Intended Audience: Grades K-5 teachers, prospective teachers, and public/private and homeschool parents.
In this video, 6-year-old Autumn shows different methods for subtracting in the context of the word problem, “If there are XXXX kittens in a barn and YYYY are adopted, how many are left?” Watch as the question degrades quickly!
The first question, answered by finding 17-8, is done using the number bond “8 is 1 and 7.” First, take away 7 from 17 to get 10, then take 1 more to get 9.
This is one of the “bread-and-butter” methods of Eureka Math because it also helps teach place value (subtract to 10, then subtract the rest). To prepare students to use this method (including Autumn!), a lot of work done in PK-1 centers around 10 frames:
This one picture shows many number relationships all at once. It corresponds to the “hand number line” in the “Learning to Multiply, Part I” video (e.g., the top row corresponds to the left hand). It shows the number bond “9 is 5 and 4” (1 left hand and 4 right-hand digits). Most important for the subtract method that Autumn used, it shows the number bond “10 is 9 and 1” (note the empty space can be counted too!). Autumn has done enough work with 10 frames that this picture is one of the pictorial representations she can visualize when doing subtraction calculations.
The answer to the second problem, 53-18, is solved using a different method. In this problem, Autumn sees that 18 is close to 20, and that 20 is easy to take away from 53: 53-20=33. She took 2 too many, though, so adds those 2 back in to get 35. As an exercise, try to draw this on a number line yourself.
The third and final method shows up in answering 114-96. Autumn imagines 96 and 114 on a number line. She then knows that the difference is just the distance between the two numbers, which is easily found by backing up 14 to go from 114 to 100, and then another 4 from 100 down to 96:
The total distance is 18, which means:
The final question is just the third method used again, and in this case, it is even easier to see: 1017-999 = 17+1 = 18.
Finally, let’s talk about the question, “If there are 1017 kittens in a barn, and 999 are adopted, how many are left?” In the Eureka Math curriculum, this is what I started calling (and which the writers have come to affectionately use as part of their vernacular):
Completely Ridiculous Artificial Problems
If used in isolation, the 1017-999 word problem in the video is absolute C-R-A-P. It’s so ridiculous that every student would see it as artificial. The writers of Eureka worked very hard to not inadvertently write C-R-A-P because it sends the very negative message that “math is only useful for ridiculous, artificial problems.” Sadly, one of the reasons many students get turned off to math is due to all the C-R-A-P in the standard Textbook School Mathematics (TSM) curricula in the U.S. If a large enough percentage of math problems are C-R-A-P, students are likely to judge that the entire enterprise of mathematics is ridiculous and artificial as well.
But, as this video shows, one can delve into the world of C-R-A-P if the teacher is honest with their students that the problem is ridiculous and made-up. In the video, we build up to the C-R-A-P problem by starting with a reasonable question (barns often have 10-100 cats due to so many mice eating grain), and slowly making the problem worse. The C-R-A-P problem then helps students understand what is a reasonable math question and what isn’t (while having a bit of fun at the same time). Enjoy Autumn’s expressions as the problems get more ridiculous.
As always, comments are welcomed!
CHANNEL: Growing up with Eureka
© 2015 Autumn Baldridge and Scott Baldridge
Supported by NSF CAREER grant DMS-0748636