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Table 3 Descriptions of CATs for division of three-digit numbers by a one-digit number

From: Teachers’ use of classroom assessment techniques in primary mathematics education—an explorative study with six Chinese teachers

Title Format Purpose
Connecting division to multiplication Red/green cards Assessing whether students can find the related multiplication problem for a division problem
Family problems Red/green cards Assessing whether students can recognize analogous problems and are aware of the relationship among the results of these problems
Choosing an answer for a division problem Red/green cards Assessing whether students can estimate the quotient
Identifying the watershed Red/green cards Assessing whether students can recognize the breaking point when the number of digits of the quotient changes
Checking divisibility Red/green cards Assessing whether students have a clue in advance whether divisions have a remainder or not
Is it in the hundreds/tens? Red/green cards Assessing whether students can estimate the quotient
Algorithm with ink blots Worksheet Assessing whether students understand how the division algorithm works
Is there a zero in the middle of the quotient? Red/green cards Assessing whether students understand the relationship between the existence of zero in the dividend and in the quotient
Correct or not correct? Red/green cards Assessing whether students can quickly check the correctness of the result of division problems without performing the algorithm
Is it in the multiplication table of …? Red/green cards Assessing whether students have the multiplication number facts available
Possible remainders Red/green cards Assessing whether students understand the relationship between divisors and remainders
Easy or difficult? Worksheet Assessing what is the easiness-difficulty range of students and whether they are aware what characteristics of a problem make it easy or difficult for them
Solving division problems without using the algorithm Worksheet Assessing whether students have a deep understanding of the division operation and whether they have, instead of the algorithm, other strategies available to solve division problems