1. The final questions in the first unit on multiplication and division, "Exploring Multiplication and Division," in the 3rd grade Math Trailblazers Student Guide, p. 103:

Your family decides to save coins in a money jar and to divide them evenly among the members of your family each month. One month, your family finds 36 dimes in the jar. How much money will each member of your family get? How much money will be left over? Write a number sentence to show your solution to the problem. You can solve this problem at home using counters of some sort, such as beans, checkers, or toothpicks.

2. The final questions in the first unit on multiplication and division, "Multiplication and Division," in the 3rd grade Singapore Math Primary Mathematics 3A, p. 103:

Mrs. Holt had 186 stickers. She gave 5 stickers to each student in her class. How many students were there in her class? How many stickers were left over?

3 students sold 243 concert tickets altogether. Each student sold the same number of tickets. How many tickets did each student sell?

3. Extra Credit:

## Thursday, June 3, 2010

### Math problems of the week: 3rd grade Trailblazers vs. Singapore Math

Why aren't Singapore Math students asked to write number sentences and given the option of solving the problems "using counters of some sort, such as beans, checkers, or toothpicks."

Labels:
math,
Reform Math,
Singapore Math

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## 8 comments:

Extra Credit answer:

By the time they get to the final questions, they don't need such items. They do use place-value discs or base-10 blocks initially. But even the initial problems, after the lesson, don't require their use. Initially, students can use them as needed until they don't need them. Besides, they are beyond 2-digit division by now; individual counters would be silly. It is possible that students who are still at dividing small numbers might need them, if all the Trailblazers have gotten to is an introduction to division. The question is not so much whether they still need counters, but what came before and the objectives before getting to final questions. However, it seems that Trailblazers does not expect students to have gotten very far if they still need the manipulatives for the final questions. They never went beyond concrete to pictorial and abstract. Maybe that was all their objective and the abstract is not until next year? In the Primary Math, nearly all lessons get to the abstract, at lest within a few days if not the first day or two of the lesson.

I don't understand the Singapore Math question. How are you supposed to answer "How many students were in [Mrs. Holt's] class?" Do you just make up any answer?

For instance, could you say, "She had no students in her class. There were 186 stickers left over."

Or do you need to assume that she gave out as many stickers as she could?

I don't love Singapore Math for word problems but I do like it for the rest of the curriculum. I use Daily Word Problems for summer supplementation for my kids and it's helped tremendously to get them comfortable with tranlating word problems into number sentences. I blog on this at http://www.pragmaticmom.com/?page_id=1927

Pragmatic Mom

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Having just assigned my DD those two problems (the Singapore ones) I can offer a second extra-credit problem: How many grade levels behind will your student be if you allow the district that chose Math Trailblazers to educate her/him?

Jennifer, I don't know the answer to your question. However, I do know that a child taught using Singapore Math from K-6 (homeschooled) can easily transition to using Larson's Algebra I text. My own 7th grade son has worked through the first 3 chapters of the textbook and the only problem we are encountering is that he can solve the problems in his head ("Show your work!). The word problems are excellent! His friends in public school are allowed to "skip" word problems - so they repeat the teenage mantra, "What do we need Algebra for..?" Larson's text clearly shows why you need and use Algebra in everyday life.

Beth -- Indeed, the wording leaves something to be desired. You have to assume that the teacher gave out as many stickers as she could. All in all, I think that the word problems are a major part of the Singapore curriculum. Working all the word problems in the Challenging Word Problems books really helps kids to develop a gut-level instinct for how to solve problems as well as the technical ability. Nonetheless, there are often problems with slightly squirrely wording, such as the one given here. Often the issue seems to be a difference between the way English is used in the US and in Singapore. I can't come up with any examples right now (and the problem Beth refers to is not an example of this difference, it's just a basic failure to be explicit). But there have been many times when my kids have not understood a problem and I find myself telling them, "The way we would say this is ...."

When I run into an ambiguous question like this (which may happen in ANY textbook, not just Singapore math), I use it as a "teachable moment". I ask the student to identify what assumption the problem is expecting us to make, or what are the possible alternate answers.

This happens fairly often with rate problems, where the "constant rate" assumption is rarely made explicit. But it can happen anywhere, because it's hard for any writer to always be aware of his/her assumptions. Sometimes it's only when you see the problem through the eyes of a child that you notice the ambiguity.

How many grade levels behind will your student be if you allow the district that chose Math Trailblazers to educate her/him?Assuming I'm remembering correctly, I may know the answer to that question.

At the end of C's 4th grade year, he placed into book 3B in the Primary Mathematics series. '3B' is the second semester of 3rd grade. C. was 1 1/2 years behind students in Singapore.

Recently, a mom here whose child has had Math Trailblazers since Kindergarten told me that she did the same thing I did: she gave her daughter the placement test at the end of 4th grade.

Her daughter placed into the middle of 2nd grade.

(I'll check with the mom to make sure her daughter was the same age as C. --- but I'm fairly sure I'm remembering correctly.)

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