Geometry: Explore, Learn, Prove

geometry headerAre you teaching a lesson on parallel lines? What about a lesson on the interior and exterior angles of polygons? If so, our Geometry lessons are the perfect resources for you!  We released our first one, Parallel Lines and Angles, this past fall. Since then, we've released four more. The lessons broaden the content of the tools in the Practice and Prove Geometry Series.

As with the lessons in our popular Algebra 1 Course, you'll find the following in the new Geometry lessons:

  • Alignment to all state standards
  • Compatibility with the PC, iPad, Chromebook, and other mobile devices
  • Interactivity and instructional feedback


Each lesson contains five sections: Get Ready, Learn, Practice, Review, and Quiz. Here’s what each section provides.

Get Ready

In Get Ready students are introduced to the lesson. They receive an overview, along with the lesson’s objectives and key vocabulary terms. Students may also practice prerequisite concepts and access guided notes.

get ready


The bulk of the instructional content is in Learn. Each page provides interactive components and guided practice. A palette is always available so that students can enter answers with appropriate math notation. As students work through the guided-practice problems, they receive immediate feedback. Congratulatory feedback reassures students; instructive feedback helps students persevere through mistakes.



To help students confirm what they have learned, practice provides additional problems similar to those found in Learn. Students receive immediate and instructive feedback. Once they finish, students can save, print, or send a summary of their results.



Review provides students with a lesson summary and access to additional practice resources and printable materials.



Finally, students assess their understanding of the lesson content with Quiz. Unlike Practice, students do not receive immediate feedback. Instead, their answers and work are submitted to a results page where they are then marked. Students can save, print, or send their results.


So check out the Geometry Lesson Series page. More lessons are coming soon!

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Successful Strategies of a Global Educator

globalEducator (1)
Regardless of grade level, subject, or academic setting, you can become a global educator and teach global competence. Here are some ideas to get you started. 

Get Informed – Start by broadening your own global citizenship and developing a multicultural awareness. Evaluate your own culture; think about your traditions, values, beliefs, and attitudes. Learn about other cultures, specifically their unique practices, and perspectives. The Global Competence Position Statement from the American Council on the Teaching of Foreign Languages (ACTFL) outlines effective practices.

Know what it means to have globally competent students and to create a classroom environment that values diversity and global engagement. Understand what encourages students to achieve the four primary capacities identified by the Global Competence Taskforce: Investigate the World, Recognize Perspectives, Communicate ideas, and Take Action.

Image courtesy of The Council of State School Officers.

Image courtesy of The Council of State School Officers.

Consider any cultural mismatches in your classroom. Culturally responsive teaching (CRT) methods use the students’ personal experiences and interests to engage learners while respecting their cultural integrity. This technique recognizes cultural and linguistic backgrounds to prompt student involvement. In Culturally Responsive Teaching Matters! Elizabeth Kozleski points out key features of CRT and how it “helps bridge the different ways of knowing and engages students from non-dominant cultures in demonstrating their proficiencies in language usage, grammar, mathematical knowledge and other tools they use to navigate their everyday lives.”

Get Collaborative –   Connect with culturally diverse people locally, nationally, or internationally. Utilize online learning and resources to foster cross-cultural experiential learning. Resources for Cross-cultural Interaction and Project Work highlights curricular tools, apps, and other technology resources that present different perspectives, authentic voices, and contextual knowledge.

Incorporate Project-Based Learning. Collaborate with colleagues to create interdisciplinary projects and inquiries. Or join interactive curriculum-based groups such as iEARN (International Education and Resource Network) to “learn with the world, not just about it.” Start by helping students learn about global collaboration. Introduce them to strategies for developing sensitive and effective communication and negotiation skills that use inclusive language to achieve fair outcomes when there are diverse points of view.

Take advantage of the collaboration between the National Education Association and VIF International Education. Together they have developed a collection of global learning lesson plans. Use their models to create new lessons or adjust your plans to build on global perspectives. The NEA also offers curriculum guides and teaching resources on global education and culturally responsive classroom activities that address different cultures and grades using the same basic framework.

Digital literacy is growing worldwide and coding campaigns such as the Hour of Code reach millions. You can collaborate with others in this exciting global movement.

Get Social – Turn to social media for professional development outlets and ideas. Here are some upcoming opportunities.

Global education is trending on social media. Be sure to check out these Twitter hashtags: #globaled, #globalclassroom, and #globaledchat.

