How to Make a Good Graph

There are some pretty basic guidelines when it comes to constructing graphs and it would be a good idea to make sure your kids know them too.

The first step is to determine which graph is appropriate for your data set. Will you make a bar graph? A line graph? A circle graph? Each type of graph presents information in a different way.

Line Graphs:

• Depict data when you want to see a relationship between two criteria- if you want to see if one variable increases or decreases as a result of a particular factor. 
• To determine the relationship, you look at the line to see if the trend is up or down or neutral. It can be up and down as well. The direction of the slope will tell you something about the trend in the data.
• They can show data over a period of time.
• These graphs can accommodate more than one set of data- you can make the lines different colors and do some comparing.

Bar Graphs:

• Bar graphs are used to show sets of data. 
• This is the graph to use when you have qualitative data to represent. Qualitative data is that which cannot be measured- so types of candy, books read, fish in the fish tank, etc. On the x axis you'd name the categories rather than making a scale of numbers.
• They can be made vertically or horizontally.
• Easily used in lots of subject areas because of the categories.

Circle Graphs:

• Represent a total amount or 100%
• The circle is divided into parts and works well when your data is broken down into percentages or fractions as they compare parts to the whole.
• This one is only used with you are graphing parts of data that make up a whole.

Every graph has to have a few things to be sure it is a well constructed graph and can be easily interpreted.

• Title- let the readers know what is depicted in the graph
• Label the x and y axis with the data set name and the units if there are any
• Evenly distribute the scale- make sure your graph begins at zero (most of the time) and counts away by a consistent amount. This is tricky sometimes to make sure you choose the right scale for your data set and sometimes is difficult for kids. A broken scale skews the data and can be misleading.
• Use a ruler! I would like to think this goes without saying, but neatly drawn lines is important in presentation and scale.
• Use color- graphs are visual representations and as such should be visually pleasing and eye catching.

Once your students are proficient at graph construction, you might consider ways to use technology to make a graph. The basics are still necessary so I think it's good practice for kids to be able to make a hand drawn graph first.

They can use a data spreadsheet (like Excel) to make their data charts and from there choose a graph they want to generate from that data. 

Now that you've made a good graph, there are a lot more ways to manipulate data (in the good way) to draw conclusions and make confident statements about what we are studying. I'll be sure to share those soon!

Using Ordinary Notebook Paper Day 3: Math Journals

Welcome to iHN's Hopscotch at Blog, She Wrote! My topic for the 10 day series is Ten Ways to Use Ordinary Notebook Paper. Thank you for joining me. Please take a moment to subscribe, so you don't miss out- you can follow, subscribe by email or RSS feed (just look to the right!) and follow Blog, She Wrote on Facebook, Twitter or Pinterest. I'd love it if you'd stay connected and visit again!

Today's notebook paper topic is: Math Journaling! Math Journaling is a great way to see how your student is processing math concepts. On a math journal page, you are trying to get your student to write about the math concept. You can use math prompts, have them explain a new concept you are ready to have them nail down, encourage drawing, etc. It's a creative way to practice math and it offers another way to learning for kids who think outside the traditional math box.

There are many resources available which will encourage a great math journal experience in your homeschool. 

• Math Journals at Blog, She Wrote- a link that takes you to posts about our math journals.
• Math Journal Pinterest Board- follow the link and check out math journaling ideas from around the internet.
• Books- There are a great many books devoted to creative math problem solving and puzzles. I've made a Pinterest board called resources for math to share my favorite math journaling resource books. I'll try to add some links on my living math page as well.
• Magazines- I often find relevant ideas in magazines that can be used in math journaling. I like to use a local regional magazine, for example, to create journaling activities. There are many ways to incorporate some math skills with some application to magazine topics.

I tasked my kids to make a geometry journal page last year.

This journal entry was an activity to accompany my fifth grader's Beyond FIAR study of Homer Price- on highways and interstates. The book is Real World Math for Hands On Fun.

This was a favorite- making a journal page devoted to all the math skills you use when you play the game Monopoly. This was especially fun after reading some strategy and history books about Monopoly. Like The Monopoly Book

If you haven't done any math journaling at your house, I encourage you to give it a try. I enjoy seeing how my kids will make a page so they can remember a concept. It's a pretty open and creative process and although my focus is on using notebook paper, don't be afraid to make the journal page interactive and use some lapbook elements as part of the page. The ideas I've shown here are just a few and are meant to illustrate that it doesn't have to be fancy and well planned to make a great page.

If you already do math journaling, tell us about something you enjoy using as a resource.

