I had coffee with another fan of Singapore Math this week and he loaned me some supplemental materials from his travels to Popular Books in Singapore. These two problems come from Accelerated Learning Primary Mathematics 3 by Ching Kheng Huat published in 1999.
The front page states:
In this book, “Accelerated Learning” fosters in pupils the ability to learn faster, to remember more and to think creatively.
The Ministry of Education has initiated IT in education for pupils. To make time for IT, pupils need to learn faster to cover the syllabus. And this requires ACCELERATED LEARNING – a new dimension in pedagogical skills. MOE has also emphasized the need to develop CREATIVE THINKING, which we have incorporated in this book.
The book has seven pages of “Infographic Images” at the beginning (visual dictionary of terms), then practice pages for 12 units. Each unit of six to seven pages has:
- two worked examples
- multiple choice practice
- short answer practice
- problem sums practice
- creative thinking problem (one or two)
Here are the Creative Thinking problems from the unit on fractions:
And a Creative Thinking problem from the unit on time:
It takes 4 h 15 min to repair 3 computer. Repairing a radio takes 47 minutes less that the time needed to repair a computer. If a worker works 9 hours a day, he needs to complete repairing 10 items that can include both computers and radios. How many computers can he repair if he needs to repair as many computers as possible?
Do you feel that these problems will help students “develop creative thinking” ?
About Cassy Turner
I neglected to mention that these problems are from the LEVEL 3 book!
I do think these kinds of problems assist with lateral thinking skills.
Should we assume those are semi-circles?
The word problem is fine, but by the time our kids get to high school, it takes ALOT of time to get them competent with dealing with them. I’ve done it and had to start with square one, super easy problems, and work up to problems at grade 9/10 level. Unfortunately there really isn’t time in the curriculum for that, so if I’m going to do that, I have to leave something else out. They will use every aversion technique ever invented to avoid doing them.
I think there are two factors that cause this. For some students, weak reading comprehension skills. For many students, they had elementary teachers who were afraid of word problems, didn’t know how to teach them, and their curricula let them get away with avoiding them.
I find the use of word problems throughout the Singapore Math materials meets those difficulties straight on.
Here’s the progression I think helps kids master math facts. First, basic multiplication & division are taught with numbers 1-5 & 10 in second grade. Then in third grade:
Double digit x single digit multiplication,
division,
then division w/remainder.
After those have been taught thoroughly, then multiplying by 6 through 9 is introduced.
The first practice is mult. by 6,
second practice is divide by 6,
third practice is divide by 6 w/ a remainder,
fourth lesson is applying multiplication & division by 6 in word problems.
The sequence follows a similar pattern for 7s, 8,s and 9s.
Great Twitter conversation today on the topic of Word Problems:
@ColleenK: I think students who learning the model method of solving word problems (Singapore Math) do not have those misconceptions later.
@JackieB: I’ll defer to you on that, as I haven’t seen any h.s. students who’ve /used/ Singapore in previous courses. My problem is that…
…they get to me w/o this understanding. Looking at the cognitive level of what we’re “supposed” to teach – it makes no sense.
@Cassyt: School in NY is using 5th & 6th gr. Singapore to remediate 8th & 9th gr. Could a SM progression be designed for WP?…
…At least to get students beyond the fear of a WP?
@k8nowak: I spend at least a week with 9th graders building WP competence. Here: http://www.box.net/shared/k8psspom9t…
…Not claiming to have written these problems. Most/all copied from various sources. I teach them SM bar models.
@ColleenK: Anecdotal but students in my program who consistently use bar models can translate Alg wp (Dolciani) by gr 7…
…Elem students immersed in a focused by highly visual math program like SM would have the tools to handle HS wp.
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3) Max of computers:4
Mrs.Yeo bought some cakes for her class pupils. The girls received twice as many as the boys. there were an equal number if
girls and boys in her class. Each boy ate 4/7 of a cake and they finished all the cakes that were given to them. Each girl
ate 1/3 of a cake and they had 8 1/2 cakes left. How many cakes did mrs.yew buy?.
There are some crystal and glass marbles in a pouch. If 3 crystal marbles are removed from the pouch, the number of crystal marbles left will be 1/6 of the glass marbles left. If 5 glass marbles are removed from the pouch, the number of crystal marbles left will be 1/4 of the glass marbles left. How many marbles are there in the pouch at first.
4 Children shared a box of chocolate bars. The first child took 1/2 of the total number of bars of chocolate and 1/2 of a chocolate bar. The second child took 1/2 of the remaining bars and 1/2 of a chocolate bar. The third child took 1/2 of the remaining bars and 1/2 of a cholocate bar. The fourth child took the remaining 7 boxes.
a)How many bars of chocolate did the third child get.
b)How many bars of chocolate were there ?.