Here are some possible mathematical problems that could be posed from the given situation:
1) The master worker can paint 1 square meter of the billboard per hour. The apprentice can paint 0.5 square meters per hour. If they work for 8 hours, how many square meters of the billboard can they paint?
2) The billboard measures 20 square meters. If the master worker and apprentice work together for x hours, write an equation to represent the relationship between the number of hours worked (x) and the area painted (y).
3) The billboard measures 20 square meters. The master worker and apprentice work together for 8 hours. How much of the billboard do they paint?
Constructivist approach of learning mathematics thiyaguThiyagu K
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Constructivist theories are about 'how one comes to know'. Todayâs constructing knowledge is tomorrows prior knowledge to construct another knowledge i.e. learners constructing knowledge are provisional. There are five basic tenets (previous knowledge, communicating language, active participation, accepted views and knowledge construction) in implication in constructivist learning. Constructivist teaching approach is the challenging one to teaching mathematics. No particular constructivist teaching approach is available to teach mathematics, here I have discussed some methods like interactive teaching approach, problem centred teaching approach may be the best approach in constructivism theory and the role of teacher is some different than other theory.
Strategies in Teaching Mathematics -Principles of Teaching 2 (KMB)Kris Thel
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Solving problems is a practical art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice. . . . if you wish to learn swimming you have to go in the water, and if you wish to become a problem solver you have to solve problems.
- Mathematical Discovery George Polya
Constructivist approach of learning mathematics thiyaguThiyagu K
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Constructivist theories are about 'how one comes to know'. Todayâs constructing knowledge is tomorrows prior knowledge to construct another knowledge i.e. learners constructing knowledge are provisional. There are five basic tenets (previous knowledge, communicating language, active participation, accepted views and knowledge construction) in implication in constructivist learning. Constructivist teaching approach is the challenging one to teaching mathematics. No particular constructivist teaching approach is available to teach mathematics, here I have discussed some methods like interactive teaching approach, problem centred teaching approach may be the best approach in constructivism theory and the role of teacher is some different than other theory.
Strategies in Teaching Mathematics -Principles of Teaching 2 (KMB)Kris Thel
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Solving problems is a practical art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice. . . . if you wish to learn swimming you have to go in the water, and if you wish to become a problem solver you have to solve problems.
- Mathematical Discovery George Polya
Foundations of Mathematics Teaching and Learning (Philippine Context) Ryan Bernido
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This presents the preliminary lessons in the course, Teaching Mathematics in the Intermediate Grades. It discusses the foundations of mathematics teaching and learning including the nature of mathematics, the five-point view of nature of mathematics, the principles of mathematics teaching and learning, and other relevant topics taken from various sources and were put together to grasp an understanding of the foundations of mathematics instruction; particularly in the context of the Philippine Mathematics Education.
Mathematics is always perceived as a difficult subject. How do teachers change the negative perception? This presentation which I presented to the staff of School of Mathematical Sciences, Universiti Sains Malaysia, shares some ideas on how to make learning Math meaningful and interesting.
Foundations of Mathematics Teaching and Learning (Philippine Context) Ryan Bernido
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This presents the preliminary lessons in the course, Teaching Mathematics in the Intermediate Grades. It discusses the foundations of mathematics teaching and learning including the nature of mathematics, the five-point view of nature of mathematics, the principles of mathematics teaching and learning, and other relevant topics taken from various sources and were put together to grasp an understanding of the foundations of mathematics instruction; particularly in the context of the Philippine Mathematics Education.
Mathematics is always perceived as a difficult subject. How do teachers change the negative perception? This presentation which I presented to the staff of School of Mathematical Sciences, Universiti Sains Malaysia, shares some ideas on how to make learning Math meaningful and interesting.
Las redes sociales y su aplicaciĂłn en la educaciĂłn.Citlali_Mena
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Las redes sociales ofrecen una gran gama de posibilidades para los docentes en tĂŠrminos de establecer interacciĂłn en diversas vĂas, empezando por colegas, estudiantes e incluso con las autoridades de sus instituciones.
problem posing merupakan strategi pembelajaran yang menekankan pada pembuatan soal atau masalah yang dilakukan oleh siswa dan untuk siswa dengan guru atau pengajar sebagai fasilitator.
Creating opportunities to develop algebraic thinking and enhancing conceptual understanding of mathematics is essential at every grade level. In this webinar, Math/Technology Curriculum Specialist Aubree Short explored the use of problem solving methods and hands-on manipulatives to guide students in the discovery of algebraic concepts at all levels of learning.
