It’s finals week here at the Triangleman Decimal Institute.

Let’s review for the final exam, shall we?

**Week 1 (Sept. 30): Decimals before fractions?**

In this week, we considered the question, *Should we treat decimals more like whole numbers or more like fractions?* Associated with that question, we strived to make explicit the ways in which decimals are *like whole numbers* and the ways in which they are *like fractions.* We covered a surprising amount of ground on these questions.

**Week 2 (Oct. 7): Money and decimals.**

Our consideration of money and decimals led us to think very, very hard about units. In the case of money, it seems that we reached consensus that the *place value *aspects of the American monetary notation system are subordinate in many people’s experience to the *different units* aspects. That is, we are more likely to think of $3.50 as *three dollars* and *fifty cents*—two different units—than as *three and fifty one-hundredths dollars*.

While both ideas are correct, this conceptual difference has fairly strong explanatory power. It helps us understand a lot of the errors we see in classrooms and in the larger world.

**Week 3 (Oct. 14): Children’s experiences with partitioning.**

In this week, we explored experiences students have with cutting things into pieces, which is the real-world knowledge children can bring to classrooms when they study fractions and decimals.

**Week 4 (Oct. 21): Interlude on the slicing of pizzas.**

Dozens of math teachers on the problem led to our documenting 6, 8 and 10 slice pizzas directly (where a slice is interpreted to be the result of *complete and equal partitioning* of a pizza). We have strong claims that other numbers of slices exist, but no photographic evidence.

**Week 5 (Oct. 28): Grouping is different from partitioning.**

We argued this week about whether moving to the right in the decimal place value system is really a simple extension of moving to the left. It seems assumptions are everything here. Maria and I brought differing assumptions to this question, and this led to some very interesting and spirited debate.

**Week 6 (Nov. 4): Decimals and curriculum (Common Core).**

In week 6, we thought about the relationship between the ideas we had been working on and standards documents.

—

This brings us to week 7.

Your final exam consists of one question and one task. The question is this:

*How can you show the world what you have learned these last several weeks?*

The task is this:

*Do it.*

And let me know what you do, OK? I need data for my funders.

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