When students start out with any confusion at all with converting between congruence statements and equations, they struggle through each next step all the way through proofs. Take time to tackle this key skill before moving on.
As a geometry teacher, this pet peeve that would pop up over and over again: I'd be grading and see students mixing up their usage of congruent and equal in lines of a proof. Since I make kids write out separate lines for each step, including converting from a statement of congruence over to an equation with the measures, missing this was really messing up their scores, along with driving me crazy. Every class, with no exception, would continually mix these up for weeks on end.
Eventually, I discovered that it was worth taking time to explicitly teach this skill. We took a while to practice converting between the two types of statements. I explained how when you describe figures you use the term congruent, and when you are describing numbers you use the term equal.
We had to bother to take time showing how to switch back and forth between a statement like "length AB = length BC" while saying aloud "The DISTANCE between A and B is a NUMBER!" and a statement showing "SEGMENT AB being CONGRUENT to SEGMENT BC." Talk these through out loud before assuming that students can see the distinction. Practice converting back and forth before you allow them to actually use these statements in a Geometry proof.
Trust me, it is worth the time.
Otherwise, you’ll see hybrids such as <2 = <5 over and over again, which leads students to stumble between steps in their proofs.
It helps to display a Reminders poster, like the one below in the room.
Then, after practicing a few examples, we work on determining if a statement uses congruent or equal correctly with statements like the ones below.
Lastly, I’d pull up the answer key, and we would discuss why each statement was either correct or incorrect.
Here is a PDF dowload version for you if you'd like to use them too.
This really comes into play in examples like the following proof:
Students MUST convert from the congruent notation in the first line into an equation in order to use substitution later on in the proof. Segment addition postulate does not blend with congruent statements. It only works with statements of equality, since addition is required. To work in an equation format, which is necessary in many proofs, students need to be able to smoothly switch from congruence statements into equations and vice versa.
Hopefully these short little downloads and this tip will help you prioritize this skill and take 15 minutes now to save yourself many future headaches and give your students a boost to help them through proofs. What's your own pet peeve when grading proofs?
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Gen Z: Tips Customized Toward TODAY'S Teens and Pre-Teens
“Kids these days!”
Don’t be that adult. Although each generation is different, as teachers, we need to see both sides- the pros and the cons. We need to look past our own biases. Realize that even though teens and pre-teens exhibit differences from your generation, not all differences are negative. I’m sure our generation wasn’t all rainbows and butterflies as teens, either!
Julian Krinsky Camps and Programs shares the definition of Generation Z. “Generation Z refers to young people who were born between 1996 and 2014. This generation stands out from the previous generations – millennials and generation X – for a ton of reasons…”
So let’s dive into Generation Z! We’ll discuss what characteristics they exhibit, why they exhibit these characteristics, and how we can adjust our teaching to overcome the challenges and enhance the positive features.
Explanations of Characteristics of Gen Z
Today’s teens and pre-teens are full of characteristics- both good and bad. It’s important to lay it all out, so you can analyze them. See if any of these resonate with your Gen Z students’ characteristics, (Hint: they will), and how some of these characteristics are interconnected.
Greater Awareness of Technology
Let’s start with the obvious, and what first popped into your mind. It’s probably not a surprise to you to hear that this generation has essentially unlimited access to technology, so they have greater awareness and a greater understanding of how it works and can improve life. Pearson Education shares that “while Millennials used three screens on average, Gen Z students frequently use up to five. Most use a smartphone, TV, laptop, desktop, and a tablet. These devices occupy ten hours of Gen Z’s daily activity." TEN HOURS!
They understand technology, and use it constantly.
They were born with the internet, and will never know life without it. They have always had all the information they needed right at their fingertips. This segues us right to the next characteristic!
Need for Instant Gratification
Do your students turn in an assignment and expect it graded and handed back the next class period? This is because they are so accustomed to instant gratification.
