The Flipped Classroom Model Explained

What is a Flipped Classroom?

How to use the flipped classroom model to boost learning outcomes, motivation and engagement

What is a flipped classroom? In a flipped classroom, teachers facilitate collaboration and provide small group instruction instead of lecturing. (Image: Mashup Math via Getty)

An effective teacher should not be a sage on a stage, but a guide on the side. -Alice King

In the traditional classroom model, students typically spend the majority of their class time passively observing direct instruction and taking notes. Under this model, students typically have to wait until class is over to apply what they have learned to solving actual problems (usually in the form of homework assignments).

Conversely, the flipped classroom model reverses the traditional model in that students use technology to access direct instruction outside of the classroom and then spend class time working on practice problems and activities that require higher-level thinking, all while a teacher is present to facilitate and answer questions as they arise.

The flipped classroom model is built around the idea that class time—when a teacher is present—should focus on applying skills and working through problems (active learning), while direct instruction should be accessed outside of class time (passive learning).

What is a flipped classroom?

The flipped classroom model—which is driven by students watching a video lesson or slideshow presentation for homework and then spending the bulk of class time working on problems and activities—is transforming the role of a teacher in the 21st Century.

Additional benefits of the flipped model include more time for activities and collaboration, students being able to work at their own pace, and teachers getting to actually teach rather than delivering a prepared lecture over and over again.

The Flipped Classroom Model vs. The Traditional Classroom Model

Given the pros of the flipped classroom model—namely giving students more time to apply what they are learning to solving complex problems under the guidance of a teacher—you may be wondering how you can incorporate this style of instruction into your classroom.

First, it is important that you acknowledge that any teacher can successfully implement the flipped classroom model to some degree.

Are you ready to make the flip?

Getting Started with the Flipped Classroom Model

Flipped Classroom Motivation and Engagement: Students use technology to access direct instruction outside of the classroom. (Photo by Thomas Park on Unsplash)

If you are intrigued by the potential of flipping but are struggling with the anxiety of taking on the challenge or simply can’t figure out where to start—it’s easier and more doable than you think!

While the following tips do not encompass every aspect of effectively flipping your classroom, they will help you to overcome some of the fears and start you on the path to shifting the focus in your classroom from teaching to learning!

1.) You're Not Alone

Flipping your classroom can be intimidating and it’s important to remember that you are not in this alone. When you begin to experiment with the flipped classroom model, let your fellow teachers, administrators, students and their parents know what you are doing and, more importantly, why you decided to do it. People will be more supportive of your endeavor and more accommodating of any missteps if they know that your intention is to create a learning environment that is better suited to meet the unique needs of every student.

2.) Expect Some Resistance

Change can be challenging. You need to prepare yourself for resistance from students and parents who are devoted to traditional models of instruction. Such resistance can be overcome by informing students and parents why you have chosen to implement a flipped classroom model and how it can enrich the educational experience. The first few weeks of flipping may be shaky, but your commitment will pay off in the long run, as early resistors often become ardent supporters once they see concrete results.

Teachers often encounter some initial resistance when they first start implementing the flipped classroom model. (Photo by Thomas Park on Unsplash)

3.) Start Small

Teachers often avoid the flipped classroom model in fear of the time, effort, and energy it takes to completely transform all of their materials and lesson plans. For anyone who shares this feeling, here’s some good news—you can start small and flip only one unit or even just one lesson! Think about a unit or concept that is particularly difficult to teach and consider flipping only those lessons. If the experience is positive, then you can continue to flip future lessons as you move through the school year.

4.) Take Advantage of YouTube

Another source of anxiety for those who are considering flipping their classroom is the demand for creating video content. Many teachers either lack the time or are simply not comfortable with filming and editing video. Luckily, there are tons of high-quality and standard-based video lessons that can be accessed for free on YouTube. Some awesome examples include Mashup Math,  ASAP Science, and National Geographic.

Did you know that Mashup Math shares over 150 free animated video lessons on our YouTube channel?

