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50 Activities For Developing Critical Thinking Skills - Kapable

Grades
4 to 12
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This article from Kapable provides a comprehensive collection of 50 practical activities designed to help develop and strengthen critical thinking skills through hands-on practice and...more
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This article from Kapable provides a comprehensive collection of 50 practical activities designed to help develop and strengthen critical thinking skills through hands-on practice and collaboration. It explains that critical thinking involves analyzing information, questioning assumptions, and considering multiple perspectives to make well-reasoned decisions. It emphasizes that activities such as debates, role-playing, puzzles, and problem-solving scenarios help learners build these skills in meaningful ways. The site highlights how these activities promote creativity, improve decision-making, and encourage adaptability by exposing learners to real-world challenges and diverse viewpoints, making it a useful resource for teachers looking to incorporate structured, interactive strategies to build students' analytical thinking and problem-solving abilities.

tag(s): collaboration (131), critical thinking (187), thinking routines (50)

In the Classroom

Set up stations with different types of challenges (logic puzzles, real-world scenarios, ethical dilemmas). Have students rotate through stations, collaborate, and explain their thinking process at each station. Have students identify a real-world problem (at the school, community, or global level) and create a solution plan. They must research, evaluate options, and present their reasoning using CER (claim, evidence, reasoning). Give students a topic connected to your ELA or social studies unit. In small groups, students can take different perspectives and support their claims with evidence.

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Thinking Interdependently - VHS Resource Toolkit

Grades
6 to 12
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This page from the Vista High School Resource Toolkit explains the Habit of Mind: Thinking Interdependently, which focuses on helping students learn to work effectively with others...more
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This page from the Vista High School Resource Toolkit explains the Habit of Mind: Thinking Interdependently, which focuses on helping students learn to work effectively with others to solve problems and make decisions. The site describes thinking interdependently as the ability to communicate ideas, accept feedback, test solutions with others, and build understanding through collaboration. It also includes strategies and activities teachers can use to help students recognize when teamwork is needed and how sharing perspectives leads to stronger learning. Suggested classroom ideas include analyzing examples of collaboration, defining the characteristics of good teamwork, and using cooperative structures, such as jigsaw activities, to help students practice working together. This resource is useful for teachers looking to build social-emotional skills, collaboration, and Habits of Mind through group learning experiences.

tag(s): collaboration (131), perspective (33), social and emotional learning (202), thinking routines (50)

In the Classroom

Divide a lesson into sections and assign each student in a group a different part to become an expert on. Have students teach their section to their group members. Provide complex tasks (STEM challenges, reading discussions, or real-world problems) that require multiple perspectives. Assign roles (facilitator, recorder, reporter) so each student contributes and the group relies on everyone's input. Have students share writing, projects, or ideas with peers for feedback. Teach them how to offer constructive suggestions and ask clarifying questions, reinforcing that improvement often happens through collaboration.

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Habits of Mind Animations: Thinking Interdependently - ASCD

Grades
2 to 8
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This short animated YouTube video, "Habits of Mind Animations: Thinking Interdependently," uses a simple and engaging story to show how working together can lead to better ideas and...more
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This short animated YouTube video, "Habits of Mind Animations: Thinking Interdependently," uses a simple and engaging story to show how working together can lead to better ideas and stronger problem-solving. The animation explains that thinking interdependently means listening to others, sharing ideas, and cooperating to reach solutions that would be harder to achieve alone. This video is useful for introducing collaboration skills, setting expectations for group work, and reinforcing social-emotional learning as students practice respectful discussion, teamwork, and helping one another succeed. If your district blocks YouTube, the video may not be viewable.
This site includes advertising.

tag(s): collaboration (131), listening (119), problem solving (279), social and emotional learning (202), teaching strategies (77), thinking routines (50), thinking skills (130)

In the Classroom

Give students brief situations that require teamwork (for example, building something together, solving a problem, or working on a group project). Have students discuss with a partner how thinking interdependently would help in that situation. Have students sit in a circle and give a compliment to the person next to them about something they do well when working with others. Students can create a poster that shows what interdependent thinking looks, sounds, and feels like in the classroom. Posters can include examples such as listening, taking turns, helping others, and sharing ideas.

