6GM21
6.GM.2.1 Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithms and finding unknown measures.
In a Nutshell
This objective has students finding the area formula of squares, rectangles, and parallelograms that can be found by using cutting techniques and graphic visualizations on grid paper. For example, by rearranging pieces of a parallelogram to form a rectangle that has the same height as the parallelogram and width equal to the parallelogram’s base, students can discover the relationship between the area of a parallelogram and the area of a rectangle. Students can then utilize both formulas in mathematical and real world problems that may require finding area and finding missing lengths given a figure’s area.
Student Actions

Teacher Actions


Develop area formulas for squares and parallelograms by making conjectures, modeling, and generalizing patterns identified through investigations using grid paper and other methods to progress to using the algorithms for finding formulas.

Develop mathematical reasoning to assess the reasonableness of area calculations by first estimating the answer for the problem.

Communicate mathematically through writing and discussion to justify strategies used to find area, including formulas for squares and parallelograms.

Develop a deep and flexible conceptual understanding of how to choose and label units appropriately.

Develop mathematical reasoning to make predictions and draw conclusions when describing how changes in the dimensions of figures affect area.
 Develop accurate procedural fluency by correctly applying the formula to find the area of squares and parallelograms.


Use and connect mathematical representations helping students make connections between the models and generalized patterns in order to develop area formulas for squares and parallelograms.

Pose purposeful questions to assess the students’ understanding of mathematical properties, ability to explain their thinking, and justify their results for problems involving areas of squares and parallelograms.

Facilitate meaningful discourse by engaging students in solving and discussing tasks that help students develop a sense of reasonableness about answers to problems involving areas of squares and parallelograms.

Use evidence of student thinking to assess progress towards understanding the difference between units and square units.

Build procedural fluency to apply area formulas for squares and parallelograms using conceptual understanding.
 Support productive struggle as students investigate mathematical ideas and relationships involving the area of squares and parallelograms. (e.g. What is the effect on area as the dimensions of a figure changes?)

Key Understandings

Misconceptions


Area is the amount of space inside a twodimensional figure.

Square units are used for area because the area of a figure represents the number of unit squares that will cover that figure.

Figures with the same area can have different dimensions.

The dimension chosen as the height of a parallelogram should be perpendicular to the base of the figure.
 The area formula for squares, A=s^{2}, can be developed for rectangles with length and width of equal measurement.


Students may confuse area with perimeter.

Students may forget that the units for area are squared.

When given an area, students may think there are always unique dimensions that will form a figure with that area.

Students may misidentify the diagonal dimension of a parallelogram as the height.

Knowledge Connections

Prior Knowledge

Leads to

 Find the area of polygons if they can be decomposed into rectangles (4.GM.2.2)

 Determine the area of trapezoids (7.GM.2.1)
 Find the area of composite figures (7.GM.2.2)

Sample Assessment Items

The Oklahoma State Department of Education is releasing sample assessment items to illustrate how state assessments might be designed to measure specific learning standards/objectives. These examples are intended to provide teachers and students with a clearer understanding of how the state assesses Oklahoma's academic standards and their objectives. It is important to note that these sample items are not intended to be used for diagnostic or predictive purposes. Ways to incorporate the items.

OKMath Framework Introduction
6th Grade Introduction
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