5.) Use Some Tools

As the flipped classroom model becomes more popular, more tech companies are producing apps and software that is specifically designed to make the flipped classroom easier for educators. One particular application, WeVideo, is a simple, yet powerful, platform that allows teachers and students to create engaging educational videos. Adobe Spark is another effective video-creation app. Similar to Microsoft PowerPoint, you can use simple drag-and-drop skills to create captivating video lessons from your desktop computer or mobile phone.

6.) Use Student Feedback

If you're flipping for the first time, then prepare to make mistakes…lots of them! Plan time to debrief with students and to collect feedback. Implementing an experimental model will require frequent course corrections and student feedback will be valuable. Effective flippers have regular debriefing sessions with students to formatively assess their experiences and to dictate future instruction.

7.) Embrace the Challenge

Flipping your classroom will be a challenge and you can count on a few missteps along the way, but that doesn’t mean it’s not worth the effort! Remember that flipping your classroom is not about technology; it’s about transforming education and redefining the role of the teacher. Becoming a flipped educator will not diminish your role as an educator—it will enhance it.

And your students will reap the benefits of a superior learning experience, while you may just rediscover your love of teaching at the same time.

Effective flipped classroom teachers make time to debrief with students and to collect valuable feedback. (Image: Mashup Math MJ)

Flipped Classroom Motivation and Engagement

On a final note, the topic of how the flipped classroom model affects student motivation and engagement should not be ignored.

Recent studies support the idea of a flipped classroom motivation and engagement boost amongst students. (Image: Mashup Math MJ)

In fact, many schools adopt the flipped classroom model as a means of motivating and engaging struggling students who are underserved by traditional instruction methods. It is not surprising why many school improvement plans adopt some form of the flipped classroom model.

As more classrooms flip, more data is becoming available on the effectiveness of the flipped classroom model.

A recent study has concluded that, under the flipped classroom model, students across all grade levels were significantly more engaged throughout their courses with a continuously increasing trend, and that the previously lowest performing students had the largest percentage of improvement.

So, if you are looking to take advantage of the flipped classroom motivation and engagement boost and try a new way to reaching your students, the flipped classroom model.

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10 Formative Assessment Examples for Your Classroom

10 Formative Assessment Examples That Work

What are effective examples of formative assessments and how do they help teachers to gauge student learning?

Enjoy this collection of the most effective formative assessment examples and activities.

If teaching your students is a journey, then formative assessments are the trail markers that keep your lessons on the right path.

Teachers use formative assessments to gauge student understanding throughout the learning process. Unlike summative assessments (like midterm exams and final projects), the input from formative assessments empowers teachers to modify instruction early in the learning process so students can have a personalized learning experience that meets their individual and collective needs.

Formative assessments also have the potential to let students take ownership of their learning by helping them identify their strengths and weaknesses. The act of self-assessment allows a student to evaluate whether or not her effort is sufficient and to make adjustments accordingly.

The most common examples of formative assessments are the simple acts of asking questions and using responses to measure whether or not students are grasping the content.

For example, asking your class does that make sense? after explaining a concept is an example of a formative assessment. If the responses reflect a strong understanding, then you can take the material to a more challenging level. If the responses reflect a lack of understanding, you can backtrack and review. 

While questioning is a useful strategy, it often falls short of reaching the unique needs of a diverse group of learners, which is why teachers can benefit from differentiating the way they formatively assess their students.

However, not all formative assessments are effective at helping teachers to assess their students’ learning at any given point in time or at helping students to self-assess, identify how well they understand a topic, and know when to ask for help.

If you are looking for examples of formative assessments that actually work, then you’re in the right place. Below is a list of Formative Assessment Examples that you can share with students of any grade level to formatively assess a diverse group of learners in a way that is inclusive, engaging, and empowering.

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10 Formative Assessment Examples

Formative Assessment Examples #1: Mini-White Boards

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Formative Assessments Examples: Having students solve problems or answer questions and display their results on a mini-white board is a great way to instantly gauge understanding.

Formative assessment is used to gauge student understanding during the learning process. As a teacher, you need to be able to assess how well your students are grasping a topic or concept before deciding to move onto something more challenging or entirely new.

