A whole-group mathematical exploration into the geometric concepts of triangles, quadrilaterals, interior angles, and sums of interior angles. The discovery lesson in this product operates under one premise: that math is not simply a set of rules learners are assimilated to follow but rather an intricate and infinite world of possibility that they can be guided to interpret on their own. Set aside your understandings about how math is supposed to be taught, learned and structured, and open your mind to a whole different kind of math lesson. One where discovery is the goal and the learners are fully responsible for it. WHAT’S INCLUDED This resource contains: -> A 3-task lesson which allows learners to discover ideas about the properties of triangles, quadrilaterals and polygons as well as their interior angles -> A detailed breakdown of what happens in each task based on what becomes the student’s responsibility and what is left for the teacher to manage -> Possible discoveries that learners can make along with key transferable ideas they’ll use throughout their future geometry explorations -> Plenty of possibility for extension, deeper discussion or lesson ideas STORY I’ve spent many years reading through textbooks and adapting the content to fit the learners I had sitting in my classroom. The rigid structure the most textbook lessons would often frustrate me as the beautiful and interconnected world of mathematics was boiled down to minute facts to be memorized, repeated and regurgitated in a specific standards-defined order. Over time, I’ve realized that a more authentic learning experience centers around learners exploring mathematical phenomenon and discovering the deeper truths for themselves. And that got me thinking, could an entire curriculum be crafted around this idea that the content could be discovered rather than memorized? And thus, our journey toward REdiscovering mathematics was born. IMPLEMENTATION This resource provides a three-task lesson with two extra pages of teacher information for implementing an organic, collaborative, exploratory lesson in geometry. As such, there are many possibilities for implementation. The tasks should be explored in the order they are given, but should not be pushed to be completed in a single sitting. Allowing learners time to make theories about the mathematics is key to the success of the lesson. POSSIBLE EXTENSIONS While this lesson does not cover all ideas specifically related to triangles, quadrilaterals or angles, it does give a great jumping off point and is suggested as the start of any inquiry into geometry at this level. Supplement this discovery lesson with problems and other ideas from your school’s curriculum. MATERIALS/PREREQUISITES Besides this resource, you may require: -> Plenty of time and space to explore these ideas -> Computer and Internet access

A small-group or independent mathematical list of graphing challenges using linear equations. This resource gives learners opportunities to push their understanding of how the coordinate plane works and how the equations we write can manipulate the lines graphed upon that plane. Learners will explore the importance of slope, how that can affect perpendicular and parallel lines, and what is required to draw a line through a specific point. WHAT’S INCLUDED This resource contains: -> Instructions for implementation -> 1-page of exploration -> Suggestions for best practices of instruction STORY After my students got a basic understanding of how the coordinate plane works, memorized vocabulary like origin and quadrant, and leaned what a y = x + 1 graph looked like, they were hungry for more. Then this activity was born to challenge them and give them more exposure to graphs. Challenge your students to push their understanding of how equations work and start some good algebra classroom discussions before they even hit their first algebra course. IMPLEMENTATION This resource provides a page of graphing challenges which can be achieved only through equations of lines that learners test and confirm. It’s implementation has a variety of possibilities. This activity can be a great intro to a further discussion on point-slope and slope-intercept form. It could be used as extra practice, an extension, or even as a small group differentiated instruction activity. More information to implement the activity in the file. POSSIBLE EXTENSIONS Continue your student’s exploration of how words, equations, tables, and graphs are related with The Fantastic Four of Algebra Exploration. MATERIALS/PREREQUISITES Besides this resource, you may require: -> Computers with Internet accessibility

A whole-group mathematical game of bingo involving solutions to multi-step equations. This resource creates the structure for practicing the simplification and solving of linear equations in one-variable and the values of the variables are represented in the numbers placed on the bingo cards. Learners will solve equations independently to mark the correct number on their own card. WHAT’S INCLUDED This resource contains: -> Blank Bingo Board Template -> 30 Linear Equations with Corresponding Answers -> Ideas for alternate or extended play STORY My competitive students absolutely love bingo. Anytime I can do a review game having to do with bingo they eat it right up. It is fairly simple to make clues and let students choose where they want their numbers. IMPLEMENTATION This resource provides blank bingo cards and a set of 30 clues. By printing the templates, you have everything you need to run one game of bingo. Learners fill in their own blank template randomly with any number in the range of 1-30. To play again, simply make a new set of clues or have the learners develop them. This is a great review game. POSSIBLE EXTENSIONS Possible extensions included in this file! MATERIALS/PREREQUISITES Besides this resource, you may require: -> A Random Number Generator – links in the file