Network with global educators through teacher training programs. Participants in the Teachers for Global Classroom Program (TGC) become global ambassadors in their classrooms, schools, and communities. Read about their experiences in the field and learn about their impact on others. Likewise, VIF  supports global educator development and has a VIF Global Schools program where teachers learn to implement global themes into everyday instruction.

So... get out there!

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When Digital Natives Become Teachers: Tech Problems Solved?

As the digital generation enters the workforce, does their technology skillset help them meet specific job-related challenges? This question has important implications for the digital-age classroom.

Writing on the future of work, David Mills notes, “the true ‘children of the internet,’ who won’t remember a life before broadband,… are headed en-masse to workplaces now.” Beginning teachers bring with them an almost instinctive comfort with technology, in particular with social media. It follows, then, that they're able to meld technology and pedagogy. Right? Hmmm. Perhaps not.

Recent findings suggest that "digital native student teachers have not necessarily become more comfortable keeping pace with the fast rate of change in technology." And an article in Educational Leadership, from the Association for Supervision and Curriculum Development (ASCD), highlights what may be the roots of the challenge.

In What's Missing from Teacher Prep? Gary Chesney and Janice Jordan discuss the discontent that beginning teachers voice about their university-level preparation programs. Here's a chief cause of that discontent: "the use of technology in preservice classrooms was limited, and training in how to integrate technology into lesson planning was virtually nonexistent." The authors recommend that teacher training programs "embed technology in their coursework in all classes." This concern casts a cold eye on digital native's "instinctive" abilities. Instead, like any job-related skill, technology integration must be learned and practiced.


Image courtesy

Related to this challenge is “technology transience,” the rapid proliferation of technology tools, the frequent update of such tools, and their ever-shortening lifespans. Writing in the Quarterly Review of Distance Education, Lin Muilenburg and Zane Berge note that it's “incumbent upon teacher preparation programs to consider how to build teacher capacity to both integrate technology and manage the challenges brought about by technology transience.” The authors note that successful integration requires TPACK:  the interaction of technological, pedagogical, and content knowledge. Their conclusion? “Effectively using technology in an ever-changing technological environment can be... quite complex.”


The need for support and training extends to the new teacher's classroom. Novice teachers face and surmount many challenges, but they can't be expected to design and implement their own high quality, standards-based lessons right from the start.  Of course, few try to accomplish this in a vacuum. In many education communities, grade-level learning teams provide some support. But even with such support, in the end, teaching is still an individual challenge.

In addition, the technology tools a teacher has mastered often differ drastically from the ones she finds in schools. For example, new teachers may be experienced Apple/iOS users presented with Chromebook carts, or Google/Android users might find themselves in a 1:1 iPad classroom. Moreover, pre-service teachers often achieve a level of comfort with a particular resource only to be presented with an entirely new, mandated program when they enter their new school. Neither of these challenges is insurmountable, but both steepen an already difficult first-year learning curve.

The implication is not that universities uniformly ignore the importance of technology in their teacher training programs. But all parties should be aware that a novice teacher’s mere familiarity with a technology does not automatically lead to effective integration in the classroom. That kind of integration requires ongoing support.

Well-implemented school and district-based technology integration plans can give teachers the support they need. In North Carolina, the Rutherford County school system has developed just this kind of program. The district's technology leadership team developed a comprehensive approach that included a 1:1 laptop initiative, professional development training, and direct support for teachers to find, evaluate, and integrate high-quality digital resources into instruction. The result was more effective use of technology across multiple middle schools and high schools in a single year.

The lesson seems clear. Assuming that new teachers automatically “get” technology is not a recipe for success. Instead, teaching educators how to use and integrate digital resources and providing a strong support system for technology integration can help ensure that classroom instruction meets the needs of digital-age learners.

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Five Things the Redesigned SAT Got Right

March came in like a lion for the high school students who were the first group to take the 2016 redesigned SAT. Now, while they wait an excruciating two months (May 17) for their scores, let’s take a moment to reflect on some of College Board’s SAT changes. We believe some key logistical and pedagogical elements of the redesign will please both students and teachers. Here’s why.

First, let's do the numbers...



What the College Board got right...

1. Logistical changes add clarity to a stressful day.

Students are happy to say goodbye to that fifth multiple choice option, and they won’t miss the ambiguity of wondering whether to “guess” or leave a question blank. So a few of those logistical changes get high marks immediately.

2. The focus is on real vocabulary.sat

Gone are the days of taking expensive courses to memorize lists of obscure vocabulary words completely out of context. Some questions even ask students to figure out a common word’s meaning based on its context.

