Balance Bender Equations Exploration

A whole-group mathematical exploration of equivalence. This resource creates space for learners to manipulate, justify, and solve equations using a basic understanding of the following properties of mathematics, each of which is introduced within its own prompt so that they can learn the process of logically reasoning through each situation. Learners are encouraged to bring ideas forward within the conversation and prove or disprove each other’s theories about the balanced equations they can create from this model. This activity is used best to push learners toward deep, critical thought about number reasoning and equivalence - skills they can start building as early as grade 3 or 4 on up through Algebra.

WHAT’S INCLUDED

This resource contains:
-> 7 balance bender explorations
-> Step-by-step instructions for you on how to lead learners into deep, critical thought about mathematics
-> Possible hints and breakthroughs for several of the prompts are included
-> Plenty of possibility for extension, deeper discussion or lesson ideas
-> An assignable Easel activity

STORY

A lot of my work this school year has led me to really pushing learners outside the usual confines of the worksheet-based industrial model of education. More than ever, I am learning how to really push my students to see beyond the obvious – making observations, developing generalizations, and justifying their theories. Learning inside my classroom has moved from something I give learners to something that my learners explore and discover for themselves. This and my other pattern exploration activities are examples of things I used this year to elicit that deep thought.

IMPLEMENTATION

This resource provides sharable whole-group prompts with plenty of opportunity for learners to explore together. It gives clear instructions for how to set up a conversation about the mathematics in play in the balanced situations. Learners will use the given balanced equations to find other equivalencies for each shape. Once they do so, they will be able to complete the comparisons below the givens based on the understood, relative value of each shape.

POSSIBLE EXTENSIONS

Possible extensions are included in the file! There is always more discussion or exploration that can be done when we are drawing conclusions about equations and algebraic representations.

MATERIALS/PREREQUISITES

Besides this resource, you may require:
-> Computer and internet access