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Peer-to-Peer Education: What It Is, Benefits & How It Works - 21K School

Grades
K to 12
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This article from 21K School, "Peer-to-Peer Education: A Collaborative Learning Approach," explains how students can learn more effectively by teaching and collaborating rather than...more
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This article from 21K School, "Peer-to-Peer Education: A Collaborative Learning Approach," explains how students can learn more effectively by teaching and collaborating rather than relying solely on teacher-led instruction. The post describes peer-to-peer education as a collaborative learning method where students share ideas, discuss topics, and help one another understand concepts through activities such as debates, group discussions, feedback, and teamwork. The article highlights benefits such as improved confidence, stronger communication skills, better social interaction, and a deeper understanding, and offers suggestions on how teachers can create a positive classroom environment that encourages cooperation and shared learning.

tag(s): classroom management (143), collaboration (131), communication (126), feedback (16), listening (119), teaching strategies (77), thinking routines (50)

In the Classroom

After a mini-lesson, have students turn to a partner and explain the concept in their own words. Each partner listens and adds anything their partner missed. Set up stations where students work in pairs or small groups to practice skills such as reading, math problems, vocabulary, or science concepts. Have students take turns being the teacher and the learner. Give each group a task that requires teamwork, such as solving a complex question, completing a research activity, or creating a project. Students should discuss ideas and agree on a solution together, strengthening collaboration and critical thinking.

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16 Variations on Think-Pair-Share to Keep Students Engaged - Edutopia

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K to 12
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This Edutopia article, "16 Variations on Think-Pair-Share to Keep Students Engaged," shares creative ways to update the classic Think-Pair-Share strategy to keep students engaged and...more
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This Edutopia article, "16 Variations on Think-Pair-Share to Keep Students Engaged," shares creative ways to update the classic Think-Pair-Share strategy to keep students engaged and actively involved in learning. The article explains how educators can expand the simple routine of thinking individually, discussing with a partner, and sharing with the class by incorporating variations such as drawing, rotating partners, collaborative writing, and small-group sharing. These strategies help increase participation, strengthen communication skills, deepen understanding, and give all students a chance to express their ideas across subject areas and grade levels.

tag(s): collaboration (131), communication (126), teaching strategies (77), thinking routines (50)

In the Classroom

Ask students a question about the lesson and have them first draw their idea rather than write it. Students can then explain their drawing to a partner before sharing with the class. Have students stand up, find a partner, and discuss a question or problem. After sharing, they find a new partner for the next question. Have students first talk with a partner, then join another pair to form a group of four, and finally share with the whole class.

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Big and Small Strategies to Harness the Power of Peer-to-Peer Teaching - Edutopia

Grades
3 to 12
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This Edutopia article, "Big and Small Strategies to Harness the Power of Peer-to-Peer Teaching," explains how students can improve their understanding and retention by teaching one...more
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This Edutopia article, "Big and Small Strategies to Harness the Power of Peer-to-Peer Teaching," explains how students can improve their understanding and retention by teaching one another. The article describes simple and structured strategies such as Think-Pair-Share, jigsaw groups, and peer tutoring, all based on the idea that students learn more deeply when they explain ideas to classmates. It offers practical classroom ideas for use in any subject and grade level to increase participation, collaboration, and confidence while building a supportive learning community.

tag(s): collaboration (131), professional development (322), teaching strategies (77), thinking routines (50)

In the Classroom

Ask a question about the current lesson, have students think quietly, discuss with a partner, and finally share with the class. After a short mini-lesson, have students turn to a partner and explain the concept in their own words. The partner listens and then adds anything missed. Divide a topic into sections and assign each group one part to learn. Students become experts on their section and then teach it to a new group.

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Choice Board Templates - Canva

Grades
K to 12
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This large assortment of choice board templates includes many free and customizable options within Canva for Education, reviewed here Choose from...more
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This large assortment of choice board templates includes many free and customizable options within Canva for Education, reviewed here Choose from a variety of styles and content options. After selecting a template, use Canva's editing tools to personalize colors, text, images, and more. Share templates digitally with your personalized link, or download as an image or PDF.

tag(s): differentiation (102), multimedia (63), presentations (41), student-centered (10)

In the Classroom

Make sure to create a free teacher's account in Canva; this gives you access to many of the paid PRO account features. Use choice boards during independent work rotations or end-of-unit projects. Create multiple versions of choice boards using the templates to accommodate diverse learners and learning styles in your classroom while still providing instruction that meets learning objectives for all students. Include a variety of activities in choice boards that engage students in learning, such as games, simulations, videos, and opportunities to share their learning by creating multimedia presentations.

