Inquiry Three: Describing Change Using T-Charts, an Introduction to Functions

Content
Information
Standards
Reviews

Type:

E-book, Other

Description:

Students move from actual physical experience with objects (variables) and their relationships (functions), toward a symbolic notion of the concepts.

Subjects:

Mathematics > General
Mathematics > Algebra
Mathematics > Applied Mathematics
Mathematics > Arithmetic
Mathematics > Graphing
Mathematics > Measurement
Mathematics > Number Sense & Operations
Mathematics > Patterns
Mathematics > Problem Solving
Science > General
Science > General Science
Science > Physical Sciences

Education Levels:

Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8

Keywords:

patterns variables functions formative assessment constructivist teaching and learning mulitple intelligence approach learning stations infinity math science

Language:

English

Access Privileges:

Public - Available to anyone

License Deed:

Creative Commons Attribution 3.0

Collections:

Patterns, Variables and Functions: Integrated, Project-Based, Science and Mathematics Inquiries for Diverse Fifth and Sixth Grade Learners

Update Standards?

SCI.6.2.C: Science

collect and record data using the International System of Units (SI) and qualitative means such as labeled drawings, writing, and graphic organizers;

SCI.6.2.D: Science

construct tables and graphs, using repeated trials and means, to organize data and identify patterns; and

SCI.7.4.A: Science

use appropriate tools to collect, record, and analyze information, including life science models, hand lens, stereoscopes, microscopes, beakers, Petri dishes, microscope slides, graduated cylinders, test tubes, meter sticks, metric rulers, metric tape measures, timing devices, hot plates, balances, thermometers, calculators, water test kits, computers, temperature and pH probes, collecting nets, insect traps, globes, digital cameras, journals/notebooks, and other equipment as needed to teach the curriculum; and

SCI.8.2.D: Science

construct tables and graphs, using repeated trials and means, to organize data and identify patterns; and

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Goal
Students move from actual or physical experience with objects (variables), and their relationships (functions), toward a symbolic notion of the concepts.

Objectives

Students see patterns when represented numerically
Understand relationships between shapes and perimeter
Describe the patterns of change among variables
Call those patterns of change a function

Time
About an hour of direct instruction from the teacher followed by up to week of self-paced exploration and expansion of the initial idea by students.

Materials

Student Observation and Reflection Journals
About 50 triangular tiles for Row of Triangles station
About 50 square tiles for Row of Squares station
About 50 pentagon tiles for Row of Pentagons station

Activity
Students rotate in groups through the following stations in order to gain more experience with relationships in the real world.

Length of the side of a square to number of squares: Squares from squares
Number of triangles to distance of perimeter: Row of triangles
Number of pentagons to distance of perimeter: Row of pentagons

Teacher models each station for the entire class.

Students make a T-Chart in each of their journals for each of the stations while gathering data.

Closure
Students respond to the following questions in their observation and reflection journals: What are the variables for each activity? What are the factors for each activity? What is the pattern or function (the rule you wrote) in each activity? What are some other patterns you noticed?

Assessment
Teacher reads and responds to journals in order to determine whether or not students are able to collect data in an organized way and if they are beginning to use the vocabulary in an accurate way. This is an opportunity for the teacher to catch misconceptions students may have and write questions to the students which may help eliminate those misconceptions.

Plan B
Students rotate one person at a time through the stations while others read silently if the groups do not work well together.