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Please visit the other bloggers participating in iHN's Hopscotch over the next two weeks. While you are taking a look at the other Hopscotchers, check out the Pin It to Win It giveaways sponsored by Prufrock Press.
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Decimals & Dolls

R11 is working with decimals. She's learning division and conversion from fraction to decimals and all the other fun things come with working with parts of a whole. I think she prefers whole numbers. Don't we all? In an effort to engage her, we've stalled in our Life of Fred Decimals and Percents to give her some increased understanding and practice.

While word problem concerning her interests are fun and easy to write, I'm going the extra mile to write problems where she has to measure and cut and make patterns and anything else I can think of to make the math problems real. Really real...not just sort of real.

I had R11 measure some items in her sewing world. I was really hoping for more decimals!

Measuring fabric to see if we can work in some division with decimals

Sometimes I'm just looking to have her convert fractions to decimals and work with the decimals.

Here's something else I must admit now. I don't make printables. There. I said it. I know there are so many homeschool bloggers out there making beautiful printables with convenient downloading at the ready. It's not really my gift. Oh sure...I can make a worksheet...used to do it all the time. But, a printable is a step up with fun graphics and for me it is not a simple way to homeschool. I waste too much time looking through membership files and websites for the perfect sheet to match our lesson and often I come up empty handed. Sometimes I do find just the sheet, but then all this time has gone by.

So, I grab a sheet of lined paper and I create. 

Fast, easy and not really professional at all, but we get to the doing. And that is what matters.

Geometry

We've been enjoying some new geometry concepts over the last couple of weeks. Last week we were focused on JrFLL and preparing for the big Expo which occurred on Saturday. Before that, we were knee deep in line segments, rays and angles. Oh my!

The list of terms which were turned into a notebook page. Illustrations by R11.

Some of the concepts on the list for R11 for geometry this year (some of them I9 will do as well. His 4th grade list is shorter):

• metric units
• coordinate planes
• volume of a cube or rectangular prism
• metric and customary unit conversion
• protractor and compass- lines and line segments, etc
• drawing angles
• drawing shapes
• congruent angles and porportion
• area of triangle, parallelogram
• Pi and the Circumference of a circle

J6 is working on measuring length, volume, weight and temperature. He will identify some more shapes as well. These concepts were taken from the Math on the Level Concept Chart. Remember I am preparing my children for Algebra and while some items on the Concept Chart are built upon other skills, some are not. The object is for my students to be ready for Algebra in 8th or 9th grade. E13 started Algebra I in the last quarter of 7th grade because he had mastered the skills necessary for Algebra success. R11 is probably more of a 9th grade Algebra student.

To add to our math journals, I had the kids make a notebook page about the new geometry terms. They did a nice job and they are doing well at remembering all the new words.

They could easily see the size of an angle by using two pencils.

We've also been using some pages from Math Mammoth Geometry I. It was a freebie recently and I grabbed it up. Math Mammoth is great for explaining new concepts and she has plenty of practice for the kids. I like to dabble in math practice sheets by the topic for my kids when I need them.

Measuring angles yesterday....this one is 180 degrees.

The kids are enjoying the unit. We do these new geometry concepts roughly three times a week and we do Life of Fred at least one other day and on the off days we do a math adventure of some sort.

Algebra I Progress

E13 has been working on Algebra I this year. We started with Saxon Algebra I (a free item on a table at co-op one week) late last school year and started up again in August. Although he was a good sport about doing 30 problems every day (writing out the whole problem) with Saxon, we have switched to using Fred primarily at this point. I was inserting Fred Beginning Algebra lessons in among the Saxon lessons a couple times a week just to change things up for E13 and to provide a different avenue for learning and remembering.

E13 does one or two Fred Companion lessons per day depending on the number of problems assigned.

When is the last time you saw our workboxes? Now the top two shelves no longer have boxes. I couldn't take it anymore- they were just not accommodating for notebooks. The binders lay flat on the top and second shelf and there are boxes for now on the bottom two. They hold projects and things- smaller items. What became of those boxes and their lids? Let's just say I was in charge of Operation Christmas Child at my church and children in 3rd world countries are now enjoying them. Win/win. No guilt...it turns out that workboxes are way to "school at home" for this borderline unschooling girl.

A look at the inside of E13's math journal

The Home Companion breaks the Beginning Algebra text into daily lessons. I highly recommend it if you are using Fred! In the last several lessons, he's been learning how to solve two variable equations with elimination and without.

Another favorite resource for him and R11- I sometimes pull out activities from here. Lots of algebraic reasoning in this book.

Last month, they played an interesting number game and we tested out a few theories at the book's suggestion.

