I. Curricular Framework

Concept:

Patterns

Essential Question:

How often do you encounter sequencing and series in your daily life?

Bridge:

Progressions

Content:

Sequence and Series

Outcomes:

II. Standards Aligned

III. Instruction and Assessment

1. Connect: Connecting to the Concept Experientially

Objective: To create an awareness for students regarding mathematical progression.

Activity: Separate students into five groups and have them re-create a thunderstorm using sound and movement or show slide presentation from "The Powers of Ten."

Assessment: Quality of reactions and participation of students.

2. Attend: Attending to the Connection

Objective: To enhance student ability to discuss what they have seen or experienced based on their perceptions.

Activity: Discuss the thunderstorm activity and how the activity related to mathematics or have student discuss and analyze the slide presentation.

Assessment: Willingness to participate in discussion and ability to listen to comments from classmates.

Assessment, Phase One, Level of Engagement, Fascination:

3. Image: Creating a Mental Picture

Objective: To add to the students understanding of the concept of sequence.

Activity: Students working in five groups will be given a bag or box with instructions for completing four tasks. The tasks include stacking cans, placing jelly beans in a jar, placing beans in a can, and cutting paper. (Two groups will stack cans.) Instructions for the tasks are as follows: Allow each group 6 to 8 minutes to complete a task before moving to the next. JELLY BEANS: Determine how many jelly beans you want to put in the jar to start. Continue putting the same number in the jar until the jar is filled or the jelly beans are gone. How many did you decide to put in each time? How many "additions" were made to the jar? What is the total number of jelly beans in the jar? Is there a way to determine this without counting all the jelly beans? BEANS: Put one bean in the jar. Put twice as many beans in the jar. Continue putting twice as many beans in the jar as previously. Continue until all the beans are gone. What starts happening to the number of beans put in each time? How do the "number" of beans compare? What is the total number of beans in the jar? How did you arrive at this figure? How many times did you "add" beans to the jar? STACKING CANS (or CUPS) Stack the cans (cups) given to you to form a pyramid. How did you start? How many cans (cups) in each row? How does the number of cans in the bottom row compare to the number of cans in the top row? What is the total number of cans in the stack? Is there a way to figure it out without counting all the cans?

Assessment: Group participation, adherence to guidelines and ability to complete each task.

Assessment, Phase Two, Seeing the Big Picture:

4. Inform: Receiving Facts & Knowledge

Objective: To define sequence and series, discuss the different types of sequences and series, and their related formulas.

Activity: Teacher presents vocabulary, new information, formulas using lecture, demonstration and discussion.

Assessment: Student notetaking and teacher checking for understanding.

Assessment, Phase Three, Success with Acquiring Knowledge:

5. Practice: Developing Skills

Objective: To reinforce understanding by practice.

Activity: Students will work sample problems in text and teacher-prepared worksheets using prescribed procedures, take quizzes and tests, and write test summaries.

Assessment: Quality and accuracy of worksheets, quizzes, tests and written summaries.

Assessment, Phase Four, Success with Acquiring Skills:

6. Extend: Extending Learning to the Outside World

Objective: To enhance student creativity and ability to work together as a group.

Activity: Students will be divided into groups. Each group will be given a recipe to increase/decrease sequentially (at least three changes). They must conclude with a required number of servings for which they will prepare a shopping list. Mathematical calculations will be required and will be shared with the class.

Assessment: Enthusiasm of students and accuracy of shopping list.

7. Refine: Refining the Extension

Objective: To follow plan in real life activity.

Activity: Take class to a local grocery store with their shopping lists. Each group will determine quantities needed and most cost effective way to purchase their supplies.

Assessment: Quality of group interaction.

8. Perform: Creative Manifestation of Material Learned

Objective: To prepare recipe and share with class.

Activity: Take class to food lab, prepare recipe, and share product with the class.

Assessment: Contribution to group effort and level of enjoyment.

Assessment, Phase Five,Performance, Creative Use of Material Learned: