TeachersFirst Data and Probability - Grades K-2

Explore this collection of resources for grades K-2. Use these resources to meet the NCTM standards in the area of Data & Probability. Help young students grasp the beginning concepts of probability, numbers, data, and basic operations. Many of these tools are ideal for use on your interactive whiteboard, math computer learning station, or in your BYOD classroom. Share these resources on your class website for students to use both in and out of the classroom. 

Explore the NCTM Standards for all Math Topics

Explore the NCTM Standards for Data And Probability for All Grades

Data and Probability Resources - Grades K-2

Data and Probability Resources - Grades 3-5

Data and Probability Resources - Grades 6-8

Data and Probability Resources - Grades 9-12

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Data grade 1 - WordWall.net

Grades
K to 2
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WordWall.net offers a collection of interactive Data games designed for young learners. Featured activities include Bar Graph Questions, Parts of a Picture Graph, a Picture Graph Exit...more
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WordWall.net offers a collection of interactive Data games designed for young learners. Featured activities include Bar Graph Questions, Parts of a Picture Graph, a Picture Graph Exit Ticket with audio support, and many others. Each game is easy to share through a direct link, Pinterest, Facebook, Google Classroom, embed code, or a QR code, making it simple to integrate into classroom activities or centers.

tag(s): addition (136), charts and graphs (194), data (210), game based learning (296), place value (43), probability (129)

In the Classroom

Students can play the featured game. Students can post their favorite game in Padlet, reviewed here. Students can create their own picture graphs using Google Drawing, reviewed here.

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Teaching Probability in Kindergarten - A Pinch of Kinder

Grades
K to 1
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In the post "Teaching Probability in Kindergarten," the author presents a thoughtfully structured six-day mini-unit designed to help young learners grasp basic probability concepts....more
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In the post "Teaching Probability in Kindergarten," the author presents a thoughtfully structured six-day mini-unit designed to help young learners grasp basic probability concepts. Beginning with foundational terms like "always," "sometimes," and "never," the unit gradually introduces additional terms, including "possible," "impossible," "certain," "likely," and "unlikely." The instruction is hands-on and meaningfully grounded so that students explore these ideas through anchor charts, sentence-writing activities, storytelling with picture books, and interactive center activities, such as creating gumball machine scenarios and conducting tally-based "bear-in-a-bag" experiments. Throughout the unit, the focus remains on using mathematical language in informal discussions to describe likelihood in everyday situations, making abstract ideas concrete and accessible for kindergarteners.
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tag(s): data (210), preK (315), probability (129)

In the Classroom

Set up a "mystery bag" with objects of different colors inside. Have students predict which color they might pull out, then record their predictions in a simple tally chart to compare them with actual outcomes. Create a classroom probability game in which students spin a color wheel or roll a numbered die, then discuss the likelihood of different outcomes using words such as "likely" and "unlikely." Follow up by having students design their own probability game to share with the class. Read a picture book that includes elements of chance, such as Pete the Cat and the Missing Cupcakes, and have students identify events that are "certain," "possible," or "impossible" within the story.

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Activities- Math at Home - Math at Home

Grades
K to 5
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Math at Home is a free website for grades Pre-K through 5th. Math at Home contains resources, activities, and games that align with mathematical concepts. After selecting a grade level,...more
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Math at Home is a free website for grades Pre-K through 5th. Math at Home contains resources, activities, and games that align with mathematical concepts. After selecting a grade level, you can choose a set. For example, grade one contains a set of "Figure the Facts" (set 5). Each set contains a selection of activities, resources, and games. Activities are in Google Docs, Seesaw, or PDFs. There are also sample problems for educators to view.

tag(s): addition (136), division (108), geometric shapes (151), measurement (126), multiplication (132), place value (43), probability (129), subtraction (117)

In the Classroom

Students can complete the lesson and activities from Math at Home. Students can complete the activities using Seesaw, reviewed here. Students can create their own math review book using Book Creator, reviewed here.

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Graphing Activities and Probability - Proud to be Primary

Grades
K to 3
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This blog post from the "Proud to Be Primary" site by Elyse highlights the excitement and accessibility of teaching data analysis through hands-on graphing and probability activities....more
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This blog post from the "Proud to Be Primary" site by Elyse highlights the excitement and accessibility of teaching data analysis through hands-on graphing and probability activities. It emphasizes that organizing real-world data helps students make sense of numbers and strengthens observation and sorting skills. It reviews different graph types, including tally charts, pictographs, pie graphs, and line plots. It offers creative, tactile activity ideas such as using Connect Four boards, sticky notes on whiteboards, Legos, human graphs, candy stacks, Fruit Loops on skewers, coin flips, dice-roll graphs, and an apple-tasting bar chart activity using student preferences. These ideas foster both visual and kinesthetic learning and make math come alive in the classroom.

tag(s): charts and graphs (194), data (210), numbers (120), probability (129)

In the Classroom

Choose a survey question (favorite recess game, type of pet, etc.) and have students physically line up in columns to represent their answers. Count each column together and discuss which category is most and least popular. Provide samples of different apple varieties. Students vote for their favorite, then create a class bar graph using Canva Infographic Creator reviewed here of the results. Using assorted Lego pieces in different colors, have students sort by color or size, then build 3D bar graphs. They can compare their graphs with classmates and discuss similarities and differences in the data.

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Probability Models - PBS LearningMedia

Grades
K to 8
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The Probability Models page on PBS LearningMedia (a K-8 Mathematics resource by WQED/PBS) offers a curated collection of lesson plans, videos, and interactive activities that help students...more
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The Probability Models page on PBS LearningMedia (a K-8 Mathematics resource by WQED/PBS) offers a curated collection of lesson plans, videos, and interactive activities that help students explore probability concepts through practical modeling tools. The materials guide learners in understanding randomness, sample spaces, and chance using real-world examples such as dice rolls, coin flips, and other simulations. Resources often include teacher support, such as discussion prompts and step-by-step guidance, to reinforce how probability can be represented and interpreted. The content is ideal for integrating hands-on experiences with conceptual discussions around outcomes, likelihood, and predictive reasoning.

tag(s): data (210), manipulatives (12), probability (129)

In the Classroom

Have students use online interactive tools (such as the "Introduction to Probability" video or simulations) to explore the outcomes of coin tosses, dice rolls, or spinner experiments. Let them record results using Visme reviewed here and compare experimental probability with theoretical predictions. Assign students to design their own simple probability-based carnival games (e.g., spinning wheels, card draws, or guessing jars), then calculate the theoretical odds of winning and test those predictions with their classmates. Challenge students to map out compound events using tree diagrams in MindMup reviewed here. For example, they can model the likelihood of flipping a coin twice or rolling two dice and identify all possible outcomes and their probabilities.

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Poll Maker - Super Survey

Grades
K to 12
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Poll Maker makes it easy to create and share polls in just a few seconds without requiring registration. Add your question and response choices in the blanks provided; options allow...more
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Poll Maker makes it easy to create and share polls in just a few seconds without requiring registration. Add your question and response choices in the blanks provided; options allow you to find and add images to both the question and the responses if desired. Additional tabs provide options for selecting and customizing a theme and personalizing settings. Setting options include security features, multiple answers as responses, and selections to hide or show results. Advanced settings allow you to set the start and end dates of polls. When ready to share your poll, copy and share the link, copy and paste the embed code onto a website, or invite users to your poll via email. Registration isn't required; however, it allows you to create and manage additional polls and view hidden results.

tag(s): data (210), Formative Assessment (45), polls and surveys (41), questioning (36), quizzes (88)

In the Classroom

Bookmark and save this handy site for many different classroom uses. Engage students when introducing a new topic by creating a poll to assess learning quickly or find students' interest in a topic. Use a poll as an exit ticket or as a formative assessment. Enhance learning by adding a link to a poll as part of a blended or flipped learning activity. For example, when delivering a flipped learning lesson using Microsoft Forms, reviewed here, include a link to a poll that asks students to reflect upon their understanding of the content learned. Extend learning by sharing the Poll Maker with students and asking them to conduct polls to gather information when learning about graphing. After completing the polls, students create graphs to share the results using online graphing resources such as the Data Gif Maker, reviewed here, or PieColor, reviewed here.

