Our Journey Westward » Math

Teaching Pi

Cindy — Mon, 12 Mar 2012 09:02:55 +0000

Did you know March 14 is Pi Day? Celebrate with some living math fun! If you can get your hands on Sir Cumference and the Dragon of Pi, it makes a great starting point to the celebration.

A lesson idea: This lesson is a quick and easy way to demonstrate Circumference = 3.1416 x diameter. Taking several sized lids, I asked the kiddos to trace five different lids on a piece of plain legal-sized paper. Using a centimeter tape measure, I asked them to measure the circumference and diameter of each lid and jot that down on their papers beside the appropriate drawing.

Using their measurements, I held my fingers on the tape measure to show the circumference and diameter of each lid. I asked them to think about what they noticed that was similar about each of the measurements. (The diameter is always about 1/3 of the circumference. You can show this by folding the tape measure in thirds each time.)

Once they saw this “almost 1/3″ measurement concretely, I told them there was a way to figure out the circumference accurately every single time. All they need to know is the diameter of the circle. I secretly held a calculator and asked them to give me the diameter of several of their lids. I would multiply the diameter by Pi (3.1416) and get their circumference measurement every time.

This, piqued their interest of course, and they couldn’t wait to find out the magic trick. So, I showed them the formula (C = ╥ · d) and allowed them to use the calculator to find several circumference measurements around the house. It was a great lesson inspired from Family Math, pg. 97!

Other lesson ideas:

These are mostly appropriate for middle school and older children, but be sure to check them out even if you have an upper elementary student.

Best Pizza Buy – money comparison activity(at the bottom of the PDF), plus another worthy idea or two

Pi Problem Solving – several problem solving prompts

How to Calculate Pi by Throwing Frozen Hot Dogs

Let Them Eat Pi – scavenger hunt, trivia research fun, cake activity and more

Tell me about your Pi Day activities!

M&M Math

Cindy — Mon, 20 Feb 2012 10:00:14 +0000

Talk about a fun week of math learning with M&M’s! Below you’ll find all sorts of activities we have done with M&M’s. Most of the ideas could easily be used with other types of candy pieces, too.

Estimation: Fill a jar with M&M’s and ask your children to estimate how many they think are in the jar. The older the child, the bigger the jar should be.

Sorting: Place a pile of M& M’s in front of each child and have them sort the candy into color groups. Older kids can sort according to various attributes, like colors containing red vs. those not containing red, for example. Let them sort as many times as they can think of a new attribute.

Counting: If you have younger children, count and tally the various color groups of M&M’s.

Add/Subtract/Multiply/Divide: Depending on the age/ability of your children, offer various operational problems to your children.

Red + Green =

R + G =

(R + G) x (Y – Bl) =

2(R + G) x 3(Y – Bl) x 12 =

Fair Shares and Division: Invite several stuffed animals over for a party. Divide the M&M’s into fair shares and determine if there are any remainders. Do this several times with varying numbers of “guests”.

Multiplication Arrays: Use the M&M’s to build multiplication arrays. (Not sure what an array is? Visit this site.)

Word Problems: If you have younger children, give oral word problems like, “You have three blue M&M’s and six yellow M&M’s. How many do you have altogether?” Use the M&M’s as manipulatives.

Older children should use the M&M’s to make up their own written word problems.

Mean, Median and Mode: A pile of M&M’s is a great opportunity to practice finding averages, middle numbers and the number occurring most often.

Fractions, Decimals and Percents: Use the pile of M&M’s to decide the fractional part of each color of M&M as compared to the entire group. For example, if you have 5 red M&M’s out of a total group of 25, the fraction would be 5/25 – reduced to 1/5. Transfer the fractions to decimals and percents, too.

Graphing: Make pictographs, bar graphs, comparison graphs, pie graphs, graphs made in a spreadsheet program on your computer. One or all, graphs are great fun. Find a printable M&M’s bar graph here.

Measurement: Use the M&M’s as measuring tools to find the length, width, circumference, radius, perimeter and/or area of various items around the house.

I’d say that’s just about enough math to rival any textbook curriculum for a week, don’t you?

I found some fun sites with other ideas for using M&M’s in your homeschool classroom.

And here are a few books that relate to candy math.

Candy Heart Valentine’s Day Math Printables

Cindy — Mon, 23 Jan 2012 06:00:39 +0000

A year or two ago, I created a couple of Valentine’s Day printables for you to enjoy with your children. I thought I’d remind you about them since V-Day is just around the corner. Simply click on the graphics to download.

The Measure of a Heart uses candy hearts to practice measuring perimeter and area. After finishing the worksheet, use your candy hearts to measure the perimeter and area of other things around the house.

(In case you need to know…Perimeter is the measurement around an object and area is the measurement of an object’s surface. To measure the perimeter of the hearts on the worksheet, place candy hearts around the edges of the hearts – the dark lines – and count how many it takes to go all the way around. To measure the area, see how many candy hearts will fit inside the hearts on the worksheet.)

