Reflection: The Broken Eggs - Section 2: Investigation


I noticed many opportunities for differentiation during today's lesson.  In this year's class, I have many special education students along with many students who have been out of school for an extended period of time. I also seem to have a few students who declare their hatred for math! This problem can be a challenging one for some students as it requires them to practice SMP 1: Make sense of problems and persevere in solving them.  I noticed during this class that many different things were happening simultaneously in order to keep students working on the problem.  

  • First, I started out with a demonstration using small cubes for the eggs.  I think this visualization of the problem helped some students to "make sense of the problem."  Some students continued with the manipulatives for a while, while other students moved on to pen and paper.


  • Two students came out with some great ideas right at the start, but had trouble incorporating those ideas into their work.  One student immediately said, well the answer has to be a multiple of seven.  We wrote up this "noticing" for the class in order to help students keep notes on their process.  Another student talked about how the answer could not be divisible by 2, 3, 4, 5, or 6.  Students were able to take the idea of not being divisible by 2 into account and ruled out any even numbers, but I noticed they were unable to do anything else with this information even though it was useful.  Later in the class, I did end up showing them a trick for how to figure out if a number is divisible by 3.


  • Students definitely needed help thinking about decimals once they got to larger numbers and were using calculators.  The way I approached this issue with most students was to ask them what an example would be of a number that would have a remainder of 1 when divided by 3.  Most students could get to the next number, 4, realizing that 1 would be left over.  We then talked about what 1/3 looks like as a decimal.


  • One student needed help organizing her information and needed a lot of encouragement to stay with the problem. We worked to create a table to organize which numbers fit the divisibility requirements of the problem.  Once students realize that there have to be more than 100 eggs, they often get frustrated.  For this reason, I think it's good to cut off the work at some point and get students writing about what they have tried so far.

  Opportunities for Differentiation
  Opportunities for Differentiation
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The Broken Eggs

Unit 1: Introduction to Algebra: Focus on Problem Solving
Lesson 5 of 14

Objective: SWBAT to make sense of a word problem and use multiple approaches to justify their answers. SWBAT be able to explain their mathematical thinking in writing.

Big Idea: Students work on their first math riddle. This lesson gives them the opportunity to solve a problem in different ways and spend some time explaining their own, unique mathematical thinking.

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Math, Patterns (Algebra), Algebra, Factoring (Number Sense), modeling, problem solving, Algebra, writing in mathematics, Number Theory
  60 minutes
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