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Are you smarter than a 2nd grader?

Under Common Core, parents are likely to see some unfamiliar terms on their children's elementary-school math homework. Here are some examples drawn from New York state's math curriculum:

-Grade 2 addition:

Solve using your place value chart and number disks, composing a 10 when necessary: 53 19

-Grade 2 subtraction:

Craig checked out 28 books at the library. He read and returned some books. He still has 19 books checked out. How many books did Craig return? Draw a tape diagram or number bond to solve.

-Grade 4 multiplication:

Represent the following expressions with disks, regrouping as necessary, writing a matching expression, and recording the partial products vertically: 3 x 24

-Grade 4 word problem:

Cindy says she found a shortcut for doing multiplication problems. When she multiplies 3 24, she says, "3 4 is 12 ones, or 1 ten and 2 ones. Then there's just 2 tens left in 24, so add it up and you get 3 tens and 2 ones." Do you think Cindy's shortcut works? Explain your thinking in words and justify your response using a model or partial products.