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 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 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 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 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 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- or whole-group science experiment designed to guide learners in calculating the molarity (concentration) of a solute in a solvent. Learners will use formulas and unit conversions to calculate and observe how the concentration of a solution can be affected by changing either the amount of solute, the solvent, or both. In addition to some meaningful mathematics, this experiment takes learners through the process of accurate measurement, molarity calculation, and data collection. In the end, learners will have created 4 different solutions of varied sugar concentrations to be compared by taste and molarity (in moles per liter). Please note: This experiment was originally designed for a unit plan in a gifted grade six classroom. As such, it contains some challenging concepts and calculations. However, the experiment is well written and with proper scaffolding, is easily appropriate for any middle school classroom. WHAT’S INCLUDED This resource contains: –> Science Education Best Practices –> 6-page Fully-Outlined Experiment Student Packet –> Experiment Answer Key STORY During the planning of my grade six chemistry unit plan, I was looking for an idea for a full lab experiment. While we didn’t have access to an actual lab or chemicals, it was challenging to come up with something viable, until we started looking at the molecule sucrose – then it hit me. So I developed this experiment to look specifically at solutions of Kool Aid and sugar. This experiment introduces my learners to the larger world of molarity including touching on Avogadro’s number, finding the molecular weight of a molecule, and tasting for themselves what “double the concentration” or “supersaturation” actually means. IMPLEMENTATION This resource consists mainly of an experiment which, through the teacher’s guidance, can facilitate great conversation about concentration, solutions, calculating molarity and supersaturation. You can begin the experiment by watching a video or reading an article explaining the “mole” and its application in Chemistry. Then, using the molecular weight of specific elements and an example of how to calculate molarity, learners will create a control and three different concentrations of the sugar and Kool Aid solution. Once all the mathematics is complete, learners will collect qualitative data, tasting the solutions to compare them. When finished, a few questions will guide their thinking and could stimulate a group conversation to make larger connections. POSSIBLE EXTENSIONS After completing the experiment, you could discuss how scientists have to repeat experiments to make sure the results are valid. Have a discussion about what could be done differently. Or, dive in head first with the entire Chemistry Science Unit Plan.