Addition using the F-L-U model

Pre-requisites:

 * Recognising numbers represented in FLU model
 * Representing numbers in FLU model
 * Knowing that when there are >10 units/longs, they must be grouped  together and replaced with a long/flat

Learning objectives:

 * To understand how the FLU  model  can be used to perform addition of  upto 3 digit numbers with and without carry-over
 * To visualize what it means to ‘carry-over’
 * To correlate the addition process using FLU model to the standard  algorithm

Materials:
Geogebra file - https://www.geogebra.org/m/k2DDxjPU, projector

Process:
Demonstration:


 * 1) The  Geogebra file uses dots and lines just as what students  were taught using the FLU  model manipulative and shows the process of addition. This  will be used to demonstrate the addition process
 * 2) Start  with two single digit  numbers <5. Ask  students to write  any number <5 in their notebooks (represented as dots).
 * 3) Facilitator  enters two  numbers  of their choice in the input box which  is automatically represented with corresponding number of  red and blue dots on the  left.
 * 4) Click  ‘Start’ to begin the process.  Both the red and blue dots move to the bottom and are arranged in a  line with the sum  indicated.
 * 5) Explain  to students that when adding, all the dots they  simply need to counts all the dots together
 * 6) Next,  ask students to look  at the number that the  person on their right has written and  write it down below their own number and add them both as was shown  on the screen
 * 7) Once  done, take another example  with one number 5.
 * 8) Before  hitting start, ask students how  they would perform the addition. They  may say count all the dots together and keep  the equivalent number of dots as the sum. Next, ask them if  the representation is correct or if anything can be grouped  together.
 * 9) Click  the ‘start’ button to demonstrate how the dots must be joined  together to form a  line(long)
 * 10) Now,  ask them to choose a number  >5 and add it in the procedure shown to the number they had  previously chosen (<5)
 * 11) Next,  demonstrate a few more  examples covering the following combinations(sum  <100)


 * A  number <20 and a single   digit number without carry over
 * A  number <20 and a single   digit number with carry over
 * Two  2-digit numbers without   carry over
 * Two  2-digit numbers with carry   over


 * 1) Addition  of numbers with sum > 100 can also be introduced in a similar  manner after students have had some practice with sums < 100.

Student Practice:


 * 1) In  pairs or small groups, students  play a game where one  student in the group says ‘start’ and another starts counting  numbers from 1 – 50 in their mind. The  1st  students can say ‘stop’ at any point of time. Then  the second student says out loud the number they stopped at and  everyone in the group write it down in the F-L-U model. This is  repeated a second time to get the second addend  and they proceed to do the  addition. Each student takes turns to repeat the same subsequently  and the game can continue  as rounds.
 * 2) Alternate:  Students are divided into  groups of manageable sizes.  Empty  chits of two different  colours, say yellow and  green, are distributed  among the students with each  child getting two  coloured chits.  Students are  asked write a single digit  number of their choice (FLU representation) on  the yellow chit and  a two-digit  number on the green  chit and  throw it all  in a  pile. In  each round, students pick  up two chits and add the numbers in them and  throw it back in the pile.

Incorporating inclusive strategies:

 * When forming groups, students who are at different  comfort levels with performing addition  can be grouped together. For students who are facing challenges, the  practice activities can be done progressively where they first  practice only addition without  carry over and then proceed to sums with carry-over. Similarly  smaller numbers cna be taken up first before moving on to larger  numbers.
 * Physical objects such as sticks, buttons, etc can be given  as aids for those who need it
 * The Geogebra file can also be used  to explain the  concept again, or by  children to solve  the given problems

Consolidated practice:

 * 1) Pair  up students who are fairly at the same level of comfort with the  F-L-U model
 * 2) Handover  a worksheet like this  to  each pair where there are numerals given on one half of the page and  the FLU model on the other. Both  students start working one  side each of the worksheet. Once done they exchange and work on the  other.
 * 3) Once  a pair has completed the  representation worksheet, handover the worksheet with addition  problems. The problems are sequenced in a manner where the  difficulty increases progressively. As in the previous case, once a  student has completed one set of problems(numerals or FLU model),  they can work on the problems in the 2nd  half of the sheet.

Incorporating inclusive strategies:

 * 1) Each  student works independently without any time constraints.   Since  they are also made to sit in pairs, there is also a sense of working  together. They may add a competitive touch to the activity and help  each other out when necessary
 * 2) Students  are grouped together roughly according to similar comfort levels,  therefore, may not feel pressured or unchallenged. The language they  speak can also be one factor to be considered when pairing
 * 3) Facilitator  can focus specifically on students who are struggling