Here's how it works:

All three problems in block A are shown here, with the work and the solutions in red. The results of problems 1, 2 and 3 are added in the bottom right corner of block A, and the sum of those numbers (2377) equals the CheckAnswer shown in the box at the top next to A.

The first example in block B asks students to select an operation symbol. Since these symbols don't have a numerical value, they cannot be added for the CheckAnswer. To get around this, we show four possible choices and an arbitrary value for each. The + sign is the correct choice, and its value is 25, so 25 is part of the CheckAnswer sum. We use this wherever answers are symbols, true/false, yes/no, etc.

*(In case you are wondering, it*

**is**possible for a student to get multiple wrong answers which add up to the correct CheckAnswer. But it's not very likely. And when we insert numerical value choices, as discussed above, we make sure that a wrong choice won't make a correct CheckAnswer.)Remainders, fractions, decimals, money and time can be included in a CheckAnswer. When we build the Lesson Sheets we are careful not to co-mingle these with any other type of math in a CheckAnswer! We don't try to resolve remainders, or round seconds and minutes up or down. Notice the examples:

Here are our original three blocks A, B, C with all the work and the answers provided. This is the view that the teacher would normally see in the Teacher Edition answer key.

The Associative Principle tells us that it doesn't matter in what order the students do the problems, or in what order they arrange the answers when adding to get the CheckAnswer. If any answers are wrong, the result is like this—they get the wrong sum and have to go back to recheck their work.

A few people feel students can exploit the CheckAnswer. They say that students can just solve the two easiest problems, do a subtotal, subtract that subtotal from the CheckAnswer, and use the remainder as the answer for the final problem.

Yes, perhaps this happens once in awhile. We still ask students to show their work. If a student is stuck, and creative enough to go through all the sub-totaling work, then able to reconstruct a problem solution backwards, I think that demonstrates ability!

Learn more about Excel Math and see sample lessons at www.excelmath.com.

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