Representation of numbers using FLU Model

Why the F-L-U model?
The FLU model incorporates the cardinality of numbers and helps visualize the ‘size’ of numbers. Units are represented as single blocks, tens as a collection of 10 single blocks and a hundred as a collection of 10 longs or 100 single blocks.

Both physical and digital versions of the model are available. The model can be replicated physically with just a sheet of cardboard/sheet of paper as well.

The F-L-U model also help to understand addition and subtraction better as the ‘why’ behind carry-over/borrowing/regrouping when working with larger numbers can be explained as the ‘putting together’ or ‘taking apart’ of the units, longs and flats when necessary.

Objective:

 * Able to understand/reinforce the base-10 structure of the number system using the FLU model
 * Able to recall the concepts of bidi(units), hattu(tens), nuru(hundreds)
 * Able to analyze how numbers can be represented using the FLU model and helps to correlate the representation to H-T-U representation
 * able to analyze the grouping of units into tens.
 * able to analyze the grouping of tens into hundreds.

Estimated time:
1 hour

Materials:
small empty chits. Geogebra file( https://www.geogebra.org/m/wwwmtx4p ), Projector, Worksheets

Process:
Demonstration:


 * 1) Ask students if they are familiar with the concept of place value and to explain what they understand of it using some examples
 * 2) Take few example numbers and discuss the nooru-hattu-biDi representation
 * 3) Next project the Geogebra file and demonstrate the representation of numbers using the F-L-U model and explain how it corresponds to the nooru-hattu-biDi representation
 * 4) Start with single digit numbers so that the students feel confident with units.
 * 5) Next take up numbers >10 represented just using the unit blocks. Use the ‘put together’ option to show how 10 unit blocks can be grouped to form a long or a ‘rod’.
 * 6) Ask for students to give some numbers <100, come to the screen and explain how it should be represented
 * 7) Next take up numbers having more than 10 rods/longs and explain how the ‘put together’ option can be used again to group them into a ‘flat’
 * 8) Reiterate that whenever there is more than 10 of a kind (small blocks/rods) they must be grouped together and exchanged for a rod/flat
 * 9) Make sure to take up examples such as X0, X0X, X00 (X are the numbers from 1-9)
 * 10) After having demonstration of number representation using the Geogebra tool, use the blackboard to show how the representation can be done similarly on paper using dots for units, standing lines for rods and squares for hundreds. Demonstrate the same examples on the board.

ACTIVITY -1
MATERIALS:

Blackboard.

PROCESS:


 * 1) In an order, ask each child have to call out numbers from 1 – 6 in an sequence order. Repeat until all children have completed the chance and tell the children to remember the number they called out
 * 2) On the board, make 6 columns and in each column, write down numbers from single digit up to 3 digit numbers
 * 3) Ask the children to look the respective column of sums written on black board that corresponds to the number they called out and represent them using the F-L-U model in their books.
 * 4) Once they are done with their column, they can move on to next columns and practice representing of numbers
 * 5) Once students have attained a level of comfort representing numerals in the FLU model, assign practice problems where they need to do it in reverse, i.e., decode numbers represented in FLU format and write their numeral representation
 * 6) The same columns used previously can be replaced with numbers in FLU format and students asked to write the numerals

ACTIVITY-2
MATERIALS:

worksheets of FLU model and Numerals.

PROCESS


 * 1) The same activity can be done by providing the worksheets like this where one of column is in FLU model and other column is in numerical form.
 * 2) This can be done in small group by telling each child have to call out numbers from 1 – 6 in an sequence order. Repeat until all children have completed the chance and tell the children to remember the number they called out
 * 3) Provide different worksheet for the children in a group and tell them to write the question on their book..
 * 4) Once they are done with first column,ask the students to try out it in reverse i.e., decode numbers represented in FLU format and write their numeral representation.
 * 5) If the child finds it difficulty the facilitator can help the child by explaining using one of the FLU model.

ACTIVITY-3
MATERIALS:

Small chits, sketch.

PROCESS:


 * 1) Split the students into smaller groups of 6.
 * 2) The facilitator provides each child 4 chits along with a sketch.
 * 3) Each child has to write 4 different numbers in 4 different chits.
 * 4) Once all the students put the chits together in the bowl, each student have to pick one chit and tell how many units- biDi, tens- Hattu, and hundreds- Nuuru is in the corresponding number.
 * 5) In a group each child gets a turn to answer it.
 * 6) This can be repeated till the chits are completed.

EVALUATION:

 * 1) Represent the number 6 using FLU Model?
 * 2) What is the numerical value for | | | | ο ο ο ο ο.
 * 3) How many units and tens is in the number 18?
 * 4) Represent the number 230 using FLU model?
 * 5) Write the Numerical value of $$\Box$$ $$\Box$$ $$\Box$$ | | ο ο ο ο ο ο ο ο.