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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

How Animals Cope With the Cold (Easy Nature Study)

December 29, 2017 | 2 Comments
This post may contain affiliate links. For more information, please see my full disclosure policy.

I was given this product free because I asked for it and couldn’t wait to use it. ALL opinions are my own and for sure I will always tell you what is on my mind. When I do accept a product it’s because I’m giddy to tell you about it. Read my full disclosure here. Now on to the fun stuff!


Winter is a wonderful season for learning about animals with kids. Animals go through so many different behavioral changes to adapt to cold temperatures and, when you can study those changes in your own backyard, it really makes scientific concepts come alive.

So I was excited to try the NaturExplorers ebook “Coping With the Cold”. I’ve been wanting to add in nature studies to our homeschool but didn’t need anything that requires a lot of fuss.

Winter is a wonderful season for learning about animals with kids. Animals go through so many different behavioral changes to adapt to cold temperatures and, when you can study those changes in your own backyard, it really makes scientific concepts come alive. Click here to grab this easy nature study!

NaturExplorers ebook “Coping With the Cold” is a Charlotte Mason-inspired nature study program for learning about how animals adapt to winter temperatures. And it’s loaded with simple DIY projects, science activities, and plenty of notebooking pages too!

Take a look at what all is included in this excellent science curriculum!

NaturExplorers Review: Coping With the Cold

Since NaturExplorers is a Charlotte Mason-style program, the curriculum includes plenty of nature study activities and hands-on learning ideas for studying winter animal behavior.

Nature Explorers Coping With the Cold

And, along with all the printed activities for kids to complete, there are loads of notebooking pages and drawing prompts so they can record what they observe outdoors.

Nature Explorers Winter Animals Notebooking Pages

Winter NaturExplorers 1080x1080 (Instagram)
What I really like about NaturExplorers is that the program encourages kids to spend plenty of time outside in nature, finding out what animals do for themselves.

Nature Explorers Migration Activity

For example, the activities about bird migration were really informational and geography-based too.

Did you know that birds actually follow “flyways” – a version of bird highways? I didn’t!

Migrating Animal Research Planning Page

This migrating animal research planner was such a neat idea, because it’s a great way to help children plan a research topic, organize their ideas, and outline an essay.

This is an excellent activity for middle school language arts.

Studying Winter Animal Adaptations

By the way, these are just some of the notebooking and journaling activities in the program!

Easy Nature Study!

Winter Animal Observation Sheets

Charlotte Mason strongly encouraged art and journaling and NaturExplorers does a fantastic job of prompting kids to draw what they see and note what it tells them about animal behavior.

It’s art and science in one activity!

Winter Adaptations Research Activity

And, because I always love to encourage reading, I was thrilled to see that the program featured an activity for kids to complete using a nonfiction book about winter animals they choose from the library. (My favorite place!)

Winter Adaptations Art Activity

Even if you can only observe one or two different kinds of animals (depending on where you live), the idea of adaptations is so thoroughly covered that kids will be able to spot other adaptations in animals they read about.

Migrating Flocks Observation Sheet

Some of the other notebooking pages include questions for kids to answer, based on their own observations, and charts for them to fill out.

Studying Winter Animal Behavior

I also loved that NaturExplorers is so open-ended. There’s no weekly schedule or layout included, so you can pick up and pause as you need to. It’s a very relaxed curriculum and you adapt it to your own schedule.

Perfect for us eclectic homeschoolers!

I’ll be sharing a few of the NaturExplorers activities in upcoming posts, but – trust me – this is a fabulous winter nature study program that you’ll love as much as the kids do!

How to Purchase It.

►Product Name: Coping With the Cold.
►Website: Our Journey Westward.
►Type of product: Ebook instant download.
►Ages: Multiple grades 1st to 8th grade.
►Price: $12.00

Winter is a wonderful season for learning about animals with kids. Animals go through so many different behavioral changes to adapt to cold temperatures and, when you can study those changes in your own backyard, it really makes scientific concepts come alive. Click here to grab this easy nature study!

See even more ways to include hands-on science in your homeschool!

  • Free Moon Journal for Homeschool Science
  • Middle School Homeschool Science: 50 Free Spring Activities
  • Free Carnivorous Plants Notebooking Pages

Hugs and love ya,

2 CommentsFiled Under: Homeschool Curriculum Review, Product Review, Science Tagged With: hands-on, hands-on activities, handson, handsonhomeschooling, hibernation, homeschoolinginwinter, middleschool, nature study, notebooking, science, winter season

How to Teach Cursive and Composition With A Fresh Perspective

December 28, 2017 | Leave a Comment
This post may contain affiliate links. For more information, please see my full disclosure policy.

When pioneers were going west, ruts served as a guide in following others. Ruts are not necessarily a bad thing. However, when you need to veer off the beaten path when teaching cursive and composition because your well-worn path is not working, then you need a fresh perspective.

The first shift in my mindset that I had to overcome when teaching cursive and composition is to realize that they are two very different skills. As teachers we can forget that they’re related, but different.

