) 3/6

What is a strategy you used to answer Question 1? Question 2?

Page 3: With your elbow partner attempt to solve the following problems.Remember: These may be new to you, try different strategies we have looked at.

1. At my favourite fruit stand in Puzzleland, an orange costs 18¢, a pineapple costs 27¢, and a grape costs 15¢. Using the same logic, can you tell how much a mango costs?

2. Take away 3 matchsticks to make this equation make sense? Can you find both solutions?

Page 4: Individually answer the following questions

1. Solve the following .

2. Discuss: Why is your answer correct?

Page 5: Individually read the following dialogue underline the fallacious statement and attempt to correct their argument.

1. You have no right to get mad at me for coming home late. Last night, Billy came in late, and you didn’t even notice.

2. Everyone eats meat – at least all normal people.

3. Capital punishment is wrong- it’s just legalized murder.

4. We don’t need to listen to Miss Boschee in Science; she’s only a Math major.

Page 6: Individually read the following phrase and then answer the questions

When Jim was taking a stroll one day, he met his father-in-law’s only daughter’s mother-in-law. What did he call her?

1. State the question in your own words.

2. What are two strategies you can use to help you solve this problem?

3. What did he call her?

With your elbow partner, compare answers and have a discussion – If you have the same answer, about how you figured it out. If you have different answers, discuss your process and see if you can find out which answer is correct and why?

Page 7: With your elbow partner, complete the following questions.

1. Which of the following is the best representation? Why?

a) ½ b) 5/10 c) 25/50

2. Which of the following is the largest? Which is the smallest? Why?

a) ½ b) 2/3 c) 20/100

3. Write the following as a decimal and as a fraction.

Page 8: Solve the following word problems with your elbow partner.

1. Jeremy is 13 years old. The sum of his age and his sister’s age is 23. How old is Jeremy’s sister? How do you know?

2. An ice-cream cone costs $2. Josephine paid $12 for ice-cream cones when she was shopping at the mall with her friends. How many friends does she have with her? How do you know?

3. What were important terms to note in each problem? What part of inquiry does this help you with?

Page 9: Individually complete the following questions.

1. Recall: What is an analogy?

2. 5 : :: :

3. Create an analogy about math class and then share it with your elbow partner. Does your partner’s analogy make sense? Could it be made better?

Page 10: Individually complete the following.

1. Using the improper fraction 9/6, make it a mixed number by:

a) Drawing a picture

b) Using division

2. Which do you find easier and why?

Page 11: Individually, complete the following problems.

1. Which set of numbers would most logically come next in the following sequence? Why?

1 0 1 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 a) 9 1 b) 9 3 c) 8 5 d) 6 7

2. How many squares of any size are in the diagram below?

Did you use a strategy of any kind to help you?

Page 12: With your elbow partner, complete the following.

1. What does the key words in a word problem mean?

2. What are some examples of key words that may be used in a word problem?

3. How do key words relate to critical thinking?

Page 13: Individually read the following statement and then answer the questions.

Fractions are important… because we use fractions everyday.

1. Defend or dispute the following ‘premise’ by creating at least three supporting arguments for your opinion.

2. Share your arguments with your elbow partner. Are their arguments logical? Why/Why not?

3. Was the original statement a valid premise? Or was it fallacious? How? Think about it and we will answer as a class.

Page 14: With your elbow partner, complete the following.

1. If TEN = 20 – 5 – 14; and MEN = 13 – 5 – 14; what does WOMEN equal by the same logic? Explain your reasoning.

2. Which set of numbers would most logically fill in the blanks in the following series? Explain your reasoning.

101, 99, 102, 98, 103, 97, , , 105, 95, 104, 94, a) 101, 98 b) 104, 96 c) 106, 99 d) none of these

Page 15: Individually complete the following.

1. What is one important characteristic you have learned about critical thinking during this unit? Explain.

2. How does critical thinking apply to other math units you have completed?

3. What is one thing you really liked about this bell work? What is one thing you disliked? Why?

Solutions:

Bell work solutions will include both problem solutions as well as discussion topics that will go along with the bell work for that day. We will delve further into strategies as well as understanding and using proper terminology such as inductive, deductive, and analogical arguments. We will also look at some common fallacies. Ongoing will be discussions of logical reasoning and how to professionally converse with our peers, what to do in a disagreement, and how to support our opinions and conclusions.

Bell Work BookletUnit 6: Equations

Name: SOLUTIONS

Page 1: Discuss questions with your elbow partner quietly.

What does it mean to think critically?

What does critical thinking have to do with this unit, Equations?

Answers and Discussion: Introductory Lesson Plan

Page 2: Individually answer the following questions.

1. What can a fraction tell you?

Part of a whole.