One of the best examples of formative assessments that are simple and easy to implement is the use of mini-whiteboards (or mini dry-erase boards) in your classroom. Students can write their responses to questions, and you can quickly walk around the room to see if your students are on the right track. Many teachers opt to ask a question, give students time to respond, and then have them hold up their dry-erase boards to instantly measure student understanding.

The instant visual feedback associated with these types of formative assessments will empower you to make changes to your lessons on the fly based on the needs of your students, which is why the use of mini-dry erase boards is one of the most popular formative assessment examples.

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Formative Assessment Examples #2: Emoji Self-Assessment

Examples of Formative Assessment: Students can use this emoji activity to self-assess how they feel about their current state of learning.

A good collection of examples of formative assessment must include activities that give your students opportunities to self-assess and make conclusions about how well they understand a topic at a given point in time.

When students have opportunities to reflect and self-assess, they are more likely to give feedback and to ask questions when they need help.

One of the most effective formative assessment examples in this guide is the Emoji Self-Assessment activity, which not only gives students a chance to self-assess, but it also lets a teacher know when her students are feeling confident, frustrated, confused, anxious, bored, etc.

This valuable input will allow you to make adjustments and to best meet the diverse needs of your students on an individual, small-group, and whole-class basis. The Emoji Self-Assessment activity is best used as an exit ticket during the last few minutes of class so you can review the responses and make adjustments to your next lesson.

You can click here to download our free Emoji Self-Assessment PDF Worksheet :)

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Formative Assessment Examples #3: Take a Poll (Digital)

Examples of Formative Assessments: Use polling software to instantly assess student understanding.

The next idea on our formative assessment examples list is digital polling (if you prefer non-digital examples, continue onto formative assessment examples #4 for a non-tech alternative).

However, if you work in a Bring Your Own Device (BYOD) school or if your students have access to digital devices in the classroom, then you can take advantage of free polling software that will allow you to ask questions and have students use a device like a smart phone, tablet, or laptop to submit their answers before seeing instant results.

This kind of input is imperative to effective data-driven instruction.

For example, take a look at the formative assessment examples below where Google Slides was used as a tool to poll student responses on two different questions (Situation A assessed understanding of prime numbers and Situation B assessed understanding of perfect cubes). Notice that, in Situation A, the majority of students answered correctly, which indicates that the class has a strong understanding of this topic, and that minimal review is needed. However, in Situation B, there is much more variety of responses and the majority of students answered incorrectly, which indicates that further review is needed.

Formative Assessment Examples: Instant feedback from polling helps teachers to decide when review is needed.

To get started using polling for formative assessment in your classroom, we recommend using Google Classroom. However, other free options include Survey Monkey, Poll Everywhere, and Kahoot.

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Formative Assessment Examples #4: Take a Poll (Non-Digital)

Examples of Formative Assessments: Polling Using Post-It Notes

If your students do not have access to internet and/or digital devices in your classroom, you can still take advantage of polling and the instant feedback it provides by using post-it notes.

These examples of formative assessment require you to post a question on the board along with several choices and then give each student at least one post-it note to write their answer/response/reasoning on (you may choose to give students multiple post-it notes if the question allows for multiple responses).

Once students have completed their response, they will stick their post-it note on top of or near their respective choice. Once all of the responses have been posted, you will have a useful visual representation of student understanding that will help you to decide how to best meet the needs of your students moving forward.

While the post-it formative assessment activity can be used at any time during a lesson, we recommend using it as an exit ticket activity where students post their responses on the way out of the classroom. This way, students have more anonymity, and they will be less inclined to change their answer due to peer pressure.

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Formative Assessment Examples #5: Venn Diagrams

Examples of Formative Assessments: Use Venn Diagrams to compare/contrast two or three topics or ideas.

When it comes to effective yet simple formative assessments examples, look no further than the Venn Diagram.

Venn Diagrams can be used to compare and contrast two or three topics or ideas related to whatever you are currently teaching. This formative assessment tool forces students to think deeply about topics and extend their understanding beyond basic knowledge of facts and definitions.