A small-group or independent mathematical exploration of expressing a number as an additive series of unit fractions. This resource creates space for learners to explore the history behind computing parts of a whole as well as the challenge around being as efficient as possible in discovering these series of unit fractions. Learners will identify patterns, draw inferences, and build their number reasoning skills. WHAT’S INCLUDED This resource contains: -> 4 pages of fraction pattern exploration -> 4 pages of hints and answer keys -> An assignable Easel activity STORY I stumbled across this story of Egyptian fractions when I was looking for supplementary resources during my addition of fractions unit in grade 5. I really liked the challenge that discovering the patterns naturally encouraged, so I developed an exploration which turned into several days of great conversation, inquiry, and discovery for my students. It was a worthwhile bunny trail from our regular curriculum as it helped many students build a foundation for understanding operations with fractions and why we might need to do it in the first place. IMPLEMENTATION This resource provides a four-page worksheet chocked full of ideas about the history and methodology of ways to split up a total. As such, there are many possibilities for implementation. Use this worksheet as an independent, standalone activity to extend learning for some students. Allow learners to partner or group up to take on the challenges together or lead the entire class in an exploration of fractions by introducing the ideas organically. POSSIBLE EXTENSIONS Ideas for extension are included in the resource. MATERIALS/PREREQUISITES Besides this resource, you may require: -> Plenty of time and space to explore these ideas -> More research on Egyptian fractions (optional websites included)

A small-group or independent mathematical exploration of the fundamentals of Algebra. This resource creates space for learners to explore the various representations of a situation in the context of Algebra. This activity is used best to offer plenty of practice for learners in order to naturally strengthen the connection between words, graphs, tables and equations within algebraic problems. This will help to strengthen their understanding of and ability to find equations in single variable, proportional relationship word problems. WHAT’S INCLUDED This resource contains: -> A 1-page graphic organizer -> 16 various practice problems -> A template page for creating your own -> An assignable Easel activity STORY Over a few years, I noticed that learners have particular difficulty in bridging the gap between reading a word problem and figuring out the algebraic equation to represent it in the years before Pre-Algebra. I decided that, to match the superhero theme of my classroom, I would attempt to teach Algebra with a metaphorical team of four heroes: words, graphs, tables, and equations. IMPLEMENTATION This resource provides sixteen different Algebraic situations and plenty of practice of the concepts. It should be used only after you have had time to teach additive and multiplicative proportional relationships with specific emphasis on writing equations for them. POSSIBLE EXTENSIONS Continue your student’s exploration of equation and graph correlation with my Equation Graphing Math Challenge product. MATERIALS/PREREQUISITES Besides this resource, you may require: -> Extra Paper or additional problems

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

A daily whole-group classroom system for assisting students with opportunities to develop their number reasoning, automaticity, and conceptual understanding of the four operations. This resource offers four types of 30-minute-a-day thought exercises specifically created to target problem solving and math reasoning skills. WHAT’S INCLUDED This resource contains: –> How-to Guide for Classroom Implementation –> 24 Weeks of Thought Exercises –> Opportunities to customize and add additional weeks –> Each week contains 4 different thought exercises –> Each thought exercise contains 30 minutes of partner and / or whole group activities –> Tips for teachers to implement this program STORY I attended a week-long mathematics professional development this last summer that opened my eyes to the importance of teaching number reasoning and reinforcing a conceptual understanding of mathematics in a world typically devoted to a get-to-the-standard-algorithm style of instruction or pedagogy based on non-conceptual shortcuts. I jumped in head first this year devoting thirty minutes of my daily teaching time to implementing this system, and I have seen fantastic results. Students are already understanding the fundamentals of multiplication and some fraction work and we haven’t officially taught multiplication or division yet this year. IMPLEMENTATION This resource gives you 24 weeks of intro-to-the-math-block thought exercises which bridge the gap from the addition and subtraction to multiplication and division. Set up the 30-minute exercises for the same time each day and allow learners the opportunity to lead deep discussions about the mathematics at play. Keep in mind this is a supplemental system for your regular math curriculum and works best if used consistently and in tandem with a regular math lesson. POSSIBLE EXTENSIONS All of the concepts included here naturally flow into your regular math lesson or can act as stand alone ideas depending on the day and student conversation. MATERIALS/PREREQUISITES Besides this resource, you may require: –> Printed hundreds charts (printable included)

