How to Add All the Numbers 1-100 In Under a Minute

Here’s a fun little math trick with a cool story behind it.  Ask the kids if they can figure out the sum of all the whole numbers between 1 and 100.  Then tell them about a kid who was able to figure it out in just a few seconds.

Carl Friedrich Gauss (1777-1855) is sometimes referred to as the “Prince of Mathematicians.”

https://upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Carl_Friedrich_Gauss_1840_by_Jensen.jpg/220px-Carl_Friedrich_Gauss_1840_by_Jensen.jpg

He was also a child prodigy.

When Carl was 9 or 10 years old in Germany, his teacher gave the class the assignment to add all the whole numbers from 1 to 100 (1+2+3+4+5 and so on) in order to keep them busy. Carl did the problem in his head almost immediately.  He wrote the answer on his slate, turned it in and sat down with his hands folded on his lap while (it is said) he teacher looked at him scornfully. When the teacher checked the stack of slates later, Carl was the only one to have the correct answer: 5050.

How did he do it?

Carl realized that he could add the numbers in pairs: 1+100, 2+99, 3+98, etc. and that every one of them added up to 101.

How to add all the numbers 1-100 in less than a minuteHe then simply multiplied 50 (the number of pairs of numbers he was adding) times 101 (the answer to every pair he added) to get 5050.

Here’s how to express this in algebra:

Use the formula Sn=n/2(a+l)

Sn is the sum of the numbers of terms

n is the total number of terms

a is the first term

l is the last term

Try it to figure out the sum of the numbers 1-10:

n= 10, a=1, l=10

So, Sn = 10/2(1+10)

= 5×11=55

Pretty cool, huh?

Fiona’s First Grade Math Goals

Fiona is loosely doing first grade this year (and some second grade).  You know we don’t strictly follow any skills lists or curricula, but I like to keep track of what kids her age would be covering in school and find ways to playfully teach those concepts through hands-on activities like using Cuisenaire rods, playing games, playing with math tools, measuring and making things, and so on.

a week's worth of fun mathI found this great resource at Houghton Mifflin that provides outlines, teaching tools, free printouts and family homework assignments to correspond with the concepts their textbooks teach in each year’s math books.  Here’s the general outline for their first grade math:

I plan to play with all of these concepts in the following months, and to make up some fun worksheets to reinforce the concepts.  I don’t generally print out worksheets and instead I write out problems myself in my kids’ homeschool notebooks.  It allows them to be more personal (I’ll often write out silly word problems or have sweet or funny copywork that is tailored to them, for instance), saves ink and cost, and makes it more fun for them.

They also provide these great teaching tools for the year:

A Week’s Worth of Fun Math Projects!

a week's worth of fun mathOne of my resolutions this year was to do some sort of fun math activity with the kids each day. I don’t care if it takes just a few minutes or what level it’s at, just as long as math play becomes a regular and enjoyable part of each day.

So far, we’ve been doing well. We’ve been playing with Cuisenaire rods, darts, dice, cards, silly word problems, made flower factors and so on.

Here are my plans for this week, in whatever order they work out. Since we have such snow and cold in Minnesota right now, I figured I would work that into some of the fun.

  1. Get a box of sugar cubes and divide them among the kids. Give them small things to measure in sugar cube units and show them how to figure out the items’ area by lining up sugar cubes along the length and width and multiplying the numbers, then have them fill in the area with sugar cubes and see if they get the same answer. Then have tea with sugar cubes.
  2. Tint some water with food coloring and fill various containers with it. Have the kids guess which containers hold more, and then measure. Compare tall, skinny, wide and oddly shaped containers. Then let the kids play at mixing the colors in the containers.
  3. Have each child guess the temperature outside and go see who’s closest. Subtract that temperature from the temperature inside to see how much warmer it is inside. Also check the temperature on the back porch, in the basement and in the refrigerator and freezer, and see how close they are to inside and outside temperatures.
  4. Sing 100 bottles of beer on the wall, the math version. Instead of taking one down, take turns singing out how many are taken down each time, and then as a group sing the answer. For instance, “95 bottles of beer on the wall, 95 bottles of beer… take 9 down, pass them around… 86 bottles of beer on the wall.” Feel free to switch out the traditional beer of the song for juice, milk, water or whatever your family chooses, of course!
  5. Give each child 25 chocolate chips. Ask them to figure out how many times 7 goes into 25 with the chips, with lines of 7 to show the answer. Eat the remainders. Then do it with 4’s, then 6’s, then 5’s and so on.
  6. Fill a measuring cup with one cup of snow, then bring it inside and let it melt. Make guesses on how much water it will melt into.  See who gets closest and subtract the difference, and talk about why snow takes up more volume than water.
  7. Play War, but make black cards positive and red cards negative.

