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math

Hands-On Middle School Math: The Pythagorean Theorem

April 6, 2018 | Leave a Comment
This post may contain affiliate links. For more information, please see my full disclosure policy.

One important mathematical concept kids run into sometime in middle school or high school is the Pythagorean Theorem. Also, look at my page homeschool middle school for more fun tips

Pythagoras, an ancient Greek philosopher and mathematician, who was born around 569 BCE is credited with the discovery.

The Pythagorean Theorem is that theorem you probably remember from your own middle school and high school years: a² + b² = c². Today we’re going to teach our kids the theorem with a hands-on activity!

Hands-On Middle School Math: The Pythagorean Theorem. One important mathematical concept kids run into sometime in middle school or high school is the Pythagorean Theorem. Pythagoras, an ancient Greek philosopher and mathematician, who was born around 569 BCE is credited with the discovery. Click here to do this EASY hands-on activity!

But first let’s take a look at what a mathematical theorem is.

Hands-On Math: The Pythagorean Theorem

A mathematical theorem is a statement that can be shown to be true by accepted mathematical operations.

This means you can’t just make up a proof and say it works. You have to use logic, reasoning, and accepted mathematical operations to show the theorem is true. Today we’ll be using squares and areas to show the Pythagorean Theorem is true.

So what exactly is the Pythagorean Theorem?

Pythagorean Theorem: The square of a square drawn on the hypotenuse of a right triangle equals the sum of the areas of the squares drawn on the other two sides.

Put another way: a² + b² = c².

In other words. If you have a right angle and measure each side, the square of side a plus the square of side b is equal to the square of the long slope we call the hypotenuse.

What You Need for This Activity:

  • Graph Paper
  • Ruler
  • Scissors
  • Pen

Directions
According to the Pythagorean Theorem, if I draw a right triangle, the square of the two sides added together will equal the square of the hypotenuse. Let’s see if this actually works!

Step 1: Pull out your graph paper and draw a right triangle on it. I’m going to use sides with the length of 3 boxes and 4 boxes.

Pythagorean Theorem for Kids

Step 2: Measure the hypotenuse.

Easy Pythagorean Theorem Lesson

Step 3: Remember square of a number is the area of a square with that length of side. So I’m now going to draw and cut out my squares. One square will have sides the length of 2 squares on the graph paper. One square will have sides the length of 3 squares, while the third will have the length I measured!

To make the next step more clear I’m going to highlight the squares in different colors. The small one will be yellow. The medium will be green. And the large one will be blue.

Simple Pythagorean Theorem Activity

Step 4: Let’s see if the area of the two small triangles will equal the area of the large triangle! We’re going to do this by laying the medium square on top of the large square.

Pythagorean Theorem Lesson for Kids

Now you have a choice. If you count the squares left over on the large triangle, you’ll notice there are 9 squares. And what’s 3²? 9! Or you can do what I did and cut the square to fit the left over area.

Pythagorean Theorem Hands On Activity

As you can see, the square of the hypotenuse is equal to the sum of the squares of the sides. The Pythagorean Theorem works!


Now let’s run through all 4 steps again with different numbers. This time I’m going to use sides with lengths of 6 and 8.

Step 1: Again we create the right triangle.

Teaching the Pythagorean Theorem to Kids

Step 2: Now measure the hypotenuse.

Measuring Triangles with Kids

Step 3: Create the squares.

Easy Way to Teach the Pythagorean Theorem to Kids

Step 4: Do the squares of the sides equal the square of the hypotenuse? The highlighter caused the sides of my squares to curl, so I used a touch of tape to force the squares to lie flat. Even so, as you can see the answer is yes!

Showing Kids the Pythagorean Theorem
Teaching the Pythagorean Theorem for Homeschoolers

Try the activity yourself using varying lengths for the sides.

No matter what the length of the sides of your right triangle, you’ll discover the squares always equal the square of the hypotenuse or a² + b² = c².

You’ve shown the Pythagorean Theorem works!

Hands-On Middle School Math: The Pythagorean Theorem. One important mathematical concept kids run into sometime in middle school or high school is the Pythagorean Theorem. Pythagoras, an ancient Greek philosopher and mathematician, who was born around 569 BCE is credited with the discovery. Click here to do this EASY hands-on activity!

Written by Sara at Classically Homeschooling.

So what lengths did you use for your right triangles?

Teach math with these other fun homeschool activities!

