## The Human Number Line

Today I’m sharing a fun activity that I like to do with my students at the beginning of the year in Algebra 2.  At the beginning of the year, I teach about subsets of real numbers.

First, get a stack of blank index cards.  I choose as many cards as I have students, so that everyone can participate.  Then, I write numbers in all forms on the cards.  Notice that some numbers that are the same, just written in a different form (ex. 1/4 and 0.25).  Also include radicals that aren’t reduced (with perfect squares as the radicand) and irrational numbers.  Really, you can do anything you want.  This should take you about 5 minutes.

Human Number Line
During class, give each student a card.  Then, direct them to put themselves into a number line.  I usually tell my students where zero is and which direction is positive and which direction is negative.  This helps the students get organized faster.

Once the students think they are in order, I start asking them questions.  I make sure I ask questions about repeating decimals.  I also ask about which number being bigger, pi or 3.14.

You could also only make half the amount of cards and have the students without cards direct and “coach” the students with the cards.

Sets of Real Numbers Sorting
Then, I have the students sort themselves into groups by their card.  First, I have them move into rational and irrational numbers.  Then, I’ll have them move into other sets (integers and non-integers, etc.).

If I have a class that seems very bright, I may try to stump them.  I’ll give them categories like real numbers and integers.  Students that are paying attention won’t know which category they fall into.

This is just a fun idea that helps liven up class at the beginning of the year.  It takes very little prep work, but gets the students talking.

## Math Teachers at Play #89

Welcome to the 89th edition of Math Teachers at Play (MTaP) Blog Carnival!  MTaP is a monthly blog carnival with a collection of tips, games, and activities for teachers of students of all ages.  If you haven’t seen the carnival before, you can read the previous posts.  I also hosted the 82nd edition.

89 is…
• the 24th prime number
• a Fibonacci number
• a Pythagorean prime
• the atomic number of actinium

89 appears in TWO Pythagorean triples!  Comment if you know what they are :)

Now, for the posts!

## Elementary Concepts and Arithmetic

Leigh, from the Applicious Teacher, explains a technique for helping students solve multi-step problems.  She also shared an interactive notebook idea to support the lesson.

Students always seem to panic when they see fractions.  Scipi uses pattern sticks to help students reduce fractions without the panic.  They can also be used to change improper fractions to mixed numbers.

Brandi, from The Research Based Classroom, shares a fun game called Help Your Neighbor.  It is a game that helps students practice adding numbers from 1 to 12.

## Beginning Algebra and Geometry

Scipi explains in her post why FOIL isn’t the best way to teach students to multiply binomials.  FOIL only works in the special case of multiplying binomials.  Scipi proposes an alternate method that works when multiplying any polynomials.

I always spend some time in Geometry with optical illusions.  This post explains why.

A post on Leaf and STEM Learning explains the faults with teaching PEMDAS.  An alternative mnemonic is shared with a foldable that can be used in interactive notebooks.

Envelopes
The National Curriculum in England and the Common Core in the US both require students to develop Fluency, Reasoning, and Problem-Solving.  Alan Parr shares an old activity made new and relevant.  It has proved successful in stimulating high-quality discussion which benefits all three.  You can follow Alan on Twitter:  @piogold

Ellie, from Middle School Math Moments, shares a discovery activity for teaching slope.  Students were asked to find relationships between equations and graphs.  She even shares the handout she used in class.

Jonathan Claydon from Infinite Sums gives a great explanation of how he teaches polar coordinates in Pre-Cal.  Not only does he explain how he teaches the lesson, but also gives activity ideas and links a great video.  If you’re teaching polar coordinates this year, you need to check out this post.

Need an idea about teaching linear regression?  Jean from Flamingo Math explains how she uses TI-84 calculators to help explain linear regression to her students.

## Mathematical Recreation

On the blog Everything Education, a fun idea is shown that can help students think creatively.  Obviously false mathematical statements can be given, and students must come up with situations where the statement might be true.  Read the post to find out more.

Denise from Let's Play Math shares a number puzzle.  What pattern can you find in the number puzzle?  Every answer is right - just be sure to explain your reasoning!  You can follow Denise on Twitter:  @letsplaymath

Do your students love Minecraft?  Rachel K shares a list of activities and games on Minecraft that can reinforce mathematical concepts.  There are lots of ideas from basic addition to area and perimeter.

Creative Cake-Cutting:  Divergent & Convergent Problem-Solving
This post by Maya is based on a non-routine problem about cake-cutting.  Two distinct solutions are presented, and various questions about their makeup are presented.  There is a little something for anyone involved in math with this post.

If you want to include math history in your classes this year, Birgid from Math Giraffe has you covered.  She will be tweeting out facts every Friday so that you can have them prepared for the upcoming week.  Read her post to find out more!