If you have fun math ideas to share, please add them in the comments!

10 Fun Ways We’ve Learned and Played Lately

It’s been a while since I posted one of these updates.  🙂 Here’s a bit of what we’ve been up to lately.

1. Fiona has been doing lots of writing and copy work.  She loves writing and fills up page after page of dollar store handwriting and spelling workbooks.

2.  Rhia is learning to play the electric guitar.  She is already a wonderful acoustic guitar player and is now excited to get an electric guitar and learn that.  She’s been practicing on a guitar that Gabe (Toria’s fiance) has lent her.  I got her an amp for solstice and she is hoping to be able to buy the guitar by her (18th!) birthday at the end of the month.  She is not just a great guitar player but also a great song writer.  With her love of music and the connection she already has with small bands in around the country, I’m pretty sure her future will be in music in one way or another.

3.  And she’s still busy with photography… Speaking of Rhia’s music connections, she took some photos for a small Mankato area band last month and she’s done some concert photography for some bands at Minneapolis and Sioux Falls concerts.  I’m pretty sure photography will be in her future, too.  Here’s her photography page on Facebook.  she’d be thrilled if you liked it!

4.  Alex has been enjoying the snow.  It’s been bitterly cold, but any time it’s above zero he’s pretty happy to be making snow forts, building snow zombies and so on.

5.  Fiona learned to play happy birthday on the lap harp.  She and Alex also learned a bunch of other songs.

View this post on Instagram

❤️

A post shared by Alicia Bayer (@magicandmayhem) on

6.  Alex has been learning to cook more meals and treats.  His latest accomplishments are 2 minute microwave GF bread (which he made about 30 batches for family in the last month) and scrambled eggs.  He also helps me cook a lot, so he’s become a great sous chef for things like taquitos.

7.  Victoria and Gabe have been in their house for a month.  They got their first utility bill today!  Luckily the house is so small and they’re so frugal that it was a fraction of what ours is.  They come over for dinner just about every night but they are settling in well and finally have reliable heat (a big thing when it’s been 20 below zero!).

8.  We’ve been doing lots of visits to the Washington Pavilion science and art center.  I took advantage of a holiday special and renewed our membership, which Alex told me he really missed.  We try to visit every time we’re in Sioux Falls, which is often since Rhia’s BF lives there and it’s also where I do my bulk grocery shopping.

View this post on Instagram

#sciencefun #scienceforkids #realworldmath #homeschooling

A post shared by Alicia Bayer (@magicandmayhem) on

They have great science presentations and Alex and Fiona got to take part in one about physics.

And last time we headed over to the art center and the kids got to do some pretty cool spin art projects.  The only thing better than messy art is messy art you don’t have to set up yourself.  😉

9.  Jack is crazy about Hamilton and it’s led to all kinds of history education.  He knows all of the songs by heart and is really excited that the show is coming to Minnesota in 2018.  I’ve come to the conclusion that I could effortlessly teach him his entire high school curricula if I could find musicals for every subject.  😉

10. We’ve been doing tons of learning with Cuisenaire Rods and other hands-on math tools.

Alex and I even tried doing long division with Cuisenaire Roads, which is really tricky to wrap your brain around!

I also published another book (affiliate link: Acorn Foraging: Acorn Foraging: Everything You Need to Know to Harvest One of Autumn’s Best Wild Edible Foods, with Recipes, Photographs and Step-By-Step InstructionsEverything You Need to Know to Harvest One of Autumn’s Best Wild Edible Foods, with Recipes, Photographs and Step-By-Step Instructions) and we’ve been reading lots of books, playing with friends, going to movies (since Daryl and Rhia work for a local non-profit movie theater, our family can go at any hour and put on whatever movies we like, which makes for some pretty fun late-night excursions!), playing music, watching shows and the usual mayhem.

Now, I’ve promised a little girl that we’d do crafts so I should sign off.  I hope everything is wonderful in your corner of the world!

 

 

Dr. Evilton and His Evil Math Problems

You know we’ve never been normal homeschoolers, and that applies to how we typically do math, too.  Ever since the first kids were little, we’ve done math through fun activities, real-world applications and lots of wacky word problems.

Daryl has always been particularly fond of doing strange math challenges in the car while we’re driving.  Since we live in the middle of nowhere, that leads to lots of time in the car and it’s a perfect opportunity to create a little math fun with our captive audience.

I’ve posted about our “mad math” challenges before and I put some of them in my homeschooling column once (reposted now at the Magical Homeschool site).  Only my husband would make up math problems involving kidnapping Minnesota Vikings and figuring out how many could fit in grandma’s swimming pool.

