Friday, August 22, 2014

Math problems of the week: Common Core word problems from New York State

An ongoing series: for all that Common Core advocates claim about what is and isn't stipulated in the Common Core goals, what ultimately matters is how actual people actually implement them in actual classrooms.

Here, via the Associated Press and EngageNY, New York's Common Core curriculum, are some sample Common Core inspired word problems:

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.


Extra Credit:
Some Common Core-inspired curriculum writers believe they have found a strategy to reach Common Core math goals. Their strategy involves requiring students to solve problems using number disks, number bonds, tape diagrams, matching expressions, vertical recordings of partial products, and explanations of their thoughts about other people's strategies. Do you think their strategy works? Explain your thinking in words, and justify your response using a model or diagram.


Auntie Ann said...

In the 3x24 problem, are they really asking kids to draw 72 circles on a page?

Considering by 4th grade, you should already have pretty much solidified your multiplication math facts, and for those students whose parents are freaked by the curriculum and have them in Kumon, it must be an incredibly frustrating worksheet. How awful to sit there drawing stupid circles with the weight of wasted time descending on your shoulders.

lgm said...

Yes, they are. This is a full inclusion setting. Advanced students who are not placed at their instructional level are not excused. If they dont do it, they wont be getting a seat in the honors middle school program, if their district has one.

Anonymous said...

No they are not. This problem is based on Singapore math. The number disks indicate place value. The students are not expected to draw anything for this problem. They will use a combination of one disks and ten disks to solve the problem.

Extra credit: People who comment on this blog claim to admire Singapore math, but when they actually see a Singapore math problem, they go ballistic. Could it be that they have no idea what Singapore math actually entails?

Auntie Ann said...
This comment has been removed by the author.
Auntie Ann said...

I looked up the page. The section with this problem starts at page 3.C.10, and the problem itself is on page 3.C.13:

Engage NY, Math, Grade 4 complete

It clearly shows that they want the kids to draw circles. Not 72 of them, but 7 to represent the tens, and another 2 to represent the ones. With regrouping, you are likely to draw slightly more than that. I ran through the problem as exampled, and drew 6 circles to represent each 24, (18 circles total), then grouped 10 of the ones, crossed them out, and drew another 10-circle. So, doing the problem took me 19 circles.

I did Singapore with our kid, and I don't remember it ever asking the kid to draw disks to answer the question. Bars, yes; disks, no. The text would use drawings of disks for explanation, and the instructor would use disks or other representations during the instruction phase, and the workbook might represent the problem with disks; but when it was time to actually do the numbers in the workbook, I don't remember the kid actually having to take the time to draw circle after circle.

Deirdre Mundy said...

Hey, since many schools no longer teach handwriting, math class has to pick up the fine-motor slack! So...drawing circles is just handwriting practice with a veneer of math!

Auntie Ann said...

Dierdre: That thought crossed my mind too!