A weekly whole-group classroom system for centers with opportunities to experience the grade 5 math topics using writing, hands-on manipulatives, small group work, independent tasks, and technology. This resource extends your students’ understanding by devoting 75 minutes a week to math rotations that will stretch their thinking and further develop their problem solving skills. This structure is used best in tandem with your regular mathematics curriculum to learn and apply the concepts in a being learned each week. WHAT’S INCLUDED This resource contains: –> 29 weeks of center rotations (5 fifteen-minute rotations per week) –> Guide to implementing the centers STORY Warm ups, writing prompts, partner work, note taking, and textbook problems are not enough to keep up a learner’s interest and full capabilities for learning in the math classroom. I decided my first year to implement a weekly rotation for math centers modeled after the “Daily 5” strategy used in language arts. Students go through 5 fifteen-minute rotations using a variety of tools to explore the current unit or topic we are working through as a class. This structure gives students something to look forward to (we always do it on Wednesdays) and also provides extra time for focused group work that goes beyond the pages of a textbook or my abilities to teach the entire class at once. Set up these rotations as a weekly structure in your class and wait for your students to wish it was centers day! IMPLEMENTATION This resource gives you 29 weeks of math rotations which explore everything from area and perimeter to fractions to decimals to financial literacy. Set up the 75-minute rotations for the same day each week according to the concepts being learned in your usual curriculum. POSSIBLE EXTENSIONS There are so many extensions to the activities, vocabulary questions, and games found in these 29 weeks of centers. MATERIALS/PREREQUISITES Besides this resource, you may require: –> Manipulatives like base ten blocks, centimeter cubes, fraction tiles, decimal tiles or paper versions of these –> Whiteboards and Markers –> Technology with access to internet (I like to use our classroom’s smart board but you can choose to structure the technology rotation around individual laptops instead) –> A teacher account to an online, interactive math game website like Splash Learn or Legends of Learning

A in-depth mathematical exploration of 110 Greek or Latin roots in the English language over eleven weeks. This resource creates space for etymology to be explored and played with by learners in themed weekly units. Over time, learners will learn to hone this skill and unlock a new world of discovering and analyzing our language. This activity is used best in tandem with your regular mathematics curriculum to learn and apply the vocabulary in a relevant context. WHAT’S INCLUDED This resource contains: –> 11 weeks of Greek and Latin Roots (110 total math-related roots) to study –> 11 weekly quizzes applying the roots in a variety of vocabulary contexts –> Printable sorting activity using all the roots and common word endings –> 3 cumulative sets of review activities (for units 1-4, 5-7 & 8-10) –> 3 cumulative sets of unit review quizzes (for units 1-4, 5-7 & 8-10) STORY In my first year as a math teacher, I worked specifically with the Reading and Language Arts teams to come up with a way that I could concentrate on vocabulary acquisition in math class without dedicating a large amount of time. We also wanted to place a specific focus on mathematics vocabulary acquisition for our English Language Learners. IMPLEMENTATION This resource gives you 110 Greek and Latin roots which influence how we use the English language today (related specifically to math). Start each week introducing learners to a new set of themed roots, then as the week goes on, give them chances to use those roots in context or time to study them. By Friday, learners will be prepared for a quiz applying their knowledge. Every couple of weeks, implement a “review” week with included daily activities for remembering and practicing the last 3 or 4 weeks of roots. Then, by Friday of the review week, the learners will be prepared for another quiz. These roots can be found in thousands of words in our modern day language and help learners with spelling, acquiring new vocabulary, and deciphering the definitions of new words. POSSIBLE EXTENSIONS There are so many extensions to using these roots once your learners have been exposed to even just a couple sets of them. These roots automatically start creeping into the classroom’s everyday language and new vocabulary words and the learners will begin noticing. MATERIALS/PREREQUISITES Besides this resource, you may require: –> Some practice together looking at what these quizzes are like or developing activities for studying and using the roots