5 Math Gems #36
Jo shares part of a series of gems posts which share five math teaching ideas.  THis post features an area maze, warm-ups, Desmos activities, pixel puzzles, and a Geogebra tool.  You can follow Jo on Twitter:  @mathsjem

Randi, from 4 the Love of Math, relates her fear of public speaking to student’s fear of math.  Math is important.  She explains how teachers can help students overcome their phobia.

My Top 7 (+1) Math Activities
Laura is a new(er) blogger who has some fantastic ideas on teaching middle school math.  In this blog post she shares some of her favorite class activities.  Many of these could be adapted for high school as well.  You can also check her out on Twitter:  @lauriebworthy

Task cards are great and keep kids engaged.  If you need any ideas on how to use task cards in your classroom, these two posts may help.  You may find a new idea to try this school year!  You can follow me on Twitter:  @mrseteachesmath

Jennifer from Teaching High School Math explains a technique for helping students become more proficient about explaining mathematical ideas.  Students have a hard time explaining math and these ideas can help!

The Carnival of Mathematics is another blog carnival that you may enjoy.  You can check it out here.

I hope you enjoyed this issue of Math Teachers at Play!

## Sets of Real Numbers Interactive Notebook Page

In my curriculum, one of the first few lessons in Algebra 2 Honors was about the subsets of real numbers.  If I were teaching this again, I would use this interactive notebook page.

I always teach the subsets of real numbers using a diagram.  It makes it SO much easier to understand.  I’ve used this color-coded diagram in the past, and it works well.

I like to give my students the formal definitions and show them the notation.  Since I had honors students, I would use the capital letter notation periodically so my students would get used to it.  If I were doing this in class, I would give my students the definitions and verbally give them a few examples.  Then, I would have them discuss with their partner to write down their own examples.

I usually follow up this short lesson with an activity or a little Algebra 1 review.

## The First Day of School 2015

This post contains an Amazon Affiliate link.  This does not effect you in any way.  However, if you make a purchase through this link, I receive a very small commission.

I’ve written about my typical first day of school before, but I thought I’d go into more detail this year.  Since I’m not actually going back to school this year (I’ll be on baby-coming-any-day countdown!), I am sharing what I’ve done in the past and how I would change it for this school year.

I always have assigned seats for my students as they walk into the classroom.  I’ve tried having student’s names written on cards and putting them on the desks between classes  (kind of like they do in elementary school).  Yeah, don’t do this, it takes forever and the kids can switch the name cards.  I’ve also tried having a seating chart projected or posted on the board and having the students find their own seats.  It works a little better, but first day anxieties don’t mix very well with reading diagrams.  I’m still looking for the perfect solution to this problem.

Then, I stand at the door and shake hands with every single student as they walk in.  Think of it as a good immune system jolt for the school year.  If it really freaks you out, squirt some hand sanitizer when the bell rings.  I got this idea from The First Days Of School: How To Be An Effective Teacher by Harry Wong.  Great book, good ideas.

As the students come in, I have something posted on the board with the class, room number, and directions.  This is what I had posted on the board last school year.  Our school colors were blue and white :)

I would use the same homework assignment that I used last year.  I loved it!  It is a free download in my Teachers Pay Teachers store.  Basically, the students tell you about themselves using numerical expressions.  I would have them start working on it at the beginning of class, and whatever they didn’t finish would be homework.

I always briefly go over expectations on the first day of school.  It was something I always expected as a student, and I feel like it’s less stressful for the students to at least give them a hint on the first day.  Then, I would launch into a brief lesson about patterns.  I’ve used this powerpoint before, but never on the first day of school.  This could also be related to any high school math class, which is nice.  The first day is exhausting enough, it would be easy to use the same lesson for each prep, but relate it to the students in different ways.

Some of the patterns are pictures, some of the patterns are mathematical, and some are just for fun :)

This pattern is my favorite.  It always takes my students for-ev-er before anyone starts to get it.  I give them hints along the way.  Most students stare or try to make it make sense mathematically, but that’s not how this pattern works.

Three
One Three
One One and One Three
Three Ones and One Three …

If I have time at the end of class, I would have students come up with their own pattern and write it on the back of their homework sheet.

I avoid the name game type stuff and the “go around and introduce yourself” activities.  I HATED them as a student and dislike them as an adult.  So, I try to help out the quiet kids and not freak them out on the first day :)

What are you planning to do on the first day of school this year?

I hope you discover a few new boards to follow!

## First Day of School Ideas

As the first day of school approaches, I thought it would be nice to share some tips for the first day of school.  I’ll share some tips that I have, but I also asked around and will share some tips from friends around the internet!

Tips for the First Day of School

Greet the kids! Just like them I am that crazy combination of nervous and excited, and I just can't wait for the year to begin!

I love to get know my students, we all take turns telling each other what we did during the summer.  I love to play music in my class, and play games like silent ball!

