Investigating Area by Folding Paper: Sentence Starters and Frames

Some ideas for sentence frames/starters that could be incorporated into your lesson are listed below. If you think a sentence frame/starter will be helpful, consider how it will support students’ mathematical learning and/or development of academic language, and decide which sentence frame/starter (from the list below or that you create) would best support students’ learning.

(part 1 and 2 of task)
To create a _____________ (square/triangle) with ¼ the area of the original square piece of patty paper, I folded:                 


(after part 2)
The way I folded the paper to create a square with ¼ the area and a triangle with ¼ the area of the original square piece of patty paper was different because: 


(after part 3)
I know that the two triangles I have created in #2 and #3 are not congruent because: 


Academic Language

Students should have opportunities to see, hear, and write key mathematical ideas during this activity. There are some specific terms that students need to understand in order to engage in this task, and there are some additional terms and phrases that may surface as the students engage with the task. You may think of additional words or phrases that are key to this activity. As the task is introduced, solved by the students, and discussed, ensure that students have opportunities to experience (i.e., through discussion, pictures, and the use of gestures) and to build understanding for key words and phrases. Examples of words and phrases that may be involved in work on this problem include:

  • Congruent
  • Area
  • Triangle; square
  • Construct a square; construct a triangle; square or triangle that you constructed
  • Side lengths are equal
  • Oriented differently
  • Base
  • Height
  • Reflection
  • Fold
  • Specified