A whole-group mathematical exploration of the Fibonacci Spiral. This resource creates space for a learning community founded on discourse, theorization, generalization, and justification. Learners are encouraged to bring ideas forward within the conversation and prove or disprove each other’s theories about the patterns they discover within this model. This activity is used best to push learners toward deep, critical thought about a mathematical scenario. WHAT’S INCLUDED This resource contains: –> 1 mathematical scenario –> Detailed instructions on how to lead students into deep, critical thought about mathematics –> 7 possible student discoveries with explanations –> Plenty of possibility for extension, deeper discussion, or lesson ideas 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 discovering how to really push my learners to see beyond the obvious: making observations, developing generalizations and justifying their theories. Learning inside my classroom has moved from something I assign to 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 drive that deep thought. IMPLEMENTATION This resource is primarily for the teacher’s eyes only. It gives clear instructions for how to set up a conversation about the mathematics in play in the Fibonacci Spiral. While seven expected discoveries are shown, it is certainly not an exhaustive list and it is not meant to be shared directly with learners. As the resource explains, the entire purpose is to have learners make the mathematical discoveries themselves. POSSIBLE EXTENSIONS Possible extensions are included in the file! There is always more research or exploration that can be done when we are drawing conclusions about sequences and patterns. MATERIALS/PREREQUISITES Besides this resource, you may require: –> Time and practice to condition your learners to know what a productive mathematical discussion looks like and sounds like –> Computer and Internet access

A whole-group mathematical exploration of a Modular Arithmetic Model. This resource creates space for a learning community founded on discourse, theorization, generalization, and justification. Learners are encouraged to bring ideas forward within the conversation and prove or disprove each other’s theories about the patterns they discover within this model. This activity is used best to push learners toward deep, critical thought about a mathematical scenario. WHAT’S INCLUDED This resource contains: –> 1 mathematical scenario –> Detailed instructions on how to lead students into deep, critical thought about mathematics –> 7 possible student discoveries with explanations –> Plenty of possibility for extension, deeper discussion, or lesson ideas 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 discovering how to really push my learners to see beyond the obvious: making observations, developing generalizations and justifying their theories. Learning inside my classroom has moved from something I assign to 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 drive that deep thought. IMPLEMENTATION This resource is primarily for the teacher’s eyes only. It gives clear instructions for how to set up a conversation about the mathematics in play in this Modular Arithmetic Model. While seven expected discoveries are shown, it is certainly not an exhaustive list and it is not meant to be shared directly with learners. As the resource explains, the entire purpose is to have learners make the mathematical discoveries themselves. POSSIBLE EXTENSIONS Possible extensions are included in the file! There is always more research or exploration that can be done when we are drawing conclusions about sequences and patterns. Or have learners create their own circular model with numerical patterns. MATERIALS/PREREQUISITES Besides this resource, you may require: –> Time and practice to condition your learners to know what a productive mathematical discussion looks like and sounds like –> Computer and Internet access