  • Hands-On Math: Factoring and Balancing Chemical Equations
  • How to Teach Limits: Hands-On Middle School Math
  • Hands-On Math: Fun and Easy Snowflake Geometry

Leave a CommentFiled Under: Ancient Civilizations, Hands-On Activities, Math Based, Middle School Homeschool Tagged With: hands-on, hands-on activities, handson, handsonhomeschooling, math, middleschool

Hands-On Middle School Math: Everyday Math Scavenger Hunt (Printable)

January 31, 2018 | 2 Comments
This post may contain affiliate links. For more information, please see my full disclosure policy.

I have a hands-on middle school everyday math scavenger hunt free printable.

My children learn best through hands-on activities.

So far, I have managed to easily incorporate experiential learning into our history, science, and language arts studies.

Math, however, has been a different story. Finding age appropriate and relevant hands-on math for my middle schooler has been a challenge.

Add to this the fact that he doesn’t see the point in doing his math work at all, and it becomes clear that I need to find an out-of-the-box approach to this subject.

Hands-on Middle School Math and printable scavenger math hunt

I knew that the first thing I wanted to incorporate was an activity that would take math out of the textbook and into everyday life.

Too often, I find myself trying to simply tell him all the ways we use math everyday.

Hands-on Math for Older Learners: Everyday Math Scavenger Hunt

I am pretty sure he hears about 10% of what I say and then I become one of the adults in the Charlie Brown movies.

Rather than lecturing him about everyday math, I decided it was time to save my breath and create an activity that would allow him to explore it on his own!

What you will need for this activity:

  • Everyday Math Scavenger Hunt Printable
  • A Pen or Pencil
  • Time to Explore and Think
Our Journey Westward


It’s super simple, to be sure, but I found it to be super effective as well!

After printing the scavenger hunt, I reviewed the different types of everyday math listed with my son.

Everyday Math Hunt for Kids

The hunt requires the learner to look for examples of:

  • Temperature
  • A Recipe with Fractions
  • A Decimal
  • Numbers Written in Word Form
  • A Number Greater than 200,000,000
  • Height and Weight
  • Percentage
  • A Price
  • Volume Measurement
  • A Repeating Pattern
  • A Graph
  • Date and Time
  • An Angle
Math Scavenger Hunt

It also asks the learner as a bonus, to find three examples of everyday math on their own.

The only rule for this activity is that no textbooks or typical “school materials” can be used. The learner must find examples of math in everyday places.

Looking for Everyday Math Examples

In order to make it a little more challenging and also a bit more fun, I asked my son to first try to find as many of the items as possible outdoors.

Hands-On Middle School Math

Looking for Everyday Math with Kids

My son did really well, and he really had to think a bit to find some of the items.

(Let’s just say percentages are not all over the place in our home – an old grocery receipt, with savings listed, did the trick, but it took a while to find.)

Overall, this was a great way to help my son understand why we learn math in the first place.

Everyday Math Scavenger Hunt

It also allowed to him to see first hand, how critical basic math skills are for his success in life.

More Every Day Math Activities

  • How to Teach Limits: Hands-on Middle School Math
  • 25 Creative and Tasty Edible Math Activities that Keep Learning Fun
  • Hands-On Math: Factoring and Balancing Chemical Equations
  • 21 Hands-On Math Activities for Elementary and Middle School

Having to critically think of how these math examples are present all around us, combined with having to come up with three of his own examples made for a math filled afternoon (with zero complaints!).

Our Journey Westward
Hands-On Middle School Math: Everyday Math Scavenger Hunt. Making homeschool math of your everyday life by doing this fun hands-on middle school math activity of a scavenger hunt. Download a free printable everyday math scavenger hunt. CLICK HERE to grab the free printable and teach your kids out of the box middle school math!

How to Get the Free Printable

Now, how to grab the free printable. It’s a subscriber freebie.

When you sign up to follow me, you get access to this freebie.

 1) Sign up on my email list to follow me and get this freebie and many others.
 2) Grab the printable.
3) Last, look for my emails in your inbox as a follower. Glad to have you.

If you’re looking for a way to bring math to life, you’ll love the book, Loving Living Math for homeschoolers. This how-to guide for parents will help you understand and implement living math principles at any grade level.

We gave this activity an A+.

Written by Shawna at Not the Former Things.

2 CommentsFiled Under: Hands-On Activities, Math Based, Middle School Homeschool Tagged With: hands-on, hands-on activities, handson, handsonhomeschooling, math, middleschool

How to Teach Limits: Hands-on Middle School Math

December 31, 2017 | Leave a Comment
This post may contain affiliate links. For more information, please see my full disclosure policy.

