# Comparison subsequence

When each comparison topic is typically taught:

• Compare 0-10 (kindergarten)
• Compare 2-digit numbers (1st grade)
• Compare 3-digit numbers (3rd grade)
• Compare multi-digit numbers (4th grade)
• Compare fractions (4th grade)
• Compare decimals (5th grade)
• Compare integers (6th grade)
• Compare ratios (6th grade)
• Compare rates (6th grade)
• Compare decimals, positive and negative (6th grade)
• Compare percents, with and without decimals, positive and negative (6th grade)
• Compare fractions, positive and negative (6th grade)
• Compare constants of proportionality (7th grade)
• Compare real numbers (8th grade)

Manipulatives can be used to compare positive numbers in any form: whole numbers, integers, decimals, percents, integers, and fractions. However, negative numbers, in any form, cannot be compared using manipulatives, because using manipulatives to compare involves comparing a number of physical objects. If we wanted to compare -5 and 3, for example, we would have 5 -1 pieces, and 3 +1 pieces. So it would seem that -5 is greater than 3, because there are more pieces, but this is not the case.

According to Piaget, when a child is in the "intuitive thought substage" of the "preoperational stage," "when two rows containing equal amounts of blocks are placed in front of a child, one row spread farther apart than the other, the child will think that the row spread farther contains more blocks." I wonder when this stage ends, because certainly if his statement is true, then we cannot teach comparison using manipulatives at this stage. If we can't use manipulatives to teach comparison, I doubt we could teach it at all, but I could be wrong on that.