Wear comfortable shoes!  You likely haven't been on your feet as much over the summer as you will be on the first day of school.
Mrs. E Teaches Math

I like to play the game "2 Truths and a Lie."  Everyone tells three things about themselves, one of which is made up.  The tale-teller gets a point if no one guesses the lie accurately, the guessers get a point if they manage to identify the lie.  I always go first with three interesting stories, so everyone doesn't just do boring stuff like "I like green. I like red. I like orange."

I always skip the syllabus on day one and do a crafty get-to-know you activity such as a collage or artifact speech.  It breaks the ice, sets the tone, and is way more interesting than a lot of things they do in other classes.  My AP Lit kids get reading homework :)

My favorite thing to do on the first day of school is memorize my students' names while they are working on a short "All About Me" activity. When the whole class has finished the assignment, I stand at the front of the class and identify each student by name before asking any of my students if they want to try. Some of my students are freaked out by the fact that I am able to learn their names so quickly, but it really sets the foundation for building a sense of community in my classes.

I give a small homework assignment on the first day, worth only a few points.  I think it sets the tone for my class and lets them know that we are there to work.
Mrs. E Teaches Math

In the classroom my class always makes a little version of themselves then we hang them up for rest of the year that way they know they are part of the class from day one.
I always plan an outfit that goes with my room theme for the first day.
We also have take out to make it a little easier on everyone at home.

I explain to my students there is only 1 rule in my classroom, which is to respect yourself and others. Together in each class, we fill out a graphic organizer discussing examples and non examples of what this looks like. It really helps set up expectations for the year in the classroom.

Play music: I like to set the tone and energy for the year. Begin by building good will and relationships so you will have the foundation you need to push your students to their very best.

I always give assigned seats on the first day.  It helps students know what to expect and sets the tone for the class.
Mrs. E Teaches Math

Play a variety of team and class building games to start building our classroom community!

I love to spend most of that session getting to know students and surveying their multiple intelligences to create an interest inventory. Then I connect their interests to the course content in tangible ways that ensure they get more from my classes.

...the name game!  The first person states his name and one thing he loves, the second person repeats that and adds her name and one thing she loves...  With a sharp class, you can ask everyone to change their seats (after the first full round) and see who volunteers to name everyone.

My favourite thing is to meet my new students.  It's always a little stressful, but it's also a real high.  I love my summers, but I'm always anxious to get back with the kids.

I like to stand in the doorway and greet each student as they walk in my classroom.  I usually shake each student's hand and introduce myself.  I feel like it shows them respect and helps some of the kids feel a little more relaxed.
Mrs. E Teaches math

I always give my students this Student Interest Survey, which can be downloaded for free here.  This tells me what their interests are, what they don't like, or don't feel like they do well, etc.

I get up and go for a run before school. This is probably the only time that will happen all year! It gives me a chance to clear my head and the first-day jitters (yes, teachers get them too), and focus. It also gives me energy to get through my day after a summer of staying up late and sleeping in!

Wear matching outfits with my collaborative teaching partner....SHE HATES IT!  I think her loathe for coordinating colors makes me love it all the more :)

I like to start off with an inquiry investigation to get them thinking about science.  The next day is when I do procedures and class expectations.  I don't have rules anymore.  I tell them that by now they have been in school long enough to know the basic rules of the school and a classroom so we work together on coming up with procedures and expectations that will help make the classroom a positive learning environment.  This puts the ownership back on the student.

Make any copies you need for the first couple of days at the beginning of inservice.  Lots of teachers wait until the end of inservice and the lines for the copy machine can get long.
Mrs. E Teaches Math

Each year I write my students a letter about me and my hopes for the coming year.  In return each student writes me a letter.  It is due the following day.  This activity gives me a quick insight into their writing abilities and gives me a glimpse of each student.

I hope you've found a tip or two that you can use for the beginning of your school year!

## Conditional Statements Interactive Notebook Page

I really like teaching Conditional Statements in Geometry.  This lesson is usually the first lesson in my short logic unit.  I actually spend a day or two on this and do lots of fun activities.

If I were teaching this lesson this year (I’ll be home with a newborn!), this is the interactive notebook page that I would use.  The foldable at the top of the page is from my Teachers Pay Teachers store.  I like having this foldable a little smaller, so that I can fit an example at the bottom of the page.  I didn’t lose any content by making it smaller, the font size is just a little smaller.

I like to color code the examples in this lesson.  I think it helps the students see exactly what is happening.

Notice that the example at the bottom of the page already has “not” in the statement.  I think this really makes the students think about what negation means.  Some of them want to have the statement say “not not”, because they just want to follow a rule.  I think this example helps them understand that the meaning of the sentence changes.  If I were teaching advanced students, I think I would make the example something like “Ants are insects.” and also have the students write the conditional statement.

Once I teach this lesson, I really like having my students play my I Have, Who Has Conditional Statements activity.  I usually split my students into teams and have them race against each other.  It’s a fun game that can be played several times in different ways.  I wrote a blog post where you can read about how I play it in my classroom.

I hope this helps you come up with an idea for your own geometry interactive notebook!