# Mr. Kugie's Curriculum

Since 2014, I've been creating innovative curriculum that cuts to the core of how children learn: based in authentic experience, organic discovery, and community learning.

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Since 2014, I've been creating innovative curriculum that cuts to the core of how children learn: based in authentic experience, organic discovery, and community learning.

7 Resources

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#### Discover Patterns in Fibonacci's Spiral

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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: –&gt; 1 mathematical scenario –&gt; Detailed instructions on how to lead students into deep, critical thought about mathematics –&gt; 7 possible student discoveries with explanations –&gt; 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: –&gt; Time and practice to condition your learners to know what a productive mathematical discussion looks like and sounds like –&gt; Computer and Internet access

#### Greek & Latin Math Roots Study

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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: –&gt; 11 weeks of Greek and Latin Roots (110 total math-related roots) to study –&gt; 11 weekly quizzes applying the roots in a variety of vocabulary contexts –&gt; Printable sorting activity using all the roots and common word endings –&gt; 3 cumulative sets of review activities (for units 1-4, 5-7 &amp; 8-10) –&gt; 3 cumulative sets of unit review quizzes (for units 1-4, 5-7 &amp; 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: –&gt; Some practice together looking at what these quizzes are like or developing activities for studying and using the roots

#### Egyptian Fractions Math Challenge

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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: -&gt; 4 pages of fraction pattern exploration -&gt; 4 pages of hints and answer keys -&gt; 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: -&gt; Plenty of time and space to explore these ideas -&gt; More research on Egyptian fractions (optional websites included)

#### Designing a New City Park Math Project

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An independent or small-group mathematics project affording learners the opportunity to desight their very own city part while managing a budget and meeting project specifications. But this is no regular end-of-year project; every aspect of this project is directly related to real-world cost, use, and application. WHAT’S INCLUDED This resource contains: –&gt; Step-by-Step Instructions –&gt; Items &amp; Specifications Page –&gt; Budgeting Spreadsheet –&gt; Building an Ideal Park Brainstorming Sheet –&gt; Map / Blueprint Printable –&gt; Extension Activities –&gt; Rubric –&gt; Project Examples –&gt; An assignable Easel activity STORY After teaching many weeks of decimal multiplication and division and getting some practice balancing budgets, I wanted a way to let my students practice these skills using a bit of their own creativity and choice. But perusing the other projects on Teachers Pay Teachers, I noticed that most of them felt like “fluff” and didn’t really get to the real-world mathematics or problem-based learning for which I was truly looking. IMPLEMENTATION This 3-week independent project is ready to implement in your classroom with many pages of step-by-step instructions for completing the project. Learners will use the equipment sold on www.gametime.com to make choices about what they wish they had in a park in their neighborhood. But building a park is more complicated than just picking a park and planting trees. Learners will have to calculate areas for a dog park, basketball courts, and even the concrete running path that they will include in their park. Students will have to consider which surfacing option for their playground will be the most effective or most cost-effective or most functional. Prices of these can vary by the ton or the cubic feet that they occupy. Learners will be converting units, calculating volumes and areas, deciding on cost effectiveness, and balancing a budget to create the most exciting park they can that still follows the city’s requirements. POSSIBLE EXTENSIONS When they finish their project designs, learners have their choice of 4 extension activities outlined in the resource including designing a radio advertisement to raise money for the park, writing a letter to the mayor, creating a project proposal for a board meeting, or designing a brochure to bring new people to the park. MATERIALS/PREREQUISITES Besides this resource, you may require: –&gt; Computers/tablets for the students to use gametime.com –&gt; Rulers for accurate map drawing –&gt; Pictures of other parks for inspiration –&gt; Calculators (optional)

#### Thought Exercises for Grade 3 Math System

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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: –&gt; How-to Guide for Classroom Implementation –&gt; 24 Weeks of Thought Exercises –&gt; Opportunities to customize and add additional weeks –&gt; Each week contains 4 different thought exercises –&gt; Each thought exercise contains 30 minutes of partner and / or whole group activities –&gt; 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: –&gt; Printed hundreds charts (printable included)