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Back to School Icebreakers Activities - Nearpod

Grades
K to 12
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This Nearpod blog post provides a collection of ready-to-use, interactive activities designed to help teachers build a positive classroom community during the first week of school....more
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This Nearpod blog post provides a collection of ready-to-use, interactive activities designed to help teachers build a positive classroom community during the first week of school. The article features icebreakers, getting-to-know-you lessons, collaborative discussions, reflection prompts, and engaging digital activities that introduce students to classroom routines while encouraging participation and relationship-building. It also highlights Nearpod's interactive tools, such as Collaborate Board, Draw It, Time to Climb, polls, and ready-made lessons, making it easy for teachers to create an engaging and welcoming learning environment from day one. Many of the featured resources are available as editable or ready-to-launch lessons for use in live or student-paced instruction.

tag(s): classroom management (143), collaboration (131), firstday (27)

In the Classroom

Use Nearpod's Collaborate Board for students to post fun facts, summer memories, reading interests, or personal goals. Encourage classmates to respond to one another to help build connections from the first day of school. Launch a collaborative Nearpod lesson where students brainstorm classroom norms using polls, open-ended questions, and Draw It activities. Turn the class's ideas into a shared digital classroom agreement. Reinforce routines such as technology expectations, transitions, or classroom rules by creating a Time to Climb quiz. Find more ideas for classroom learning activities at Nearpod, reviewed here.

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Using Humor in the Art Room - The Art of Education University

Grades
4 to 12
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This podcast episode from The Art of Education University discusses how teachers can use humor in the classroom to build relationships, increase engagement, and create a safe learning...more
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This podcast episode from The Art of Education University discusses how teachers can use humor in the classroom to build relationships, increase engagement, and create a safe learning environment, especially in the art room. The speaker explains that humor can help students feel comfortable and more willing to take risks. Still, teachers should be thoughtful about how they use jokes, sarcasm, and playful comments, as students may interpret them differently. The episode shares examples such as intentionally making mistakes during demonstrations, using lighthearted comments to keep students engaged, and choosing humor that supports learning rather than embarrassing students. Overall, the message encourages teachers to use humor intentionally to make class enjoyable while maintaining a respectful, supportive atmosphere.

tag(s): classroom management (143), humor (20), podcasts (169), teaching strategies (77)

In the Classroom

Start a lesson by intentionally making a funny mistake during a demonstration, such as using the wrong color, holding a tool incorrectly, or pretending to forget a step. Ask students to catch the mistake and explain how to do it correctly. Use lighthearted class discussions about appropriate humor, asking students when jokes are helpful and when they might hurt someone's feelings. Try a teacher-student improv activity where students quickly add a funny detail to a drawing, story, or idea the teacher starts.

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Why Can't Teachers Be Funny in School? - Trainers Warehouse

Grades
3 to 8
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This blog post from Trainers Warehouse explains how using classroom humor can make learning more engaging, memorable, and enjoyable for students. The article encourages teachers to...more
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This blog post from Trainers Warehouse explains how using classroom humor can make learning more engaging, memorable, and enjoyable for students. The article encourages teachers to include funny activities, jokes, games, and playful routines to help students relax, participate more, and feel comfortable taking risks while learning. Suggestions include using silly introductions, humorous writing activities, improv games, movement breaks, funny prompts, and lighthearted classroom challenges to keep energy high and attention focused. The post also notes that laughter can reduce stress, improve mood, strengthen relationships, and help students remember what they learn, making humor a powerful tool for building a positive classroom environment.

tag(s): blogs (82), classroom management (143), humor (20), teaching strategies (77)

In the Classroom

Use content-based humor activities like Mad Libs, limericks, or funny captions related to the topic you are teaching. For example, students can fill in missing words in a paragraph about the lesson or write a humorous rhyme using vocabulary terms. Begin a lesson with a funny introduction activity, such as having students introduce themselves using emojis, memes, or silly voices. Incorporate movement-based humor activities like funny walks, freeze poses, or short dance breaks.