STI Course A Closer Look at Singapore Math by Yeap Ban HarJimmy Keng
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This weekend course conducted at Scarsdale Teachers Institute, New York focused on the use of anchor problem to enhance the teaching and learning of mathematics.
This study aimed at analyzing and describing Various Methods used by mathematics teacher in solving equations. Type of this study is descriptive by subject of this study comprised 65 mathematics teachers in senior, junior, and primary schools respectively 15, 33, and 17 in numbers. The data were collected from the answer to containing four problems of equation. Data Coding was conducted by two coding personnel to obtain credible data. The data were then analyzed descriptively. It has been found that the teachers have implemented a method for solving equation problems by means of operation on one side of equation and procedural operation. This method has been dominantly used by the teachers to solve to the equation problems. The other method was doing operation on both sides of the equation simultaneously by focusing on similar elements on both sides of the equation.
A Case Study of Teaching the Concept of Differential in Mathematics Teacher T...theijes
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In high schools of Viet Nam, teaching calculus includes the knowledge of the real function with a real variable. A mathematics educator in France, Artigue (1996) has shown that the methods and approximate techniques are the centers of the major problems (including number approximation and function approximation...) in calculus. However, in teaching mathematics in Vietnam, the problems of approximation almost do not appear. With the task of training mathematics teachers in high schools under the new orientations, we present a part of our research with the goal of improving the contents and methods of teacher training
How to Create Map Views in the Odoo 17 ERPCeline George
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The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Palestine last event orientationfvgnh .pptxRaedMohamed3
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An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Model Attribute Check Company Auto PropertyCeline George
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In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
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Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
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This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
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In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as âdistorted thinkingâ.
Operation âBlue Starâ is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
6. ď˘Silver
described problem
posing as it is refers to both the
generation of new problems
and the re-formulation of given
problems, posing can occur
before, during or after the
solution of a problem (Silver,
1993).
7. ď˘Stoyanova
has defined
mathematical problem posing
as the process by which, on the
basis of concrete situations,
meaningful mathematical
problems are formulated
(Stoyanova, 1996).
8. SKILLS IN PROBLEM POSING
1) Use problem-solving strategies to investigate and solve the
posed problems.
2) Formulate problems from every day and mathematical
situations.
3) Use a proper approach for posing problems up to the
mathematical situations.
4) Recognize relationships among different topics in mathematics.
5) Generalize solutions and strategies to new problem situations.
6) Pose complex problems as well as simple problems.
7) Use different subjects' applications in posing mathematical
problems.
8) The ability of generating questions to improve problem posing
strategies like:
- How can I finish the problem?
- Can I pose another questions?
- How many solutions can I find?
9. HOW ARE PROBLEM-POSING SKILLS
RELATED TO PROBLEM- SOLVING SKILLS?
ď˘ Silver
and Cai found that studentsâ problemsolving performance was highly correlated
with their problem- posing performance.
Compared to less successful problem solvers,
good problem solvers generated more, and
more complex, mathematical problems.
10. BENEFITS OF PROBLEM POSING
ď˘ It
frees learners from the one-answer
syndrome.
ď˘ It enables learners to view common things in
uncommon ways.
ď˘ It legitimizes asking questions.
ď˘ It fosters the predicting, conjecturing, and
testing of hypotheses.
ď˘ It builds a spirit of adventure, intellectual
excitement, and class unity.
ď˘ It demonstrates the spiraling nature of inquiry
learning. No problem is really solved.
ď˘ It develops a sense of personal ownership and
responsibility for mathematical investigations.
11. WAYS TO CHANGE A PROBLEM
Some ways to change a problem to create new
problems
ď˘ Change the numbers.
ď˘ Change the geometry.
ď˘ Change the operation.
ď˘ Change the objects under study.
ď˘ Remove a condition, or add new conditions.
ď˘ Remove or add context.
ď˘ Repeat a process.
12. CHANGE THE NUMBERS
ď˘
This is the most obvious way to change a problem.
Give your students one or more problems and ask
them to identify any stated or implied numbers.
ď˘
When considering numerical changes to a
problem, many different domains and
representations can prove interesting.
13. CHANGE THE GEOMETRY
ď˘
Any problem with a geometric setting is ripe for
new variants. The simplest problem-posing
maneuver is to change the shapes involved.
ď˘
Different categories of shapes that suggest
possible substitutions include polygons and their
number of sides, regular versus non-regular
polygons.
14. ď˘
Changes of dimension can yield exciting
challenges and patterns.
