Activity 1: A Tool for Inquiry
Algebra with Manipulatives

Manipulatives as tools to support mathematical inquiry:

An exploration from the Video Studies in Math Education and Empowering Teachers: Mathematical Inquiry Through Technology (ETMITT) Project, Ricky Carter and Fadia Harik, BBN Learning Systems and Technologies.
Students in grade school commonly use tools to think about numbers. Base 10 blocks model our number system of units, tens, hundreds, and thousands with unit blocks, rods of ten, flats of one hundred and cubes of a thousand units. These tools aid in gaining a conceptual understanding of place value and the meaning of addition and subtraction. In most transitional algebra courses this key conceptual transition is omitted. Understanding of symbol manipulation is built as a house with no foundation of meaning. Manipulatives can provide that foundation. We will start with pattern blocks.
how long will it take? One hour, including viewing a fifteen-minute classroom case study video.
Assignments:
Readings
There is no reading for this assignment. Do the Hands On and view the Pattern Block Train video.
Hands-On
Activity 1
TO DO Checklist
__ Print this page!

Readings & Hands On
__ Complete the hands on assignment.

Initial Thoughts
__ Post your initial comments on Activity 1 and read some of the module-based discussion in the Algebra Discussion area. Check out the personal Introductions and Tech FAQ discussions there too.

Local Study Group Meeting
__ Attend LSG meeting where colleagues share their new "tools" for inquiry. Doing your presentation this week? Here are the notes you'll need.

Further Reflection
__ Visit the Algebra Discussion area to read more of the dialogue and post additional comments.

This Hands-On Activity consists of two parts. Work with pattern blocks yourself first, then view the video.

Goal: To build understanding of the meaning of symbols and a sense of perimeter as a function for transitional algebra students.

Materials: (Available from the Site Coordinator, for use with this activity.)

  • Pattern Blocks
  • Pattern Block Train video

Part 1:
Instructions for building Pattern Block Trains

Consider square blocks only to begin the exploration:

Pattern blocks are placed in rows.

square train

View the SQUARE TRAIN animation above:

  • The 1 - SQUARE TRAIN consists of one square block. Its perimeter is 4 units, where one side is counted as a unit.
  • The 2 - SQUARE TRAIN consists of two square blocks in a row. Its perimeter is 6 units, where one side is counted as a unit.
  • The 3 - SQUARE TRAIN consists of three square blocks. Its perimeter is eight units, where one side is counted as a unit.

CHALLENGE ONE:

  • What perimeter would a 10 square train have?
  • What about a 100-square train?
  • What about an N-square train?

What is a triangle pattern block train?
What can be generalized?

Triangle pattern blocks are placed in rows. triangle train
View the TRIANGLE TRAIN animation above:

  • The 1 - TRIANGLE TRAIN consists of one triangular block. Its perimeter is 3 units, where one side is counted as a unit.
  • The 2 - TRIANGLE TRAIN consists of two triangular blocks in a row. Its perimeter is 4 units, where one side is counted as a unit.
  • A 3 - TRIANGLE TRAIN consists of three triangular blocks. Its perimeter is 5 units, where one side is counted as a unit.

CHALLENGE TWO:

  • What perimeter would a 10-triangle train have?
  • What about a 100-triangle train?
  • What about an N-triangle train?

CHALLENGE THREE:

Explore on your own HEXAGON TRAINS. An animation of hexagon trains is shown below.

hexagon train

FINAL CHALLENGE:

Part 2: View the video

Watch the 15-minute video, Pattern Block Train. See how a teacher uses the activity with a 6th grade class.

This material is derived from the work of Ricky Carter and Fadia Harik for the ETMITT Project, BBN Learning Systems and Technologies.