3. All reading is evidence-based reading, and data analysis is a form of reading.

In the past, SAT reading questions often focused on identifying details in isolation. As the name suggests, the new Evidence-Based Reading and Writing section ask students to identify evidence as they answer questions across disciplines. Some reading passages address literature, but many topics focus on science and social studies. In parts of the Math section, students read a graph or table and then revise an associated passage to make the text consistent with the data presented. Text and number literacy work together just as they need to in the real world.

4. Correct answers are not the end of the story.

After students answer an interpretive question, the following question will sometimes ask them to explain why they chose that answer. This rewards the highest level of authentic comprehension. These questions often take this form: “Which choice provides the best evidence for the previous question?”

5. Primary-source documents are relevant again!

You remember those random paragraphs on obscure topics like language acquisition, the rationale for breeding endangered animals in zoos, or (worst of all) those rambling personal narrative passages the SAT used for reading comprehension questions in the past? In the new SAT every Reading section will include at least one primary-source document from American History. Founding Documents like Federalist Papers or The Declaration of Independence are particular favorites so Hamilton and Jefferson are back! Most students have already encountered these documents in their regular courses, so it's easy to be fully prepared the day of the test

(psst: Our Explore! Primary Sources tool is a great resource for helping students read and interpret primary sources. Check out this text and audio clip of  Barbara Jordan's famous 1974 speech to Congress, highlighted in the College Board sample question.)

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SAS Curriculum Pathways Teacher Institute


**The application is now CLOSED. We are currently reviewing applications.**

We at SAS Curriculum Pathways are excited to announce our inaugural Summer Teacher Institute! The application is open and ready for your submission.

We always say "in-service teachers are our number-one source for new features and vital to our development process." For these reasons, we are excited to host a cohort of educators this summer at SAS headquarters in Cary, NC. The cohort will work closely with our team for 8 weeks to critically evaluate our current resources, consult on future features, and iterate on their own ideas for the next big edtech resource.

Why should you apply?

There are plenty of reasons to apply; here are our top 5:

  1. To get paid for doing what you love--designing, developing, and evaluating edtech resources!
  2. To collaborate and network with other teaching professionals in the greater Raleigh-Durham area.
  3. To expand your working knowledge of our over 1,500 FREE resources.
  4. To develop or refine your software engineering skills.
  5. To get hands-on experience with the latest edtech gadgets--robots, 3D printers, iBeacons, tablets, and more.

But most of all, to work with great people at a great company.

Hurry! The deadline for applications is April 24th, 2016, at 11:59 pm EST. Start your application here.

Frequently Asked Questions

Do I have to be in Cary to participate?
Yes. All participants are expected to work on SAS campus in Cary, NC, for the 8-week institute. Participants are welcome to commute, but travel expenses will not be paid by SAS.

What will a day in the life of a Summer Institute participant look like?
We hope no two days will look alike. From resdesigning and updating current resources to consulting on new features and products, participants will be busy putting their classroom experiences and expertise to work with our team.

My school doesn't let out until late June (or starts back early August), can I still participate?
No problem. The institute schedule has a built-in flex week. The institute will run for 9 weeks (June 15 - August 17), but participants are only expected to work 8 of those weeks.

I have a beach week planned, can I still go on vacation?
Of course! The institute schedule has a built-in flex week. The institute will run for 9 weeks (June 15 - August 17), but participants are only expected to work 8 of those weeks.

I submitted my application, now what?
Stay tuned! We expect to have applications reviewed by the middle of May. We will be in touch soon via email.

I have a question about my application, can I contact you?
Absolutely. Send us an email:

Please use the comment section or email us with additional questions.

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#Edtech Planning: Why Implementation Matters

My high school calculus teacher once asked the class, “When do you know that your new shoes have just become your normal shoes?” Answers varied: “when the majority of the shoe shows wear or dirt,” “when you buy a newer pair of shoes,” “when the season changes.” I mused, “When you’re no longer excited about wearing them.”

Like finding Flyknits on markdown, everyone loves something sparkly, new, and functional. This tendency to revere and promote what is most current is not only incredibly human; it’s ubiquitous, particularly in regards to technology.

It’s indisputable that advances in technology have made indelible marks on the way we communicate, organize, and learn. Some of these changes have been incredibly positive: the internet has made it possible for anyone with an iPad and Wi-Fi to access torrents of information about subjects as varied as plant evolution and Persian poetry. Online communities provide some of the best informal learning and/or safe spaces for people invested in particular subcultures. While equitable access to web-enabled technologies and resources remains a domestic and international issue, the fervor with which people have embraced computer-based technology in their personal and professional lives is mirrored in the burgeoning ed-tech industry.