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LiveGap Charts - Livegap

Grades
K to 12
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Create charts in several formats using Livegap Chart creator; no registration required. First, select a form to enter data manually or from a spreadsheet to begin. Next, customize colors,...more
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Create charts in several formats using Livegap Chart creator; no registration required. First, select a form to enter data manually or from a spreadsheet to begin. Next, customize colors, text, font, and more to personalize the look and design of your content. When finished, save your chart as an image, as an animation on a web page, download a video file, or save online and share the link for others to view. Although registration isn't required, it offers you the opportunity to save charts for later use.

tag(s): charts and graphs (194), data (210), noregistration (78)

In the Classroom

Save this handy chart creation tool in your bookmarks and on student computers for various classroom uses. Enter data on the site, then demonstrate how to represent the information through multiple formats and representations. Collect data in your classroom and quickly create a graph to express it, then choose another design to share the data in another way. Share your charts by adding links or uploading images to blogs, wikis, or websites--share graphs on an interactive whiteboard or projector for better data analysis by the class. Graph results of a test, answers from students, favorite foods, fictitious budgets, class schedules, and anything applicable in your classroom. Use an informational text, and have students create a pie chart to understand how to read charts accompanying the nonfiction texts. Have cooperative learning groups create graphs to share with your class. Create quick pie charts on your interactive whiteboard whenever you count class votes or encounter other data so students "see" data visualized regularly; visual students will have another way to absorb the information. Keep the link handy on your web page for you and your students to access it quickly in or out of class.

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Spinner Wheel - spinnerwheel.com

Grades
K to 12
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Spinner Wheel isn't just your ordinary customizable spinner; it offers the ability to include several spinners to use simultaneously. Add spinners and customize colors, text, select...more
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Spinner Wheel isn't just your ordinary customizable spinner; it offers the ability to include several spinners to use simultaneously. Add spinners and customize colors, text, select images, and themes. Customize backgrounds by color or select images from Unsplash, reviewed here. Creating an account isn't necessary, but it allows you to save and share wheels. Scroll down the page for complete directions and a selection of examples shared for inspiration on using this resource. .

tag(s): preK (315), probability (129), statistics (128), Teacher Utilities (205)

In the Classroom

Simultaneously spinning multiple wheels opens the door to unlimited uses to engage students. For example, create six wheels with the numbers on dice as a virtual dice roller. In addition, customize wheels for creative story writing prompts that include options for random characters, setting, and story theme. Use this tool to practice math facts by creating wheels that prompt players to solve math problems based upon a spin of the wheel. Engage students when reviewing for upcoming quizzes and tests by creating wheels to check facts. For example, in social studies, create one wheel with names and another with characteristics such as date, place, important event, other characters involved, etc. Use during math lessons on probability to have students record outcomes when spinning the wheel.

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Data GIF Maker - Google News Lab

Grades
K to 12
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Create and share data with the different GIF formats offered by Google News Lab. Choose from the three theme options - rectangles, circles, or donut to begin. Follow the prompts ...more
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Create and share data with the different GIF formats offered by Google News Lab. Choose from the three theme options - rectangles, circles, or donut to begin. Follow the prompts to add a title and data values. Add data as a percentage or numerical values then customize your GIF by selecting from different color options. When finished, save as an HQ (high quality) or LQ (low quality) GIF. Once created, save the GIF to your computer or share using the provided link.

tag(s): data (210), images (263)

In the Classroom

This tool provides you and your students an excellent resource for engagingly sharing data. Use the Data GIF Maker to create a visual display when collecting data. For example, begin using this tool by polling your class to find out their favorite type of pizza and then enter the data to create a GIF. Use the same data in all three included formats to compare and contrast how the information looks based on the type of chart used. Take this same information and have students calculate the percentages and create GIFs to compare and contrast this information with your original images. Once you and your students are familiar with how to use this site to create GIFs, use it to enhance student learning by including GIFs within your presentations for students to evaluate and to visualize any data. Create GIFs to document student reading logs, the amount of time spent on homework, or time spent on community service. Have students include GIFs when annotating images using Image Annotator, reviewed here, or within presentations created with tools such as Sway, reviewed here.

