Monday, February 16, 2009

Grade 5 Division and Everyday Math in Seattle

In grade 5 EDM lists as a developing learning goal division with one and two digit divisors. Unfortunately this is a long way away from the WA State Math Standards 5th grade expectation of students having a secure mastery of the standard algorithm for long division with a two digit divisor.

Here is what appears to be going on in grade 5 of the Seattle Public Schools if the EDM pacing plan is followed:

Division is covered in Unit 4 (pp. 230-272 in teacher's guide) of Everyday Math in 5th grade:


4.1 Division Facts and Extensions - Reviewing multiplication and division facts and apply basic facts to division w/ 1-digit divisors.

4.2 Partial Quotients Division Algorithm - Review algorithm w/ whole numbers

4.3 American Tour Finding Distances on a Map ( I don't know what this has to do w/ division as defined in WA Standards)

4.4 Partial-Quotients Algorithm Strategies - Providing practice w/ algorithms

4.5 Division of Decimal Numbers - Providing experience w/ magnitude estimates for quotients and using partial-quotients algorithm w/ decimals

4.6 Interpreting the Remainder - Interpreting remainders in story problems

4.7 Skills Review w/ First to 100 - game where 2 dice are rolled and the product found and it is multiplied by variable to get answer. If one gets correct answer then they get to keep the product of the two dice just rolled. ( there is an entire section about this with lots of games and calculator activities.) So what is happening to the Standard Division algorithm? As near as I can tell it is not present in Grade 5 EDM.

4.8 Progress Check 4.

It seems that in EDM, there are not too many 2-digit divisor problems. The only method shown is partial quotient or calculator use. Students are encouraged to estimate using multiples of 10. At one point in the "Informing Instruction" teachers are encouraged to have the child make the following list if divisor is 6:
5 x 6
10 x 6
20 x 6
50 x 6
100 x 6
200 x 6

This list is supposed to get students to go beyond using multiples of 10.
In perusing the problems a lot of "friendly numbers" for 2-digit divisors such as 11, 25, 50, etc. This must be intentional as in EDM it is likely that many of the students haven't memorized multiplication facts to a level of automaticity.

Have I missed something here?

What is the District doing to meet the following performance standard for grade 5?

Fluently and accurately divide up to a four digit number by one- or two-digit divisors using the standard long-division algorithm.

In the EDM standard pacing plan, it appears that EDM avoids the standard long division algorithm in favor of partial quotients and calculators.

Is there a revised pacing plan that shows how the WA State Math grade level performance expectations as posted on the SPS website are being met?

I've asked this question of the SPS hopefully there is a a good answer about how the needs of the students are being met.

Charlie Mas followed this with Seattle Schools Blog material at:

Nice work Mr. Mas.


Anonymous said...

5 x 6
10 x 6
20 x 6
50 x 6
100 x 6
200 x 6

Here is the problem with a list such as this - there isn't one rule and it is iterative ( must be written recursively). This is a non-standard pattern - meaning there are two rules (not one). Teachers in Singapore do not give problems like this one, because it is confusing and unnecessary.

Simplest method using multiplication

Start with 5
Double twice
Multiply by 2.5
Repeat step 2

5, 10, 20, 50, 100, 200
30, 60, 120, 300, 600, 1200

What most people overlook when they review Core Plus is that not only do students write the equation of lines using a non-standard form: y = a + bx

BUT, they also have to describe the rule with an iteration (rule) using tables they create on the graphing calculator. The work is difficult, tedious, and unnecessary. Most adults don't have a clue what the authors are doing. Very little explanation is given - you have to search the calculator resource book, since its not found in either the teacher's edition, nor the student textbook.

The authors are complete hacks.

Anonymous said...

Just to test your readers, who might be skeptical or hadn't wondered why Core Plus avoids instruction on parabolas. Try this!

Write an iteration for generating a parabola using the table mode in a graphing calculator. Without any instructions from the authors. It must have been divine inspiration, because I still puzzle over that bit of nonsense. then imagine having to stare at a college entrance test that has parabolas. Mind boggling.

Anonymous said...

How about a formula for working over MathematicallySane, preferably in a dark alley? What does MS do for education in general other than gripe about how their textbooks get no respect.

Multiplication Worksheets said...

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