Additionally, formative assessment activities that are highly visual cater to students with a visual learning preference who typically struggle to express their understanding verbally or through traditional written responses.

By differentiating this way, students have the freedom to express their understanding without boundaries, and their responses are usually surprisingly creative!  

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Formative Assessment Examples #6: Create Your Own Questions

Formative Assessment Examples: Give students an answer and have them create their own question(s) related to the topic.

Looking for more formative assessment examples that give your students opportunities to be creative and gain a different perspective on whatever it is that they are currently learning?

The Create Your Own Questions formative assessment activity takes a Jeopardy-style approach to questions and answers where, like the host of Jeopardy, the teacher gives students the answer (or answers) and the students, like the contestants on Jeopardy, must respond with a question.

This type of formative assessment allows for higher-level thinking and creativity while simultaneously providing the teacher with valuable insights into how students are understanding and thinking about a given topic.

This formative assessment activity can be differentiated in many ways, and you can choose to have students provide only one question or three questions (easy, medium, and hard) as shown in the sample student response below.

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Create Your Own Questions: Sample Response

You can click here to download our free Create Your Own Questions PDF Worksheet Template

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Formative Assessment Examples #7: Exit Tweet

Formative Assessment Examples: Have students summarize what they have learned under the constraints of a 280 character-limit resembling a twitter post.

Examples of formative assessment that incorporate things that students are interested in—like social media—are great for boosting student interest and engagement.

For this activity, students are tasked with an exit ticket activity that requires them to summarize, in words, what they have learned under a 280-character similar to a twitter post (or tweet). The exit tweet activity forces your students to express the main ideas in a clear and concise matter.

The activity also forces students to carefully think about what they plan on writing before they even start because they must adhere to a character restriction that has real-world implications (since the same restrictions are placed on twitter posts).

You can click here to download our free Exit Tweet PDF Template (there are three exit tweets per page to help you save on paper; simply scissor-cut each page into three activities).

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Formative Assessment Examples #8: ELI5

Examples of Formative Assessments: Have students explain their understanding of a topic as if they were teaching it to a 5-year-old. (Image: Mashup Math MJ)

If you’re not acquainted with popular internet slang and acronyms, then you probably don’t know that ELI5 actually means “explain it to me like I am a 5-year-old.”

By teaching others what they have already learned, students can organize their thinking, express their thoughts in words, and identify any gaps in their understanding. These benefits are why many teachers have their students work in groups and teach each other what they have already learned—because it works!

Using ELI5 as a formative assessment is simple. Give students a topic and have them describe the key concepts, ideas, and procedures—in writing—as if they were teaching it to a 5-year-old.

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Formative Assessment Examples #9: Making Predictions

Examples of Formative Assessment: Gauge your students’ understanding of how topics are related by having them predict what they will be learning next.

Another important activity type on our formative assessment examples list is assessing how well your students understand how different topics are connected to each other and what direction their learning is going in.

One great way to gain insights into how students perceive the direction of their learning is to have them make predictions about what they will be learning next and explaining why they feel that way.

For the predictions formative assessment activity, simply have students express in writing what they think they will be learning next (based on what they have already previously learned) and explain why. You will likely be surprised by the depth of student responses, which will help you to give your students a more coherent and interconnected learning experience.

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Formative Assessment Examples #10: Thumbs Up / Thumbs Down

Formative Assessment Examples: The classic thumbs up/down activity is a great way to instantly gauge student understanding and how to proceed with your instruction.

The final formative assessment idea on this list is the classic thumbs up/down activity. This type of formative assessment requires the teacher to ask a question such as:

• Does that make sense to everyone?

• How do we feel about that last example?

• Are we ready to move onto a more challenging problem?

Then, students are instructed to respond non-verbally by raising one hand showing a thumbs-up, thumbs-down, or thumbs-sideways, each of which represent the following:

• Thumbs Up: I understand, I am confident, Yes

• Thumbs Down: I do not understand, I am not confident, No

• Thumbs Sideways: I am not sure, I partially understand, I am a little confused

While this may be the simplest of formative assessment examples on this list, the practice is incredibly effective as it gives you an immediate idea of how your students are feeling and whether or not you should take your lesson to the next level or backtrack and review before moving on—which is precisely what good formative assessment activities are supposed to do.