Cursive is a fine motor skill and requires physical dexterity while composition is a mental process.

When both work together, it is an out of body experience as my son told me one time. Okay, okay, it is a total body experience.

Bottom line is that it can be flat out hard. Telling your child to pick his pencil up and start writing can be the demise of him.

For example, a child may be mastering fine motor skill, but needs help with ideas on what to write.

On the flip side, a child may be excited to write creatively, but his fine motor skills are holding him back.

Both skills are needed for a child to be an effective writer.

How to Teach Cursive and Composition With A Fresh Perspective. When you need to veer off the beaten path when teaching cursive and composition because your well-worn path is not working, then you need a fresh perspective. Click here to read these valuable tips!

Honing both skills need to be done simultaneously as well as individually for both to emerge strong.Let me get one more idea out of the way too. Cursive is both hard to teach and to learn, but print can be harder.

As the parent, you are the only one to know if the problems you’re having with your child are because of attitude or aptitude.

Some children do better when typing, but before you give in to teaching only typing, read on about my experience.

Cursive takes patience, consistency, and fortitude to teach.

Devices today are suppose to speed up the time we have, but they don’t. They can make both children and adults overly anxious.

They also teach us to instantly master whatever it is that we’re learning.

Teaching and learning cursive rubs opposite of the educational grain being thrown at us today. It’s a slow process and not instant gratification. Parents are left wondering if their child has a special need when in fact they may be developing fine.

How to Rock Teaching Cursive

Look at these tips for teaching cursive from a fresh perspective.

1.) Don’t teach cursive later. Big mistake. I hear it all the time: “I’ll wait until my child is in 3rd grade or 5th grade.” 

The best time to teach cursive is soon after he gains control of his fine motor skills. The rule of thumb is about half way through first grade.

One side note is that your child is still malleable and willing to learn cursive the younger he is.

By the time, he is in third grade or later, he may be too embarrassed or not patient enough to learn.

I started each child halfway through first grade and had plenty of time to teach it. Later is not better in this instance. Of course, this means if your child has no developmental issues.

By 3rd grade, my kids had a good handle on cursive and of course I expected them to use it all the way through to high school. And yes, they learned to type along the way.

How to Teach Cursive and Composition With A Fresh Perspective. When you need to veer off the beaten path when teaching cursive and composition because your well-worn path is not working, then you need a fresh perspective. Click here to read these valuable tips!

2.) Don’t teach cursive and composition at the same time.

Direct teaching is very different from practice.

For example, in the beginning while your child is learning cursive don’t make him agonize in how to spell or how to be creative. Just give him the answers and move on while he focuses on the physical part of writing.

3.) Don’t teach composition or cursive back to back in the day.

Whatever you do, don’t do two back to back heavy assignments.

If your child is struggling with both of these skills then space them out in the day.

Do cursive practice work first thing in your day.

Then, switch gears and do other subjects. Add in composition later after your child’s hand has had time to recover.

4.) Strengthening fine motor skills goes beyond practicing cursive.

  • Coloring is a great way to naturally strengthen skills. And coloring something worthwhile like science pages or history pages will make learning time productive. Check out the 10 Westward Expansion History Fun Coloring Pages and 20 Ancient Civilization History Coloring Pages.
  • Copywork is timeless for teaching beautiful penmanship and again worthy of your child’s learning time. Poems, scriptures, history, or science are straight and clear prose which are practical for copywork. Look at my article, Free History Copywork – A Roundup of History Resources.
  • Drawing and writing. Be sure to not criticize, judge, or grade these fun activities. But make sure they do BOTH writing and drawing. My sons wanted to draw a picture first and then the words swelled up from the inside as they viewed their magnificent drawings.

Teaching composition is equally teacher intensive. There are no short cuts. Learning how to express ideas clearly doesn’t just happen. It is modeled by the teacher.

It reminds me of summers I spent with my granny when she was alive. I watched a southerner master cook whip out the most delicious recipes I fondly remember to this day. As I stood beside her, I wrote down her ideas.

I added a few ingredients to her pot under her supervision and then learned to cook delicious meals like her.

Teaching Composition that Goes from Limp to Life

Composition can be the same way. Don’t make it an event where all life goes limp. Make it a time that is memorable for the right reasons. Tears are not a good sign.

Composition starts off as a shared project when your kids are just learning.

You start the “pot”, let them stir it by adding a few key ingredients.

As you model how to write, your kids learn by watching and participating.

Look at these ways to teach composition that are out of the box.