2. Which fractions are the same?

a) ½ a and d

b) 7/14

c) 1/3

d) 3/6

What is a strategy you used to answer Question 1? Question 2?Previous knowledge. Math. Drawing.

DISCUSSION: How to defend your answer basically, why does you believe what you do. Then, using your answer, does it actually work or does it need adjustment? Brainstorm problem-solving strategies.(Pearson. (2007) Math makes sense. Unit 6: Equations. Pearson Education Canada.)Page 3: With your elbow partner attempt to solve the following problems.Remember: These may be new to you, try different strategies we have looked at.

3. At my favourite fruit stand in Puzzleland, an orange costs 18¢, a pineapple costs 27¢, and a grape costs 15¢. Using the same logic, can you tell how much a mango costs?

Orange = 6 letters, Pineapple = 8 letters, Grape = 5 letters. Find this pattern therefore each letter is 3 cents. So, Mango = 5 letters so 5x3 = 15 cents

4. Take away 3 matchsticks to make this equation make sense? Can you find both solutions?

1+7=8; 7+1=8DISCUSSION: Considering and applying strategies. Understanding the problem. Discussing reasoning.

(Salny, A. (1989). The mensa genius quiz a day book. New York, NY: Perseus Books)

Page 4: Individually answer the following questions

1. Solve the following . 1.a 2.c

2. Discuss: Why is your answer correct?Discussion: Using prior knowledge, and how to put mathematical knowledge into words. Logical Reasoning(Small, M. & Lin, A. (2010). Great ways to differentiate secondary mathematics instruction. New York, NY: Teachers College Press. )

Page 5: Individually read the following dialogue. Underline the fallacious statement and attempt to correct their argument.

1. You have no right to get mad at me for coming home late. Last night, Billy came in late, and you didn’t even notice.

Fallacy of Two Wrongs. Two wrongs do not make a right!

2. Everyone eats meat – at least all normal people.

Fallacy of Popularity. Just because it is popular does not make it true/right

3. Capital punishment is wrong- it’s just legalized murder.

Begging the Question. Repeating the premise.

4. We don’t need to listen to Miss Boschee in Science; she’s only a Math major.

Ad Hominem. Just because she is a math major does not mean she is not knowledgeable in science.

Discussion: Picking out fallacies and correcting it to make it more logical.(Balin, S. & Battersby, M. (2010). Reason in the balance: An inquiry approach to critical thinking. McGraw-Hill Ryerson Limited.)

Page 6: Individually read the following phrase and then answer the questions 6.3

When Jim was taking a stroll one day, he met his father-in-law’s only daughter’s mother-in-law. What did he call her?

1. State the question in your own words.

What did Jim call his wife’s mother-in-law? What did Jim call his father-in-law’s only daughter’s mother-in-law? (Cut out unnecessary information to better understand problem)

2. What are two strategies you can use to help you solve this problem?

Change wordingDraw a picture

3. What did he call her?MOM

With your elbow partner, compare answers and have a discussion – If you have the same answer, about how you figured it out. If you have different answers, discuss your process and see if you can find out which answer is correct and why?DISCUSSION: Logical Reasoning. Understanding the problem, using strategies, coming to a conclusion. Stating and debating your conclusion. PROCESS OF CRITICAL THINKING

(Salny, A. (1989). The mensa genius quiz a day book. New York, NY: Perseus Books)

Page 7: With your elbow partner, complete the following questions.

1. Which of the following is the best representation? Why?

a) ½ b) 5/10 c) 25/50All the same however, simplified is best so ½

2. Which of the following is the largest? Which is the smallest? Why?

a) ½ b) 2/3 c) 20/100 2/3 largest 20/100 smallest.Because ½=15/30, 2/3=20/30, 20/100 or 1/5=6/30

3. Write the following as a decimal and as a fraction.

1/10 and 0.1Discussion: Defending your conclusion. What type of argument did you use? Were there any fallacies in your partner’s reasoning? Did it make sense?

(Pearson. (2007) Math makes sense. Unit 6: Equations. Pearson Education Canada.)

Page 8: Solve the following word problems with your elbow partner. 6.4

1. Jeremy is 13 years old. The sum of his age and his sister’s age is 23. How old is Jeremy’s sister? How do you know?

J=13; j+s=23 -> 13+s=23 -> 13+s-13=23-13 -> s=10

2. An ice-cream cone costs $2. Josephine paid $12 for ice-cream cones when she was shopping at the mall with her friends. How many friends does she have with her? How do you know?

12/2 = 6 means 6 ice-cream cones. Assuming Josephine buys one for herself, that leaves 5 cones. She has 5 friends with her.