#### Astronomy & Space 4-Week Unit Plan

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This 4-week unit plan will give you a great framework for a unit in discovering the secrets and science of Space. Using these resources, you’ll debunk a few misconceptions about the cause of seasons, moon phases, distances between and sizes of planets, and the levels of our atmosphere. This unit plan offers multiple lessons involving great technological resources for conceptualizing the ideas. Inside this .zip file you will find a Read Me.pdf that will guide you through the 4 weeks of the unit. See the “What’s included” section below for the details. This is an all-inclusive unit plan! Although this was designed and implemented in a sixth grade classroom, it can be easily modified to fit a fifth grade or seventh grade classroom as well. WHAT’S INCLUDED This resource contains: –&gt; A planning &amp; pacing guide –&gt; Four comprehensive, technology-integrated activities –&gt; A group research project &amp; presentation –&gt; Group rubric and peer evaluation rubric for the project –&gt; A simple assessment (for use as a pretest) –&gt; A in-depth assessment (for use as a summative) –&gt; Reteaching resources for all 6 major topics of the unit –&gt; Answer keys and teacher implementation info included for each rubric STORY I originally developed this unit plan to address a variety of concepts surrounding the wonder and science of Space. I weaved in situations where practice with the scientific method could be included as well. IMPLEMENTATION This unit plan contains a guide for a suggested path through the scientific content. In addition, each activity or project has a teacher forward detailing options for how to implement the activity in any classroom. There are also resources for effectively reteaching concepts from the unit. From start to finish, this plan has four weeks of science learning in your classroom covered. POSSIBLE EXTENSIONS The reteaching materials included in this file are a great, multi-day possibility for extending learning and curiosity. MATERIALS/PRE-REQS Besides this resource, you may require: –&gt; Computers with internet access –&gt; Meter or yard stick –&gt; Construction, butcher, or printer paper for one activity –&gt; Wooden skewers or stakes for one outdoor activity

#### Math Centers for Grade 5 (29 Weeks)

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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: –&gt; 29 weeks of center rotations (5 fifteen-minute rotations per week) –&gt; 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: –&gt; Manipulatives like base ten blocks, centimeter cubes, fraction tiles, decimal tiles or paper versions of these –&gt; Whiteboards and Markers –&gt; 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) –&gt; A teacher account to an online, interactive math game website like Splash Learn or Legends of Learning

#### Discover Patterns in Sierpinski's Triangle

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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: -&gt; 1 mathematical scenario -&gt; Detailed instructions on how to lead students into deep, critical thought about mathematics -&gt; 7 possible student discoveries with explanations -&gt; 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: -&gt; Time and practice to condition your learners to know what a productive mathematical discussion looks like and sounds like -&gt; Computer and Internet access

#### Discover Patterns in a Magic Square

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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: -&gt; 1 mathematical scenario -&gt; Detailed instructions on how to lead students into deep, critical thought about mathematics -&gt; 7 possible student discoveries with explanations -&gt; 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: -&gt; Time and practice to condition your learners to know what a productive mathematical discussion looks like and sounds like -&gt; Computer and Internet access

#### Classroom Solar System Model

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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: –&gt; Step-by-step instructions for accurately scaling down the diameters of the planets and distances from the Sun –&gt; 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: –&gt; Computers with internet access –&gt; Meter or yard stick –&gt; Construction, butcher, or printer paper for creating planets

#### Discover Patterns in Mathematical Models Bundle

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A whole-group mathematical exploration of seven different mathematical models. This bundle of resources 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. These activities are used best to push learners toward deep, critical thought about a mathematical scenario. WHAT’S INCLUDED This resource contains: –&gt; 7 mathematical scenarios –&gt; Detailed instructions on how to lead students into deep, critical thought about mathematics –&gt; 7 possible student discoveries for each model with explanations and lines of questioning –&gt; 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 learning 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. These 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 each of the seven models. While seven expected discoveries are shown for each, 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: –&gt; Time and practice to condition your learners to know what a productive mathematical discussion looks like and sounds like –&gt; Computer and Internet access

#### Simple and Compound Machines Exploration

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A small-group or independent, scientific exploration of purpose and prevalence of simple machines in our daily lives. This resource offers opportunity for learners to experience brainstorm items that contain the six simple machines in four different areas of a home. Then, they will examine everyday household items that contain 2 or 3 simple machines considering the purpose of how these systems assist our lives. WHAT’S INCLUDED This resource contains: –&gt; 2 different activities exploring simple and compound machines –&gt; Possible answers are included for both activities STORY After watching Bill Nye’s episode about simple machines, my students were interested in exploring more on the topic. Our discussion also moved into the realm of compound machines. The next day, I created for them this activity and we had a group competition to see who could name the most household items containing simple machines. IMPLEMENTATION This resource consists mainly of a worksheet that can help students navigate an exploration of simple and compound machines in their homes and at school. Choose to frame this as an independent or small group activity for learners to extend their understanding of the six simple machines. In any case, push learners to continue inquiring about how science is used to make our lives easier - specifically within systems. POSSIBLE EXTENSIONS After completing this activity with your class, you can also have students think of an item and let classmates guess which simple machines can be found in it. In class, this was my lead up to conversations about potential and kinetic energy. In that unit, we had students build Rube Goldberg machines, and this knowledge was very helpful in the successful creation of those machines. MATERIALS/PRE-REQS Besides this resource, you may require: –&gt; Some knowledge of simple machines –&gt; Sample simple / compound machines for students to consider