Pearson Education talks about the way technology consumes Gen Z’s time. “The constant stimulation and access to all the world’s information at their fingertips has given them an eight-second attention span and has trained their brains to expect instant gratification.”
Even when analyzing their behavior as consumers, this generation demands instant gratification. “A few decades ago, quality was the most prized attribute. Then it became “quick and easy.” In the current environment, the demand is for “right now;” according to Huff Post.
Tendencies Toward Attitudes of Entitlement
You might recognize this trait in your own students. The Odyssey shares, “The biggest criticism of Generation Z would be that they are an entitled group of individuals who expect people to cater to them. They are often associated with narcissism and how their narcissistic entitlement leads them to believe good things will come their way because they are deserving of them. Some might also harshly label them as clueless as to how the real world operates.”
Not only do they want their assignments graded and handed back instantly, but they expect it. Of course, not all young people have this characteristic. But more and more, we need to specifically teach AGAINST this attitude in order to prevent it. Without being on guard for entitled attitudes and constantly addressing this, we as parents and teachers may allow kids to default to feeling entitled. Luckily, we can combat this by teaching gratitude.
Lack of Accountability
Do your students ever turn in work late, and expect it to be ok? This goes hand in hand with entitlement. Many students may expect you to cater to their needs.
The worst part is that sometimes even their parents encourage this behavior! I’ve had countless parents reach out to me, on behalf of their child, and ask for an extension. But for many students, this door does not swing both ways. Some expect teachers to have work graded immediately (pointing back to the instant gratification), even if they turned it in late. It can be really frustrating as a teacher to have a student walk up after only one class period has passed and ask whether you graded the work they handed in earlier that morning that was a week late! We know how often this happens in the current school atmosphere.
Ok, let’s get to the positives. We can certainly be aware of the above challenges and how serious they are, and we do need to address them. But the intent here is not to bash today’s children. They are wonderful people, and as much as we can criticize their deficiencies (in a very generalized way), we need to praise and admire their beauty!
This group has such promise in so many ways!
Desire to Make a Difference/Create Culture
I don’t know about you, but this trait makes me breathe a sigh of relief for the sake of humanity!
The Atlantic tells us Gen z has already shown evidence of an “active social conscience.” For example, Afghan teen Malala Yousafzai is an activist for female education around the world. At age 18, she became the youngest person ever to win the Nobel Peace Prize. There are many lesser-known activists, as well.
Read more about Malala here.
These kids and teens CARE about the earth. They have such a strong desire to see the world as a better place in the future. They know how to spring into action and take advantage of the web at their fingertips to use it to impact society.
Independent and Autonomous Tendencies
According to Julian Krinsky Camps and Programs, “they do not rely on their parents as much as previous teen generations did. The reason is that the internet and technologies allow gen Zers to start earning money at much earlier age than their parents.”
In fact, many don’t have a “typical teenage job,” but instead, have a creative side hustle. They do things like teach in-home piano lessons or review video games on youtube, etc. The opportunities are as extensive as their creativity!
By feeding their creative spirits, we can unearth the wonderful passions that will transform the world in the very near future!
Strengths in Visual Learning
Education Week shared an article on Gen Z’s preference for Youtube when learning something new. This signals a rise in visual learning; students find it easier to grasp concepts when they have a visual reference.
Expertise in Multitasking
Gen Z kids can scroll through instagram, send texts, gossip with a friend, and successfully study for a test all at once! Okay, that may be an exaggeration, but you get the idea. Basically, these kids are so accustomed to getting information and entertainment instantly, that they are excellent multi-taskers as a result.
How to Teach Gen Z
Teaching Generation Z requires thoughtful consideration to both adjust your teaching to overcome the challenges, and take advantage of their positive features.
Adjust to Overcome
“It's very simple, and it has improved my classroom management and instruction, and above all, my quality of life. Are you ready for it? Here it is:
I don't take late work.”
