About a Primary 5 Problem

I came across this P5 question:

There are altogether 405 boys and girls. Each boy is given 35 sweets, each girl 23 sweets. In total, boys have 255 more sweets than girls. How many boys are there?

I can solve using algebra and trial-and-error, but the students (my nephew) was taught to apply this 'formula':

If it were all girls: 405 X 23 = 9315 sweets
Add the 255 difference: 9315 + 255 = 9570
Each girl and boy has 23 + 35 = 58 sweets
No. of boys = 9570 / 58 = 165

I can see that mathematically it works, but what kind of method is this, and how should this be taught to the students (by applying the formula blindly?) This was never taught to us during our school days???

Chuck

I hope this is not taught as a formula! This formula is not general enough to warrant students learning it. there are so many problems and it is not productive to teach kids formula for each problem type.

I would not really if they were all girls. It is more like suppose everyone boys and girls each was given 23 sweets first.

There are altogether 405 boys and girls. Each boy is given 35 sweets, each girl 23 sweets. In total, boys have 255 more sweets than girls. How many boys are there?

If you use an algebraic method, you might let b = number of boys and set up this equation: 35b - 23(405 - b) = 255 which simplifies to 35b - 23 x 405 + 25b = 255 or 58b = 23 x 405 + 255 and hence b = [23 x 405 + 255] / 58. This is exactly the method that the teacher taught the class.

Question: How do we explain the algebraic solution? Why 23 x 405? Why plus 255? Finally why divide by 58 to get the number of boys?

Dividing a number by 58 to get the number of boys suggest that each boy got 58 sweets. But each received only 35 according to the problem! Why?

This method is actually one that many high-achieving students use and it is actually quite interesting and, at least to me, impressive that an 11-year old or 12-year old is capable of.

What is done is to give each child, boys and girls, 23 sweets. Thus 23 x 405 sweets are given out. Each girl got 23. Each boy also got 23. The 255 comes from the number of sweets the boys got (when each got 35) minus the number of sweets the girls got (when each got 23). So 23 x 405 + 255 tells us 23 x 405 (the number given to every child when each got 23) + 35b (the number the boys got when each got 35) - the number the girls got (when each got 23). The result gives number of sweets that the boys got (23, at first) + 35.

See?

This method is quite clever in that if pretends to give each boy 23 first before the 35 that the problem requires. It also explains the algebraic solution that most adults are familiar with.

Lesson Study and Project Approach

What is the difference between Lesson Study and Project Approach (Lilian Katz)?

Kindergarten Educator in Singapore

"A project is an in-depth investigation of a topic worth learning more about. The investigation is usually undertaken by a small group of children within a class, sometimes by a whole class, and occasionally by an individual child. The key feature of a project is that it is a research effort deliberately focused on finding answers to questions about a topic posed either by the children, the teacher, or the teacher working with the children. The goal of a project is to learn more about the topic rather than to seek right answers to questions posed by the teacher."

This is taken from http://ceep.crc.uiuc.edu/eecearchive/digests/1994/lk-pro94.html

For example, students may learn about founding fathers in class. Some of them (or the whole class or one child) may become interested to learn more about Lee Kuan Yew. They may do internet research or read relevant books appropriate for their age or ask their parents questions about Lee Kuan Yew. They may pose questions that they can ask Mr Lee should they actually get to meet Lee Kuan Yew. This is an example of the Porject Approach that many eary childhood educators are familiar with - thanks to Katz. It is a teaching and learning strategy.

Lesson Study is a professional development activity where teachers 'study' lessons by discussing a lesson plan, by observing students and talking about what they see and so on.

As you can see it is possible to do Lesson Study on different teaching and learning strategies including the Project Approach.

Engaging Students During Problem Solving

I was wondering...what are some ways that teachers in Singapore engage students while teaching problem solving?

Educator in the US

I understand that you teach math at college level? A good way to engage students while teaching problem solving is to ask students to suggest their way of solving the problem. Thus, students will see solutions of various degree of sophistication and choose one that is appropriate for themselves. For more difficult solutions, teachers can scaffold the process by asking questions and giving hints. The choice of problem is important - it must cater to a range of students. Focus on the process and not the final answer. In planning the lesson, anticipate how the students will respond.

See Marshall Cavendish Institute Facebook or http://singaporelessonstudy.blogspot.com/ for an example used with junior high school (grade nine)students in Japan.

Problem-Solving Approach

Question
What is a problem-solving approach?

This presentation made in Penang provides answer to this question.

mathz4kidz for parents

View more presentations from jimmykeng.

About Mastery of Basic Facts

Question

I have written a post on a blog regarding fact fluency and have received feedback that I am mistaken in that students in Singapore learn their basic facts to mastery...meaning with speed and automaticity. It was suggested to me that in fact, students in Singapore don't focus on facts and recalling them automatically is not an important focus of the program. True?

A teacher in the US

Answer
you are right that in singapore students are expected to learn their basic facts (1+1 to 9+9 and 1x1 to 9x9) to mastery.

true - that is not the focus of the program. the focus is problem solving and thinking - visualization, number sense and patterning. but that not not mean they are not expected to master basic facts.

the only thing teachers may want to note is that they have a fairly long time to do it.

students master addition facts in grade one, starting with number bonds and then they get lots of practice because they kept on using these in subsequent chapters.

for multiplication facts, they get a concrete and pictorial meaning making of multiplication before they are taught simpler basic facts such as multiplication of 2, 5 and 10 (and also 3).

plus, they get to learn how to figure out 3 x 6 from 2 x 6. also, 7 x 6 from 2 x 6 and 5 x 6 or 9 x 7 from 10 x 7. see any singapore textbooks - look for the dot diagrams (primary mathematics, my pals are here, shaping maths, math in focus, pensar sin limites - all have these dot diagrams)

all these are done over two years - grade two and three.
subsequently they get plenty of practice in larger number multiplication.

hope this helps

Question About Use of Notebook

Hello teacher Ban Har, I am one of the teachers in the course to apply the Singapore method in Santiago de Chile conducted recently. I now have to help 13 teachers next week in using the Singapore method textbooks. I have a question: how to use a note book, apart from the textbooks?

Marcela, a teacher in Chile

Hola Marcela. As we did in the course, we often use one problem in the development part of the lesson. At this point, the students are not likely to be opening the textbooks. They would be given the problem and asked to solve it usually in pairs or groups. They are likely to record their solutions in the notebook. After about 5 to 10 minutes, they will be asked for their responses which are used by the teacher to help students develop the key concept. By the end of the development, if you have attended one of my lessons before, you will see the board filled with different ways to solve the problem. Students can record this in their notebook. Sometimes there is also a conclusion. They will also be asked to write this in the notebook.

At this point the teacher will ask students to do consolidation tasks from the textbooks. These can be done in the notebook.

At the end of the lesson, students can do their reflection (e.g. write a letter to a friend about the lesson) in the notebook.

The notebook is an important tool for students to learn how to organize ideas.

Question About 4 x 4 = ___ + 7

Second grade students have some difficulties with tasks such as 4 x 4 = ____ + 7. They are students in billingual school and use Spanish and English.

A teacher in Chile

It is expected that students who do not understand the meaning of the equal sign (=) to give 16 as the answer to 4 x 4 = ____ + 7. The teacher can ask students: "What is the value on the right hand side?" (16 + 7) which is 23 and "What is the value on the left hand side?" which is 16. They should realize that these are not equal.

You could read the number sentence this way: 4 x 4 is equal to 16 which is what plus 7.

The task requires a two-step process and students need some metacogntion to complete the task. Use drawing and concrete materials to help the students.