A lot of teachers who have been using this activity have added a little paper airplane flying contest to their class time afterward.  Such a fun idea!  If you have time, this could be a great follow-up, and you can plot / track the distances as well, depending on your grade level.

​Here is a quick peek at how it works:

Depending on what graphing skills your students need to practice, you can switch it up!  I have been adding to this activity and have a few options. 

Graphing Linear Equations, Reflecting Lines, etc.

The original one has a few versions centering around practice graphing linear equations.  Three variations of the worksheet are included.  All three offer practice graphing using slope-intercept form.   After graphing the lines, students follow the directions to fold along the lines and create a paper airplane. 

3 versions you can try:

- graphing using a given equation and by reflecting a previous line (plus writing equations)

-  graphing using given equations in slope-intercept form  (plus completing a chart identifying slopes & y-intercepts)

-  manipulating equations before they are in slope-intercept form (then graphing)

If you know which one would be best for your class, just choose that version.  Or, if you want to easily differentiate, print some of each! Print one worksheet and one coordinate plane sheet per student.

Plotting Points on the Coordinate Plane

This set is for the younger crowd.  If your kids are still just working with points on the coordinate plane, they can try one with just plotting ordered pairs, or the version with plotting and reflecting points.

They'll still get all the fun of folding their final product into a paper airplane if they plotted it all correctly!

Links:

Graphing Linear Equations "Coordinate PLANES" set (slope, y-intercepts, equations of lines, etc.)

Plotting Points "Coordinate PLANES" set for middle school (ordered pairs on the coordinate plane)
​

To Read Next:

Benefits of Creativity in Math Class
 
Creativity does not tend to take center stage in many typical math classrooms, although it has been proven to have many benefits.  According to The Lab School, “the educational community largely embraces the notion that creative expression is an important aspect of a student’s learning experience. We also know that exposure to the arts and arts-integrated instruction has positive educational benefits, especially for learners who have not succeeded in typical learning environments.”
 
Creative thinking skills help develop intrinsic motivation and help your middle and high school students become lifelong learners.  Teens should be given the opportunity to seek out new experiences and experiment with new ideas.
 
 They should be taught to ask questions and investigate to help develop critical thinking and problem solving skills; art encourages this.
 
In addition to all of the brain-based benefits, creativity has the added bonus of fun and relaxation.   Students love to have the opportunity to relax and use their creative sides.  School days can be monotonous for our middle and high school students, so art and creativity in math class is the perfect way to break up the day!

Creative brains
 
According to an article, Study Reveals How Creative Brains are Wired, a new study reveals that creative people are wired differently than most.  An important finding of this study is discovering that creativity doesn’t simply come from the left or right side of the brain; “it is a whole-brain endeavor.”
 
Creativity is not something where you have it or you don’t.  This tells us that we need to encourage both hemispheres of the brain in math class to really maximize the benefits of creativity.

How to Up the Creativity in your Math Class
 
So, now that you know why creativity should have a place in the classroom, especially math, here are some ideas on how to incorporate creativity in the upper grades!

Encourage doodles and sketches during note-taking (and even on tests!)  Let kids explain and explore concepts using creative images.  Doodling and coloring in a left-brain oriented class like math encourages communication across the corpus callosum, the bundle of nerve fibers that divides the two hemispheres of the brain; the proven benefits of this communication include focus, learning, memory, and even relaxation.
 
A recent study proved that doodling actually INCREASES focus and the ability to recall new information.  With these color-it-in, doodle-friendly note methods, your students can use their colored pencils and the right side of their brains, and then remember key vocabulary, math examples, and new concepts more easily.

Incorporate coloring, hand lettering, and creative graphic organizers whenever possible.  Coloring can improve memory, learning, and retention.  It even offers the additional benefit of stress relief.  The relaxation that comes from coloring decreases activity in the amygdala, which is the part of the brain affected by stress.
 
It is possible that this is partly due to an unconscious reminder of childhood, a time of lower stress.  It is great to add just a touch of coloring (in a purposeful way) to a math activity.  This can help students to relax and focus while still learning.
 
A few of my favorite ways to do this are:

• When working through "Always True, Sometimes True, Never True" critical thinking challenges, I have kids color statements red for "never", blue for "always," and green for "sometimes."  (Added bonus - I can check for accuracy in two seconds by arranging the statements in a pattern.)
• Students shade or color answers in "GridWords" puzzles to reveal the mystery words.  Then, I include either an action word as the GridWord or a mathematical connection throughout a series (for example, all the words in my polynomial factoring GridWords series turn out to be places that the Golden Ratio is found in nature.  It's fun to see them try to figure out this connection with each new word they color - "Hmm, how are "pinecones" and "fingers" related??")  The GridWords for prime factorization and simplifying expressions are action words, so the kids clap, hum, tap, etc. when they reveal the word.
• When teaching geometry, I like to have my students incorporate color-coding their notes and work.  For example, if I’m teaching special angle pairs, students can color specific types of angle pairs certain colors (or even use patterns, like stripes / polka dots).

