# dreambox continued

Posted on October 27, 2011

Seems they *might* have something similar to my “put the numbers together” game — “Build up to 50 Optimally: Students build and identify numbers from static and flashed sets of 1 to 50 objects, using the least number of mouse clicks.” (Then the same for bigger numbers.)

They’ve got this one for second grade: Add & Subtract Landmark Numbers: Students add or subtract two numbers by jumping to the nearest multiple of ten, then adding additional tens and leftovers (45+28 becomes 45+5+10+10+3).
Finding Groups Of Tens: Students group numbers into tens and multiples of ten when adding up to 12 addends. I kinda hope they also have the option of adding ten at a time (so 45 + 28 = 25 + 20 + 8), but of course, if we’d thoroughly learned the ten combos it would be easier to do their thing.

However, I don’t understand why this part is green, indicating fully covered; they’re supposed to understand the equations all turned inside out — where my guys totally break down, so I care. TO wit: “Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?”

Welp, the activity which “completely covers this” is:

Multiplication & Division Situations: Students use various tools and groupings to develop an understanding of multiplication and division.
Multiplication: Doubling: Students double known basic facts to find the product of more challenging basic facts.
Multiplication: Partial Products: Students use the sum of two known basic facts to determine the product of a more challenging problem.
Multiplication: Double & Halve: Students use known basic facts and double one factor and halve the other to determine the product of a more challenging problem.
Multiplication: Adding or Removing Groups: Students add or remove a group from a known basic fact to determine the product of another basic fact.

Excuse me, but don’t **all** of these strategies do things to determine a product – as in, multiply?

This is where that “part to whole” thinking could go… now, I have no earthly idea how well it would carry over into the third grade mind. It could be they’re not ready for that kind of abstraction. If not, though, I can’t see how they’re going to get from finding products to finding the other factor in a multiplication problem.

Using the “part to whole” concept, though, students could identify whether they were looking for the whole thing (the product) or one of the parts (the factor) and what the appropriate operation woudl be to find that.

The problem completely repeats itself in a later, similar goal (IMO the same one — to find the missing number in a times fact, given two out of three, except if they stated it that baldly it would obviously be the rote process it is). All the activities to reach that goal involve finding a product.

The final third grade goal … words fail me:
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Yea. I don’t know much about the third grade mind, but … I’m pretty sure that’s *got* to morph into rote procedure.

I love and adore that there’s visual practice with learning things like doubling one number and halving the other in multiplying gets teh same answer (so 16 x 5 is the same as 8 x 10). I just hope that actual exploration and mastery (you know, the stuff constructivists **say** it’s all about) is included in practice, instead of “oh, we’ll skip the manipulation — here’s the process; that will be quicker…”

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