A small- and whole-group exploration geared toward creating a to-scale model of the solar system that fits within the walls of a classroom. By leveraging their understanding of ratios and scale factors, learners can scale down the actual distances between planets and the diameters of those planets to a reasonable size for display from the ceiling. WHAT’S INCLUDED This resource contains: –> Step-by-step instructions for accurately scaling down the diameters of the planets and distances from the Sun –> Teacher guide for strategic implementation in the classroom, leaning on the learners to provide the mathematical reasoning for building accurate models STORY In an effort to create a fun, visual representation of the Solar System during my astronomy unit, I came up with this activity. Instead of just being another art project, I decided to have learners flex their mathematical reasoning muscles to discover scale factors. IMPLEMENTATION This resource consists mainly of an activity which, through the teacher’s guidance, can facilitate great conversation about the connections between proportional reasoning and a scale model of the Solar System. Using two separate scale factors, learners will create a model with scaled planet diameters and distances from the Sun. With this, you will be able to create an accurate model for drawing deeper conclusions together in class. POSSIBLE EXTENSIONS There is always more research or exploration that can be done about the things scientists have discovered in our Solar System. MATERIALS/PRE-REQS Besides this resource, you may require: –> Computers with internet access –> Meter or yard stick –> Construction, butcher, or printer paper for creating planets

A whole-group mathematical exploration of a Magic Square. This resource creates space for a learning community founded on discourse, theorization, generalization, and justification. Learners are encouraged to bring ideas forward within the conversation and prove or disprove each other’s theories about the patterns they discover within this model. This activity is used best to push learners toward deep, critical thought about a mathematical scenario. WHAT’S INCLUDED This resource contains: -> 1 mathematical scenario -> Detailed instructions on how to lead students into deep, critical thought about mathematics -> 7 possible student discoveries with explanations -> Plenty of possibility for extension, deeper discussion, or lesson ideas 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 discovering how to really push my learners to see beyond the obvious: making observations, developing generalizations and justifying their theories. Learning inside my classroom has moved from something I assign to 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 drive that deep thought. IMPLEMENTATION This resource is primarily for the teacher’s eyes only. It gives clear instructions for how to set up a conversation about the mathematics in play in a Magic Square. While seven expected discoveries are shown, it is certainly not an exhaustive list and it is not meant to be shared directly with learners. As the resource explains, the entire purpose is to have learners make the mathematical discoveries themselves. POSSIBLE EXTENSIONS Possible extensions are included in the file! There is always more research or exploration that can be done when we are drawing conclusions about sequences and patterns. MATERIALS/PREREQUISITES Besides this resource, you may require: -> Time and practice to condition your learners to know what a productive mathematical discussion looks like and sounds like -> Computer and Internet access

A whole-group mathematical exploration of Sierpinski’s Triangle. This resource creates space for a learning community founded on discourse, theorization, generalization, and justification. Learners are encouraged to bring ideas forward within the conversation and prove or disprove each other’s theories about the patterns they discover within this model. This activity is used best to push learners toward deep, critical thought about a mathematical scenario. WHAT’S INCLUDED This resource contains: -> 1 mathematical scenario -> Detailed instructions on how to lead students into deep, critical thought about mathematics -> 7 possible student discoveries with explanations -> Plenty of possibility for extension, deeper discussion, or lesson ideas 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 discovering how to really push my learners to see beyond the obvious: making observations, developing generalizations and justifying their theories. Learning inside my classroom has moved from something I assign to 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 drive that deep thought. IMPLEMENTATION This resource is primarily for the teacher’s eyes only. It gives clear instructions for how to set up a conversation about the mathematics in play in Sierpinski’s Triangle. While seven expected discoveries are shown, it is certainly not an exhaustive list and it is not meant to be shared directly with learners. As the resource explains, the entire purpose is to have learners make the mathematical discoveries themselves. POSSIBLE EXTENSIONS Possible extensions are included in the file! There is always more research or exploration that can be done when we are drawing conclusions about sequences and patterns. Or have learners create their own shape with fractional pieces. MATERIALS/PREREQUISITES Besides this resource, you may require: -> Time and practice to condition your learners to know what a productive mathematical discussion looks like and sounds like -> Computer and Internet access