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PictureStem Project - Tamara Moore, Kristina Tank, and Elizabeth Gajdzik

Grades
K to 3
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The PictureStem Project offers STEM teaching units for grades K-2 incorporating the engineering process and correlated to science standards. These three units - one each for grades...more
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The PictureStem Project offers STEM teaching units for grades K-2 incorporating the engineering process and correlated to science standards. These three units - one each for grades K, 1, and 2 include modular features that contain content within different lessons throughout the school day. Each lesson within a unit provides science concepts based upon literary connections using picture books. Select any unit to view and download the entire unit including printables.

tag(s): animal homes (53), animals (270), design (76), engineering (136), geometric shapes (151), main idea (8), measurement (126), numbers (120), patterns (80), phonics (52), preK (315), reading comprehension (145), STEM (353)

In the Classroom

Enjoy these free, high-quality STEM units to use in your elementary classroom. As you teach lessons found on this site, enhance learning using a portfolio-creation tool like Seesaw, reviewed here, to share student work and reflections. Upload images of student projects then use Seesaw to add video reflections, students' written responses, and more. Share Seesaw portfolios with parents during parent/teacher conferences to demonstrate student learning. If you are unable to use the complete units in your classroom, be sure to look through the many lessons to "mine" for shorter activities that work in your teaching situation.
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Open Middle - N Johnson, R Kaplinsky, B Anderson, D Luevanos, and Z Miller

Grades
K to 12
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Open Middle is a terrific resource to find challenging math problems for all grade levels. The problems on this site offer multiple options for finding the solution. Many initially...more
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Open Middle is a terrific resource to find challenging math problems for all grade levels. The problems on this site offer multiple options for finding the solution. Many initially appear to be easy; however, they become more complex as they are solved. Use links at the top of the page to find problems by grade level and concept or use filters to browse by Common Core Standards. Each question includes a hint when necessary and answers.

tag(s): logic (162), problem solving (268), statistics (128)

In the Classroom

Bookmark this site to find math problems correlating to your teaching standards or content. This site is perfect for finding materials to differentiate instruction with different student ability levels. Have students share their results and discuss their problem-solving process on your interactive whiteboard. Take screenshots of the different solutions and include on your class website. Another option is to take a picture of student's written solutions, then use Voxer, reviewed here, to extend student learning by having them add an audio recording describing their mathematical thinking. Share their Voxer to your student's digital portfolio on Seesaw, reviewed here, or another portfolio creation site. As students become more proficient in sharing their mathematical thinking and problem-solving activities, consider using their math talks as part of an ongoing podcast using Buzzsprout, reviewed here, as a way to extend student learning and promote math conversations and help students understand that there may be many different ways to arrive at the right answer to a problem. Buzzsprout features free and easy to use tools including the ability to create and schedule podcasts to be released on any date and time you desire.

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Monarch Lab - University of Minnesota

Grades
K to 12
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This site serves as a comprehensive hub for monarch butterfly conservation and offers a wealth of free scientific data and educational materials for K-12 classrooms. The site features...more
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This site serves as a comprehensive hub for monarch butterfly conservation and offers a wealth of free scientific data and educational materials for K-12 classrooms. The site features downloadable handouts, species fact sheets, and high-quality webinars that cover everything from life cycles and migration patterns to habitat restoration. Users can access the Monarch NECTAR Hub to find self-paced courses or explore a curated collection of lesson plans that align with national science standards. The platform also hosts the Integrated Monarch Monitoring Program, which provides the tools and protocols necessary for students to participate in real-world citizen science by tracking milkweed and monarch populations in their own communities.

tag(s): animal homes (53), butterflies (14), citizen science (43), data (210), habitats (103), insects (62)

In the Classroom

Introduce a unit on ecology and environmental stewardship by having students explore the interactive migration maps to predict when monarchs will arrive in your local area. After researching the specific needs of pollinators, students can use the site's habitat guides to design a school pollinator garden. To share their findings and advocate for conservation, students can create digital flyers or social media graphics using Canva, reviewed here, to highlight the importance of native milkweed. For a more collaborative project, have students document their garden's progress and record observations of local butterfly activity by building a class website with Google Sites, reviewed here.
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MathGames - TeachMe, Inc.

