August 17, 2008

Member Rating

Curriki Rating

On a scale of 0 to 3

3On a scale of 0 to 3

The resource has been added to your collection

Self-paced, inquiry-based learning

- 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

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

Curriki Rating

On a scale of 0 to 3

3On a scale of 0 to 3

This resource was reviewed using the Curriki Review rubric and received an overall Curriki Review System rating of 3, as of -0001-11-30.

FileChecker2 FileChecker2

This resource received a 3* rating because it is part of Patterns, Variables and Functions: Integrated, Project-Based, Science and Mathematics Inquiries for Diverse Fifth and Sixth Grade Learners, which received…In Collections #### Patterns, Variables and Functions: Integrated, Project-Based, Science and Mathematics Inquiries for Diverse Fifth and Sixth Grade Learners

Table of Contents

- Introduction
- Goals
- Overview
- Rationale
- Context
- Assessment
- Inquiry One: The "Infinite" Across the Disciplines
- Inquiry Two: Discovering Relationships Among Variables
- Inquiry Three: Describing Change Using T-Charts, an Introduction to Functions
- Inquiry Four: Introduction to Exponents
- Inquiry Five: Describing Functions and Solving for Variables
- Inquiry Six: Magic Squares
- Inquiry Seven: Variables and Functions We Notice in the World
- Inquiry Eight: Using Graphs, Words and Pictures to Describe Functions

View Content *Inquiry* *One: The "infinite" across the disciplines*

*InquiryThree: Describing relationships using T-Charts, an introduction to functions*

*Inquiry Four: Introduction to Exponents* Exponents are a key idea used in math and science to describe patterns of change between variables. Students are presented with a chart that shows the relationship between the powers of ten and ways of writing 10, 100, 1000, etc. Students may later draw on their experience with exponents when describing patterns (functions) they discover in the graphs they'll later make of observed phenomena.

In the first inquiry, students will explore the concept of "the infinite" as a way to grasp the idea that some events, such as a ball of tinfoil being launched from a catapult made of Popsicle sticks, would go on forever unless something gets in its way (e.g., gravity). Students' background knowledge is first activated through opportunities to brainstorm what they already know about the infinite. Through group discussion of interdisciplinary paradoxes of of the infinite (in home and expert jigsaw groups), students will discover there is often "something which keeps something else" from going on forever. Those "somethings" become the foundation for the vocabulary to be introduced in the next inquiry (e.g., the weight of an object, force of the catapult, or air resistance).

*Inquiry* *Two: Discovering relationships among variables*

The next inquiry presents students with opportunities to use their intuitive definitions of **patterns**, the **infinite**, and **variables**, while exploring the properties and relationships of objects in a variety of contexts. Through this guided, but self-paced discovery, students will move between the following stations exploring the relationship between:

- Buoyancy and weight in the
*Lifeboat Inspection* - Gravity and weight in the
*Flipsticks*activity - Amount of liquid and pitch in the
*Physics of Sound*activity - Length of string and weight of an object in the
*Pendulum*activity (above activities adapted from Foss kits)

Students are encouraged to move from actual or physical experience with objects (variables), and their relationships (functions), toward a symbolic notion of the concepts. 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: Number of squares in the
*Squares from Squares*activity. - Number of triangles: Distance of perimeter in the
*Row of Triangles*activity - Number of pentagons: distance of perimeter in the
*Row of Pentagons*activity - Number of hexagons: distance of perimeter in the
*Row of Hexagons*activity

(from Marilyn Burns, About Teaching Mathematics)

*Inquiry* *Five: Describing Factors and Using Variables*

Using tiles, markers, and "hundreds" charts, students create patterns which "grow" by the same factor. Students write a rule to describe their pattern or function. Repeated exposure to the concepts of patterns, variables and functions provides multiple opportunities for students to see relationships. Students practice computing patterns of numbers by completing "textbook" problems.

*Inquiry* *Six: Magic Squares*

Students are individually presented with magic squares in which variables appear. They replace the variable with a number, which then creates an equal sum, whether one adds the numbers horizontally, vertically, or diagonally. Students complete "textbook" problems as practice in finding the value for the missing variables.

*Inquiry* *Seven: Variables and functions we notice in the world*

Students brainstorm possible sets of objects or events whose relationships cause an observable pattern, or function. Examples are given from the teacher during the brainstorming class brainstorming time, such as the size of an image on a screen to the distance of the projector from the screen, or the number of cars to the amount of carbon dioxide pollution. Students create collages that describe relationships they discover in the world through looking at newspapers and scientific magazines.

Inquiry Eight:*Using graphs, words and pictures to describe functions*

Using spreadsheet software, students enter data they collected from one or two experiments they conducted in Inquiry Three. Each person generates one or two graphs, a written explanation in English, other pictures if they wish as well as mathematical/symbolic descriptions.

Or

Our Terms of Service and Privacy Policies have changed. By logging in, you agree to our updated Terms and Policies.

Are you sure you want to logout?

Or