Please click on the thumbnail to enlarge the photo.
To leave a comment, you have to click on the word "comment" in the comment counter at the bottom of the blog :-} I smell candy!
All of these samples of student work show how creative and efficient students can be when asked to solve basic multiplication and division problems. All of these students used very efficient strategies to carry out work that is usually a very scripted set of steps (Traditional algorithms allow for very limited flexibility in mathematical thinking).
Equally important, the students were able to create their own word problems that could be answered by solving the numerical problems. This is always a very tricky situation for students of this age, (in truth, it is for students of any age) as students are so used to solving numerical problems that are written for them. Many start by imitating problems that they have read in math books. However, when students start to create problems that are really relevant to their lives, they gain a very deep insight into what multiplication and division really are.
These are works in progress, and there are some very simple errors, especially in the division problems (usually because of faulty subtraction), but the kids are showing a pretty deep understanding of what the answers really mean. In most math books, the remainders of division problems are just written as a fraction or a decimal amount, but in the real world, remainders mean something. Remainders can be valuable or inconsequential, and contrary to popular opinion, not all remainders can be split into equal pieces.....kids, puppies, and crunchy potato chips included!
In photo number 1, there is a subtraction error. 835-690 = ?
In photo number 2, one factor pair, 26 X 20, was left out.
In photo number 3, the remaining $17 could, and probably should, become 50 cents extra per person, although giving the money to charity is admirable :-}
In photo number 4, 3135-2300 = ?
As you can see, there is a ton of input to manage, but the concepts are coming together!
