Got subtraction?

A type of algebraic expression that befuddles legions of students is the following:

6x – (2x + 3)

Standards writers, in particular those that are charged with reshaping education, should carefully consider those areas that are known to cause difficulty, and address them.

We’re not here to introduce a foolproof method for teaching every student to get this right (because there is none), but we think a curriculum sequence that allows students to recognize underlying concepts, discover patterns and make connections, and build fluency, can and should begin long before algebra class.


CCSSI is unduly worried that students won’t be able to add and subtract.  1.OA.1, 1.OA.4, 1.OA.6, 1.NBT.4, 1.NBT.5, 1.NBT.6, 2.OA.2, 2.NBT.5, 2.NBT.7, 2.NBT.8, et al., all involve addition and/or subtraction of two numbers.  We previously discussed our plan for addition and subtraction.

Even CCSSI’s focus on mental math such as adding 10 at a time does nothing more than require students to add and subtract two digits without a calculator, a skill that they should be learning anyway.  If we want to make mental math a priority, we should teach students anzan.

Barely gaining CCSSI’s attention, though, is the possibility that you might require operations with more than two numbers, and the opportunity that presents.

1.OA.2 states ``Solve word problems that call for addition of three whole numbers...’’
2.NBT.6 states, ``Add up to four two-digit numbers...’’

Even with these standards, CCSSI is strangely devoid of situations that combine three or more numbers and involve subtraction, which creates far more complications than addition.

Ann has 12 marbles.  She gives 3 marbles to Jack.  Then she gives 4 marbles to Jill.  How many marbles does Ann have left?

Under CCSSI, students won’t face such a problem.  We find this troubling.

Posing such a (seemingly basic) question creates opportunities for more sophisticated math connections to be made, even in the first grade.  Because you can subtract 3 from 12, and then subtract 4, but can also group 3 + 4 together before subtracting, this kind of problem and the thought processes it engenders form a precursor to a real (not rote) understanding of the algebraic expression we posed at the beginning.

We’ve said it before: CCSSI has not only the opportunity, but also the obligation to address the difficulties that have long plagued American math education.  We don't see it happening.