ď˘
Continuous and discrete spaces (e.g., the lattice of
points with integer coordinates) usually require
distinct methods of solution and offer contrasting
conclusions
15. CHANGE THE OPERATION
ď˘
Algebraic: We can switch between addition,
subtraction, multiplication, division,
exponentiation, and roots. We can also change the
order of operations.
ď˘
Geometric: We can change between scaling,
translating, rotating, and other transformations.
We can construct medians rather than
perpendiculars. We can trisect or n-sect rather
than bisect an angle, segment, or area.
16. ď˘
Analytic: We can change the function involved
(example make it exponential rather than linear)
ď˘
Probabilistic: We can substitute a predictable
behavior for a random one). For example,
Juancho, a fifth grader, altered the Connect the
Dots problem so that the jump size was chosen
randomly for each step;
17. Start with a circle with 16 points, equally spaced:
You are going to make a shape by jumping around
this circle. Pick a number, j, that determines how
far you will move around the circle with each
jump.
Start at the top point (labeled 0), and draw a
segment to the point j steps away.
Begin each new jump where the previous one ends
and continue this process until one of your jumps
returns to the starting point, 0.
18. CHANGES THE OBJECTS UNDER STUDY
ď˘
Rather than just look at real numbers, we can
consider vectors, matrices, or functions (e.g.,
polynomials) as the operands.
ď˘
For example, elementary school students often
discover that 2 + 2 = 2 * 2, but find no further
examples (except perhaps 0 and 0).
19. REMOVE OR ADD CONTEXT
ď˘
If a problem comes with a particular setting, we
can make it abstract by removing any nonmathematical details.
ď˘
Alternatively, we can add a story to an otherwise
abstract problem. For example, it is easy to dissect
a rectangle into four equal pieces, but when that
rectangle becomes a cake and there are four kids
who each want their fair share, a whole realm of
new and difficult mathematics problems emerge
20. ď˘
You can turn each problem-posing method into a
practice activity. Ask students to superimpose a
story or context on an abstract problem of their
choosing (e.g., a geometric construction or a
system of equations they find by scanning through
a textbook).
21. REPEAT A PROCESS
ď˘
iteration can lead to surprising and beautiful
mathematical questions and results.
ď˘
We can repeat any operation, such as squaring a
number, bisecting a side, or rotating a figure, to
yield ever more complicated objects or sequences
for study.
22. WITH STARTING POINT IN SYMBOLIC SCHEMES
The teacher gives the formula a+b=x and requires as many
examples of exercises as possible. Then the teacher asks for the
formulation of varied problems. The position of the unknown is
changed ( a+x=c; x=a+b ; x+b=c ; etc.) with the same requirements
(proposing various exercises and problems). The same procedure
is carried out, starting from one of the models a-b=x, a+b+c=x, a-bc=x, etc., or from graphical models, diagrams, tables.
ď˘Children were asked to do the tasks described above in a gradual
progression of internalizing, which emphasizes recurrent cycles of
understanding: orally, mentally, in writing (without or with
minimum verbalization, and the result is required for checking).
Letters are to be used just accidentally, or gradually, depending on
the studentsâ level and teacherâs knowledge about their
appropriate use. Usually, instead of a,b,c,x, other symbols â more
familiar to children â were used as âboxesâ or âshellsâ for the
substitutions.
23. EXAMPLE 1
ď˘
1+1=?
ď˘
Assume the student has already figured out that
the result is 2.
ď˘
By increasing a term on the left by 1 the total on
the left is increased.
ď˘
In order to get the equality back, one should
increase by 1 the right side as well.
24. Applying the enlightening idea repeatedly, the
student may even conceive of the notion that
adding any number on the left can be balanced by
adding the same number on the right. The left
hand side is a sum of two terms.
ď˘ A second observation can be made to the effect
that it does not matter to which of the terms the
number has been added. And then a third one that
the number does not have to be wholly added to
one of the terms - it can be split in any way
imaginable.
ď˘
25. EXAMPLE 2
ď˘
One of two brothers is 7 years old while the other
is only 5.
ď˘
As you can see, the sum of their ages is 12.
ď˘
Please invent another problem and solve it.
ď˘
Even if the following was obtained as (7 + 1) and
(5 - 1)
26. ď˘
One of two brothers is 8 years old while the other
is only 4. As you can see, the sum of their ages is
12.
ď˘
One of two sisters is 7 years old while the other is
only 5. As you can see, the sum of their ages is 12.
28. PROBLEM
The mathematics teacher assigns an assignment
to her students. The boy asked the Monster to
answer his assignments in his behalf.