Eventually kids run into the concept of limits during their math classes. In traditional classes, it’s common to use graphs to explain this idea. Also, look at my page homeschool middle school for more fun tips.

But when you homeschool, you can make learning a bit more hands-on, which is how I prefer to teach my children.

This fun hands-on math activity is a great (and simple) way to explore this concept with middle school students!

How to Teach Limits: Hands-on Middle School Math

Sometime around 450 BCE, Zeno of Elea, one of the ancient Greek Philosophers, gave a puzzle to his students.

How to Teach Limits: Hands-on Middle School Math. It's common to use graphs to explain how to teach limits. But when you homeschool, you can make learning a bit more hands-on. Click here to see how to bring this math concept alive

A tortoise came up to Achilles and proposed a race.

You know who Achilles is, right? The hero of the Illiad (think Trojan War). The guy who died of an arrow in his ankle. The mighty hero himself!

Well we’ve met the tortoise in Aesop’s Fables. He’s a pretty smart guy.

So the tortoise comes up to Achilles and proposes a race. Achilles fell down laughing. A slow, crawling, reptile is challenging ME to a race?

Why yes. However I need a head start. 10 meters should be enough.

Achilles laughs harder, even with a head start he’d quickly catch the tortoise!

Then the tortoise begins to explain.

No matter how fast you run, you will only catch up to where I WAS, not where I am now. After you’ve run the 10 meters, I will have moved farther ahead.

No matter how fast you run, you will only run to where I have been. Not where I will be. I will have always added a small distance before you reach where I am. So you can never catch up to me.

Achilles sadly conceded the race.

So let’s take a look at this concept on the kitchen table.

Pull out your Achilles and Tortoise. We used two different Lego minifigures.

Set the Tortoise ahead of Achilles. Place a piece of tape or use a piece of posterboard to mark the spot where the tortoise is standing.

Simple Math Limits Activity

Now move “Achilles” to the designated spot, but move the “tortoise” slightly ahead.

Hands On Math Limits Activity

Do this again and again and again. No matter how fast Achilles runs, he always ends up where the Tortoise WAS, not where he is.

Teaching Kids About Math Limits

In the pure world of mathematics, Achilles will always run the where the Tortoise WAS, not where the Tortoise IS. Achilles will get close to the Tortoise. He may be atoms away from the Tortoise, but he will never catch Achilles.

The tortoise is the limit for Achilles in the race.

A limit is the value that a function or sequence approaches as the input, or index, approaches some value.

Achilles can approach the tortoise but never quite reaches the tortoise. The tortoise is the Achilles limit!

Isn’t the pure world of mathematics fun!

Let’s take another look at limits through a joke my math professor once told us.

An engineer, physicist, and mathematician were placed on one side of the room. A line was drawn on the other side. They were told they could only go halfway each time.

So the engineer whipped out a calculator and measuring tape. After a few measurements and calculation, he quickly crossed the room.

The physicist pulled out a slide rule and a yard stick. After a few measurements and scribbled calculations, she quickly crossed the room as well.

The mathematician…. well the mathematician has yet to arrive!

So again, we pulled out the LEGO figure to take a look at what’s going on.

First you place one figure at one end of the table. Now measure the table and go halfway.

Learning About Math Limits for Kids

Measure the table and go halfway again!

Learning About How Math Limits Work

As you can tell, if you only go halfway each time, you’ll never reach the end of the table.

The measurement of the table is the limit of the infinite series 1/2(table) + 1/4(table) + 1/8(table) + 1/16(table) + 1/32(table) and so on. Once you reach infinity, supposedly you’ll have reached the end of the table.

But not until then!

Hence our poor mathematician is trapped trying to get to the other side of the table.

Try again moving the mathematician 1/4 or 1/8 of the way each time. Does it change the limit or does the limit remain the length of the table?

How to Teach Limits: Hands-on Middle School Math. It's common to use graphs to explain how to teach limits. But when you homeschool, you can make learning a bit more hands-on. Click here to see how to bring this math concept alive

Written by Sara at Classically Homeschooling.

Limits is a fascinating and fun concept to explore with kids!

Check out these other math activities for homeschoolers!

  • Hands-On Math: Fun and Easy Snowflake Geometry
  • 21 Hands-On Math Activities for Elementary and Middle School
  • 25 Creative and Tasty Edible Math Activities That Keep Learning Fun

Leave a CommentFiled Under: Hands-On Activities, Math Based Tagged With: hands-on, hands-on activities, handson, handsonhomeschooling, math, middleschool

Hands-On Math: Factoring and Balancing Chemical Equations

December 22, 2017 | Leave a Comment
This post may contain affiliate links. For more information, please see my full disclosure policy.