The evidence suggesting “gadgets in the classroom don’t improve learning…hasn’t stopped the educational technology market’s steady upward climb.” Not only has the overall market value risen to over $8 billion in 2014, rising school expenditures in ed-tech products have encouraged investors to pour money into related startups.

US Edtech Funding
This has led to a corresponding shift in the way that schools interface with ed-tech companies. In lieu of the lengthy but standard request-for-proposal process, many companies now benefit from demonstrating products in classrooms before they launch. Innovation centers, both public and nonprofit, exist to match schools and ed-tech companies based on mutual need.

Fundamentally, all this investment, hard work, and good intention exist to promote innovations that promise to solve, or at least ameliorate, some of education’s most intractable problems. But, amid all the buzz, we might recognize a tacit but tangible notion that ed-tech solutions are universally good and should be widely adopted, sans alteration or rejection, as an example of pro-innovation bias.

Pro-innovation bias is not a new phenomenon. Everett Rogers coined the term in his 1963 capolavoro, Diffusion of Innovations, but it remains an understudied facet of innovation theory today – probably because it’s a total buzzkill. It’s that voice inside your head that, facing something with a lot of promise, tells you not to get your hopes up or to proceed with caution. It’s not fun, but it does give good advice.

Namely, that implementation matters.

The success of any new endeavor, technological or otherwise, is undoubtedly shaped by how well it aligns with the culture of your organization. If you’re a teacher with students who love working in groups, think about the capacity of your technologies – be they devices, physical spaces, or applications – to promote collaboration in real time as opposed to reward individual success. If you’re an administrator in an informal professional environment, consider how formal performance reviews might impact employees, as well as the way you prefer to manage. These kind of mismatches – individual tools in collaborative environments, formal evaluations in informal environments, processual reforms in innovative spaces – tend to curb the duration and degree to which people use new things.

Also, resources matter. A shiny set of new laptops is certainly a boon to any teacher or administrator, but there must be logistic support in place to ensure that the laptops are kept in working order and that their users – including students, teachers, coordinators, and specialists – know how to use them effectively and efficiently. Certainly having the funds to cover technical support and training is an important component of implementing technology successfully, and yes, schools are notoriously resource-scarce, but simply communicating a clear plan of who is responsible for what goes a long way toward alleviating frustration down the line. Is there a go-to person on staff for technical issues? Do you have a colleague who is familiar with the app you’re using? Can go to her if you have questions? Do you know how to access training materials, and do you have them on hand? Is there a well-understood process for reserving time with devices?

Finally, innovations with lasting power tend to be flexible. With personalization and modification, innovations can become optimized for your or your organization’s use. It’s important though, in this process of mutual adaptation, to strike a balance. Too little modification and the innovation ends up controlling you. Too much modification, and you may compromise the parts of it which promise the greatest reward. Think about those formal performance reviews. If you administer them by the book, your run the risk of alienating your employees. Conversely, if you don’t take them seriously enough, you run the risk of communicating that performance isn’t important.

None of this is to say that technology doesn’t have a space in education. Clearly, we’re in favor of it. But next time you’re considering changing things up or wondering why everyone stopped using that note-taking app three weeks after you introduced it, maybe it’s worth assessing whether you’ve introduced the wrong thing or implemented the right thing wrongly.

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Four Tips for Helping Students Unpack an Argument

Perhaps it’s the frenzied primary campaign season that’s to blame. But for some reason, I’ve been thinking a lot lately about the state of our public discourse. More specifically, I’ve noticed that our political candidates are increasingly unwilling—or unable—to answer questions with logical, detailed answers. When asked to explain why they have taken a certain position on an issue, many tend to present shallow arguments with skimpy evidence. They rely instead on platitudes and emotional rhetoric.

The challenge for teachers, then, is to help students negotiate a world where clear language and well-structured arguments seem to be diminishing in importance.

The good news is that we can provide students with the knowledge and tools they’ll need to navigate the mish-mash of arguments and opinions thrown at them each day. For example, SAS Curriculum Pathways offers four lessons in a series called Quick Tutorials: Clear Thinking. Students learn to reason carefully, recognize faulty logic, and construct and assess written and spoken arguments.

Each tutorial is built on a crucial tip for helping students analyze the arguments they’re hearing every day—from televised political speeches and newspaper opinion pieces to conversations with their parents and peers.

