Category Archives: student work

Smart as a 5th grader using structure

Zoe 5th Grade 10 times

Helping students with homework can be easier with examples rather than rules.

10 times as much as  vs. 1/10 of  can be clarified by using better numbers:

so we chose 6 as our better number
6   is 10 times as much as 0.6 and 1/10 of 60

Now we know how to answer each column by comparing it to our easy example of 6!!

CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
Once we see how 6 worked with 0.6 and 60, we can extend that idea to the harder decimal numbers given.







Student work: How much is 12/0?


So how much is 12/0?  Go here to ask Google’s calculator: Google Calculator
oogle says Infinity

Now try the calculator from Web 2.0 Calculator
eb 2.0 says “Error: Divide by 0”

Desmos says “Infinity”

went through a lot of online calculators until I found this:  It says error and also says division by zero is not defined

Wolfram Alpha says “complex infinity”

Try your cell phone calculator(s) and post any other interesting answers here by leaving a comment…this student meant to write Undefined but wrote something super close 🙂

You Make the Call!! 4th Grade Division


It used to be that Math was lots of number crunching but Elementary Math has changed –my theory is the advent of the calculator and Google.  Homework can no longer be a page of straight division problems as they can be Googled for the answer and even for all the steps involved!!!
I came across this working on homework with a 4th grader. Is it 9 divided by 2?  or 9 divided by 4?  Both have a remainder of 1.

See the diagram below for these two ways of interpreting division (albeit division without remainder).Partition division vs Quotition division diagram

Here is another example:

13 can also be grouped by quotition division see above with 3 groups of 4 with remainder 1.  This method will yield the same Math results EXCEPT  for problems like 12 divided by 5 which is 2 remainder 2.  But divide 12 by 2 and we get 6 not  5 remainder 2 b/c the remainder goes in one more time (same goes for divide 21 by 6  is 3 R3 but 21 divided by 3 is exactly 7 not 6 R3.).  So be aware that division these days is about interpretation and not computation.