Math Teachers at Play #82

Welcome to the 82nd 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, I would encourage you to read the previous posts.

First, some information about the number 82!

82 is...

•  the product of prime numbers 2 and 41

•  a happy number

•  the atomic number for lead

•  the international direct dial code for calls to South Korea


Now, on to the posts!

Elementary Concepts and Arithmetic

7 Ways Kids Can Learn to Make a Graph - Anna, from The Measured Mom, shares 7 Ways Kids Can Learn to Make a Graph.  She shares ways she teaches her young children about bar graphs using toys, food, and coins.

Math Games with Dice - Help students practice their math skills with dice!  Rachel K, from Rachel K Tutoring, gives 18 ideas for fun educational dice games.

How to Teach Homeschool Addition with Understanding - Some homeschool moms tend to think that the only way to master the math facts is to memorize and drill.  Kate from Kate's Homeschool Math shares a more interesting and effective way to tackle one set of math facts that can be difficult for kids.  Bonus:  There's a free printable!

Unlocking Fractions for the Confused and Bewildered - Scipi has shared her tips about teaching fractions on her blog, Go Figure!  Scipi has been teaching math “since the earth cooled” (her words, not mine) and currently teaches math at the college-level.  Even in college, students are still scared of the dreaded F-word (FRACTIONS!).  Her tips can hopefully help contribute to the cure of math-phobia.

Using Clothespins in Math - Jen, from Runde's Room, used clothespins to help students understand fractions.  Students hung the clothespins on a number line for a great hands-on lesson.

Cuisenaire Squares - Simon, from Following Learning, used cuisenaire rods to help students investigate number patterns.  This post also explains how Twitter can be a great place for teachers to connect and share ideas.

Multiplying by 10: Why you can 'just add zero'  - Students must understand why tricks work, and not just blindly follow them.  This post by the Digi-Block does a great job explaining why you can 'just add zero' when multiplying by 10.  

Beginning Algebra and Geometry

Awesome Quadrilateral Project - This year, at the end of my quadrilaterals unit my students did the coolest project - EVER.  I had them create a social media page (of their choice) for a quadrilateral.  My students were required to give 10 properties in their page.  They were so creative!

Using the Ladder Method to Factor Expressions - Middle School Math Moments has a great post about helping students understand factor expressions.  Her 6th grade students are off to a great start in pre-algebra!

Transformations Summative Assessment - Would you like to give your students a fun assessment instead of a regular quiz?  Jan from Equation Freak created a very cute and thorough project for transformations.  Her students graphed pictures, colored, and transformed.

Moving Negative - This post by John at Math Hombre explains using a human scale number line to develop intuition for signed numbers and the representation.  It also includes a fun game :)

Angles in a Triangle - This is a walk-through of Euclid's proof of the theorem that the angles of a triangle sum to 180 degrees.  This would be a great addition to a lesson in a geometry class.

Advanced Math

Inverse Trig Graphing - Shireen from Math Teacher Mambo used patty paper to help her students understand inverse trig graphs.  She also includes a great idea for an interactive notebook.

Function Operations Sum 'Em Activity - Need a fun activity to help students with function operations?  I shared this free sum 'em activity to help students practice operations and compositions of functions.

Mathematical Recreation

10 Unusual Ways to Explore Math - Christina, from Interested-Led Learning, says she never really liked math in school.  Sadly, I know where she’s coming from.  On her blog post, she shares different and interesting ways to get kids interested in math that they typically don’t learn in school.

Non-Transitive Grime Dice - In his post, Mike played around with some non-transitive dice.  He shared a neat little activity with a surprising result.

2015 Mathematics Game - Denise, from Let's Play Math, gives a fun way for people of all ages to play with numbers.  Use the digits in the year 2015 to write mathematical expressions for the counting numbers 1 through 100.  There are versions of the game for all ages and levels.

New Year Party Challenge and How to Make a Binary Abacus - The year 2015 is a palindrome in binary!  Christy from Thriving Stem shares a tool to help figure it out.  With this abacus, young children can figure out small numbers, elementary students could work on place value, and adults can play with an unusual binary challenge.