3. What were important terms to note in each problem? What part of inquiry does this help you with?

Sum means +, is means =, How oldCost $2, Paid $12, How manyDiscussion: Understand the problem by understanding terminology. How can we figure out what terms mean? What is a strategy we can use to help understand the problem? – Underline/Highlight(Pearson. (2007) Math makes sense. Unit 6: Equations. Pearson Education Canada.)Page 9: Individually complete the following questions.

1. Recall: What is an analogy?

An argument form where two similar events/ideas/concepts are compared so that the properties/evidence of one will be the properties/evidence of the other.

2. 5 : :: 3 :

3.Create an analogy about math class and then share it with your elbow partner. Does your partner’s analogy make sense? Could it be made better?

Discussion: Analogical distance. Are the cases reasonably comparable? What would make it better? Is it logical to make this comparison?

Page 10: Individually complete the following.

3. Using the improper fraction 9/6, make it a mixed number by:

c) Drawing a picture

d) Using division

9/6 = 1 r 3 so 1 and 3/6 or 1 and 1/2

Which do you find easier and why?ALL useful. Again, personal preference.

Discussion: This time, we are looking for fallacies in the others argument. What are these fallacies? Can you tell what kind of argument was used? Can we improve your partners argument? How?

(Pearson. (2007) Math makes sense. Unit 6: Equations. Pearson Education Canada.)

Page 11: Individually, complete the following problems.

1. Which set of numbers would most logically come next in the following sequence? Why?

1 0 1 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 a) 9 1 b) 9 3 c) 8 5 d) 6 7

2. How many squares of any size are in the diagram below?

25 1x1; 16 2x2; 9 3x3; 1 5x5; 4 4x4 = 45 Did you use a strategy of any kind to help you?

Color, one kind at a time, etc.

Discussion: Strategies and improving these strategies. Looking for patterns. Explaining your reasoning.

(Salny, A. (1989). The mensa genius quiz a day book. New York, NY: Perseus Books)

Page 12: With your elbow partner, complete the following.

1. What does the key words in a word problem mean?

Helpful terms that tell you what you need to do in the problem.

2. What are some examples of key words that may be used in a word problem?

Sum, Equal, Product, Quotient

3. How do key words relate to critical thinking?

Can help you identify the issue and potential fallacies. Focus words to help you research.

Discussion: Diagnosing the problem to aid in research

Page 13: Individually read the following statement and then answer the questions.

Fractions are important… because we use fractions everyday.

1. Defend or dispute the following ‘premise’ by creating at least three supporting arguments for your opinion.

When we cook we use fractions and you need to cook to eatTime is a fraction and we use time everydayMoney is a fraction and we need money

2. Share your arguments with your elbow partner. Are their arguments logical? Why/Why not?

3. Was the original statement a valid premise? Or was it fallacious? How? Think about it and we will answer as a class.

Either Or Fallacy. Discussion: Fallacies again as well as argument types. Are their arguments strong/valid/fallacious. Can their partner pick this out? How can they fix their mistakes?

Page 14: With your elbow partner, complete the following.

1. If TEN = 20 – 5 – 14; and MEN = 13 – 5 – 14; what does WOMEN equal by the same logic? Explain your reasoning.

T= 20th letter in alphabet, E= 5th, N= 14th; M= 13th, E=5th, N=14th;W= 23rd, O=15th, M=13th, E=5th, N=14th. WOMEN= 23-15-13-5-14

2. Which set of numbers would most logically fill in the blanks in the following series? Explain your reasoning.

101, 99, 102, 98, 103, 97, , , 105, 95, 104, 94, a) 101, 98 b) 104, 96 c) 106, 99 d) none of these-2,+3,-4,+5,-6,+7,….

Discussion: How is the term logic used in math, in critical thinking? How are patterns in word problems like patterns in arguments?

(Salny, A. (1989). The mensa genius quiz a day book. New York, NY: Perseus Books)

Page 15: Individually complete the following.

4. What is one important characteristic you have learned about critical thinking during this unit? Explain.

5. How does critical thinking apply to other math units you have completed?

6. What is one thing you really liked about this bell work? What is one thing you disliked? Why?

Discussion: Why certain terms came up multiple times, hopefully “logical”.

References

Balin, S. & Battersby, M. (2010). Reason in the balance: An inquiry approach to critical thinking. McGraw-

Hill Ryerson Limited.

Salny, A. (1989). The mensa genius quiz a day book. New York, NY: Perseus Books

Salvardodi, M. & Wright, J. (1998). Math games for middle school. Chicago, Il: Chicago Review Press.

Small, M. & Lin, A. (2010). Great ways to differentiate secondary mathematics instruction. New York, NY:

Teachers College Press.

Pearson. (2007) Math makes sense. Unit 6: Equations. Pearson Education Canada.