The Candy Pattern worksheet (which didn’t transfer to a jpg well and is MUCH nicer in the PDF download) allows your child to make various patterns using candy hearts.

(In case you need to know…each of the letters on the worksheet (A, B, C) represent a different colored candy heart. So, for instance, an ABA pattern, where A represents pink and B represents green would look like: pink, green, pink, pink, green, pink, pink, green, pink. Your child gets to decide which colors represent each letter of the pattern.)

You can find several other fun math related V-Day ideas at Googol Learning.

I’ve been pinning fun ideas on my Valentine’s Pinterest board, too!

For those of you interested in learning how to add more living math into your homeschool, consider Loving Living Math.

Positive Negative Symmetry Art

Cindy — Thu, 19 Jan 2012 10:00:10 +0000

An art lesson that promotes mathematical thinking – oh joy. With the main focus being on the art concept of positive and negative space, throwing symmetry into the mix gave a nice extra punch to the lesson.

Positive space is the area on a piece of art which the subject occupies, while negative space is the area around the subject. You can see in this symmetrical example that the positive space is the pink on the left, but changes to yellow on the right.

The method is quite simple.

1. Find two contrasting colors of the same sized paper.

2. Fold both papers in half to establish the line of symmetry.

3. Set one paper aside.

4. Cut the 2nd piece of paper in half on the fold you just made. Discard one of the halves.

5. Draw 1/2 of a shape. (Like you would do if you were making paper hearts and planned to open the paper up once the heart was cut out. Except, in this case, you’ve already discarded the other half.)

6. Cut out your shape, keeping all pieces.

7. Place the positive space pieces on one side of the line of symmetry on the 2nd sheet of paper. Place the negative space pieces on the other side. Situate all the pieces so that they meet the line of symmetry perfectly and match up with one another.

8. Glue.

This lesson was inspired by Dick Blick and is one of the many integrated math and art lessons I’ve pinned on my Living Math Pinterest Page!

(Sorry, not the best photo, but I wanted you to see the possibilities.)

Candy Math and Science

Cindy — Wed, 02 Nov 2011 14:08:25 +0000

Got candy? We do, and we’re having so much fun using it during living math lessons! This year we added a little science classification to the mix, too. Fun! Fun! Fun!

Math

My preschooler made a concrete graph with his candy.

He had to sort the candy into groups before we could graph them and he created the group names all by himself – gum, chocolate, suckers, crunchy, chewy and hard.

After completing all sorts of averages based on different groupings of the candy, Caleb (6th grade) created this graph using Excel. (This is another great computer integration activity for those of you who’ve asked me to share more about how we use the computer in our homeschool!)

Science

Not a great picture, but I wanted you to see the entire concrete classification system my 6th grader made with his candy. {A classification system is otherwise known as a taxonomy, which we compared to the classification system for plants and animals.}

Beginning with the main group of ‘candy’, Caleb decided how to break the large group into two smaller groups. He came up with ‘chocolate’ and ‘non-chocolate’ as his descriptions.

For each new category, he continued breaking the groups down into two new categories until he ended up with each specific type of candy in it’s own pile.

Finally, we walked through each candy’s “classification”. An example from our taxonomy chart -Candy; chocolate; bright wrappers; made with peanuts; made with peanut butter, crunchy, Butterfinger. Besides being a science activity, this also fits into the category of logic!

Check out some other candy math lessons we’ve posted in the past, too!

Pumpkin Math

Cindy — Mon, 31 Oct 2011 09:00:16 +0000

We always enjoy a living math lesson with pumpkins! All our children participated according to their abilities – from the 4yo to the 14yo. The 11yo and 14yo were expected to measure with complete accuracy, while the 4yo dabbled in learning how to measure. He used standard (rulers) and non-standard (blocks) measuring tools.

We measured the height and width of each pumpkin.

We measured the weight with our bathroom scale. A nice kitchen scale (which we don't own) would've provided more accurate measurements.

We measured the circumference and the big kids used formulas to determine the diameter and radius.

Here's the beginning of Mahayla's record keeping.

When Eli saw his big brother and big sister keeping records, he insisted that he have a record keeping sheet, too. W = wide and T = tall.

We did a water displacement activity to find the volume of our pumpkins (you'll see below), but we didn't have a big enough container marked with measurements to make the pumpkin displacement accurate. To demonstrate the correct way to find volume, we used a measuring cup and potato. At least this gave them a better idea what we were doing wrong in measuring the volume of our pumkins.

In measuring the volume of our pumpkins, we made our own measurement bucket for estimations, but realized our measurements probably were not perfect, nor could we see through the bucket to see exact water levels. At least they have the experience and understand the flaws in our trial.

Of course, we couldn't end the lesson without carving our pumpkins! Through this process, we continued to measure width of the skin, depth of the cavity, and such. We also talked "science" as we discussed the pumpkin parts and their functions.

And, we couldn't end the lesson without a pumpkin treat. These are simple pumpkin bars that are so moist, they don't even need icing!