About Teaching Math

Incorporating Writing in Math - I’ve been trying to incorporate more writing and literacy in my classes.  I have found that it has not only helped my students writing skills, but has also helped them create a deeper understanding of mathematical concepts.  I incorporate writing in math mostly as my student’s warm-ups.

Math in the Ferris Wheel - It’s important that we, as teachers, help students see all the math around them in their everyday lives.  The Math Manic did exactly that in her post.  She shares her experience asking students to find the math in a photograph she took.  This is a great idea that could be expanded to any level classroom.

Rolling Throne: An Exponent Game - The Results - Simplify With Me did an experiment to see if playing games in the classroom was worthwhile.  She had one class period play a game and lectured and gave a worksheet to the other class period.  Read her post to see her results!

Top 10 Problem Solving Strategies - The collaborative blog, Upper Grade Memoirs, shared 10 strategies for helping students solve problems.  This is a good read for any level math teacher!

Reviewing Beyond A(nother) Worksheet - Elle from The Spectacular World of Secondary Math says she's always looking for other things than just worksheets to review with her students.  She tries to make her classes interactive, especially the review days.  In this post she shares some of her favorite ways to review.


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!

Clip art credit:  Kady Did Doodles

How I Teach the Quadrilateral Family Tree

When I first started teaching Geometry, the quadrilaterals unit was a little overwhelming.  There were several shapes all with a bunch of properties, and I found myself forgetting some of them.  #teacherfail  It was not my favorite unit.  My second year, I pieced together this little story and have shared it with my students ever since.

Disclaimer:  I have seen a few cute stories floating around the internet.  This is not one of them.  My story could be considered slightly risqué.  However, my kids think it is funny and remember it.  Use common sense before deciding to share this with your class.  :)

If you read my post about my student’s awesome quadrilaterals projects, some of my students mentioned family relationships.  They were referring to this story as they made their projects.

At the risk of writing this in an annoying way, I’m going to try to share this exactly as I share this in class.  It’s better if you ham it up a lot.  I usually try to make it sound like a soap opera (I make my own sound effects).  By this point in the year, my students are used to my craziness.  I do not use a powerpoint or anything, I just draw it on the board.  As I go, I also list the properties off to the side.  I write them in shorthand as I’m telling the story.

The Story

“Put your pencils down for a few minutes.  I’m going to tell you a story.  You’ll have time to write any notes that you want in a few minutes.

We’ve been talking about quadrilaterals.  What are the properties of quadrilaterals again? 

So, in the quadrilateral family, there were three kids: parallelogram, trapezoid, and kite.  What are the properties of parallelograms?  What are the properties of trapezoids?  What are the properties of kites?

Now, in your family, you have a lot of the same traits as your parents.  My dad has green eyes and I do too.  I know you’ve talked about genetics in Biology.  Well, in the quadrilateral family all of the kids have the same traits as the parents.  Notice, that parallelograms, trapezoids, and kites all have four sides.  Their interior angles all sum to 360.

Parallelogram got married and had two kids: rhombus and rectangle.  Since rhombus and rectangle are parallelogram’s kids, they have all the same traits.  Their opposite sides are parallel, their opposite sides are congruent, etc.  They also have the same properties of their grandfather, quadrilateral.  

All right y’all, this is where things kind of get sketchy.  So, rhombus and rectangle…  Well, they had a kid, named square.”

**At this point, some kid is going to make a comment.  I let them, as long as it’s relatively PG.  Usually, they say something about incest.**

“Square’s mom and dad are from the same family.  So, square doesn’t have any extra properties.  He’s just a little bit special.

Trapezoid only had one child.  He named his son, isosceles trapezoid, after him.  Isosceles trapezoid has a few extra properties.

Kite didn’t have any children.

So, this is the quadrilateral family tree.  Just like all families, they have some issues, however, they all get along and are happy together.”

If you don’t end up sharing this story with your class, I hope it at least inspires you to do something interesting to help your students remember the properties of quadrilaterals.

