Solving word problem without using algebra (physical chemistry, geometry, science, teacher)
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I taught Singapore math in the early 2000's in the inner city of Houston. I was fully invested,and my kids scored very well on problem solving. However, as the grades progressed the teachers weren't invested. It broke down and was eventually abandoned for the most part.
The problem is not the program chosen.
It's teachers being invested and staying long term in a school district.teacher turnover is high and it's expensive training.
Then you have huge numbers of students coming and going during the school year. They often seek free rent specials at apartments, and then don't pay and are evicted. Students can have 3-5 teachers per year in some districts due to movement. I've gotten students with a few weeks left in the year. Those kids often have huge gaps in learning.
Top all of that with shifting admin, who jump from program to program for the district. One admin. Brought in a new program to "save" the district. I told him most of us were trained in that ten years ago. Identical trainings.
For Singapore to work, you need a stable population of teachers, admin, and students.
Joe sets up a kiosk in a book fair to sell Donald Trump's new book. The book's price is $20. Young ladies will get 25% discount. At the end of the day, Joe reports to his boss.
"Mr. Trump, I sold 152 books and total sales is $2695." Joe says.
"How many books were sold to young ladies?" Trump asks.
"I, .. I don't have the number, yet." Joe stutters.
"You must figure it out in 3 minutes or you are FIRED!" Trump raises his voice.
Your mission, should you choose to accept it, is to assume Joe's identity, answer Trump's question and save Joe's job. Trump is not a math whiz. Keep it simple and good luck!
Man! You are fast. It is 69, Donald's favourite number.
Thanks. Donald would probably be more impressed by a teenager cranking out the answer quickly on a graphing calculator, using a system of equations entered in a 2x3 matrix with the rref function.
I've been teaching the Singapore bar graphs to my daughter over the past week in response to this thread. So when I saw this problem, I naturally just drew a bar graph. Took about 30 seconds to figure out the answer this way, with nothing more than addition and an understanding of fractions. Wow powerful. I minored in math in college, but I still wouldn't have been able to do this before last week.
I have 2 kids in public elementary schools. Their math homework have no depth. For the topic of "average", there is nothing more than "add them up and divide". I have been searching for better math problems all over the web to supplement there homework. I am glad that I found this thread. Solving the Singapore math problem in the 1st post is way better than doing 100 times of "add up and divide". Ever wonder why our kids are behind Asian kids at math? Not only they have better teachers and curriculum, they also do lots of really great exercises.
Some posters said those word problems are convoluted and have no real world connection. I disagree. IMO, its purpose is to help kids develop their logical reasoning skills. It is a game to play Sherlock Holmes. Are you smarter than a 4th grader? Try this.
There is a 4-digit number. The digit in the hundreds place is thrice the digit in the ones place. The digit in the thousands place is the smallest even number. the sum of all digits is 21. What is the number?
I have 2 kids in public elementary schools. Their math homework have no depth. For the topic of "average", there is nothing more than "add them up and divide". I have been searching for better math problems all over the web to supplement there homework. I am glad that I found this thread. Solving the Singapore math problem in the 1st post is way better than doing 100 times of "add up and divide". Ever wonder why our kids are behind Asian kids at math? Not only they have better teachers and curriculum, they also do lots of really great exercises.
Some posters said those word problems are convoluted and have no real world connection. I disagree. IMO, its purpose is to help kids develop their logical reasoning skills. It is a game to play Sherlock Holmes. Are you smarter than a 4th grader? Try this.
There is a 4-digit number. The digit in the hundreds place is thrice the digit in the ones place. The digit in the thousands place is the smallest even number. the sum of all digits is 21. What is the number?
2973 is the answer, but I didn't use a particularly algorithmic method to solve it, just recognized that the no digit but 9 would work for the hundreds place and still add to 21.
Back to the thread topic, I cannot really see the distinction between the arithmetic solution and the algebraic solution. If I was writing code to solve any of the algorithms, I would be using the exact same operators. I am obviously missing something due to my familiarity with basic algebra, but I am interested in learning the nuances to help my students. However, it seems to me that the "arithmetic" solution seems to be just a combination of algebraic steps where a series of operations are combined rather than evaluated individually. I understand the value of mental math, I guess I am just not seeing the value in slinging together a line of ratios when each algebraic step is so simple and logical.
regular book sales + discounted book sales = total book sales
20(152-X) + 20(100%-25%)X = 2695, X = 69
In Asia, 5th graders use arithmetic reasoning.
number of discounted books = total discount ÷ discount per book
(152×20-2695) ÷ (20×25%) = 69
Which one do you prefer?
I would solve this algebraically with a system of equations, but I'm curious about the arithmetic method. Is there a way to learn how to do this or start thinking like this? Maybe using bar modeling?
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1st ever word problem created by myself