Grades
K to 8
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MathGames offers a large variety of math activities and interactive questions for grades preK-8 all fully aligned to Common Core Standards. Choose a grade to start, or choose by skills....more
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MathGames offers a large variety of math activities and interactive questions for grades preK-8 all fully aligned to Common Core Standards. Choose a grade to start, or choose by skills. Other options allow you to choose by grade level standards. Registration isn't necessary to play individual games; however, enrollment as a teacher provides additional features. Input your class to receive detailed progress reports as well as leaderboards and student competitions.

tag(s): addition (136), charts and graphs (194), differentiation (86), division (108), equations (132), estimation (36), fractions (179), game based learning (296), geometric shapes (151), measurement (126), mental math (18), multiples (15), multiplication (132), patterns (80), pi (27), preK (315), ratios (52), statistics (128), subtraction (117), time (94)

In the Classroom

MathGames is perfect for practice with many different math concepts. Include a link to games on your class website or classroom computers. Be sure to share games with parents for play at home. Take advantage of the free registration to register your class to follow student progress and challenge students to increase scores. Enhance learning goals by asking students to write blog entries sharing their learning and understanding for each game using Telegra.ph, reviewed here. This blog creator requires no registration. If you are teaching younger students and looking for an easy way to integrate technology and check for understanding, challenge your students to create a blog using edublogs, reviewed here. Take this a step further and extend students' learning by picking the game they learned the most from and make a feature video about it using FlexClip, reviewed here. If you teach using Common Core Standards, MathGames is excellent for finding practice activities aligned to the standards. Measure student growth for Common Core Standards using Edulastic, reviewed here. MathGames is perfect for remote or blended learning due to its detailed progress reports.

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Learn - PBS Kids - PBS Kids

Grades
K to 3
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Learn offers resources and activities to accompany several popular PBS Kids shows including Peg & Cat, Scratch Jr., Ready, Jet, Go! and several others. View the different show options...more
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Learn offers resources and activities to accompany several popular PBS Kids shows including Peg & Cat, Scratch Jr., Ready, Jet, Go! and several others. View the different show options by clicking the arrows, then click on any show to see available resources. Resources include show clips, games, printable worksheets, and more. Some of the favorite shows, like Peg & Cat, even have their own website.
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tag(s): counting (66), emotions (62), geometric shapes (151), insects (62), numbers (120), planets (124), plants (140), preK (315), social and emotional learning (155), solar system (122)

In the Classroom

Take advantage of the many free resources available on Learn. Share show clips on your interactive whiteboard, then have students complete an accompanying activity. Learn is perfect for sharing with parents. Include a link to activities on your class website along with suggestions on how to use activities at home.

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Peg & Cat - PBS Kids

Grades
K to 4
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Join Peg & Cat on their math adventures with this entertaining site. Watch videos, play games, or check out the latest adventures. Each activity explores math skills such as counting,...more
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Join Peg & Cat on their math adventures with this entertaining site. Watch videos, play games, or check out the latest adventures. Each activity explores math skills such as counting, fractions, or shapes through real-world lessons. Don't miss the link to activities located under the main part of the homepage; this includes recipes, coloring pages, crafts, and more.

tag(s): addition (136), fractions (179), geometric shapes (151), number sense (73), numbers (120), operations (71), preK (315), subtraction (117)

In the Classroom

Use this site as a learning station or center. Be sure to include a link on your class web page for use at home. Ask a volunteer to come into your classroom to help students make crafts or fix a recipe from the site. Film your students discussing math concepts and share them using a tool such as SchoolTube, reviewed here.
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Zearn - zearn.org

Grades
K to 5
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Zearn Math is a complete math program that provides Common Core aligned math lessons, personalized to individual learners, and based on Eureka Math / Engage New York. Lessons focus...more
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Zearn Math is a complete math program that provides Common Core aligned math lessons, personalized to individual learners, and based on Eureka Math / Engage New York. Lessons focus on three critical components: deep understanding, fluency, and problem-solving. Self-paced lessons allow for mastery of concepts before unlocking lessons providing the next level. Math lessons provide video instruction similar to a small group lesson. Lesson Labs include drag and drop activities followed by quiz questions. Zearn currently offers K-8 lessons. Create a class account and add students using an Excel sheet or manually input student names to receive custom reports on student progress.

tag(s): addition (136), classroom management (125), data (210), decimals (94), differentiation (86), division (108), fractions (179), geometric shapes (151), measurement (126), multiplication (132), numbers (120), operations (71), subtraction (117)

In the Classroom

Use Zearn on a projector or an interactive whiteboard to demonstrate specific concepts or use as weekly math centers for student practice. Zearn provides data to target instruction to specific students or concepts needing additional reinforcement. Since Zearn is a complete math program, with individualized lessons for students to work on, teachers can conduct small group instruction while others work independently. Zearn is perfect to use for gifted or advanced students, allowing them to work at their own pace. Be sure to put a link to Zearn on your class web page for students to use at home. Zearn does not support Android devices but will work on all other devices with a browser and Internet access.
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Progressions Documents for the Common Core Math Standards - Achieve the Core