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More K-8 Math Resources You Will Love:

Why Am I So Bad At Math? (and How to Get Better!)

Why Am I So Bad at Math? (And How to Be Good at Math)

Why am I so bad at math? Harmful misconceptions about your ability to learn may be to blame. (Image: Mashup Math via Getty)

Why Am I So Bad at Math?

Learning math can be incredibly challenging and students who struggle with mathematics often question why math is so difficult and often conclude that they may not be capable of being successful in the math classroom.

Unfortunately, there is a harmful misconception about the ability to understand math. Over 50% of people in the United States ages 18 to 34 say that they can’t do math according to a conducted by Change the Equation.

It’s no wonder why so many people learn to accept a false idea that understanding math is reserved only for “math people.”

So, before you conclude that the answer to the question why am I so bad at math? has something to do with you being unable to learn math no matter how hard you try to improve, understand that the cause of your frustration and struggles is more likely due to negative misconceptions about math than it is about your ability to learn.

Sadly, these misconceptions are often passed down to children from parents who also struggled with mathematics when they were students. In fact, children with parents who have math anxiety underperform in math compared to children whose parents are not math anxious according to a study by the University of Chicago.

The “math person” misconception leaves lower achieving students feeling disinterested, frustrated, and unable.

Such harmful misconceptions and the idea that only certain people are capable of understanding mathematics are also product of traditional teaching methods that focus entirely on fixed outcomes, like letter grades and standardized exam scores. Students who do well on exams are labeled as “smart” and those who perform poorly are led to believe that they are not.

Many students learn to believe that they are not capable of being successful in math. (Image: Mashup Math via Getty)

Under so much pressure to perform and general anxiety surrounding the subject, it’s no wonder why so many students feel like they are unable to learn math and avoid the subject at all costs.

But giving up on math is not a good option in the big picture. More and more desirable jobs require a high degree of math fluency, understanding, and comfort. Careers in STEM (science, technology, engineering and math) are the fastest growing sector of jobs in the United States. However, 35% of all bachelor’s degrees in STEM in the United States are earned by nonresident aliens, according to a study by the department of education.

What can you do to change the situation? If you are wondering, why am I so bad at math? The fault is likely due to you having a fixed mindset for learning, which is often a product of being negatively affected by harmful misconceptions about your ability to learn math.

A Fixed Mindset is based on the idea that you only have a limited amount of intelligence, and no amount of hard work or effort can lead to improvement. With a fixed mindset, you believe that looking smart is more important than learning new things and that having to try hard means that you have low natural ability. Under this mindset, you are easily discouraged and afraid of taking on new challenges out of fear of making a mistake.

Does this sound like you? If you are feeling discouraged and questioning why am I so bad at math?, then you may be struggling due to a fixed mindset.

However, there is a path to how to be good at math, and it starts with a shift from a fixed mindset to a growth mindset.

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How to Be Good at Math? Mindset is Everything

How to Be Good at Math

Students who struggle with math are often not held back by their ability, but by their mindset for learning.

The truth about learning math is that, just like learning how to read, every student is capable of understanding mathematics. We need our students to approach math with a growth mindset that values learning over intelligence and effort over final results. 

With a Growth Mindset, you value learning new things over appearing smart. With this mindset, you see growth is equated with success and challenges are embraced as new opportunities to learn. When you approach math with a growth mindset, you learn to love solving problems and you celebrate your mistakes because you know that they are necessary steppingstone along the path to learning.

The idea of a growth mindset was pioneered by Stanford University Professor, Carol Dweck. Her studies have shown that students who believed that their ability and intelligence could grow, and change outperformed those who thought that their ability and intelligence were fixed.

Dweck’s research has shown that increasing focus on the process of learning, rather than the outcome, helps increase a student’s growth mindset and ability.

How can YOU embrace a growth mindset for learning math? You can start by learning more about growth mindsets and applying the key concepts to your everyday life. Anytime that you are trying to learn something new, approach the situation with an open mind, a belief that effort and making mistakes is necessary for learning, and without a fear of failure or not looking smart.

