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.

]]>Here are five pieces of digital content a teacher might choose from our library to support and enhance the teaching of: CCSS.Math.Content.3.G.A.1

*Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.*

A teacher could use this virtual manipulative with students on an interactive whiteboard and choose relevant shapes to start a discussion about how one shape can have different names. (square, quadrilateral, polygon, parallelogram)

**Exploring Shape Classification**

A teacher could use this activity to challenge students to sort shapes into four different diagrams based on their characteristics. (Choose the Shape Classification Tab.)

A teacher could use this activity with students to encourage students to think about multiple categories a shape could belong in as they sort shapes into a Carroll Diagram.

A teacher could use this activity to challenge students to find *all* of the shapes that match the given characteristic.

A teacher could use this resource to challenge students to sort shapes into a triple venn diagram without knowing the categories. Then students are asked to figure out the categories.

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