I hope you’ll find a few leftover pumpkins at the market and have your own living math lesson!

Abstract Art and Living Math

Cindy — Thu, 06 Oct 2011 09:00:30 +0000

Thanks to Pinterest, I am finally able to remember all those fun ideas I come across while surfing the Internet! This activity was stolen from Heather over at Blog, She Wrote. Thanks, Heather!

I love incorporating math with other subjects. In this simple activity, math and art come together to make a pretty spectacular finished product.

Use watercolors to make whatever design you like on card stock.
On the back of the dried artwork, use a ruler to make a grid of one-inch blocks.
Cut the blocks apart and mix the pieces up.
Lay the blocks randomly on another piece of card stock to create an abstract picture.
Glue the pieces down securely.

We didn't have carstock, so I substituted old folders. I would definitely plan to use cardstock next time for easier measuring.

Since math is part of the lesson, be precise in creating the grid and cutting the squares so the pieces fit together nicely in the final product.

Mahayla's fiished artwork.

Caleb's final artwork.

Cold Measurement

Cindy — Tue, 19 Jul 2011 23:25:36 +0000

I love to incorporate more than one subject at a time when possible. It not only saves time, but makes connections that are so important for children to understand.

Making measurement notes.

Last week, we were blessed with a dry snow that led to lots of snow drifts. I sent the kids on their merry way with a clipboard and measuring tools in hand. Their job was to find and measure as many snow drifts and icicles as possible, noting measurements on a scrap piece of paper.

Measuring icicles on the van.

Measuring icicles on the watering trough.

Measuring a small snow drift near the house so mom could get a picture from her cozy perch inside.

Preschoolers and dogs enjoy helping, too!

After a warm cup of hot chocolate, I pulled out these two notebooking pages from the Snow and Ice NaturExplorers study. (For the record, the pages within the unit are in color. I was out of color ink, so copied them in gray scale.)

On The Measure of Snow, they took their snow drift measurements and created a graph to display the information. My daughter began with a line graph, then changed her mind to watercolor a bar graph. Thus the eraser marks!

On Interesting Icicles, I had them order their measurements from shortest to longest and draw a picture of an icicle up-close. My oldest had to create her own graph from the icicle information, too.

They LOVE this kind of math – hands-on, active, meaningful, real. And, I didn’t have one complaint as they joyfully learned about and practiced accurate measuring, ordering mixed/decimal numbers, and completing/creating graphs. Ah, a fun time of math and nature study, indeed. (And I didn’t have to get out in the cold to boot!)

The Pumpkin Patch

Cindy — Tue, 19 Jul 2011 22:00:23 +0000

A yearly visit to the local pumpkin patch with our church’s family ministry is a highlight this time of year. And a great nature study outing, too!

As a homeschool teacher, I don’t let my kids often get away with only carving their pumpkins! Although, since we’ve been so busy this season, I did let them get away with only carving them just this once. What do I usually make them do? Fun math and science/nature study, of course!

Measure the circumference
Calculate the diameter and radius using only the circumference measurement
Weigh the pumpkins
Compare weights
Measure heights and widths
Measure the volume
Estimate the amount of seed
Count the seeds
Examine and open the seeds
Observe the difference between the inner and outer pumpkin shell
Measure the thickness of the shell
Examine the stem
Look for signs to see where the pumpkin touched the ground
Follow a recipe to make roasted pumpkin seeds

If you have any questions about how to do any of the math tasks I’ve suggested, just ask! They’re all very easy really.

This is a wonderful activity to supplement the NaturExplorers study of Fruits and Nuts this season!

Logic Giveaway!

Cindy — Mon, 23 May 2011 20:03:39 +0000

Giveaway Closed.

I just finished the manuscript for Homeschooling Gifted Kids and sent it to the publisher! WooHoo!! How about a giveaway to celebrate?

Prufrock Press (my publisher) is partnering with me for a living math giveaway! Today’s your lucky day because I’m going to offer ONE wonderful logic book to TWO lucky winners!

My son, Caleb, and I have used and loved both of these books. Don’t think I’m giving away my copies because they rest on my bookshelf waiting for Eli. The winners will get their very own brand-new copies!

Primarily Logic by Judy Leimbach is a fantastic book full of analogies, syllogisms, if-then statements, all-none statements and deductive reasoning for 2nd-4th graders. My son loved the fun worksheet challenges and I loved that each page provided plenty of examples and practice. I also appreciated the step-by-step approach to understanding each type of logic.

Logic Safari (Book 2) by Bonnie Risby is written for 3rd and 4th graders. It’s full of excellent logic matrix puzzles that Caleb (and Mahayla) simply devoured. We love these! This series is available in three different books that are appropriate for 1st-6th grades.

You have until Friday, May 27th to leave a comment on this post for a chance to win one of the books!

If your children are older than 2nd-4th grades, don’t worry. I’ll be giving away two more books very soon which are appropriate for 5-8th graders!

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