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How to Easily Infuse More Humor into Your Classroom - Beginning Teacher Talk with Dr. Lori Friesen

Grades
K to 8
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This video explains how teachers can use humor to create a positive, engaging classroom environment and build stronger relationships with students. The speaker shares practical ideas,...more
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This video explains how teachers can use humor to create a positive, engaging classroom environment and build stronger relationships with students. The speaker shares practical ideas, such as telling jokes, using funny voices, adding silly props, creating playful routines, taking brain breaks, and leaving surprise notes, to help students feel relaxed and connected. The video emphasizes that humor helps students feel safe, increases engagement, and improves classroom management by making them more willing to participate in a fun, supportive atmosphere. Teachers are encouraged to try small strategies that match their personality and gradually add more lighthearted moments to make learning enjoyable. This video is hosted on YouTube. If your district blocks YouTube, the video may not be viewable at school.
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tag(s): classroom management (143), humor (20), teaching strategies (77)

In the Classroom

Start the day with a joke or a funny daily announcement to create a positive classroom mood. Use silly writing prompts or creative challenges connected to your lesson. For example, ask students to write a story funnily using vocabulary words, such as "What would happen if a dinosaur became the principal?" Create a class mascot, puppet, or character that gives directions, asks questions, or leaves notes for students. The mascot can review content, introduce lessons, or offer hints, making learning more memorable and increasing student engagement.

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Fractivities - Fractal Foundations

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K to 12
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The Fractivities page from the Fractal Foundation offers a collection of free, hands-on classroom activities that help students explore fractals through math, science, and art. Each...more
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The Fractivities page from the Fractal Foundation offers a collection of free, hands-on classroom activities that help students explore fractals through math, science, and art. Each activity includes step-by-step instructions, worksheets, and teacher guides that demonstrate how repeating patterns appear in nature, geometry, and real-world systems. The lessons align with the Common Core State Standards in math and English language arts. The activities encourage teamwork, creativity, and problem-solving while building large-scale designs, exploring nature, or creating models. The activities range from simple paper projects to outdoor investigations, making the site useful for a wide range of grade levels and classroom settings.

tag(s): collaboration (131), commoncore (62), patterns (79), problem solving (279)

In the Classroom

Have students work in groups to create a large fractal design, such as the Sierpinski Triangle, using paper shapes or index cards. Each group can build a small part, then the class combines the pieces into one large pattern. Have students design their own fractal artwork using drawing, coloring, or digital tools such as Google Drawings, reviewed here. They can repeat shapes, zoom in on patterns, or create symmetrical designs inspired by the examples on the site. Use one of the Fractivities worksheets to explore how fractals relate to fractions, multiplication, or geometry. Students can calculate how many shapes are added at each step and predict what will happen next.
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Monica AI Podcast Generator - Hongyuan Cao

Grades
5 to 12
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Monica AI Podcast Generator is an AI tool that converts a website, YouTube video, PDF/file, or long text into a podcast. When creating your podcast with a free account, you ...more
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Monica AI Podcast Generator is an AI tool that converts a website, YouTube video, PDF/file, or long text into a podcast. When creating your podcast with a free account, you must sign in. There are two hosts: Emily and Michael. You can also create your podcast in various languages, including American English, British English, Simplified and Traditional Chinese, French, Spanish, and more. After creating your podcast, share it via a link, on Facebook, Twitter, and LinkedIn, or by scanning a QR code on a phone. The free plan features 40 accesses to basic daily models, a limited trial for image/video generation, ChatPDF, and AI Agent.

tag(s): artificial intelligence (335), differentiation (102), podcasts (169)

In the Classroom

Students can create podcasts summarizing a book, create dialogue between two characters, or write a different ending to a book. Encourage students to create a podcast on a science topic they are learning to teach others. Use the Monica AI Podcaster Generator for students to create a podcast as an exit ticket to demonstrate what they learned about a specific topic.

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GoComics A to Z - GoComics

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4 to 12
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GoComics A-Z is an extensive online collection of classic and contemporary comic strips, featuring hundreds of popular titles that appeal to a wide range of readers. Browse beloved...more
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GoComics A-Z is an extensive online collection of classic and contemporary comic strips, featuring hundreds of popular titles that appeal to a wide range of readers. Browse beloved favorites such as Peanuts, Garfield, Calvin and Hobbes, Big Nate, Ziggy, and many others, or discover new comics organized alphabetically for easy exploration. Each comic includes an About section that provides background information about the series and its creators, helping readers better appreciate the characters and themes. Because the collection includes comics intended for audiences ranging from children to adults, teachers should preview selections before sharing them with students to ensure the content is appropriate for their grade level and classroom setting.
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tag(s): comics and cartoons (67), media literacy (130), satire (7)

In the Classroom

Students can share their favorite comic on Padlet, reviewed here. Students can use Cartoon Comic Maker, reviewed here to create their own comic with their favorite comic cartoon. Students can use Kiddle, reviewed here, to learn more about the comic creator.