29. PROBLEM POSING WITH PLOT
Examples:
ďList actions in a logical order
ďClues to identify a part of the story
ďCompare actions
ďMake predictions based on evidence
ďConnect the plot to a math concept
ďRedesign the plot to include mathematics
ďA âmath walkâ through the story
ďExplore conjectures, estimations, generalizations
30. MATHEMATICAL TASK WITH PLOT
Letâs pretend that
the Monster in our
story charges the
boy 35¢ for each
multiplication
problem and 60¢ for
each division
problem he solves.
How many types of each
problem did the Monster
solve if the boyâs bill is
$15?
How many different
solutions can you find?
31. PROBLEM POSING WITH CHARACTER
ď
Make the Character(s) come to life
ď
Put the Character(s) in the studentsâ classroom,
bedroom, kitchen, or community park
ď
Make the story real to children: what open-ended
tasks can characters face?
32. MATHEMATICAL TASK WITH CHARACTER
Letâs pretend that the
Monsterâs Magic Calculator
has broken.
Only the 5, the 2, the Ă, the
â, and the = buttons work.
How did the Monster
use the Magic
Calculator to get the
homework answers of:
-10
1
3
10
24
100
33. PROBLEM POSING WITH ILLUSTATIONS
Illustrations can:
ďCapture studentsâ interest and imagination
ďVisualize the mathematics
ďEnhance the details of the narrative
ďPlace mathematics in a meaningful context
34. MATHEMATICAL TASK WITH ILLUSTRATIONS
How many different
monster faces can you
make from 4 different sets
of scary eyes, 3 different
eerie noses, and 3 different
sets of pointy teeth?
35. PROBLEM POSING WITH SETTING
Consider how the students can relate to the setting.
Settings help to create integrated teaching units.
Students can begin to see the mathematics in the
everyday.
36. MATHEMATICAL TASK WITH SETTING
Respond to our class survey
about the places where we do
our math homework.
1)At the kitchen table
2)In my room at home
3)At the library
4)At a friendâs house
Draw a graph to display
the results.
37. PROBLEM POSING WITH OBJECTS
ď
Familiarity (and unfamiliarity) with objects in the
story provide learning opportunities.
ď
Objects in stories can be compared, contrasted,
sorted, and classified. (Got Van Hiele?)
ď
Objects in stories can be described or constructed
with 2D and 3D shapes
38. MATHEMATICAL TASK WITH OBJECTS
To do the boyâs math
homework, the Monster
requires a very special type
of pen.
⢠Which store has the
better buy, Pens-R-Us or
Pen-Mart? How do you
know?
Pens-R-Us sells 2 pens for
$1.40
⢠Which store would you
go to to buy 24 pens?
Show your thinking in
words, numbers and
pictures.
Pen-Mart sells 3 pens for
$1.99
39. PROBLEM POSING WITH TIME FRAME
The TIME FRAME of a story:
ď
Builds understanding of time measurements
ď
Creates the necessity for standard units
ď
Can bridge a students imagination and reality
ď
Allows for comparisons and contrasts
40. MATHEMATICAL TASK WITH TIME FRAME
Before the boyâs teacher
realizes that the Monster is
doing the math homework,
the Monster has spent
1,725 minutes doing
homework.
⢠How long is this in
hours?
⢠How long is this in
days?
⢠How long is this in
weeks?
41. SILVER AND CAI (2005) IDENTIFIED THREE CRITERIA
THAT ARE COMMONLY APPLICABLE TO MOST PROBLEM
POSING TASKS:
1.Quantity - refers to the number of correct responses
generated from the problem posing task.
2.Originality - is also another feature of responses that
can possibly be used as a criterion to measure studentsâ
creativity.
3.Complexity - refers to the cognitive demands of the
task. It can be categorized as low, moderate, or high.
42. Low complexity
⢠Recall or recognize a
fact, term, or property
⢠Compute a sum,
difference, product, or
quotient
⢠Perform a specified
procedure
⢠Solve a oneâstep word
problem
⢠Retrieve information
from a graph, table, or
figure
Moderate complexity
High complexity
⢠Represent a situation
mathematically in more
than one way
⢠Provide a justification
for steps in a solution
process
⢠Interpret a visual
representation
⢠Solve a multiple-step
problem
⢠Extend a pattern
⢠Retrieve information
from a graph, table, or
figure and use it to solve a
problem
⢠Interpret a simple
argument
⢠Describe how different
representations can be
used to solve the problem
⢠Perform a procedure
having multiple steps and
multiple decision
points
⢠Generalize a pattern
⢠Solve a problem in more
than one way
⢠Explain and justify a
solution to a problem
⢠Describe, compare, and
contrast solution methods
⢠Analyze the
assumptions made in
solution
⢠Provide a mathematical
justification
43. Task objective: From the information below, construct
mathematical problems, and solve them, to
demonstrate your competency in using the basic
rules for manipulating inequalities to simplify and
solve simultaneous inequalities or inequalities
involving linear, quadratic or modulus functions.