Written by Kim at The Learning Hypothesis.

Hands-on Chemical Equations Fun!

Chemistry requires a lot of algebraic thinking in order to be successful and it’s easy to incorporate hands-on chemical equations. Chemistry includes formulas, proportions, and the basis of the balanced chemical equation includes math concepts like the lowest common multiple, factoring, and the distributive property.

Balancing equations is necessary to satisfy the law of conservation of matter and simple means that what goes into a reaction comes back out.

The number of atoms on one side of the yields sign will equal the number on the other side.

Learning this kind of advanced math can be a bit tricky for students, so I like to make it as hands-on as I can.

Middle & High School Hands-On Math: Factoring and Balancing Chemical Equations. Chemistry requires a lot of algebraic thinking in order to be successful. It includes formulas, proportions, and the basis of the balanced chemical equation includes math concepts like the lowest common multiple, factoring, and the distributive property. Look at this fun hands-on idea to bring math alive!

This hands-on balancing chemical equations activity was a great way for my kids to visualize the concept as they learned.

How to Factor and Balance Chemical Equations

Let’s talk about the 3 mathematical concepts that are necessary to balance these equations:

  • Lowest common multiple
  • Factoring
  • Distributive property

The lowest common multiple (LCM) is the smallest number that 2 (or more numbers) are factors of.

Factoring is the process of determining what combinations of numbers can be multiplied to create a specific product. It looks like this.

Factoring Numbers

Distributive property says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately.

In the case of balancing equations it means that when we add (or change) coefficients that the change will impact all of the elements in the formula.
Example

Balancing Chemical Equations

In this equation, there are 2 atoms of oxygen on the reactants side and 1 atom on the product side.
Reminder: the only thing that can be changed is the coefficient.

The LCM of 1 & 2 is 2. The factors of 2 are 1 & 2 so 2 is the first coefficient to try.

How to Balance Chemical Equations

That 2 will multiply the 2 hydrogens and the 1 oxygen atom resulting in 4 hydrogen and 2 atoms.

Now the hydrogen are unbalanced. There are more hydrogen on the product side.

The LCM between the two sets of hydrogen is 4. The factors of 4 are 1 & 4 and 2 & 2.

To make the hydrogen on the reactants side equal the number on the products side we will use a coefficient of 2 on the reactant side. This results in 4 hydrogen atoms on both sides.

Balancing Chemical Equations for Kids

All balanced.

Now if all of that math, made your head spin. Let’s look at a hands-on way to work through balancing these chemical equations.

Hands-On Activity for Balancing Chemical Equations

Make Factor Trees:

Do a quick lesson/review on creating factor trees. This is something many students have done since upper elementary. This is a great review of factor trees.

I like to actually multiply the number of atoms to get a common multiple and use factor trees to determine the lowest common multiple and the coefficients needed for that number of atoms.

This is a quick example…

How to Make Factor Trees

The factor trees make it easier to determine both the lowest common multiple and the coefficients (the factors of the LCM will be used in conjunction with the subscripts in the formulas

For instance if you were trying to balance an element with 4 atoms on the reactant side and 6 atoms on the product side, you can multiply those together to get 24.

Do a factor tree and quickly discover the lowest common multiple is 12 and the factors of 12 that will be used as coefficients.

Create a Chemical Equation Balance

Making a Math Balance

Supplies:

  • ruler
  • paper clips (colored are best)
  • binder clips
  • pencil

Directions:

  1. Place the binder clips on the opposite ends of the ruler.
  2. Count the type of atoms in your equation.
  3. Now count the number of each atom and add it to the corresponding binder clip (Use a different color for each element)
  4. Use the factor trees to help determine how to best balance the equation by adding atoms (paper clips)
  5. The ruler will be flat (balanced) when the number of atoms is balanced.

Using the example from above. This is the balance in action.

Hands On Math Balancing Equations Activity

Unbalanced equation:

This balance activity uses green paper clips for the hydrogen atoms and blue paper clips for the oxygen atoms.

To balance the oxygen, we added the coefficient to the product side to balance the oxygen.

The result is that hydrogen is now unbalanced. There are 4 atoms (paper clips) on the product side and only 2 on the reactant side.

The balance is leaning to the right.

Balancing Chemical Equations Activity

To completely balance the equation add the coefficient to the hydrogen on the reactant side.