It was the game of Euclid which Dan is still trying to figure out why they think it's a game! The kids thought it was fun. I'm pretty sure that is what counts!

Great news for Fred Beginning Algebra fans! Dr. Stan has just come out with a book on a Zillion Practice Problems for Beginning Algebra. I can't wait to get my copy as we continue on our Algebra journey with Fred!

10 Days of Science with Math: Relevant Resources

Today I want to share with you another great resource for math in your science. I discovered Yummy Math sometime during the last school year and it is really good stuff! I like to just see what is up on the home page because it always has seasonal items and current events right there. However, you can always search the site for topics that relate to what you are studying right now.

This is primarily middle school math, but you could modify the activities for younger kids. Lots of pre-algebra skills and beyond. Last year my then 7th grader was graphing lines and conic sections...how can you go wrong with an activity that asks your student to graph the parabola he is going to make as he shovels snow in the driveway? How?

Here are a few fine examples so you can have a guided glimpse!

• Hurricanes
• Earthquakes- this one popped up after the funky east coast earthquake from August
• Why Does It Stay in Orbit? a look at how the space shuttle stays in orbit in honor of Endeavor's last launch
• The Geometry of Flooding

I could go on and on! Seriously, this is an amazing resource for applied math. You won't be disappointed when you go looking for something relevant for math in your science.

Thanks for stopping by. If you have another resource to share, please leave a comment. I'd love to hear from you!


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Be sure to visit these brilliant women during our 10 days adventure between November 7th-18th! I love these ladies and we know you will too.

10 days of Character Studies | Confessions of a Homeschooler
10 days of Christmas Countdown Ideas | Milk & Cookies
10 days of Creative Writing | Chocolate on My Cranium
10 days of Crockpot Meals | The Happy Housewife
10 Days to a Godly Marriage | Women Living Well
10 Days of Growing Leaders | Mom's Mustard Seeds
10 Days of Homeschooling High School | Weird Unsocialized Homeschoolers
10 days of I Wish I Had Known | Fruit in Season
10 days of Keeping Your Marbles | The Tie That Binds Us
10 days of Kid-friendly Food | Planner Perfect
10 Days of Language Arts Lesson Planning | Jimmie's Collage
10 Days of Learning Apps | Daze of Adventure
10 Days of a Mason Jar Christmas | Cajun Joie de Vivre
10 Days of More JESUS in Christmas | Preschoolers and Peace
10 Days to a Peaceful Home | Raising Arrows
10 Days of Raising a Life-Long-Learner | Bright Ideas Press
10 days of Science with Math | Blog, She Wrote
10 days of Teaching Values | Our Journey Westward
10 days of Winning your Child's Heart | I Take Joy

Math Lessons

If you've been reading here a while, then you know that about two years ago I gave up using Horizons Math and began using Math on the Level. While Horizons was a very good fit for my computational whiz and problem lover, E13. It was a horrible fit for R11- the hands on artsy girl. There's only so many times you want to pay for a workbook (even if it's only $10) and whittle down how many problems are required only to watch the ones you did assign get finished only after hours and after a lot of tears. It really wasn't about the workbook anyway. It's not how I wanted our homeschool to look. We needed to make a change. Additionally, it was WAY too easy to send the kids away with their assigned set of problems and spend very little time in creative instruction. If I had to follow the manual for 3-4 different grades, that would have been a lot of time spent on math instruction alone. So, I decided on a more living math approach through Math on the Level.

One of our math resources- this is a great book for working with several kids of different skills and ages.

In this lesson, I was giving them differing amounts and asking them to find as many ways as they could to come up with that amount.

R11, in 6th grade, could find the most and this was a great activity for her.

She ran out of money before she ran out of ideas for combinations. Note that I used REAL money!

J6 was working on this too- never been taught with lots of lessons the value of coins or addition, but play pays off ladies! He rocked this activity. He found lots of coin combinations that added up to the total I gave him. Then I created a writing portion of the lesson for him.

This year my focus with him is on handwriting. However, he wants copywork more and I found success with a word list. I think his drawings of the coins look pretty good too!

This is a typical math day right now. We are focusing on money and decimals to start the year. Once the lesson is over, the older kids do their "5-A-Days" which is a set of five practice problems I give them based on what they need to review. I use the MOTL auto spreadsheet for this. Basically, it's an Excel spread sheet which I used to list out the concepts my kids have already been taught. Then when I tell it how often I want it reviewed, it generates a daily list of what types of problems my kids get each day for that week. It's a slick piece of programming let me tell you!

