TITLE:    Calendar Patterns
 

CONTENT  AREAS:    Algebra
 

GRADE  LEVEL:   
 4-6

MATERIALS   NEEDED:    Calendar
 

KEY   CONCEPTS:    Understand a pattern to develop a rule describing the pattern which may include a single arithmetic operation.
 

EALR'S (Make the connections clear and specific):  Solve a problem that uses a pattern with a single operation.  
 

GOALS (Remember the difference between goals and objectives): Students will be able to use arithmetic operation with 100% efficiency.
 

OBJECTIVES:    Students will derive a general rule for adding three consecutive numbers. 
 

PROCEDURES:  (Label each step in the process:  Activating Prior Knowledge, Disequilibration, Elaboration, Crystallization)

• Introduction/Preassessment

(Disequilibration):  Pose problem to class: “What is the sum of the first 100 consecutive numbers?”  Assess class reaction to this question.  Students will feel confused and think that it will take a long time to figure out a way.  Make sure all students understand that consecutive means three numbers that appear next to each other.  Ask students to look around the room for three numbers that appear next to each other.  Students can refer to the calendar for consecutive dates. 

• Activity

Ask students to add any three dates that appear next to each other and look for a pattern.

Ask students to write their number sentences on the board or on index cards to be posted.

After students have posted several examples, ask if anyone has found a pattern.  Students should see that the sum of three consecutive numbers is the same as the middle number added three times:  9+10+11=10-1+10+10+1.

Ask why that equation is true (The first number is 1 less than the middle, and the last number is 1 more, sot they add to 0).  Middle-1 + middle + middle+1=middle + middle + middle.

They may express this as: sum=m+m+m, or sum=3 x m.

Then ask students to see if this equation will work for the question posed at the beginning of the lesson.  Students should note that 1-100 is an even amount of #’s.  They should test their equation on an even # of consecutive #’s first.  They will have to find the middle value (for example 1+2+3+4=10, 2.5 is the middle value and 4x2.5=10.   Have students work alone or in pairs to figure out the middle value between 1 and 100.  Then using the formula derived, find the sum of the first 100 consecutive numbers.   

• Closure

  Discuss with students the process of problem solving this question.  List steps on the board (define problem (what are the first 100 consecutive numbers and what does consecutive mean),  devise a plan (use smaller amount to generate formula), carry out the plan (try formula), look back or evaluate the solution (does the answer seem reasonable).   
    
 

POST-ASSESSMENT