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**I**n administering the concepts test to young children, you may read the first three items to them; however, refrain from giving them any hints or prompts. Allow as much response time as deemed appropriate. Record the results on the form provided on the next page. Tally the types of responses and then total the tally marks. For example, 15 “trues” and 7 “falses” for the first question would be recorded as follows:

The items on the concepts test are subtle. Items 1-3 test for an understanding of equals as “balanced” or “is the same as.” Many children don’t think of it that way. They think it means “get the answer,” like on a calculator, or “write the answer,” like on a worksheet. If they still think that when presented with algebra, they’ll be puzzled and at a disadvantage with equivalences such as a + b = b + a. Teaching the is a first step in preparing them for algebra.

Item 4 tests for “always carrying a 1,” a habit that many children develop because of rarely adding more than two numbers at a time in the early grades. All that matters for this item are the responses to the *last* problem. The first three problems just lead up to it. Teaching in the Fair Lands™ key overcomes the habit.

Item 5 checks for the realization that context matters in working with numbers. A surprising number of children answer 2 feet 5 inches for this item. They add 7 and 8, get 15, put down the 5 and “carry the 1.” They don’t take into account that 12 inches—*not* 10—make a foot. Teaching the addresses the issue of working with different exchange rates.

Item 6 tests for an understanding of base 10 numeration. The first two problems are just warm-ups exercises. The third one checks for the common mistake of always subtracting the smaller number from the larger one and getting 22. The fourth one is simply difficult for most children with many of them leaving it blank (or again subtracting the smaller number from the larger one). Poor results for this problem indicate the need to teach the Fair Lands™ key and —the standard subtraction algorithm except with *understanding* and no shortcuts like sprinkling 1s about.