| 
  • If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.

  • You already know Dokkio is an AI-powered assistant to organize & manage your digital files & messages. Very soon, Dokkio will support Outlook as well as One Drive. Check it out today!

View
 

6-GM-1-1

Page history last edited by Brenda Butz 6 years, 1 month ago

6.GM.1.1 Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm.


In a Nutshell

Area can be defined as the amount of space inside a two-dimensional figure.  Area formulas for squares and parallelograms can be developed by recognizing both of the figures’ connection to rectangles. The area formula for squares can be developed through rectangles with length and width of equal measurement.  Using grid paper will help students find that the total number of unit squares in the square can be found by multiplying the equal lengths and widths of the square, s, which leads to the formula A=s2.  Students should also have the opportunity to develop the area formula of parallelograms using cutting techniques and graphic visualizations on grid paper. 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.  For example, if the total area of a parallelogram is 140 cm2 and its base is 14 cm, what is the height of the parallelogram?  Students must use the area formula of A = bh to set up the equation 140=14h and solve for the height.  This objective aligns closely with 6.A.3.1 and 6.A.3.2

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.

  • 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 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 and ability to explain their thinking and justify their results for problems involving area of squares and parallelograms. (Ex: Can you make a model (drawing) to help you solve this problem?  Do you see any patterns that can help you solve this?)

  • Facilitate meaningful discourse by engaging students in solving and discussing tasks that help students develop a sense of reasonableness about answers to problems involving area 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 area of squares and parallelograms. (Ex:What is the effect on area as the dimensions of a figure changes?)

Key Understandings

Misconceptions

  • Area is the amount of space inside a two-dimensional 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.

  • To apply the formulas for finding the area of a square and a parallelogram.  

  • The dimension chosen as the height of a parallelogram should be perpendicular to the base of the figure.

  • Confuse area with perimeter.

  • 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.
  • Identify the diagonal dimension of a parallelogram as the height.


OKMath Framework Introduction

6th Grade Introduction

 

Comments (0)

You don't have permission to comment on this page.