Reflection: Intervention and Extension Area of Composite Shapes - Section 6: Closure and Ticket to Go

Some students struggled on the ticket to go from the previous lesson where students learned about finding the area of triangles.  At the beginning of this lesson, I briefly went over the previous night’s homework.  I presented answers that made some of the common mistakes students had made on their tickets to go and had them correct me.  Here are a few examples of students who struggled on the Area of Triangles ticket to go and demonstrated progress on the Area of Composite Shapes Ticket to Go.

Student A:

On her triangles ticket to go, she struggled to differentiate and calculate perimeter and area.  To calculate the perimeter of the triangle, she multiplied 6.2 inches by 8.4 inches.  She mistakenly thought that this was a right triangle, instead of identifying the base and height as 10 inches and 5 inches.  She also struggled to multiply with decimals, forgetting to count the 1 she carried and forgetting how to put back her decimal in her final answer.  For area, she first doubled each measurement, including the height inside the triangle.  Then she added these numbers up.  My guess is that she applied her strategy of finding perimeter of a rectangle, where there are 2 pairs of matching sides, to this triangle.  Needless to say she ended the lesson with many gaps in her understanding.

On her composite shapes ticket to go the next day, this student demonstrated a significant amount of growth.  She was able to correctly calculate the area of the rectangle as well as the triangle.  She is still struggling on identifying the base of a triangle.  She labeled the hypotenuse as 20 feet, instead of the base that is one of the sides of the rectangle.

Student B:

On his triangles ticket to go, he struggled to find the perimeter of the triangle.  He mistakenly added the base and the height together to get 15 inches.  For area, he correctly identified the base and height.  He multiplied them together to get 50 and then divided it by 2.  He made a mistake in his long division, writing that 5 – 4 = 0.  The student should have checked his work and recognized that 2 square inches cannot be ½ of 50.

On his composite shapes ticket to go the next day, he was able to correctly found the area of the rectangle and the triangle. He also accurately divided 160 by 2.  Like Student A, he did not correctly identify the base of the triangle.  He also forgot to include units with his answer.

Student C:

On her triangles ticket to go she confused perimeter and area.  She was able to correctly identify the base and height of the triangle.  She used the formula to find that the area of the triangle was 25 square inches, but she thought that was the perimeter.  For the perimeter she simply listed the height of the triangle.

On her composite shapes ticket to go the next day’s ticket to go she was able to correctly calculate the area of the rectangle as 160 square feet.  She was able to find the area of the triangle by multiplying 20 x 8 and then divide 160 by 2 to get 80 square feet.  I am unsure why she placed “64” inside of the triangle.  Instead of adding the area of the rectangle and the triangle together she just wrote down the area of the triangle.  She needs to make sure she carefully reads the problem to make sure she answers the correct question.

Next Steps:

Although these students showed growth, each of them still has areas that they need to continue to work on.  At the beginning of the next lesson I will pass back these tickets to go so students can see their growth and correct mistakes.  I will also continue to check a couple homework problems as a class before passing them in.  This gives me another opportunity to commit common mistakes and have students correct them out loud.  I will also take this data into consideration when I make my small groups for the Area, Perimeter, and Circumference lesson.

Intervention and Extension: Making Progress from Triangles to Composite Shapes

Area of Composite Shapes

Unit 8: Geometry
Lesson 4 of 19

Big Idea: How can you find the area of this shape? Students apply their knowledge of area to find the area of composite shapes.

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Standards:
Subject(s):
Math, Geometry, area of parallelogram, area of rectangle, area of triangle, 6th grade, master teacher project, area of composite shapes
50 minutes

Andrea Palmer

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