Grades
1 to 12
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Explore the progressions of the Common Core math standards throughout the grade levels. Look at different areas of mathematical standards, numbers and operations, base ten, counting...more
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Explore the progressions of the Common Core math standards throughout the grade levels. Look at different areas of mathematical standards, numbers and operations, base ten, counting cardinality in algebraic thinking, numbers and operations for fractions, geometry, and measurement and data in grades kindergarten through grade five. In grades six through eight explore statistics and probability, expressions and equations, the number system, ratios, and proportional relationships. In high school discover the progressions in algebra, functions, and modeling. Find resources for further development of programs offered to support Common Core mathematics. Discover research, periodicals and groups using Common Core math.

tag(s): commoncore (61)

In the Classroom

Strengthen your teaching of Common Core mathematics. Having an understanding of the knowledge students enter with or without, leads to better preparation for where the students will explore later. Use this as an individual study or even as a professional learning group study with your grade level and department.
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Preschool and Kindergarten Games - Sheppard Software

Grades
K to 2
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Choose from many preschool and kindergarten interactives to develop and reinforce basic academic skills. This highly colorful site includes: animals, alphabet, numbers, colors, and...more
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Choose from many preschool and kindergarten interactives to develop and reinforce basic academic skills. This highly colorful site includes: animals, alphabet, numbers, colors, and shapes. Most activities are very simple. Simply roll the mouse over objects to hear the object name and color, or click on arrows to view flashcards. Play alphabet activities to learn letters. Test your skills with a quick quiz. Choose from an extensive array of activities in the animal portion of the site sorted into categories of look, create, play, learn, find, and count.
This site includes advertising.

tag(s): alphabet (46), animals (270), colors (61), geometric shapes (151), numbers (120), preK (315)

In the Classroom

Demonstrate games on your interactive whiteboard or projector before students play on their own. Demonstrate how to choose games while avoiding advertising on the site. Bookmark specific games or activities on classroom computers for students to explore and discover during center time. Be sure to share this site with parents for fun learning at home! List this site on your class website or in your class newsletter.

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Curious George - PBS Kids

Grades
K to 1
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Join Curious George in his adventures with the Man in the Yellow Hat. Enjoy the antics of Curious George through online games, printables, and videos. Games feature matching, numbers,...more
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Join Curious George in his adventures with the Man in the Yellow Hat. Enjoy the antics of Curious George through online games, printables, and videos. Games feature matching, numbers, sounds, categorizing, shapes, Spanish, movement/dance, and animal sounds. Earn stickers with successful completion of each game.

tag(s): animals (270), dance (42), geometric shapes (151), matching (8), numbers (120), preK (315)

In the Classroom

Use the video clips or activities on your projector or interactive whiteboard. Use this site at centers to reinforce skills (counting, matching, learning shapes, and more). Share this link on your class website for students to access at home.
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Virtual Number Rack - Math Learning Center

Grades
K to 4
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Practice number sense skills using beads on the virtual number rack (similar to an abacus). Movable beads encourage you to think in groups of fives and tens while practicing addition,...more
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Practice number sense skills using beads on the virtual number rack (similar to an abacus). Movable beads encourage you to think in groups of fives and tens while practicing addition, subtraction, multiplication, and division strategies. Add or subtract rows of beads using links provided. Display up to 100 beads at one time. Use the shade key to hide beads or drag the corner of the bead to move or change its size. Use the start over button to clear the rack and start with a new set of beads. Be sure to visit the information portion of the site for free resources, including a 10 page activity book for use with the virtual number rack. Click on the lowercase "i" at the bottom right for complete directions.

tag(s): addition (136), counting (66), division (108), manipulatives (12), multiplication (132), number sense (73), numbers (120), operations (71), preK (315), subtraction (117)

In the Classroom

View the virtual number board together as a class (or a center) on your interactive whiteboard or projector to practice counting and basic operational skills. Use this with younger students learning to count to 10 or 100. Create a link on classroom computers for students to explore and practice on their own. Share a link to the site on your class website or blog for students to practice at home. When finished, have students draw the problems they created and include the appropriate number sentence for each drawing.

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