  • Take a week and brainstorm topics instead of writing a composition. In order to have your child’s ideas flow abundantly, you take control of the physical act of writing.
  • Let your child record his ideas on his phone. Then play them back and write them down. This breaks this hard process down into two steps.
  • Have your child use his phone or your phone to take pictures of objects that might interest him. Go on a scavenger hunt. Scrolling back through the pictures is not only fun, but gets your child excited about what to write.
  • Also, I would find a funny picture or some other picture that I thought would evoke a strong emotion and muse with one of my sons about what the title should be. How many titles or ideas can your child come up with?
  • Make writing a group effort. One activity we did was to have each child write part of the story. This is not only fun, but it takes the pressure off of coming up with the whole story.
  • Another thing I did was to write story starters on a strip of paper and have each child draw a topic from a jar. Some kids like the element of surprise and challenge.
  • For one son, he loved it when I wrote as he dictated to me. He had beautiful prose, but his handwriting held him back. So I would write as he focused on his thoughts. When I finished the draft, he would copy it. Eventually, his physical dexterity caught up with his creative mind.
WriteShop

Also, there are many writing programs that I have used through the years, but one of my favorite writing programs that not only taught writing well, but gave me support is WriteShop.

WriteShop has a unique way of helping the homeschool parent because it was written by homeschooling moms.

Not only does it have a fun way of helping the littlest budding writer, but it gives you practical tips in how to teach.

WriteShop Primary

A lot of writing programs can assume that you have a professional background as a teacher. I do not.

From the time you open the curriculum and read about setting a realistic schedule and see a visual of one to how to grade upper grade compositions, WriteShop guides you in every step.

Ruts can be valuable to a routine, but they can also hem you in.

How to Teach Cursive and Composition With A Fresh Perspective. When you need to veer off the beaten path when teaching cursive and composition because your well-worn path is not working, then you need a fresh perspective. Click here to read these valuable tips!

Fresh ideas in how to teach cursive and composition need to be nurtured. Try one or two of these ideas above and let me know how it works for you.

What do you do when you need a fresh perspective?

Also, I know you’ll find these other posts super helpful!

  • 3 Ways to Choose the BEST Writing Curriculum (for a Growing Homeschool Family)
  • How to Rock Creative Writing When Homeschooling (and when you don’t feel like THAT creative mom)
  • Cursive Matters; Handwriting Style Doesn’t + Free Resources

Hugs and love ya,

Leave a CommentFiled Under: Teach Homeschool Language Arts Tagged With: composition, cursive, handwriting, language arts, languagearts, teachingwriting, writing

2018 New Year New Goals Printable (Get It Together Girl)

December 24, 2017 | 1 Comment
This post may contain affiliate links. For more information, please see my full disclosure policy.

Today, I have ready the 2018 New Year Goals Free Printable ready.

I love this form because it not only reminds me to keep goal setting simple and not pen in a lot of goals so that I can reach them, but most important I remind myself to have Less of This.

It’s important to remind myself that some things I need to let go.

I don’t want to have pie in the sky goals, but to be reminded to homeschool and live simply.

New Year New Goals

I can only do that when I let go of things that are not working at the end of the year.

2018 New Year New Goals Printable (Get It Together Girl).I love this form because it not only reminds me to keep goal setting simple and not pen in a lot of goals so that I can reach them, but most important I remind myself to have Less of This. Click here to download this FREE and BEAUTIFUL form!For some years, the goals have been to be less critical of myself, to be less hard on my kids, or to be less judgmental.

As homeschoolers we’re constantly criticizing ourselves and can be our own worst enemy when it comes to meeting goals. We push ourselves to do more and more.

Goal Setting Means Doing LESS OF THIS

I’ve learned doing more means that I have to let go of something. Different things can weigh me down. I mentioned being too critical of myself is one thing that holds me back.

Letting go each year or at least reminding myself to let go each year, I can start with a fresh slate.

Also, I am renewed to keep homeschooling.

Maybe this next year you need to do more of something which is productive. Just remember that being productive means doing less of something. It means making room for it.

What are you going to be doing LESS OF this next year?

Grab the form below. It’s easy to fill out because it requires few words! Keep goal setting simple.

Download here the 2018 New Year New Goals Printable (Get It Together Girl)

Also, you may like my 2 page per month Appointment Keepers calendar pages to keep you on track. Grab what you need below.

2018 New Year New Goals Printable (Get It Together Girl).I love this form because it not only reminds me to keep goal setting simple and not pen in a lot of goals so that I can reach them, but most important I remind myself to have Less of This. Click here to download this FREE and BEAUTIFUL form!Hugs and love ya,

Are you ready to begin building your UNIQUE Homeschool Planner? There is NOT another one like it because YOU created it!

7 Easy Steps – “Tons of Options & Pretty Color” Begin building your planner

Step 1. Choose a Pretty Front/Back Cover

Step. 2. Choose Calendars/Appointment Keepers

Step 3. Choose Goals/Objectives

Step 4. Choose Lesson Planning Pages Right For You!

Step 5a. Choose Unique forms JUST for You! Not a kazillion other people

Step 5b. Choose MORE Unique Forms JUST for You!

Step 5c. Choose MORE MORE Unique Forms Just for You!

Step 6. Personalize It

Step 7. Bind it! Love it!

 

1 CommentFiled Under: 2. My FREE Organizing Printables {Any topic}, Curriculum Planner, Home Management Binder, Homeschool Planner Tagged With: calendar, curriculum pages, curriculum planner, freecalendars, freeprintables, goals, homeschool planner, lesson planner, lessonplanning

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

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