3-2-1 Sunday Scoop

So I mentioned several weeks ago that I'm headed to Disney World with some students.  The students are taking some classes through the Disney YES program.  We're all really excited.  Well, the time is here!  I leave at 6am tomorrow morning!

In honor of my trip, I thought I'd complete the Sunday Scoop with the Teaching Trio, to let you know a little bit about my day!

I need to go to the grocery store to get some snacks for myself and get food for my husband so he's not eating out all week.

I'm hoping to get to bed early because I need to be at the airport at 6am in the morning!  Ahhh!

I hope ya'll have a good week!

Name That Parent Function!

I like to use this powerpoint as a quick activity to help my students recognize parent functions.  

I usually ham it up a little and pretend like it’s a game show (think: Name That Tune!).  I have a pretend microphone and I get it out when we do this.  Yep, my students always roll their eyes.

Anyway, I get out my whiteboards and have my students write the answer and hold it up as we go through the powerpoint.  That helps me quickly check their answers and give feedback if needed.

The first section of the powerpoint gives a graph and the students name the parent function.

The second section of the powerpoint gives an equation and the students name the parent function.

Enjoy!

You may also be interested in:   

How I Teach Function Notation

Parent Functions Matching Activity

Function Operations Sum ‘Em Activity

Going Off on Tangents

Thoughts on Partial Credit

I’ve been thinking about partial credit a lot this year.  I want grades to accurately describe my student’s level of knowledge, but I also don’t want them to feel discouraged.  Remember, I only have honors students.  All of my students would make an A in an on-level course, no problem.  My goal is to challenge them, without making them want to drop the course in order to get the “easy A”.  

Side Note:  At my school students can choose to move from an Honors/AP course into an on-level course at any point during the school year.  We are on a 5.0 scale and they get to bring their GPA points with them.  For my less motivated Honors students, it can be a challenge to keep them in Honors, where they need to be.

Reasons I Like Partial Credit:

•  It keeps my students from getting too discouraged (especially my freshmen!).  My tests can be difficult.

•  It helps me differentiate from students that understand the concept, but make computation errors vs. students that have no idea what they’re doing.  Computation errors are very different mistakes than, say, forgetting exponent properties.  Those types of errors should be treated differently.

•  It encourages my students to show their work neatly.  My freshmen really struggle with this.  So many of them struggle with writing down their work, even though they are honors-level students.

Reasons I Don’t Like Partial Credit:

•  Getting an answer is just as important as the process.  Our AP Calculus teacher uses the following example:  If you were going in for open heart surgery, would you want your surgeon to get 90% of your surgery right?  He got most of it, he just made a few “little” mistakes.  While I understand that high school isn’t “the real world”, I totally understand this example.  We need to stress the importance of the correct process AND the correct answer.

•  Grading takes much longer.

•  It can give students (and parents, and future teachers) a false representation of their skills.  Students in my course should make an A because they understand the concepts and can solve problems.  Students should not make an A because they can get 90% of any problem correct.

My Current Solution:

Currently, I give partial credit on tests and quizzes.  However, I make the key and decide how partial credit will be awarded before I give the students the assessment.  There are usually questions on every test or quiz that do not receive partial credit.  When I’m grading, I grade one page of each test at a time.  That way, I’m concentrating on grading one or two problems at a time.  I grade all tests without looking at the student’s name.  I feel this is the only way I can be fair.  This is working for me, but I wonder if there is a better way.  I know some people have moved to SBG (standards based grading), and this could be the answer for me, eventually.  However, I'm just not there yet.

What Would You Do?  

Keep in mind, these are all Honors-level students.  Would your answers be different if this were an on-level or remedial class?

This student has the right idea, but doesn’t remember the correct vocabulary.  Would you give partial credit for “having the right idea”?  Would you give no credit?  Would you give full credit and write a comment?

This student understands the concept and has the correct answer.  However, they did not use the correct notation.  Do they get full credit?  Would you take off points for incorrect notation?  Would you only write a note?

This student uses the correct vocabulary, but also includes something that’s not quite right.  Would you take off points?  Would you give full credit and write a comment?