*This is the fourth in a series of posts dedicated to helping teachers understand specific changes the Common Core requires them to make in their instruction and sharing how StarrMatica’s content can help facilitate that transition. The first three posts can be viewed here, here, and here.*

One of the major Common Core Math shifts is that students will be required to demonstrate an understanding of mathematical concepts. Perhaps the most obvious example of being able to “do the math” without understanding the underlying concept is a student’s ability to correctly add two numbers in a multi-digit addition problem with re-grouping and arrive at the correct answer without being able to explain why they are regrouping.

Here is an example of a former standardized test question paired with a Smarter Balanced Assessment question.

*Previous Standardized Test Question:*What is 23.46 rounded to the nearest tenth?*Smarter Balanced Assessment Question:*Five swimmers compete in the 50-meter race. The finish time for each swimmer is shown: 23.42 23.18 23.21 23.35 23.24 Explain how the results of the race would change if the race used a clock that rounded to the nearest tenth.

Both questions are ultimately asking students to round decimals; yet they are distinctly different. In the first question, if the student knows a rounding procedure, they can find the answer. The second question requires students to think about the implications of rounding decimals and to explain how this concept is applicable in a real life situation.

The first step for many teachers in the concept building process is leading students to develop their own number sense and mathematical reasoning. Ask your students to share ways they would group a set of 23 objects to make them easier to count. (Instead of telling them to group by tens and ones.) Ask your students to share what strategy they would use to mentally subtract 82-64 (Instead of showing them the algorithm.) Challenge your students to figure out how 3 friends would share 4 cookies equally. (Instead of telling them what a fraction is.)

This type of instruction takes careful planning of a series of properly sequenced varied experiences paired with strategic questioning and opportunities for meaningful distributed practice. Once a concept is developed, students should be able to explain their thinking by constructing viable arguments in mathematically precise language.