It may take time to develop this new mindset for learning, but the payoffs just may take you from thinking that you are bad at math to believing that you are becoming better and better every day.

If you want to learn more about developing a growth mindset, click here to learn more about the fundamentals of a growth mindset (and how to overcome a fixed mindset) and watch the above video of Stanford Professor and Researcher, Carol Dweck, presenting on Growth Mindsets and the Power of Yet.

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How to Help My Child with Math at Home

How to Help My Child with Math at Home: 7 Tips

How to help my child with math at home. (Image: Mashup Math via Getty)

Many parents want to understand how important mathematics is for their child’s future and they genuinely want to excel in the subject.

But many parents also struggled with mathematics when they were students, and they don’t feel confident in supporting their child’s math learning outside of the classroom.

In fact, studies show that parents with math anxiety can actually undermine their children’s math achievement by spreading their negative attitudes towards the subject to their kids.

When parents push too hard, their child can feel overwhelmed and stressed. When parents are too hands-off, then their child may not value the importance of mathematics at all.

As a result, far too many students learn to view math as a chore instead of an invaluable life skill.

If you are a parent wondering how to help my child with math at home, then the following tips will help you to support your child’s math learning and prevent you from passing on any negative attitudes or math anxiety.

The following collection of tips will not require you to spend hours relearning tricky elementary math topics like the order of operations or simplifying fractions. Instead, the focus will be on developing a positive attitude for learning mathematics combined with a reliable support system to ensure that your child continues to pursue math education beyond the point where many give up.

How to Help My Child with Math at Home

Tip #1: Keep Your Cool

How to help your child with math at home: There is a growing body of research suggesting that playing games can support the development of mathematical thinking skills. (Image: Mashup Math MJ)

The idea that only certain people are capable of learning math is a harmful misconception.

The idea of being a math person has caused an extreme amount of damage to student attitudes and has given many of them an excuse to quit learning mathematics prematurely.

This idea, however, is simply untrue. Just like it is completely reasonable to expect every student to become skilled in reading and writing, we can expect every student to be able to think and solve problems mathematically.

While you may have fallen victim to out-of-touch teaching practices that failed to meet your needs as student and, as a result, have adopted this belief that you are simply not a math person, it does not mean that your child has to suffer the same fate.

A recent study showed that sharing negative feelings with our children can severely increase anxiety and degrade their attitude towards learning math. Education has been continuously evolving over the past few decades and no longer resembles the environment that many parents were exposed to.

Modern students think about and learn mathematics in very different ways. Parents do their children a disservice when they impart their negative experiences about math education onto them.

If you want to help your child with math at home, then you need to leave your past negative experience with mathematics behind and approach the situation with an open mind.

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Tip #2: Understand the Purpose

How to Help My Child with Math at Home: Help them understand why math is important. (Image: Mashup Math MJ)

Just because you do not remember the ins-and-outs of fractions or even algebra does not mean that you cannot support your child with math at home.

It is, however, necessary that you reinforce why learning math is useful and advantageous. When you say things like “you are never going to use this in life,” your children respond by devaluing the skills they are learning.

While your child will likely never have to simplify a square root in the real world, he or she will have to solve complex problems. To be successful in life, students must develop into creative problem solvers who can think critically and mathematically.

If you want to help your children with math at home, then you need to help them to understand why they are learning it in the first place.

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Tip #3: Hire a Tutor

Studies show that children who meet regularly with a tutor have reduced math anxiety. (Image: Mashup Math MJ)

Wondering how to help your child with math at home? Hiring a tutor is a good place to start.

This tip for supporting your child’s math education may seem obvious, but many parents do not fully appreciate the impact that a one-on-one tutor can have.

NPR recently reported on a study that focused on the effect of one-to-one tutoring relationships on student anxiety and math test scores. The conclusion of the study was that students who had regular meetings with an individual tutor had significantly lower levels of academic anxiety than students who did not. Students with a one-to-one tutoring relationship were also better able to get through areas of difficulty without becoming discouraged.