#### Discover Patterns in a Modular Arithmetic Model

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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: –&gt; 1 mathematical scenario –&gt; Detailed instructions on how to lead students into deep, critical thought about mathematics –&gt; 7 possible student discoveries with explanations –&gt; 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: –&gt; Time and practice to condition your learners to know what a productive mathematical discussion looks like and sounds like –&gt; Computer and Internet access

#### The Speed of Animals Math Exploration

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A small-group or independent mathematical exploration of the animal kingdom. This resource creates space for learners to explore the relative size and speed of animals in comparison to their own. This activity is used best to reinforce data collection, proportional reasoning, and unit conversions within a relevant, real-world context. Learners will calculate their own land speed to make comparisons with other animals using data from www.speedofanimals.com. WHAT’S INCLUDED This resource contains: -&gt; A 4-page worksheet -&gt; Suggestions for Best Practice in implementation STORY One day at recess, my math class students were racing each other outside. I made a comment to say that they weren’t nearly as speedy as most of the animal world. Then, we needed a little exploration to prove it. IMPLEMENTATION This resource provides a structured exploration of rates, unit converstions, data collection, and data representation. Learners will begin by heading outside and being timed while running a set distance. From there, the class will work together to calculate their average running speeds. Then, they will choose ten animals from www.speedofanimals.com with which to compete. Finally, the worksheet provides the required structure to walk thorugh several other mathematical tasks to draw some interesting conclusions about how fast animals can be. POSSIBLE EXTENSIONS Possible extensions are included in this file! MATERIALS/PREREQUISITES Besides this resource, you may require: -&gt; Stopwatches or timers -&gt; Computers or tablets with internet access

#### M&M Melting Design-Your-Own Sci Experiment

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A small- or whole-group science experiment designed to allow learners the chance to craft their own experiment following the Scientific Method. The experiment begins with watching an old M&amp;M commercial stating the oldest and perhaps most popular M&amp;M slogan, “Melts in your mouth, not in your hand.” Learners will decide on the variables and conditions of the experiment before conducting it and gathering data. They will leverage their own creativity in the specific design of their experiment and conduct it themselves in tandem with the other groups in the class. WHAT’S INCLUDED This resource contains: –&gt; Experiment Walkthrough and Notes –&gt; Experiment Handout STORY This experiment came about when I wanted a way to highlight the Scientific Method and independent and dependent variables with very few materials. A usual class favorite, this experiment has repeat value over many years. Plus, allowing learners to both design the experiment and base it off of M&amp;Ms boasts great engagement. IMPLEMENTATION This resource consists mainly of an experiment which, through the teacher’s guidance, can facilitate great conversation about conducting experiments, the importance of variables, the importance of establishing a control, and much more. You can begin the experiment with several included discussion starters for introducing the exploration. Then, the class will gather their ideas and set out designing experiments, conducting them, and compiling data. When finished, a larger conversation can be had reflecting on the M&amp;M slogan and the validity of the experiments just carried out. Specific examples from my classroom for each step of the experiment’s implementation have been included for reference. 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 (coming soon to TES).

#### Linear Equation Graphing Math Challenge

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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: -&gt; Instructions for implementation -&gt; 1-page of exploration -&gt; 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: -&gt; Computers with Internet accessibility

#### Discover Patterns in the Multiplication Table

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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: -&gt; 1 mathematical scenario -&gt; Detailed instructions on how to lead students into deep, critical thought about mathematics -&gt; 7 possible student discoveries with explanations -&gt; 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: -&gt; Time and practice to condition your learners to know what a productive mathematical discussion looks like and sounds like -&gt; Computer and Internet access

#### Discover Patterns in the Hundred Chart

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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: -&gt; 1 mathematical scenario -&gt; Detailed instructions on how to lead students into deep, critical thought about mathematics -&gt; 7 possible student discoveries with explanations -&gt; 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: -&gt; Time and practice to condition your learners to know what a productive mathematical discussion looks like and sounds like -&gt; Computer and Internet access

#### Discover Patterns in Pascal's Triangle

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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: -&gt; 1 mathematical scenario -&gt; Detailed instructions on how to lead students into deep, critical thought about mathematics -&gt; 7 possible student discoveries with explanations -&gt; 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: -&gt; Time and practice to condition your learners to know what a productive mathematical discussion looks like and sounds like -&gt; Computer and Internet access