DIY Balancing Chemical Equations Activity

Changes the number of hydrogen from 2 to 4 which completely balances the equation and the balance.

Middle & High School Hands-On Math: Factoring and Balancing Chemical Equations. Chemistry requires a lot of algebraic thinking in order to be successful. It includes formulas, proportions, and the basis of the balanced chemical equation includes math concepts like the lowest common multiple, factoring, and the distributive property. Look at this fun hands-on idea to bring math alive!

Make learning math fun and easy with these other hands-on activities!

  • 25 Creative and Tasty Edible Math Activities That Keep Learning Fun
  • 21 Hands-On Math Activities for Elementary and Middle School
  • How to Shake Up STEAM with Geography for Middle School

Leave a CommentFiled Under: Hands-On Activities, Math Based, Middle School Homeschool Tagged With: hands-on, hands-on activities, handson, math, middleschool

Hands-On Math: Fun and Easy Snowflake Geometry

December 15, 2017 | Leave a Comment
This post may contain affiliate links. For more information, please see my full disclosure policy.

I have an easy snowflake geometry activity.

With the onset of winter weather, we’ve experienced the first few snow flurries in our area.

Just the mention of the word snow and kids of all ages get into a tizzy that brings delight and happiness.

I really wanted to bring that feeling of magic into our lessons, so I began hunting for ideas for my older kids.

Hands-On Math: Fun and Easy Snowflake Geometry. With the onset of winter weather, we’ve experienced the first few snow flurries in our area. Add a bit of math and science together to make these easy snowflakes and study a bit of geometry too. CLICK HERE to make this easy hands-on math craft!

When my kids were younger, we did a lot with crafts.

Crafts are a great way to make lessons hands-on and fun.

The more ways you can make math an art activity, the more kids can connect with the concept.

It’s also nice to connect other subjects and make lessons more efficient and engaging.

Because my kids are older, we’ve fallen away from crafts. However, it had become my goal to find a learning craft to tie into both math and science for the winter season.

Easy Snowflake Geometry

The following craft was the perfect lesson to review angles and geometrical shapes.

To get in our science skills at the same time, we learned a little about the science of weather.

Winter can be a hard time to keep focused with lessons, so this activity can be a great way to keep up your schooling stamina.

Hands-On Math: Simple Snowflake Geometry

Break out the smocks, paint, and craft sticks!! It’s time to get crafty! Here is a fun DIY decoration for your kids to make for their rooms, for a friend, or for a party.

For this craft, you will need the following materials:

  • craft sticks
  • protractor
  • liquid glue or a hot glue gun
  • any color of paint
  • paper to cover work space
  • paint brushes
  • decorative ribbon
  • double stick foam tape

We began this lesson by reviewing the different types of angles. We measured out and drew a 30 degree angle using the protractor.

Making a Simple Math Geometry Craft

Then we used 6 craft sticks to glue together a star shape. We were careful to make sure our angles measured at 30 degrees.

Winter Snowflake Geometry Craft

Next we added the points to our star in the form of diamonds or rhombuses.

At this point, a few of the kids got off of their measurements which resulted in the creation of their own shapes.

Painting a Geometric Snowflake

The kids then chose a color of paint to paint their snowflakes.

Making a Geometric Snowflake

You’ll love these living books for winter which bring learning alive when your kids hit the doldrums.

Winter NaturExplorers 940x788 (Facebook)


There are many ways to extend this activity:

  • Use the book Snowflake Bentley to learn about the man who studied snowflakes and invented the photomicrographic technique.
  • Research the science of snowflakes. Learn how snowflakes are made and what determines the shape of snowflakes.
  • Learn the seven shapes of snowflakes and then identify all of the shapes found in each snowflake type.
Hands-On Math: Fun and Easy Snowflake Geometry. With the onset of winter weather, we’ve experienced the first few snow flurries in our area. Add a bit of math and science together to make these easy snowflakes and study a bit of geometry too. CLICK HERE to make this easy hands-on math craft!

Add more math learning fun to your winter studies with these hands-on activities!

  • 21 Hands-On Math Activities for Elementary and Middle School
  • STEM: Build a Da Vinci Parachute Activity
  • 25 Creative and Tasty Edible Math Activities That Keep Learning Fun

Leave a CommentFiled Under: Hands-On Activities, Math Based Tagged With: earthscience, hands-on, hands-on activities, handson, handsonhomeschooling, homeschoolinginwinter, homeschoolscience, math, science

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