A gardener is planting a new orchard. The young trees
are arranged in the rectangular plot, which has its
longer side measuring 100m.
44. SAMPLE 1 OF PROBLEMS SHOWING LOW
MATHEMATICAL COMPLEXITY
ď˘
If a fence around the orchard measures more than
330m, and the area of the orchard is not more than
7000m2, find the range of values of the shorter side.
45. SAMPLE 2 OF PROBLEMS SHOWING MODERATE
MATHEMATICAL COMPLEXITY
ď˘
The gardener decides to divide the plot of land into
three sections for growing three different types of
plants. It is given that section C is representative of a
quadrant and the area of section C is bigger than that
of section A. The various sections require different
types of soils of different prices. If the gardener has a
budget of $400 for buying soil for the orchard, what is
the maximum value of x?
46.
47. SAMPLE 3 OF PROBLEMS SHOWING HIGH
MATHEMATICAL COMPLEXITY
ď˘
It is given that the width of the orchard is 50m.
Starting from point B, a worker P walked along the
edge in a clockwise direction and back to B at a speed
of 2m/s. Another worker, Q, started from point A and
walked along the edge in the clockwise direction and
back to point A at a speed of 1 m/s. What is largest
possible area of triangle BPQ?
48. EXAMPLE PROBLEM
Ann has 34 marbles, Billy has 27 marbles,
and Chris has 23 marbles. Write and
solve as many problems as you can that
uses this information
49. STUDENTS ARE ABLE TO POSE PROBLEMS SUCH AS
THE FOLLOWING:
How many marbles do they have altogether?
ď˘ How many more marbles does Billy have than Chris?
ď˘ How many more marbles would they need to have
together as many marbles as Sammy, who has 103?
ď˘ Can Ann give marbles to Billy and Chris so that they
all have the same number? If so, how can this be
done?
ď˘ Suppose Billy gives some marbles to Chris. How many
marbles should he give Chris in order for them to
have the same number of marbles?
ď˘ Suppose Ann gives some marbles to Chris. How many
marbles should she give Chris in order for them to
have the same number of marbles?
ď˘
50. MATHEMATICS CONTENT: LINEAR EQUATION WITH
ONE UNKNOWN
ď˘
Situation: A factory is planning to make a billboard. A
master worker and his apprentice are employed to do
the job. It will take 4 days by the master worker alone
to complete the job, but it takes 6 days for the
apprentice alone to complete the job.
ď˘
Studentsâ Task: Please create problems based on the
situation. Students may add conditions for problems
they create.
51. ď˘
Problem 1. How many days will it take the two
workers to complete the job together?
ď˘
Problem 2. If the master joins the work after the
apprentice has worked for 1 day, how many
additional days will it take the master and the
apprentice to complete the job together?
ď˘
Problem 3. After the master has worked for 2 days,
the apprentice joins the master to complete the job.
How many days in total will the master have to work
to complete the job?
52. ď˘
Problem 4. If the master has to leave for other
business after the two workers have worked together
on the job for 1 day, how many additional days will it
take the apprentice to complete the remaining part of
the job?
ď˘
Problem 5. If the apprentice has to leave for other
business after the two workers have worked together
for 1 day, how many additional days will it take the
master to complete the remaining part of the job?
53. ď˘
Problems 6. The master and the apprentice are paid
4500Pesos after they completed the job. How much
should the master and the apprentice each receive if
each workerâs payment is determined by the
proportion of the job the worker completed?
ď˘
Problem 7. The apprentice started the work by
himself for 1 day, and then the master joined the
effort, and they completed the remaining part of the
job together. Finally, they received 4900 Pesos in total
for completing the job. How much should the master
and the apprentice each receive if each workerâs
payment is determined by the proportion of the job
the worker completed?
54. ď˘
Problem 8. The master started the work by himself
for 1 day, and then the apprentice joined the effort,
and they completed the remaining part of the job
together. Finally, they received 4500 Pesos in total for
completing the job. How much should the master and
the apprentice each receive if each workerâs payment
is determined by the proportion of the job the worker
completed?