Thursday, May 14, 2009

Math problems of the week: 3rd grade Everyday Math vs. French Math

1. The last five addition problems in the second (and final) Everyday Math 3rd grade workbook, Student Math Journal Volume 2, p. 316:

2,384 + 1 =
2,384 + 10 =
2,384 + 100 =
2,384 + 1,000 =
2,384 + 10,000 =

2. The last five addition problems in a French 3rd grade (CE2) math workbook, Cahiers d'activites mathematiques, p. 22:

57 + 19 =
84 + 29 =
164 + 19 =
315 + 29 =
36 + 39 =

3. Extra Credit:

What do these problems suggest about who learns more about place value by the end of 3rd grade?


Anonymous said...

My particular ninth graders struggled with defining a 2-digit number.

Solve using algebra (without guessing) Find a two digit who's digits add up to 11. When you add 9 to the number you get a new number with the same digits but reversed. What is the number?

To solve this problem with algebra, students must know
N = 10x + y (And most don't)

N + 9 = n
10x + y + 9 = 10y + x
9x + 9 = 9y
x + 1 = y
(11 - y) + 1 = y
12 = 2y
y = 6
x = 5

This is from a third grade Singapore textbook - the problems are different of course, but you should see some parallels - the Singapore authors are emphasizing place value and students are deducing what the number is while practicing their multiplication.

Primary Mathematics 3A, including the 3A workbook.*

"Challenge Problem" from Intensive Practice 3A:

I am a three-digit number. All the three digits add up to 9. My tens digit is twice my hundreds digit and my ones digit is three times my tens digit. I have no zeros. Who am I?
(page 10)

Ans: 126


Now where do you think you would see this same problem in Saxon? Intermediate Algebra

Saxon Algebra 2, at the end of the book. [update: RJ and Cheng noted that the sum of the digits of their two-digit counting number was 9. If the digits were reversed, they found that the new number was 27 less than the original number. What was the original number? Saxon Algebra 2, Second Edition, p. 432, no. 1.]

These are considered key problems because they are clearly identifiable and you find them everywhere except in the DOE's exemplary? textbooks. Why not?

In fact you will find these same problems in Wentworth's New School Algebra (1898) which if you read carefully on p. 81, Saxon uses identical symbols, t for 10's place and u for unit's place.


I happenned to read some of the Amazon reviews for Saxon 2 and I would not believe a word of their nonsense.

My only prejudice would be for the US using either Singapore or Challenging Mathematics (published in 4 languages) but CM originated in Quebec and is easy to verify from their TIMSS scores. Plus the classes are fun to observe.

lefty said...

Anonymous--Thanks so much for all these problem excerpts and references! And for your fascinating and valuable post. I'm going to order the Wentworth algebra. Do you have any other references for old algebra or arithmetic texts? Also, any pointers to how I can order Challenging Mathematics? It seems that no online booksellers carry it...

Anonymous said...

This will point you where you want to go.

Anonymous said...

This is better...the textbooks were created originally for immigrant children learning English and French in Quebec. The authors integrated weekly chess lessons into the books. When the children were mainstreamed into French speaking classes, the parents and students demanded the books. The results were so striking that the TIMSS investigators had to disaggregate the data into two groups: French-speaking Canadians and English-speaking Canadians.

Quebec had the youngest student ever to win a chess game against a grandmaster. Neat story.

The program has been adopted in other provinces; although you are right, you can't find it easily on the internet. Also, I have some instructional materials the authors make for pre-school age children that are fascinating! Cheers.

Challenging Mathematics
by Michel Lyons, Robert Lyons
Hardcover, Mondia Editeurs, ISBN 289114418X (2-89114-418-X)
More editions of Challenging Mathematics:

Challenging Mathematics: Hardcover, Mondia Editeurs, ISBN 2891144643 (2-89114-464-3)
Challenging Mathematics: Hardcover, Mondia Editeurs, ISBN 2891144724 (2-89114-472-4)
Challenging Mathematics: Hardcover, Mondia Editeurs, ISBN 2891144783 (2-89114-478-3)
Challenging Mathematics: Hardcover, Mondia Editeurs, ISBN 2891145364 (2-89114-536-4)
Challenging Mathematics: Hardcover, Mondia Editeurs, ISBN 2891145771 (2-89114-577-1)
Challenging Mathematics: Hardcover, Cheneliere/McGraw-Hill, ISBN 2894612508 (2-89461-250-8)
Challenging Mathematics: Cycle 1
by Michel Lyons, Robert Lyons
Hardcover, Cheneliere/McGraw-Hill, ISBN 2894618700 (2-89461-870-0)
More editions of Challenging Mathematics: Cycle 1:

Challenging Mathematics: Cycle 1: Hardcover, Cheneliere/McGraw-Hill, ISBN 2894618719 (2-89461-871-9)
Challenging Mathematics, Cycle 1: Hardcover, Cheneliere/McGraw-Hill, ISBN 2894618727 (2-89461-872-7)
Challenging Mathematics: Cycle 1: Hardcover, Cheneliere/McGraw-Hill, ISBN 2894618735 (2-89461-873-5)

Anonymous said...

Something you might be interested too is that I've used chess to teach children with autism. Here's a link that has lots of useful information for interested parents.

I am convinced there are two secrets to writing math curriculum. First, is to design curriculum for non-native speaking students and then cross over to your native speakers during the implementation phase. Second, design your curriculum in reverse - How proficient do you want your students to be in mathematics when they leave high school? This is not the same as saying success for all students. That's being unrealistic.