                                          

For additional creativity, allow students to choose their own colors and create a key in the top corner of the page!  This way they are not restricted in their coloring choices, can choose colors that can individually help them, and you are keeping the creativity purposeful to learning.
 
Try having kids explore (and/or display) their learning goals by creating anchor charts.
 
Have kids explore a problem in more creative ways, like the video above shows.  Try the Socratic Method.  Try structuring your class period in a completely different way.  See how you can change things up to get the kids' creativity to come forth.  Students are naturally creative and will try new approaches if you just leave open some opportunities for this to happen.
 
The options are endless!
 
Add your own thoughts and specifics for us!  How do you get your students’ creative juices flowing?  Leave a comment below!
 
Creativity in math class is a definite no-brainer!  Subscribe through email to hear more from me:

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Using ANS (Approximate Number System) to Build a Cognitive Foundation for Theoretical Math

The Study
 
Park & Brannon developed a hypothesis:  Complex math skills are fundamentally linked to rudimentary preverbal quantitative abilities.  This provides the first direct evidence that ANS and symbolic math may be causally related, and raises the possibility that interventions aimed at the ANS could benefit children and adults who struggle with math.  They developed 2 different experiments to test their hypothesis. 
 
            Experiment 1
           
In the first experiment, they used a training study with a pre- and post-test design to assess whether performance on a non-symbolic arithmetic task would improve over repeated testing and whether improvement would transfer to symbolic arithmetic.   Adult participants had to add or subtract large quantities of visually presented dot arrays without counting.   
 
They gave all participants a set of multi-digit addition and subtraction problems both before the first training session and after the tenth training session.  The approximate arithmetic training resulted in a substantial improvement in symbolic math performance. 
 
            Experiment 2
 
In the second experiment, to account for a possible placebo effect, they included a training group that received world knowledge training over the course of multiple lessons.  They also aimed to test the relative efficacy of the ANS-based training compared to other training based on symbolic numerical associations.  They randomly assigned participants to various training groups- Approximate Arithmetic (AA), Numerical Ordering (NO),and Knowledge Training (KT). 
 
As in Experiment 1, there was substantial improvement on the non-symbolic approximate arithmetic task.  To assess the transfer effects, they compared the standardized gain scores in symbolic math performance across the three training groups using one-way analysis of variance.  This analysis revealed significant differences on the math gain scores across the training groups; the AA training group showed higher increases than the NO and KT groups.

            Results
 
The study’s findings were important in a few ways.  First, the results were the first to show that ANS training improves symbolic arithmetic.  Second, there was a striking transfer between the approximate addition and subtraction task and the symbolic math test.  Thirdly, this link suggests important directions for math interventions.

How it Affects Students
 
So, in short, ANS training is directly linked to how we should approach math.  It shows that when students’ ANS improve, so does their symbolic mathematics.
 
            Visual Approaches
 
The findings from this study show the value of taking a visual approach to math.  Viewing large arrays of dots and quickly making estimates has a lot benefit to symbolic mathematical abilities.  That’s not to say symbolic math isn’t significant; ANS training is key to getting there.
 
How to Apply
 
There are a number of ways you can increase ANS training in your classroom, and, although it’s important to lay this foundation in younger students, the study shows us it can improve arithmetic of students of any age, even adults!
 
           Estimate Challenge
 
For students of any age you can hold a “Guesstimate Challenge.” Fill up a jar with marbles and have your students give their best estimate of the number of marbles.  It’s an easy, simple way to get kids to work on and develop their ANS!
 
Keep in mind that this will not take much time at all!  Consider making this a weekly challenge and allowing students to make their guesses whenever they have time during the week.
 
            Partner Cards
 
To quickly add a bit of ANS training to your classroom, incorporate partner cards with different amounts of dots. Randomly pass out sets of dot cards- Figur8 provided cards to download here, and have your students swiftly partner with the student who has the same number of dots.   They will have to estimate the number of dots by using their ANS. 
 
Partner cards are a great way to quickly partner up your students, and since you already are spending time partnering up the class you’re not wasting any time.  
 
I hope you found this study as cool as I did!  Do you have any great ways to train your students’ ANS?   Don’t forget to subscribe in the box below!