In another post (soon) I will explain the math concept target lists (the ones in my planner) and how I use them to design instruction and guide our way through the math year. I'll explain how often we do lessons on new concepts vs math adventures and how we record it all.

Fun with Math & Books

My kids really enjoy reading math books that have challenges in them. When I find them, I just set them out and at some point they will be discovered. This one is called, Go Figure! (A totally cool book about numbers) by DK Publishing.

I always leave a book I want my kids to find in conspicuous places like our living room coffee table- somehow they always gets noticed and poured through afterward!

With topics such as:

• Where do NUMBERS come from? A look at numbers in different cultures
• MAGIC Numbers- cool number tricks and special numbers like Pi, nature's numbers, and Pascal's Triangle
• SHAPING Up- a fun look at shapes in the world
• The World of MATH- probability, fractals, chaos theory, and the art of math

My kids had a great time looking through and learning about some fun concepts in math. I feel a math journal page or two coming on! I think one is due on Prime Numbers and how they are special and what they are used for. Do you know? Prime numbers are used in encrypting because the really large ones are so unbreakable in codes.

Some other fun math books we've enjoyed include, Cool Math, The Math Book for Girls (and other beings who can count), and Real World Math for Hands On Fun. We have others, but we haven't gotten a chance to use them yet.

This is a fun way to add to your math journal! I checked on my math journal link above to see what is up with the missing pages and have fixed it. If you've visited my math journal link before and thought it wasn't much, please visit again! You will find more examples of our math journaling now. We will definitely be scheduling in a math notebooking day this week. My 8yr old will doing a page on equivalent fractions. Stay tuned!

Sewing Math: Finding the Area of an Irregular Shape

R10 is working on transforming a little girl slipper pattern to an 18 inch doll slipper pattern. Her brother suggested finding the area of the shape and working from there...I believe we are working on "similar" shapes with this one.

So, we looked it up and decided the way to go was to divide the irregular shape into rectangles, squares and triangles and find the areas of those. So, she did and measured the sides. Then she got to practice:

• changing mixed numbers into improper fractions
• multiplying fractions
• changing fractions into mixed numbers
• reducing fractions
• area of a rectangle
• area of a triangle
• dividing fractions
• reciprocals

She got more than she bargained for, but she is still plugging away!

The Pattern- divided into common shapes and measured out

Our trusty Math on the Level manual for Geometry and Measurement- we reviewed the proper procedure here. I like the format of the quick reference for the teacher with MOTL.

Area of a triangle

I made this paper for her after showing her on scrap paper. I laid out the steps nicely so she could repeat it with each section. So much of what I am doing right now involves me quickly writing out an assignment for a child- not fancy but they are learning a TON!

learning to divide fractions by multiplying by the reciprocal

Sewing math is continuing to be a HUGE motivator for R10. More proof that using math instead of just doing math all the time is really effective. I'll have to update you when the smaller pattern is finished.

Felicity's Stitching

“Lissie my love,” said her mother. Her gentle voice sounded tired. “Look at this apron you sewed. I’ve had to rip out the hem on it again. It’s supposed to be 20 stitches to the inch, Lissie. And in a line. Yours fly all over. Your sister Nan sews more carefully, and she is but six years old.”

When I opened the first Felicity book to check on some vocabulary, this is the first paragraph I noticed. And I immediately thought- lesson!

R10 tries to make her stitches tiny

This was R's assignment- she had to draw a one inch line and try to draw 20 stitches along it. Then for some multiplication practice she had determine how many stitches Felicity would make in a 24 inch hem at 20 stitches per inch. Finally, I had her try it!

Here are the results! On the left is her hand sewn bag. Her first inch was more like 11 stitches, then she was able to tighten it up to 26 after that. We also decided to compare what the sewing machine would do with a standard stitch setting. 11 stitches to the inch. Priceless lessons all around on this day.

In the end, she had made two new sachet bags with the leftover potpourri from co-op (that she and sewing pal Betsy had ground together on a sewing day) Hey- I think I still need to blog about that...

It is amazing to me how much sewing we can squeeze into R10's daily lessons and how well she responds to it. Not only did we get to do some great applied math, but this has really improved her hand sewing skills as well! This is also a great lesson in just allowing time for opportunities to arise in your school day. Too much scheduled in doesn't leave the margin for these teachable moments in our day that are far better than the ones we had planned!

Measuring Investigations

In math we are doing a unit on geometry and measurement. We started with some simple investigations of measurement- specifically length and volume this day.

R10 is counting out her steps across the room

The kids recorded their estimates and results on our chalkboard. I love a good chalkboard.

