Grades 3-4 Video Solutions 2022-2022_3-4

Video Transcription

Problem number 13. Aladdin has a square carpet. There's the same number of dots arranged in two lines along each of the four sides of the carpet.  Unfortunately, one side of the carpet got folded over. How many dots are there on Aladdin's carpet? A 48, B 44, C 40, D 36 or E 32?  The problem tells us that there's the same number of dots along each of the four sides of the carpet. We can see along this side, which is fully visible,  that there are six dots along the line. If the whole carpet was covered with dots like this, it would form a square that had six rows and six columns of  dots. If we multiply those together, that would mean there were 36 dots. We also know that the carpet isn't fully covered. There are only two rows. So we have the  two rows here and there would be two rows on this side. Likewise, there are two rows on this end and two rows on this end. So right in the middle, there are  only two rows and two columns of dots missing, or four dots that are missing. 36 minus 4 is 32. So there are 32 dots on this carpet. You can also notice that once  you figure out that there would be 36 dots if the whole carpet was covered, and we know that there are not 36 dots, but there are fewer, the only answer that makes sense is E.

Video Summary

Aladdin's carpet has an equal number of dots on each side, forming a pattern of six dots per side. The fully visible six-dot rows suggest a potential 6x6 dot pattern across the whole carpet, totaling 36 dots. However, the actual pattern comprises only two rows per side, with two rows effectively missing from the center, leading to four missing dots. Thus, subtracting these from 36 yields 32 dots. The correct answer is option E, where the reasoning confirms that while 36 dots would be possible if fully covered, folding results in a total of 32 dots on the carpet.

Keywords

Aladdin's carpet

dot pattern

6x6 grid

missing dots

32 total dots