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 and another >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 1^st 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 2^nd 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