It’s simple, yet effectively solves the problem. This idea can span across various situations, like when students expect an assignment handed back instantly. Simply explain to them at the beginning of the school year that you will do your best to keep up with assignments and grading, you want them to succeed, but you have your own life outside of school. They will get it back whenever it fits into your schedule.
Take Advantage of Positive Features
Do you have any thoughts to add, or tips to share on teaching Gen Z? Feel free to share below.
If you do teach this generation, be sure to register for the free "Teaching Teens" email series - It includes information, advice, and resources that you can print and use right away!
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A class set of clipboards is one of the most underrated teaching tools out there. I want to share some of the ways to use them if you have them, and encourage you to get a set if you do not! These are so handy to have if you just get used to using them well.
Don't worry - I used to have no idea how valuable these are too! Years ago, a wonderful mentor teacher left me a set of 30 clipboards when I taught middle school. At first, I had no idea if I would ever use them. I shoved them in a closet and continued on with my day.
At the time, I had a couple of sixth graders who had what I called a "popping-up" problem. These two boys happened to be in the same class, and physically could not stay seated. They were great kids! It was not intentional, and eventually I started to feel bad for how often I'd have to say "sit back down!" They were very lovable and did not even realize it, but would suddenly be standing! Constantly.
The two who did this all the time would very sheepishly sit back down any time I pointed it out. They seemed to not even realize that their rear ends had left the seat. They just could not stay in the chairs! They'd be hunched over taking notes way down at the desk level.
Once I realized that they were just more comfortable standing, I gave up and accepted it. I just moved these students to the back row so everyone else could still see. Then, I remembered the clipboards. At least they could work without hunching way down to work at the low desk. Once I pulled out a couple of clipboards, suddenly I was finding uses for them everywhere!!
Another group of students loved to camp out on the floor right up close to the smartboard. I'd let them gather there, where they could see clearly and hear me easily when they asked. The clipboards started to come in handy again! I started leaving the whole basket out so that kids could grab them and sit (or stand) wherever they needed to.
I even started reaching for them when I needed somewhere to stack and layer all the different class periods of make-up quizzes. I found more and more uses for the set and started adapting!
Here are a few ways to use a set you may have lying around.
Clipboards are amazing for streamlining the make-up quiz process. During the regular quiz time, immediately label a blank quiz with the name of each absent student. Then, clip it to a board right away. Lay it along the chalk ledge with just the name visible. You can group and organize them by class period.
When students come in during recess time (or after school) to make up the quiz, you'll never again have to stop working with students you may be tutoring. The kids will know to come in, grab their quiz, and find a quiet place to work. No more fumbling around to find the right make-up quiz instead of focusing on grading, planning, etc. And BONUS! -- If you need to send one into the hall, they have a work surface already attached. No more dragging desks back and forth to the hallway.
If you slide the stack closer together so that only the names and class periods are showing, none of the quiz will be revealed ahead of time. You can even add a cover sheet to the top one.
If each student has a clipboard, you can spread out more for group work. Kids this age LOVE to sit on the floor. If you are trying some task card activities or scavenger hunt-style worksheets, clipboards will help a lot. Send one group to the back of the room and two to spread out in the hall, and suddenly group work is SO CALM!
During stations, scoot activities, games, etc. they will love not having to cart around a book to hold under their work. I even have learned to start color-coding groups of clipboards to kill two birds with one stone. Just hand out the clipboards, and you can have built-in partnering or grouping.
Being able to sit on the floor with a clipboard helped students even in cases I did not expect. Sending someone out in the hall to do missing work while everyone else goes over the answers used to mean dragging a desk out. Even after offering both options, I've yet to see a single student ever prefer a desk, surprisingly. I used to feel so bad having them sit on the floor until I realized how much they loved it. They sit in chairs all day and sometimes just need some variety. It can feel more relaxed for them to work lounging on the floor with a clipboard and finally get a break from the school chairs.