We went outside to record steps across the yard in several directions and recorded the results.

We measured the volume of water using both non-standard and standard measurements.

We've been using some of the Math Mammoth Measurement 1 materials. The kids have been enjoying it.

During our family math time, we’ll be doing various activities with measurement. The older kids will be working on circle geometry in addition to conversions both within the English system and between it and the metric system.

After we did the measurements in the yard, we walked up and down our street to determine the length and we found that it's about a third of a mile. We used pedometers, but this weekend I'd like to try it with marking a bicycle wheel. We'll determine the number of rotations and then once we know the circumference we can do some distance calculations.

FAQ: Math on the Level

Our use of Math on the Level seems to be a very popular subject recently. In my inbox right now there are no less than three different notes asking about Math on the Level. So, I think it's time to do another update on MOTL and how we use it, why we like it that sort of thing. You can read more about why we chose to go with MOTL here. In fact, definitely check out that link. I talked about the program plenty there as well.

So, here is the FAQ Math on the Level style:

• Is it teacher intensive? Yes! Let's just get that out of the way first. By its very nature, Math on the Level requires some work from the teacher. This program is NOT for the person who likes the lessons and everything else spelled out for them. This is a GREAT program for people who want to individualize math instruction based on what their child needs. Therefore, the program provides you with many resources. It does not tell you what order or how or when you should teach it.
  
• Is it teacher overwhelming? No, I don't think so. BUT, I'm up for the task. I enjoy the challenge of putting things together for the kids to make math come alive. I don't spend tons of time putting lessons together. I do spend more time than I did when I had a box math curriculum.
• What about the price...seems expensive? Yup, it's pricey at first glance. $315 with shipping which takes roughly three days maximum. You'll have it in no time! BUT, this is a curriculum for kids preK through pre-algebra (grade 7 or 8). There are no consumables. If you invest in it and it works...that's it. You won't be paying this yearly.
• What about resale? Well, MOTL definitely holds its value. First though, you can use the program for 60 days and still send it back for a full refund. I've seen used sets going for $250 or more and selling. I think the purchases is worth the risk and the author allows you to sell on the yahoo group.
• Do I need the whole thing? Yes, eventually you will. You can buy it in different combos, but I think the best bet is to buy it all at once. I waited until I could. You need the entire set to take advantage of the math maturation concept. The author promotes the viewpoint that kids should be able to learn different concepts in math when they are ready and not necessarily in order except where that is important. For example, kids can learn basic geometry without knowing all their math facts. You can't explore this if you don't have all the instructional volumes.
• Can I do this without the program? Sure you can...Kendra at the Pumpkin Patch does a really fine job at this. MOTL is GREAT for when you want to leave behind the conventional programming, but don't want to be totally out on your own. It's a set of resources- the manuals provide the background you need as a teacher and some ideas for teaching a concept. They have sets of problems at the back that you use to create the 5-a-Days (more on those later). They have concept charts that show you what all your children need to know when they are through pre-algebra. The Math Adventures and Math Resources books give you charts, graphs, etc that you may need and give you ideas on how to do math with unit studies and how to create math experiences that are more applied in nature. The record keeping books is what it sounds like- it shows you the various ways you can keep track of what concepts your student is mastering. There is also a large excel file form you can use to automate the process of keeping track of concepts.
• What are 5-A-Days? These are the five problems you will create for your student to do each day to practice new concepts and review older ones. There are only 5 problems and you make them and rotate them. You can use the record keeping chart to mark when a problem is mastered and how often it should be rotated into the review.

I think that covers most of the questions that come up. In another post, I will go over how we use it and what our week looks like with MOTL. You know...the nuts and bolts of using MOTL on a daily basis.

Basically, I think it boils down to how you want to teach math. Do you want to work with your kids where they are and individualize their math or do you want to teach a boxed curriculum that dictates when and how concepts are taught. When you don't tailor math then ultimately for us, with our differing learning styles, we weren't using the program to its fullest. I would either resort to opening the book to the next set of problems or I would skip tons of repetition and then I'm not using all the resources I'd purchased.

When you think, "Can I do this?" You really need to think about your approach to teaching math. Is the extra time worth it? Will it be successful?

I still like Jim Trelease's quote from The Read Aloud Handbook when he says, "Parenting was not meant to be a time saving activity." This was in response to a parent telling him that reading separate books to his kids would take more time. I feel the same way about homeschooling- this was not meant to be a time saving endeavor. It's important to meet the needs of our kids. Even when it's not convenient or easy. Otherwise...I could send them down the road to the local brick building. That would save me lots of time.