The document discusses teaching techniques for multiplying four-digit numbers by 11, introducing alternative methods to enhance students' mathematical skills and confidence. It includes step-by-step examples demonstrating these methods, along with verification processes to prove the efficacy of the conjectures presented. The researcher concludes that these techniques can also be applied to larger four-digit numbers with regrouping.

1. DOUBLE X
NAILYN R. CABUDOL
Investigator
SIOASIO INTEGRATED SCHOOL

2. II. INTRODUCTION
Math tricks help pupils learn techniques on how
to solve questions quickly and can help pupils
develop greater confidence in Math, improve Math
skills and understanding (cuemath.com). Many
Mathematics tricks call on learners to compute
the four basic operations. In the context of Math
magic, computational practice is fun. If a trick
works for some learners and not to others, it’s
amazing how eager they can be to find and fix
their mistakes so the trick will come out right.

3. III. STATEMENT OF THE PROBLEM
The researcher of this mathematical
investigation would like to determine the
following;
A.Multiplying four-digit numbers by 11.
B.Using different way of finding the product
of four-digit numbers by 11.

4. IV. CONJECTURES
To find the product of 4325 and 11 using
different way.
4325
X 11
47,575
Steps:
1.First, copy the digit in ones place of the multiplier which is
5. It will be written in the ones place of your product.Then add
the digit in ones place by the tens place(5+2=7).The answer will
be in the tens place of your product.
2.Next, add the digit in tens place to the hundreds
place(2+3=5). Then the answer will be written on the hundreds
place.
3. After that, add the digit in the hundreds place and
thousands place(3+4=7). Then the answer will be written on the
thousands place.
4.Lastly, just copy the digit (4) in the thousands place and will
be written as the thousands digit of your product.

5. V. VERIFYING CONJECTURES
Find the product of 6327 and 11 by using
different way. Follow the previous steps.
6327
X 11
69,597
Steps:
1.First, copy the digit in ones place of the multiplier which is
7. It will be written in the ones place of your product.Then add
the digit in ones place by the tens place(7+2=9).The answer will
be in the tens place of your product.
2.Next, add the digit in tens place to the hundreds
place(2+3=5). Then the answer will be written on the hundreds
place.
3. After that, add the digit in the hundreds place and
thousands place(6+3=9). Then the answer will be written on the
thousands place.
4.Lastly, just copy the digit (6) in the thousands place and will
be written as the thousands digit of your product.

6. V. VERIFYING CONJECTURES
Find the product of 6327 and 11 using the
traditional way of solving.
6327
X 11
6327
6327
69,597
*At this stage, the conjecture has been
tested and supported.
*Conjecture was proven.

7. VI. JUSTIFICATION
Let’s Try again!
5418
X 11
59, 598
4453
X 11
48,983
*In finding the product of four digit numbers by 11, it is applicable to
use other way in solving by following the steps.

8. VII. SUMMARY
After investigation and verifications, the
researcher found out that there is other way to
multiply 4 digit numbers by 11.

9. VIII. POSSIBLE EXTENSIONS
 How about if we multiply 4 large digit
numbers by 11 using the other way of
solving?
6875
X 11
61415125
6875
X 11
7 5, 6 2 5
1. First, copy 5 in the ones
place of the product.
2. 5+7=12
3. 8+7+1=16
4. 8+6+1=15
5. 6+1=7
*Just regroup if the product
is 10 or more .

10. VIII. POSSIBLE EXTENSIONS
It’s the same result. We can conclude that
it can apply in finding the product of large
4 digit numbers by 11 with regrouping.

11. REFERENCES
https://www.cuemath.com
https://math4teaching.com

12. THANK YOU FOR LISTENING!