Problem Set 1: Systems of Numbers & Operations
Problem Set 1: Systems of Numbers & Operations
Problem Set 1: Systems of Numbers & Operations
Cabalida
ID NO: 2019-6730
I. Study the given algorithm below. The algorithms used involved the rules and
concepts of place value. Use your understanding of these concepts to explain these
algorithms.
a. Continue the steps given. Explain why this algorithm works. Illustrate the process
of “carrying on” (5 points).
Name: Jeralyn T. Cabalida
ID NO: 2019-6730
b. Extend also why “borrowing” works in subtraction. Explain why this works.
Represent the process of this borrowing (5 points).
Answer:
13
2 3 12
3 4 2
- 1 5 7
1 8 5
II. Solve the various word problems below. Use different modelling approach that you
learned to represent your solutions (2.5 points each).
a. Michael and Nicko each picked a number from a box. Nicko’s number is twice as
large as that of Michael’s. The sum of their numbers is 42. What is Nicko’s
number?
Given:
X + y = 42 (Nicko’s number + Michael’s number = 42)
2x = Nicko’s number which is twice as large as Michael’s.
Solution:
2y+ y = 42
3y = 42
Y = 14
So, Michael’s Number is 14.
X + y = 42
X + 14 = 42
X = 42 – 14
X = 28
Therefore, Nicko’s number is 28.
b. Raffy has Php750. He spent Php256 on food, Php125 for his fare, Php345 for his
project and saved the rest. How much did he save?
Name: Jeralyn T. Cabalida
ID NO: 2019-6730
Given:
P750.00 (total money of Raffy)
P256.00 for his food
P125.00 for his fare
P345.00 for his project
Solution:
P256 + P125 + P345 = P726
P726 – P750 = P24.00
So, Raffy saves P24.00 from his money.
III. Explain the versatility and usability of the array representation technique in
multiplication and division. Study the figure below.
Name: Jeralyn T. Cabalida
ID NO: 2019-6730
IV. Solve the various word problems below. Use different modelling approach that you
learned to represent your solutions (2.5 points each).
a. Myrine has twice as many marbles as Mirel while mirel has thrice as many
marbles as Machel. If Machel has 8 marbles, how many marbles do the girls have
in all?
Given:
8 marbles – Machel
Solution:
8 x 3 = 24 Marbles ( Mirel)
24 x 2 = 48 Marbles (Myrine)
8 + 24 + 48 = 80 Marbles
b. 58 Children and 6 teachers went to a fieldtrip. They took private cars which can
carry 8 passengers. How many cars did they use? Are all the cars filled up with 8
passengers?
Given:
58 children
6 teachers
Solutions:
V. Research on (indigenous) teaching manipulatives and technologies that you can use
in encouraging reasoning among students. Give a brief narrative for each (5 points)
a. Description of the Manipulative/Tool/Technology.
+ Teaching indigenous people requires sensitivity and respect towards their
special needs and traditional views. We should allow them see the different
context in education and help them learn. Whatever the circumstances of our
school and local Indigenous community, we can incorporate Indigenous
perspectives into our teaching. Thus, by letting Indigenous People engage to
different teaching manipulatives and technologies will help develop their
understanding towards the modern approach to learning. For instance, using
concrete manipulatives is the first step toward the use of mental images and
models. When students demonstrate understanding of the concept at this
physical, or concrete, level, they are ready to move on to the next level, where
they can apply their knowledge using representations of the objects instead of
the actual objects.
b. Identify any concept discussed this week (place value, numbers, operations) and
describe how you can use that technology to teach and model concepts and
promote reasoning.
+ According to Fuson (1988), the concept relating to numbers are cardinal,
ordinal and measurements. Cardinal is a cardinally set that tackles about the
amount or the ‘many-ness’ of an objects, things and circumstances. Ordinal on
the other hand, is all about the ordering, arranging and sequencing objects, just
like for example books arrangements in a shelf’s. And measurements involves
the measurements of one thing, example is hours spend washing dishes. To
incorporate this concept in a classroom effectively, I will use technologies as a
Name: Jeralyn T. Cabalida
ID NO: 2019-6730
manipulative tools to help develop their reasoning skills. For instance, with the
use of smart tv’s to show concepts and find tv shows that highlights numbers.
VI. Create your own problem on one of the 4 operations. Use a relevant context for this
problem. The problem must involve at least 3 steps in solving, and or provides for
reasoning. If you can create an open-ended problem, that will be better. (5 points)
Problem Solving:
Submission Guide:
Name: Jeralyn T. Cabalida
ID NO: 2019-6730
The submission may be hand-written or typed. You can use as much as 6 pages of paper
(of your choice) to answer each of the mega-item. Each paper should have in the top
the following details: Name & ID Number. Submit only a Google Drive Link
Example:
I.a.
#Solution Solution … (page 1)
II.a.
#Solution Solution … (page 2)