Fiveton   a brief description of a mathematical unit aimed at the development of understanding of place value and renaming in addition and subtraction

The Fiveton unit is based in chip trading and is aimed primarily at increasing students' understanding of place value and renaming (carrying and borrowing in addition and subtraction).   A story that takes place in the imaginary kingdom of Fivton is the basis for approximately 11 days (30 - 60 minutes each day) of instruction and activity.   Ideally, this instruction should take place as students begin to work with the addition and subtraction of multi-digit numbers but before they have been introduced to the traditional algorithms for these procedures. This will probably take place in second grade but can be adapted to first or third. Facility with single digit addition and subtraction will enhance results but is not a prerequisite for the unit.   Students will get considerable practice in this area.   Manipulatives (chips / counters) are used to enable the development of conceptual understanding of place value and renaming.   This development takes place in a base five number system, the context for which is naturally developed in the story.   A shift to base ten is made near the end of the unit.   Teachers who wish to do so will find many opportunities to integrate art, social studies, literature and other related aspects of the primary curriculum.  

Mark Roddy, Ph.D.
Seattle University
(206)296-5765
mroddy@seattleu.edu

Here are links to all of the elements of the Fiveton curriculum.
If you decide to use them in your classroom I would like to know how it goes.

The Whole Story (pdf 396 KB)

Day One in which the context of the story is established. Several key characters are introduced.

Day Two in which the dragon is encountered.   (A frieze depicting the kingdom may be started today.)

Character worksheet (pdf 32 KB)

Day Three in which they are building a house for the dragon and so are buying materials and so need money and so we solidify the System of Trades.  

Trading Rules Poster (pdf 24 KB)

Day Four in which Talic and Melinda buy supplies for the dragon's house and so encounter a number of problems that must be worked out.   The mats are first introduced.   We make up and do a story problem.   Students write one on their own for me.

Trading Mat (pdf 16 KB)

Dragon Supply Data (pdf 40 KB)

Day Five in which there are additional problems that arise when the king and queen plan to visit the dragon and buy two paintings.

Day Six in which the king and queen visit the dragon.   Talic and Melinda are doing math problems with the dragon.   The king does some with them.  

Fiveton School Math Problems Worksheet (pdf 68 KB)

Day Seven in which Talic and Melinda go home and observe Emmeline going down the well, doing her job for the Dragon Defense Fund.

Trades worksheet with ten problems (pdf 44 KB)

Day Eight in which the "First Growth Festival" and "Sprout Day," a day of gift giving, are introduced.  

Gift Problem Cards Worksheet (pdf 228 KB)

Day Nine in which the dragon needs a name!   Hence a test of the students' ability and resolve.  

Practice Problems (pdf 44 KB)

Problems to be used in the Naming Test (pdf 36 KB)

Day Ten in which the dragon is named (Garth) and all is well.   There is much Rejoicing. Party!   Bingo!

Bingo Card Maker fromTeachnology

Bingo Problems (pdf 36 KB)

Day Eleven (the last) in which the children and Sir Gollub journey over the mountains to Tenton to see Garth's parents.  

Tenton Worksheet (pdf 64 KB)