A whole-group mathematical exploration of the Multiplication Table / Times Table. This resource creates space for a learning community founded on discourse, theorization, generalization, and justification. Learners are encouraged to bring ideas forward within the conversation and prove or disprove each other’s theories about the patterns they discover within this model. This activity is used best to push learners toward deep, critical thought about a mathematical scenario. WHAT’S INCLUDED This resource contains: -> 1 mathematical scenario -> Detailed instructions on how to lead students into deep, critical thought about mathematics -> 7 possible student discoveries with explanations -> Plenty of possibility for extension, deeper discussion, or lesson ideas 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 discovering how to really push my learners to see beyond the obvious: making observations, developing generalizations and justifying their theories. Learning inside my classroom has moved from something I assign to 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 drive that deep thought. IMPLEMENTATION This resource is primarily for the teacher’s eyes only. It gives clear instructions for how to set up a conversation about the mathematics in play in the Multiplication Table. While seven expected discoveries are shown, it is certainly not an exhaustive list and it is not meant to be shared directly with learners. As the resource explains, the entire purpose is to have learners make the mathematical discoveries themselves. It makes the most sense to bring in this activity before students are formally familiar with multiplication and the structure of the table. Even so, this model differs slightly from the traditional layout and display allowing for the focus to be on finding patterns than recalling “how the times tables work.” POSSIBLE EXTENSIONS Possible extensions are included in the file! There is always more research or exploration that can be done when we are drawing conclusions about sequences and patterns. MATERIALS/PREREQUISITES Besides this resource, you may require: -> Time and practice to condition your learners to know what a productive mathematical discussion looks like and sounds like -> Computer and Internet access

A whole-group mathematical exploration of the Hundred Chart from https://mathforlove.com. This resource creates space for a learning community founded on discourse, theorization, generalization, and justification. Learners are encouraged to bring ideas forward within the conversation and prove or disprove each other’s theories about the patterns they discover within this model. This activity is used best to push learners toward deep, critical thought about a mathematical scenario. WHAT’S INCLUDED This resource contains: -> 1 mathematical scenario -> Detailed instructions on how to lead students into deep, critical thought about mathematics -> 7 possible student discoveries with explanations -> Plenty of possibility for extension, deeper discussion, or lesson ideas 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 discovering how to really push my learners to see beyond the obvious: making observations, developing generalizations and justifying their theories. Learning inside my classroom has moved from something I assign to 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 drive that deep thought. IMPLEMENTATION This resource is primarily for the teacher’s eyes only. It gives clear instructions for how to set up a conversation about the mathematics in play in this very special Hundred Chart. While seven expected discoveries are shown, it is certainly not an exhaustive list and it is not meant to be shared directly with learners. As the resource explains, the entire purpose is to have learners make the mathematical discoveries themselves. POSSIBLE EXTENSIONS Possible extensions are included in the file! There is always more research or exploration that can be done when we are drawing conclusions about sequences and patterns. Or have learners create their hundred chart with numerical patterns. MATERIALS/PREREQUISITES Besides this resource, you may require: -> Time and practice to condition your learners to know what a productive mathematical discussion looks like and sounds like -> Computer and Internet access

A whole-group mathematical exploration of Pascal’s Triangle. This resource creates space for a learning community founded on discourse, theorization, generalization, and justification. Learners are encouraged to bring ideas forward within the conversation and prove or disprove each other’s theories about the patterns they discover within this model. This activity is used best to push learners toward deep, critical thought about a mathematical scenario. WHAT’S INCLUDED This resource contains: -> 1 mathematical scenario -> Detailed instructions on how to lead students into deep, critical thought about mathematics -> 7 possible student discoveries with explanations -> Plenty of possibility for extension, deeper discussion, or lesson ideas 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 discovering how to really push my learners to see beyond the obvious: making observations, developing generalizations and justifying their theories. Learning inside my classroom has moved from something I assign to 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 drive that deep thought. IMPLEMENTATION This resource is primarily for the teacher’s eyes only. It gives clear instructions for how to set up a conversation about the mathematics in play in Pascal’s Triangle. While seven expected discoveries are shown, it is certainly not an exhaustive list and it is not meant to be shared directly with learners. As the resource explains, the entire purpose is to have learners make the mathematical discoveries themselves. POSSIBLE EXTENSIONS Possible extensions are included in the file! There is always more research or exploration that can be done when we are drawing conclusions about sequences and patterns. Or have learners create their own triangle with numerical patterns. MATERIALS/PREREQUISITES Besides this resource, you may require: -> Time and practice to condition your learners to know what a productive mathematical discussion looks like and sounds like -> Computer and Internet access