4.NF.B.4c Hand Puppet Problem

In order to solve this hand puppet problem, I gave each of my 4th graders a sheet of 2-cm graph paper and 18 snap cubes. 

The cubes were arranged in sets of 6 and included 3 different colors to help each child connect with the fabric colors in the story problem.

 Immediately, the discussion began with “How much is 5/6^th of a yard?” After Eligio determined that he could represent this with 5 of the 6 snap cubes, then Fatima struggled with “How much is 3 times 5/6^th of a yard?”

Patricio said that  3 x 5/6  was 15/18, but Rigoberto disagreed. Rigo showed the class that “three times a number” was the same as adding it 3 times. Therefore,  
5/6 + 5/6 + 5/6 = 15/6.

Martha saw that each cube (1/6) was worth $2, because there were 6 cubes (6/6) in a yard and each yard cost $12.

Esmeralda wrote, “The girls need to buy 2 ½ yards of felt. It will cost $30. I know this for sure, because 1/6 = $2 and $2 x 5/6 = $10. So $10 x 3 yd. = $30 and that’s how I know.”  She confused the 3 times 5/6 with 3 yards, but was definitely making progress in her understanding. 

Patricio showed the class that he could move 2 cubes from the third 5/6 of a yard to make 2 complete yards, plus ½ a yard. “That equals 2 ½ yards of felt,” he beamed. “Each block costs $2 and 15 x 2 = 30. I got the 15 from each block.” It was obvious that he had clarified his earlier thinking that multiplying 5/6 by 3 was not the same as multiplying 5/6 by 3/3. He also realized that ½ a yard was $6 and not ½ a dollar or 50 cents.

The children agreed that problem solving was messy work, but they enjoyed the social aspect of working together and helping each other be successful in finding the solution.