Hiring a private math tutor for your child can have huge benefits, but it can also be cost- and time-prohibitive for many, which is why the next tip offers an effective and more accessible alternative.

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Tip #4: Build a Relationship with Your Child’s Teacher

How to Help My Child with Math at Home: Stay in touch with your child’s teacher by phone or email on a bi-weekly basis. (Image: Mashup Math MJ)

One thing that every parent can do to support their math education at home is to establish consistent and positive communication with their child's teacher.

Why? Because staying in tune with what your child is learning and being aware of how he or she is responding to classroom instruction will help you to understand where and when support is needed.

Most teachers have regularly scheduled before or after-school hours (which is essential free private tutoring) for your child to gain extra help and small-group or even one-on-one instruction.

Additionally, teachers tend to give more attention to students whose parents are more involved.

This extra attention is not a matter of treating students unfairly, but when a teacher regularly communicates with one of her student’s parents, then, as a result, she starts to spend more time thinking about ways to better meet that student's individual needs.

Parents should be aware that teachers have limited time and refrain from bombarding them with phone calls and emails. A weekly or bi-weekly phone or email conversation is perfectly sufficient, in most cases, for establishing regular and meaningful communication. 

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Tip #5: Use Online Resources

How to help your child with math at home: Virtual Math Manipulatives (or digital hands-on activities) are a great resource for exploring difficult math concepts in a visual way at home. (Image Source: Mashup Math MJ)

Many parents do not take advantage of so many helpful free online math resources made specifically for children.

One math resources—ranging from practice worksheets to virtual hands-on activities to animated video lessons—give children opportunities to explore and learn difficult math procedures and concepts and procedures at home.

Here are a few links to free online math resources that you can start using with your child at home today:

• Free Virtual Math Manipulatives Library

• Free Animated Math Video Library for Grades K-8

• Free Math Puzzles and Worksheets (with Answer Keys)

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Tip #6: Gamify

How to Help My Child with Math at Home: Utilize hands-on activities—like building fraction kits out of construction paper—as opportunities to explore and learn math at home. (Image: Mashup Math ST)

There’s to practicing, exploring, and earning mathematics than completing worksheets.

There are tons of benefits to working on hands-on activities that are fun, engaging, and powerful opportunities for your child to explore challenging math concepts and build meaningful conceptual understanding of topics like fractions, probability, and geometry.

While even activities like Sudoku puzzles or building structures using Legos can help your child to develop problem solving, creative thinking, and spatial awareness, there are even further benefits to hands-on activities specifically designed to help your child to develop math skills through play.

Here are a few links to fun hands-on math activities that you can start using with your child at home today:

• Building a Fraction Kit at Home

• Exploring Area and Perimeter Using Cheez-Its

• Starburst Probability Activity

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Tip #7: Become a Student Again

Your child can deeper her understanding of math concepts by teaching them to you at home. (Image: Mashup Math MJ)

 One of the best ways to better understand something is to teach it to someone else—and mathematics is no exception. This idea is often used to support the use of peer tutoring, where teachers group struggling students with higher performing classmates.

When you have to teach something to someone else, then you have to stop and think about the best way to express your understanding, which ultimately strengthens your grasp of the material.

As a parent, take advantage of these benefits by allowing your child to teach you what they have learned in school. Work through practice problems together and ask thoughtful questions. In this role reversal, your child will be the teacher and you the student.

You may just be pleasantly surprised by how much of a difference such a simple practice can make on your child’s academic development. 

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How to Factor a Trinomial in 3 Easy Steps

How to Factor a Trinomial in 3 Easy Steps

 Learning how to factor a trinomial is an extremely important and useful algebra skill, but factoring trinomials can also be very tricky.

This free How to Factor a Trinomial step-by-step guide will teach you how to factor a trinomial when a=1 and when a does not equal one (more on what a refers to later) using a simple three-step process.

Before you learn how to factor a trinomial, let’s do a quick review of some very important vocabulary and definitions related to trinomials.

