Reflection: Complex Tasks Halloween Candy to Zombies - Section 1: Warm Up

 

This lesson came from my first year  attempting to implementing some of these more open ended problems and I would definitely do it differently in the future. Until the class started working on this problem I didn't realize how many avenues it contained for further and deeper exploration of the math. I treated here as a problem to do on the side, but it really needs to be the central focus.

Because it is so open ended it provided all kinds of opportunities for my students to experiment and raise questions. They were very engaged and curious about the math and it also created opportunities to intervene and develop gaps in prior learning.

Even if my students knew how to calculate, they didn't often understand the reasons why the calculations work the way they do. Their understanding of the definitions of operations, the relationships between them, and the relationships between the numbers was lacking. This problem allowed them to explore questions like:

  • what's the biggest/smallest number we can make with these four numbers? 
  • Is it better to use a particular number as an exponent or a multiplier? 
  • What difference do grouping symbols make? 4x3+2+1 vs. 4(3+2+1)
  • When is adding more powerful than multiplying? 4x3+2x1 vs. 4x3+2+1
  • How do you get the biggest bang for the buck with the number 1? (addend, base,exponent?)

 

Exploring these questions not only gave them deeper understanding of the operations, but also allowed them to experiment and "discover" number properties like the identities, distributive, etc. The open ended problems with multiple avenues of deeper math explorations don't always look like complex problems on the surface. They greatest value is that they promote student curiosity and questioning. The teacher then has to determine which questions will lead to big ideas.

  Complex Tasks: Make this a separate lesson
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Halloween Candy to Zombies

Unit 3: Equivalent Expressions
Lesson 4 of 23

Objective: SWBAT use and understand the use of distributive property with variables.

Big Idea: Students will understand how to represent the distributive property on unknown quantities with variables using a real world context.

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Subject(s):
Math, Expressions (Algebra), distributive property with variables, white boards
  54 minutes
variables and
 
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