Tip #1: Beware of distractions.

Sometimes speakers—through carelessness, laziness, or even dishonesty— intentionally disguise a weak argument by distracting their audience with calculated errors in logic. Clear Thinking: Distracting the Reader surfaces and explains these errors, including false dilemmas and slippery slope arguments. It also shows students how to spot arguments from ignorance (the illogical assumption that if something hasn’t been proven true, then it’s false) and complex questions (the connecting of unrelated ideas with the assumption that both are true).

Tip #2:  Make sure the evidence leads to a logical conclusion.

Clear Thinking: Missing the Point shows how a speaker sometimes provides evidence that fails to prove that the conclusion is true or relevant to the argument. When that happens, the argument is said to miss the point.

Another way a speaker might form a faulty conclusion is by begging the question.  In this case, she bases the argument on premises she mistakenly assumes the listener will agree with.

Tip #3: Watch for someone unfairly changing the subject when challenging an argument.

Clear Thinking: Changing the Subject shows how a “shifty” listener might challenge an argument by shifting the focus. For example, someone presenting an argument might be unfairly attacked by the listener, who might change the subject by attacking the character or motivation of the arguer rather than confronting the merits of the argument itself. These shifty characters might also change the subject by side-stepping the evidence and offering unrelated counter-arguments.

Students learn to spot a case of faulty logic called style over substance. When someone ignores an argument’s conclusions and attempts to counter with persuasive words and beguiling body language, then the response to the argument sadly relies on style, not substance.

Tip #4: Reject arguments that rely on emotions rather than reasons and evidence.

Clear Thinking: Looking for Evidence makes the case that strong arguments are supported with reasons and facts. Students learn to look for several types of emotional appeals. The appeal to pity, for example, occurs when a speaker lists reasons that the listener should pity him or his condition. Similarly, arguers sometimes apply the appeal to popularity, claiming that a proposal is true simply because many people believe it is true.

Students also learn about the appeal to force and the appeal to consequences. In both cases, the arguer threatens the listener by warning that failing to accept the argument will possibly lead to an unfortunate consequence. And if neither of these appeals does the trick, some people use loaded words (e.g., all reasonable people will agree…) to advance their argument.

Of course, none of these emotional appeals has anything to do with the merits of the argument.

Want to learn more about how to help students unpack an argument, check out these resources:

Political Palaver and the Passive Voice
Active Listening

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Putting Students on the Write Path

One of my goals for 2016 is to become a blogger. I’m not a writer. I deal with numbers not words. So panic often sets in when I start to write. But then I realized that—panic or not-- I have to step out of my comfort zone if I want to grow professionally. And so I did! In the past few months, I’ve written several blogs about math.

Five Ways Parents Can Help Students in Math Class
Our Free Algebra 1 Course: The Basics
Without Order, There’s Chaos

Although writing blogs is not an easy task for a person like me, a "math" person, and it may not be easy for your students, writing is a critical skill. Writing teaches students to organize their thoughts logically, to clarify their understanding of concepts, and to sharpen their communication skills. So it is important to encourage writing in the math curriculum. Here are three easy ways to kick-off writing in your math classroom.


Read in Class
I know, reading in math class sounds strange, but it doesn’t have to be strange. And it doesn’t necessarily mean reading a novel, although students may find Flatland: A Romance of Many Dimensions, by Edwin A. Abbott a motivating book. Another interesting book—this one nonfiction—is Innumeracy, by John Allen Paulos. The book is full of riveting examples of how math is essential to our daily lives and how—for an educated citizen—numeracy is as important as (and related to) literacy.

Research shows that reading impacts writing and writing impacts reading. As Clare Heidema states in her article Reading and Writing to Learn in Mathematics: Strategies to Improve Problem Solving, “Mathematics is about problem solving, and reading comprehension is an important component, especially for word problems.” While it’s important for students to be able to read through short problems (e.g., finding a number such that the sum of twice the number and 7 is 13), don’t shy away from those long word problems. Use them frequently. Read them aloud in class. Have students deconstruct them individually or in groups. And then have students reflect on the problem-solving process used through writing.

Please Explain
A great way to get math students to express themselves in writing is to say, “Explain.” It’s that simple. Such a small word, but a powerful one. Students can show true understanding by justifying their thoughts in writing. Asking students to explain in detail how they solved a problem is a valuable form of mathematical writing. Start small by asking students to explain an answer on an assessment or their response to an opening assignment. While this task alone will not necessarily turn your students in writers, it’s certainly an excellent way to start them on the right path.

