We've all been in the situation where the math in the curriculum seems too easy for a group of students. For example, in Grade 2 Ontario's curriculum calls on students to "...solve problems involving the addition and subtraction of two-digit numbers, with and without regrouping". We have students explore the concept with and without manipulatives and using both student-generated and standard algorithms. We lead students to explore these skills in single-step problems and then introduce multi-step problem solving situations. And what then? When all of this seems to no longer be problematic to students, what do we do? Of course, we move them along to three-digit numbers! But...

My hunch is that the students have become very comfortable with and skilled at solving "result unknown" problems that involve the addition and subtraction of two-digit numbers.

If Tom has collected 27 marbles and Sue has 34 marbles, how many marbles are there when they join their two marble collections? 27 + 34 = ???

Are students as comfortable when the structure of the problem is changed to be a "start unknown" problem?

There are 61 marbles in the marble collection that Tom and Sue share. If Sue added 34 marbles to the collection, how many did Tom add? ??? + 34 = 61

While neither the numbers nor the context of the problem changed, the mathematical reasoning that must happen to solve the second problem is quite different than that needed to solve the first.

When we move students along to larger numbers without having given them opportunities to make sense of the various problem structures, we miss an opportunity to have them really make sense of some important mathematical concepts. It's this sense-making and reasoning that will serve them well when they are required to use their math skills outside of math class and in society.

My hunch is that the students have become very comfortable with and skilled at solving "result unknown" problems that involve the addition and subtraction of two-digit numbers.

If Tom has collected 27 marbles and Sue has 34 marbles, how many marbles are there when they join their two marble collections?

27 + 34 = ???

Are students as comfortable when the structure of the problem is changed to be a "start unknown" problem?

There are 61 marbles in the marble collection that Tom and Sue share. If Sue added 34 marbles to the collection, how many did Tom add?

??? + 34 = 61

While neither the numbers nor the context of the problem changed, the mathematical reasoning that must happen to solve the second problem is quite different than that needed to solve the first.

When we move students along to larger numbers without having given them opportunities to make sense of the various problem structures, we miss an opportunity to have them really make sense of some important mathematical concepts. It's this sense-making and reasoning that will serve them well when they are required to use their math skills outside of math class and in society.

To learn more about various problem structures, refer to the Types of Problems from Ontario's

A Guide to Effective Instruction in Mathematics (Kindergarten to Grade 6) -- Volume 5: Teaching Basic Facts and Multi-Digit Computations