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Teaching for Understanding in Mathematics

Activity 1: Warm-up: The formula A=P+Prt can be used to find the amount of money (A) in a savings account, where P is the initial deposit, r is interest rate, and t is the time in years. Joquin deposits $400.00 into a new account with an interest rate of 3%. He makes no other deposits or withdrawals. How much money will he have in the account after 1 year?
(Estimated time: 10 minutes)

• Step 1: Write the equation A=400+400*.03*1 by substituting the appropriate values in for each variable.
  
• Step 2: Solve the equation by completing the computations on the right side of the equation
  
• Step 3: A=$412

Technology: TI 83 Calculator
Materials: Blackboard, pencil and paper
Student product or performance: Solving problem on their own and attentiveness during student explanation of solution.

Activity 2: Warm-up: Using Math Connections Manual page 19.You go to the store to buy some sodas. Each bottle cost $1.o5. If you buy 4 bottles, how much will it cost? If you buy 6? If you buy 12? If you buy 15? Set up a table to represent the data above. How would you head your columns? Which represents the independent variable in this situation? Which represents the dependent? Remember that the dependent value changes as the independent variable changes.
(Estimated time: 20 minutes)

• Step 1: Get the answers to each question.
  
• Step 2: Set up the table using correct headings.
  
• Step 3: Explain the concept of dependent and independent variables

Technology: Calculator
Materials: Paper and pencil
Student product or performance: Correct table set up.
Scoring: Through teacher observation and participation in group discussion.

Activity 3: Practice identifying independent and dependent variables: Students will discuss which is the independent and dependent variable in the following situations, giving reasons why which is which.

1. hours worked and amount paid.
   
2. area of a square and the length of each side.
   
3. weight of a book and the number of pages.
   
4. size of steak ordered and cost of meal.

(Estimated time: 10 minutes = Due to discussion of other factors that could influence the dependent variable)

Scoring: Observation as students participate in the discussion.

Activity 4: Written classwork which students will work on independently.
(Estimated time: 25 minutes)

• Step 1: Using the Formula F=1.8C+32 where F represents degrees Fahrenheit and C represents degrees Celsius, set up a table where C starts at 0 and increases in 5 degree intervals to 35.
  
• Step 2: Graph the table on the coordinate plane, labeling each axis correctly and using reasonable intervals.
  
• Step 3: Explain why the independent and dependent variable were labeled as they were in this problem. Make sure to use the formula in your explanation.

Technology: Calculator
Materials: Paper, graph paper, straightedge, and pencil
Student product or performance: Table, graph and written explanation.
Scoring: See Scoring Rubric

Activity 5: Summary: What distinguishes the dependent variable from the independent variable? Have the students discuss this question as they finish their graded assignment.
(Estimated time: 5 minutes)

Discuss homework directions as classwork is collected.
Homework: In Prentice Hall Algebra 1- Pages 71 and 72-#7,8,9,10 and 12b and d
(Estimated time: 5 minutes)

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Organize: On the classwork BCR that was assigned to the three classes being taught this information, the following breakdown was observed.

A total of 65 students submitted the work:

• 4 out of 65 received a 0, which was 6%.
  
• 2 out of 65 received a 1, which was 3%.
  
• 46 out of 65 received a 2, which was 71%.
  
• 13 out of 65 received a 3, which was 20%.

Breakdown by individual classes:

Period 2

• 3 out of 27 received a 0, which was 11%.
  
• 1 out of 27 received a 1, which was 4%.
  
• 18 out of 27 received a 2, which was 67%.
  
• 5 out of 27 received a 3, which was 18%.

Period 5

• No students in this class received a 0 or a 1.
  
• 11 out of 17 received a 2, which was 65%.
  
• 6 out of 17 received a 3, which was 35%.

Period 10

• 1 out of 21 received a 0, which was 5%.
  
• 1 out of 21 received a 1, which was 5%.
  
• 17 out of 21 received a 2, which was 81%
  
• 2 out of 21 received a 3, which was 9%
  

Reflect: I feel all three classes need work on how to determine the independent variable from the dependent variable using a formula. Some review in the form of drill, incorporation into future examples, classwork, and homework are needed for filling in a table using a given formula and constructing a graph from that table. All this will be infused in future lessons as review and reinforcement.