Subtraction using Place value and Standard Algorithm

Objective

 * able to solve single digit,two digit,three digit addition without carry over.
 * able to recognize the minuend and subtrahend.
 * To analyze how to solve subtraction using standard algorithm.
 * Able to compare the flat long units in solving subtraction.
 * able to recall subtraction without carry over
 * able to recognize the minuend and subtrahend.
 * able to analyze the unit number of minuend is greater or lesser than the subtrahend.
 * Able to predict why one tens is broken into ten units.
 * Able to subtract the minuend number units and tens with the subtrahend units and tens.
 * Able to solve more number of sums with carry over/ re-grouping.

Materials
geogebra file: https://www.geogebra.org/classic/uENt3Tj8, https://www.geogebra.org/m/uuk3mjne , black board,

 https://www.geogebra.org/m/av6psbf7#material/xt3yPtRg 

 https://www.geogebra.org/classic/ZBnCfzbA 

Subtraction of the numbers lesser than 10.
Procedure :

Before starting with subtraction without carry over the facilitator started recalling of the place value taking to addition of numbers then subtraction was introduced. To know the previous knowledge of the children in subtraction few questions were asked to the children based on their daily life like


 * Ramu’s mother asks him to bring 3 packets of 5 rupees biscuits by giving 20 rupees, how much rupees Ramu get back from the shop keeper?
 * Rithika has 57 rupees and she likes to eat an ice-cream of rupees 45, then how many rupees is remaining with her?

From these questions the facilitator made the students why are we subtracting or what is remaining when two numbers are subtracted, this concept was explained using flat long units. In the given two numbers for example the facilitator wrote 8 dots and the children answered as 8 later the facilitator wrote 3 dots which the number is 3. now the facilitator tells to remove 3 units out of 8 units and ask what is the remaining units the children came up with the answer as 5 units.

o o o o o ø ø ø  , so here the students observe that 3 is removed out of 8 which gets 5 as number.

Another example was given to the children, if 4 units has to be removed out of 6 units then how many units are remaining the children will solve and came up with answer as 2. Few similar questions was explained to the students. Later it was connected to the standard algorithm of subtraction to solve the sums.

From the above example: 6-4=2, the facilitator explains which number is subtracted from the fixed value. From the above example 4 is a subtrahend that gets subtracted from the minuend 6 which gets 3 as a difference.

It helps students to co-relate that both the answers are same. At the end some of the sums was given to practice it.

For the same concept different methods were used like grouping the students and telling them to write the numbers in a chit and passing the chits to different students to solve it,students themselves had to choose the number and solve it, the facilitator gives different representation to all the students and have to solve it.

For example: 9-5=4; 6-4=2; 6-3=3.

Subtraction of the numbers greater than 10.
The facilitator recalls the subtraction numbers less than 10 and consider greater than 10 numbers such as 89 and 57, tell the students to write in the form of flat long units and the students come up with their answers as 8 tens and 9 units, 5 tens and 7 units. The facilitator shows the same example on geogebra file and explains how the units and tens are removed from the minuend. Here among 9 units 7 units are removed so that 2 units are left and in tens out of 8 tens 5 tens is removed so 3 tens are remaining that mean 32 is the difference.

This was also explained by showing the geogebra file how the units and tens of the subtrahend are removed from the minuend, where the subtrahend is just considered as a reference number to remove the number from the minuend which get as a difference.

Similarly few more examples were explained for their better understanding and few sums was given for all the students in the form of flat long units and instructed them to solve it. Once the students were comfortable the facilitator explains subtraction using standard algorithm by considering an example such as

28

- 15

13  or  this can also be written as 28 – 15 =13

The facilitator writes the sum on the board as written above and tells to solve always from the units. The facilitator asks what is the value of 8-5 the students came up with the answer as 3, again the facilitator asks what is the difference of 2-1 the students came up with the answer as 1. so the difference of the minuend and the subtrahend is 13.

similarly few more sums was explained and given for the practice, this helped the students to get exposure to different methods of solving subtraction sums.

For example:

27 – 13 = 14; 42 – 21 =21; 68 – 23 = 45;

Subtraction with carry over/ re-grouping:
Materials:

Black board, geogebra file https://www.geogebra.org/m/av6psbf7#material/xt3yPtRg .

Procedure :

From the previous knowledge of the students in subtraction the sums of regrouping was introduced by considering any two number such as 26 and 19.

Now the facilitator tell the students to write it in the form of flat long units for the given numbers. Now the facilitator ask, Is it possible to remove 9 units out of 6 units. The students answered “No”. The facilitator asked then how do you solve it? Students thinks. The facilitator explains from the tens place one ten has to be broken into ten units then in the units place there will be totally 16 units which is shown in the  figure. The facilitator ask Now is it possible to remove 9 from 16? The students answered “yes”. Then what’s the difference of 16 and 9? the students said 7.yes !!

In the tens place from 2 tens 1 tens was already broken into ten units therefore only 1 ten is remaining. Now we will find the difference of the tens place value that is 1-1=0. The facilitator tells so the difference of 26-19 is 7. this was also explained by using standard algorithm of subtraction. Few sums were solved with the interaction of the students. And few sums were given to students for the practice.