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?

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

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

Desmos says “Infinity”

went through a lot of online calculators until I found this: http://www.calculator-tab.com/.  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

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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

http://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/continuum/pages/earlydiv225.aspx

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.