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Using Comics to Teach the 4 Cs - edutopia

Grades
4 to 12
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Edutopia's Using Comics to Teach the 4 Cs shares how comics can foster the 4Cs: creativity, critical thinking, communication, and collaboration skills in both elementary and secondary...more
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Edutopia's Using Comics to Teach the 4 Cs shares how comics can foster the 4Cs: creativity, critical thinking, communication, and collaboration skills in both elementary and secondary classrooms. The article shares how comics develop each of the 4Cs, including resources and tools to use. In addition, comics also enrich verbal and visual skills as students use and create them.

tag(s): collaboration (131), comics and cartoons (67), creativity (89), critical thinking (187), thinking skills (130)

In the Classroom

Students can use Witty Comics, reviewed here to create a comic about their favorite book scene. Students can use Comic Strip Templates by Canva, reviewed here to teach about a significant historical event. Students can use Witty Comics, reviewed here to create political cartoons.

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TickTick - TickTick Team

Grades
7 to 12
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TickTick is an organization and planning tool with several features to help develop and maintain positive lifestyle habits. Use TickTick to create multiple lists to categorize different...more
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TickTick is an organization and planning tool with several features to help develop and maintain positive lifestyle habits. Use TickTick to create multiple lists to categorize different subjects or extracurricular activities. Within each list, the free version supports adding up to 99 tasks, including subtasks, priority levels, and descriptions. Another useful component is the integrated Pomodoro timer, which helps focus on specific tasks for set intervals. The platform also includes a habit tracker to build consistent routines and a basic note-taking feature for quick thoughts.

tag(s): calendars (36), DAT device agnostic tool (132), organizational skills (91)

In the Classroom

In addition to using TickTick for your personal and professional use, share this site with students to use to organize their busy schedules. Demonstrate how to manage long-term projects using the list and subtask features to break down a complex research paper into manageable steps, such as finding three sources or writing the introductory paragraph. Encourage students to use the Pomodoro timer during independent study blocks to stay focused and track how much time they dedicate to specific subjects. To extend learning, students can use Blogger, reviewed here to reflect on their productivity habits or share time-management tips with their peers. For visual learners, suggest that students take their project deadlines from the platform and create a visual representation of their progress using Timeline Infographic Templates, reviewed here. This combination helps students move from simply listing tasks to actively analyzing and visualizing their academic workflow.

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Iditarod Education Portal - Iditarod Trail Committee

Grades
3 to 12
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This section of the official Iditarod site offers free educational resources focused on the famous Alaskan sled dog race for students in grades 3-12. Explore a variety of lesson plans...more
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This section of the official Iditarod site offers free educational resources focused on the famous Alaskan sled dog race for students in grades 3-12. Explore a variety of lesson plans and activities that cover core subjects like math, science, social studies, and language arts through the lens of the Last Great Race on Earth. Additional features include a virtual museum, engaging articles written by K9 journalists, and a dedicated section for Teacher on the Trail updates that bring real-time race events into the classroom. Also available are printable worksheets, reading lists, and interactive tracking tools that allow students to follow individual mushers and their dog teams across the tundra. Make sure to check out the IditaRead program, which encourages students to reach their own reading goals by moving an avatar along checkpoints in the race.

tag(s): alaska (22), animals (278), iditarod (5)

In the Classroom

Bring the excitement of the Iditarod to life by having students participate in a cross-curricular simulation where they adopt a musher and track their progress using the site's live GPS maps. Enhance the experience by having students use Google Sheets, reviewed here, to record daily statistics such as miles traveled, weather conditions at checkpoints, and average speeds to create comparison graphs. For a language arts connection, ask students to write daily journal entries from the perspective of their musher or a sled dog, then compile these narratives into a digital book using Book Creator, reviewed here. Students can even record audio reflections or trail reports to embed within their digital books, allowing them to share their understanding of the physical and mental challenges faced during the race.
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Examples of Maths Magic Found in Nature - Akribian