Encourage Reflection
Finally, encourage reflection. Have students start a math journal to record their thinking, their challenges, and their accomplishments. Math journals will give students a chance to articulate their feelings about math and allow them to clearly express what they’ve learned (or to discover gaps in their learning). For some students, the structure of the math journal will be important. That is, you may want to devise entry questions for them. These questions should be clear and concise. While the main idea is to express themselves in writing, students should also be allowed to do so through modeling. If your journal question is a specific math question, try using one that has multiple solutions or calls for several paths to reach the solution. Remember, you want students to think! Check out these math journal prompts for a start.

There are many ways to encourage writing in a math classroom. I hope these suggestions are a good starting point. And remember, ultimately, math isn’t simply about equations any more than philosophy is about diagramming sentences. The goal in both subjects is the same: understanding.

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Elementary Spotlight: Songs and Social Studies

Bedtime stories and Disney movies are great, but how do you get young readers to start embracing nonfiction, historical fiction, or even primary sources? And how should parents and educators introduce them to these new genres?

Explore! Primary Sources is the brand new repository of original text and audio, provided with historical context and comprehension questions to encourage active reading and text analysis. The primary-source collection stretches across four centuries. It includes founding documents, speeches, letters, patriotic songs, personal letters, and more. Many documents are excerpted for early readers taking their first steps into the world of active reading of a primary source.

If your child is saying, “Wait a minute. Just to be clear, what is a primary source???”  There’s a short video tutorial that explains all of that.


Start with something familiar. Reading is only one important way to enjoy primary sources. You can also listen to them! Some primary sources are best consumed as audio! Active listening is just as important as active reading! Use the Grade Level filter to search for K-5 resources and the Primary Source Type filter to search audio.

Songs are great for helping students tackle the text reading in a rigorous, yet very fun activity. Learn about a mule named Sal while exploring the geography and trade routes of the Erie Canal!


Primary sources require active reading. Students apply knowledge of the historical context to gain perspective on the writer’s point of view and begin reading to uncover evidence. Students get to be like a detective gathering evidence to obtain a clearer picture of time period they are investigating. This excerpt from Captain Preston’s account of the Boston Massacre will help them understand point of view.


Here are just some of our K-5 Primary Sources for younger readers to start exploring:

Yankee Doodle
The Star-Spangled Banner
The Battle Hymn of the Republic  
Pledge of Allegiance
Wade in the Water
Letter from Abigail Adams
Declaration of Independence
Preamble to the Constitution of the United States
George Washington's Character

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From (A)rea to (Z)ero: 18 Quick Math Tutorials

Starting a new lesson and need a quick overview of the upcoming concepts? Or are you starting a new lesson and want students to quickly review prerequisite skills? Well, these 4-6 minute tutorials are just what you need.

Why are some numbers rational and some irrational? That’s an important question for all students to understand. The tutorial, Real Number Hierarchy, guides students through a comparison of the two types of numbers using examples.

Many students are familiar with the Pythagorean Theorem, but do they understand why the theorem is true? The Pythagorean Theorem tutorial animates a proof of the theorem using squares, and then shows them how to use the theorem in a real-world situation.


Pythagorean Theorem - Quick Launch #1351

Starting a lesson on probability? Use the tutorial, Basic Probability, to engage students in conversation. After students listen to a thorough definition of probability, stop the tutorial at the 1:33 mark and allow them to discuss in groups whether or not the probability can ever be greater than 1. Once students have discussed an answer, continue the tutorial’s explanation.


Basic Probability - Quick Launch #1400

Have you discussed triangle congruency and are now ready to discuss that corresponding parts of congruent triangles are congruent? Use the CPCTPC tutorial to explain how to use the statement to complete proofs and solve problems involving congruent triangles.

Each tutorial concludes with a short online quiz to check student knowledge—perfect if you want to use these tools as part of a flipped lesson or to check prerequisite understanding.


Every SAS Curriculum Pathways tutorial includes a short quiz.

Check out these other math tutorials.

Solving Absolute Value Equations
Midpoint Formula
Vertical and Horizontal Lines
Division by Zero
Simplified Radicals
Systems of Linear and Nonlinear Equations
Real-World Examples of Quadratic Functions
Evaluating Expressions
Area and Circumference of a Circle
Area of Triangles and Quadrilaterals
Surface Area of Prisms and Cylinders
Parallel and Perpendicular Slopes
Similarity and Proportions
Measures of Central Tendency

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