As we all know, middle schoolers are always begging to go work outside. This can be a pain and is sometimes asking for trouble. To make this work in situations were it was beneficial (like measuring shadows when doing scale, right triangles, etc.), I put blank paper on every clipboard, threw them all in a basket, and took everyone out with no hassle. All they needed was a pencil.
With doodle notes, it can get frustrating to carry coloring supplies around if you do want to do some chill doodle time outside with a new lesson. I've stumbled across a solution for keeping a few coloring tools on hand without dropping everything. Here's how I have adapted a brand new set of clipboards to make all these systems more perfect. Get ready for a fun project!
Ok, here comes the fun, crafty part!
To use the clipboards for grouping, it's nice to have colors, numbers, and symbols/icons (I used animals) on each. This way, you can group in different ways. I used stencils for both the pictures and numbers, but you can do stickers to keep it easier!
Groups of 4: Color-code. Students can gather into groups of four by color to work or complete stations. My set has 28 clipboards, so I grabbed 7 different paint colors. For this, I just used tape and number stencils. The foam dabbers work MUCH better than a brush for stenciling. Pro Tip: Keep your foam dabber super dry for trickier shaped stencils. Just dab over it lots of times with less paint, rather than soak it, or it will ooze through and make the stencil print messy.
Once you peel off the tape, you'll have both the coloring and the numbering done, if you do it this way. Remember, another option is to just use stickers or sharpie for the numbers, and you can add colored tape to keep it simpler. I was going for a fun, more bold graphic design, so I chose paint and arranged the tape differently to make each one unique. It does not have to be complicated. This was pretty quick for me, though, because with these little jars of paint, I did not pour anything. Just dabbed right into the jar for each one.
Two big teams: Sometimes, you need to split your class into two large groups. When you want to do this for a review game or something, have students with even numbered clipboards go to one side of the room, and students with odd numbers on the other. They can keep scorecards, notes, game sheets, etc. on their clipboard, and keep all other reference materials, calculators, phones, etc. out of the playing area. Having just the clipboard makes games run really smoothly.
Partners: So many math activities are perfect when done in pairs. Get the "math talk" going and team kids up! To pair up matching sets of clipboards, I stuck with my paint and stencil plan, but you could just use stickers instead. For mine, each pair of matching animals on the boards means those two students will work together.
Numbers: Just a side note, you can also of course just use the numbers to randomly call on a student, determine an order for presentations, etc. There are a lot of possibilities. You can also use these to have kids sign out a clipboard and see which one is missing.
Another note: I tried to make the animals "partner up" boards from two different color groups. That way, if you want to use both grouping options in the same day, everyone can keep their clipboard and still work with a totally different person.
Elastic Headbands: I use a clipboard myself all the time. Lately, it has been driving me crazy to try to carry my work along with a few pens or pencils. Especially with doodle notes, we need to have a handful of coloring tools right with the page, and even though clipboards are supposed to make this portable, I end up dropping the colored pencils. Or I try to line them up and balance them below the clip and tilt it just the right amount so they won't slide as I walk very carefully.
Sometimes, I even put my phone face down to "trap" the other end of my stack of colored pens. I finally found a little trick to help this frustration a bit. If you slip an elastic headband over the end, it will allow you to slide a little handful of colored pencils in and keep them somewhat secure to travel around with the clipboard. Usually, about 5 colors is enough for a doodle note page. I like to choose a coordinating color combo, and a lot of kids do too.
They can slide them right inside the headband and keep them handy. (Tip: Be careful if you use the headbands with the strip of clear rubbery silicone. Those would probably grip the pencils better but could also grip and rip the paper.)
Notice, you can tilt the page almost completely vertically and it still holds them pretty well! So handy for working on doodle notes together on the floor, in groups, spread out in the hallway, or even outside!
This particular set of clipboards is going to a teacher in need as part of my "Supply Sprinkle" where I am gifting materials and teaching tools to a math classroom that is lacking the funds they need. If you or someone you know could use this type of gift showering for their math classroom, apply here!
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