Trinomial Definition

A trinomial is a polynomial that has three terms. The first time is an x^2 term, the second term is an x term, and the third term is a constant (just a number).

Furthermore, when discussing trinomials, you will see references to vales for a, b, and c., where:

a = the x^2 term coefficient

b = the x term coefficient

c= the constant value

For example:

For this trinomial: a=1, b=5, and c=6.

Note that, when a=1, the coefficient will not be written in front of the x^2 term.

Factoring Trinomials: a = 1

For the first few examples, let’s learn how to factor a trinomial when a, the leading coefficient is 1.

How to Factor a Trinomial Example #1

For the first example, let’s factor the trinomial: x^2 + 6x + 8

Again, note that a=1 in this example.

Now let’s factor the trinomial:

Step 1: Identify the values for b and c.

In this example, b=6 and c=8.

Step 2: Find two numbers that ADD to b and MULTIPLY to c.

This step can take a little bit of trial-and-error.

For instance, you could pick 5 and 1 because 5+1=6. But 5 x 1 does not equal 8, so these numbers would not work.

However, if you chose 4 and 2, you could easily confirm that:

4 + 2 =6 (the value of b); and

4 x 2 = 8 (the value of c)

Step 3: Use the numbers you picked to write out the factors and check

For this example, the factors would be (x+2) and (x+4)

Final Answer: (x+4)(x+2)

You can check your answer by multiplying the two factors (binomials) together to see if the result is the original trinomial as follows:

Notice that 2x and 4x are like terms that can be combined.

Multiplying the factors results in the original trinomial.

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How to Factor a Trinomial Example #2

Let’s get more practice factoring trinomials when a is 1.

Factor: x^2 + 9x + 20

Step 1: Identify the values for b and c.

In this example, b=9 and c=20.

Step 2: Find two numbers that ADD to b and MULTIPLY to c.

Finding the right numbers won’t always be as easy as it was in example 1.

To make factoring trinomials easier, write down all of the factors of c that you can think of.

In this case, c=20, so:

20 x 1 = 20

10 x 2 = 20

5 x 4 = 20

Remember that the two numbers have to multiply to c AND add to b.

The only factors of 20 that meet both of these requirements are 4 and 5.

Step 3: Use the numbers you picked to write out the factors and check

The last step is to write out the factors: (x+5)(x+4)

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How to Factor a Trinomial Example #3

Factor: x^2 - 5x -24

Notice that this example includes subtraction signs, but the process of factoring is still the same.

Step 1: Identify the values for b and c.

In this example, b= -5 and c= -24.

Step 2: Find two numbers that ADD to b and MULTIPLY to c.

Again, you have to find two values to ADD to -5 and MULTIPLY to -24.

This step can get tricky when you’re dealing with negative numbers. Remember that a negative times a negative is positive, so only one of the values can be negative if the product has to be -24.

After writing out all of the possible factors, you can conclude that:

-8 x 3 = -24

and

-8 + 3 = -5

Step 3: Use the numbers you picked to write out the factors and check

The last step is to write out the factors: (x-8)(x+3)

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How to Factor a Trinomial when A does not equal 1

How can you factor a trinomial when the leading coefficient does not equal one? This free video tutorial will show you how:

How to Factor a Trinomial Using the Completing the Square Formula

Finally, there is an alternate method to factoring a trinomial that is called completing the square. This method applies to factoring quadratic equations (when a trinomial equals a value, namely zero).

You can learn more about factoring using the completing the square formula by checking our free step-by-step guide.

This Complete Guide to the Completing the Square includes several examples, a step-by-step tutorial, an animated video mini-lesson, and a free worksheet and answer key.

Click here to access a free Completing the Square step-by-step guide.

Conclusion: How to Factor a Trinomial

You can factor a trinomial of the form ax^2 + bx + c, when a=1, by using the following 3-step method:

Step 1: Identify the values for b and c.

Step 2: Find two numbers that ADD to b and MULTIPLY to c.

Step 3: Use the numbers you picked to write out the factors and check

Please review the above examples, watch our video on how to factor a trinomial when the leading coefficient, a, is not 1, and check out our free guide to factoring by completing the square.

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