Grades
4 to 8
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This article shares examples of mathematical patterns found throughout nature and provides simple examples that help students see how math connects to the real world. The page describes...more
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This article shares examples of mathematical patterns found throughout nature and provides simple examples that help students see how math connects to the real world. The page describes how shapes such as circles, spirals, and repeating patterns appear in everyday natural objects like bubbles, raindrops, and tree rings, helping learners understand that math is not just numbers on paper but something that exists all around us. It is a useful resource for teachers who want to introduce mathematical thinking through observation, discussion, and real-world examples, making math more engaging and meaningful for students

tag(s): geometric shapes (154), patterns (79), pi (27), symmetry (31)

In the Classroom

Have students look at pictures from the website and identify mathematical patterns such as spirals, symmetry, or repeating shapes. Students can record what they see in a chart and explain the different math patterns they find. Students choose one example from the site, such as a shell, a flower, or a honeycomb, and draw it, labeling the mathematical features they notice. Take students outside to look for natural objects that show math patterns, such as leaves, rocks, clouds, or tree bark. Students can sketch or photograph what they find and describe the shapes, symmetry, or patterns they observe. After learning how nature uses math, students can design their own nature-inspired object, such as a strong bridge based on honeycomb shapes or a spiral design based on shells. Students explain how math helped their design work.

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Clothesline Math - Chris Shore

Grades
K to 12
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Clothesline Math offers a visual, hands-on approach to understanding basic number sense, algebra, and statistics through a dynamic number line. This resource, ideal for students from...more
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Clothesline Math offers a visual, hands-on approach to understanding basic number sense, algebra, and statistics through a dynamic number line. This resource, ideal for students from elementary through high school, provides everything needed to implement this hands-on strategy in the classroom. The site includes a comprehensive library of downloadable clothesline cards that cover various mathematical concepts, such as fractions, decimals, square roots, and algebraic expressions. You can find detailed instructional videos and lesson plans that explain how to facilitate student discourse as they place values on the line and justify their reasoning based on spacing and relative magnitude.

tag(s): equations (129), mixed numbers (8), negative numbers (14), number lines (31), number sense (74), numbers (122), ratios (50), statistics (128)

In the Classroom

Transform a standard lesson on equivalent expressions or rational numbers by having students physically arrange cards on a string stretched across the room, which encourages students to engage in mathematical modeling and peer-to-peer discussions as they argue for the correct placement of values like $2/3$, $0.6$, and $sqrt{0.5}$. To enhance the collaborative aspect of the lesson, have students use Figjam, reviewed here, to create digital versions of their clotheslines where they can leave sticky note justifications for their placements. Extend the learning further and have students record their mathematical reasoning using ScreenPal, reviewed here, explaining the logic behind their spacing and the relationships between the numbers they placed.
 This resource requires PDF reader software like Adobe Acrobat.

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10 Fantastic Examples of Fractals in Nature - Mathnasium

Grades
4 to 8
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The Fractals in Nature article from Mathnasium explains how mathematical patterns called fractals appear throughout the natural world. The page describes fractals as repeating shapes...more
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The Fractals in Nature article from Mathnasium explains how mathematical patterns called fractals appear throughout the natural world. The page describes fractals as repeating shapes that look similar at different sizes and shows real-life examples such as rivers, snowflakes, plants, shells, and clouds to help students see how math connects to science and nature. The article is written in student-friendly language and can be used to introduce geometry, patterns, and problem-solving while showing how mathematics helps us understand the world around us. This resource works well as a reading activity, discussion starter, or enrichment lesson when studying patterns, nature, or real-world math connections.
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tag(s): geometric shapes (154), patterns (79), problem solving (279)

In the Classroom

After reading the article, have students look for fractal patterns in pictures or outside on the playground. Students can sketch or photograph examples such as leaves, trees, clouds, or shells and explain how the pattern repeats. Teach students how to make a simple fractal design, such as a repeating triangular or square pattern or a branching tree, using paper folding or drawing. Students can color-code the repeating parts to clearly show the pattern. Students can create their own fractal-inspired artwork using markers, rulers, or digital drawing tools such as Draw.to, reviewed here. Encourage them to repeat the same shape in progressively smaller sizes to demonstrate the fractal effect.

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