As with many of my peers, this week, my students were given a pre-assessment to help guide my GLT unit planning. My assessment was a former Everyday Math teacher's volume for formative assessments for third grade. The assessment was designed to be administered at the end of "Unit 2" instruction. Nearly half of the assessment consisted of an input/output table in which students were supplied with the rule for completing the missing values in the table. For each table, nearly half of the values were filled in to help students more easily see how the rule functions: ie "Rule is +8 so in=7 out=___" My focus student successfully completed nearly every output question in the tables, however, determining an input was more of a challenge. Therefore, this student was likely more comfortable when the initial value was given for which the rule was to be applied to. When the output value was given, it involved using the number in the rule with the reverse operation to determine the input value. In order to further this student's thinking/level of understanding I would explicitly teach how to reverse the given operation to reach the input value. Additionally, I would utilize input/output charts in more "real-world" contexts, such as a receipt showing sales tax added followed by the total.
Rather than explicitly teaching the "rule" or method, you might ask this student to try to find the "input" by any means necessary (using a drawing or manipulatives, etc.). At that point, you might have students compare their different methods for solving such a problem, allowing the student to make the connection between his current method / understanding, and the more "efficient" strategy.
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