It’s nice to know that some things don’t ever change.  We took the little ones to the science museum in Sioux Falls earlier this week, and on the drive Daryl started asking Alex all kinds of math questions involving yet another mad scientist (Dr. Evilton) and all of the jobs he wanted Alex to do for him as his henchman.

There were genetically engineered animals with extra body parts, hover cars of various weights and with various materials needed, budgets to figure out for evil inventions, energy sources with different needs, and so on. If Alex was taking a long time to answer, Daryl would caution him, “Careful, Dr. Evilton is coming closer to your desk with his henchman-whacking stick!”.

Alex did a remarkable job with even really complicated problems, and Dr. Evilton rewarded him with the promise of a cookie on his desk each day next week.  When Alex asked if they’d be gluten-free since he’s allergic, Daryl said that one would be.  But he wouldn’t know which one, because he is evil, after all.

That’s what you get when you work for evil scientists…..

chemist-2025955_640

50 Ways to Use a Pumpkin for Homeschooling

50 educational ways to use pumpkinsI should be doing a million things and need to drive part of the family to Mankato soon, but I miss this space and you all (or you one person perhaps at this point!) so I thought I would bop in here for a quick post.

Yes, only I would decide to post 50 ways to use a pumpkin for homeschooling off the top of my head for a quick post!  LOL  Some people play video games to get their minds off things and have fun.  I write.  🙂

So here goes….  All kinds of crazy ways to learn with that pumpkin before it goes in the compost pile or pie.

  1. Measure the circumference
  2. Guess its weight
  3. Roast the seeds and experiment with different seasonings
  4. Do a rubbing of its skin
  5. Find a recipe for stuffed pumpkins and bake dinner in it
  6. Draw it
  7. See if it floats in water
  8. Use a mallet and golf tees to poke a pattern of holes (immensely satisfying if not terrible educational)
  9. Write a haiku about it
  10. Print out these pumpkin life cycle printables
  11. Roast it and bake with it
  12. Leave it outside and see how it changes over time
  13. Finger paint on it, clean and repeat
  14. Plant some of its seeds
  15. Figure out its capacity (how much it holds)
  16. Think of an alternate way to figure out its capacity
  17. Compare its weight to other foods
  18. Bake two different pie recipes for pumpkin pie and see which one is better
  19. Write out pumpkin on a paper and see how many other words you can make with the letters (pump, kin, pin…)
  20. Write a short story about a pumpkin
  21. Use the seeds for math manipulatives
  22. Use the seeds for a collage
  23. Look up how to say pumpkin in another language
  24. Read books or stories about pumpkins
  25. Write letters on clean pumpkin seeds and use them to spell words
  26. Look up the history of jack-o-lanterns
  27. Look up the nutritional information for pumpkins
  28. Watch videos of pumpkin trebuchet launchers
  29. Or instead of launching pumpkins, use mini pumpkins to make small pumpkin catapults
  30. Build your own (or a small scale one for smaller objects)
  31. Make a list of as many words as possible to describe a pumpkin
  32. Estimate how many seeds a pumpkin will have and then see how close everybody got
  33. Read these pumpkin riddles and try to make up your own
  34. Write a song about pumpkins
  35. Make construction paper jack-o-lanterns with all kinds of faces
  36. Write the word pumpkin in your fanciest handwriting
  37. Think of 10 ways to use pumpkins besides for carving or baking
  38. Give a short report on the history of pumpkins and/or jack-o-lanterns
  39. Predict and observe what the inside of a jack-o-lantern looks like before and after having a candle in it for several hours
  40. Take artistic photographs of pumpkins
  41. Write or tell a funny short story about what it was really like for Cinderella to ride a pumpkin coach to the ball
  42. Put pumpkin seeds outside near a window and watch to see what kind of wildlife eats them
  43. Use pushpins and rubber bands to make a geoboard on a pumpkin
  44. Challenge the kids to think up other things you could make jack-o-lanterns out of besides pumpkins
  45. Ask the kids to describe a pumpkin using all 5 senses
  46. Invent a pumpkin spice drink or dessert together
  47. Use a small pumpkin as a ball for playing catch outside
  48. Use a small pumpkin as a planter and plant seeds in it
  49. Write a pumpkin acrostic poem (write the letters PUMPKIN down the side of the page and each line starts with the corresponding letter)
  50. After Halloween, cut your jack-o-lantern into one-inch pieces and put pieces in all different environments and record how they change (freezer, fridge, outside, in a plastic bag, uncovered at room temperature, in vinegar…)

Got more?  Leave them in the comments!  Happy Halloween!

Where Did Our Food Originate?

I stumbled onto this fantastic infographic showing where many of our foods first originated, and tracked it back to a scholarly article, Origins of food crops connect countries worldwide, published by The Proceedings of the Royal Society B (Biological Sciences).

Origins of food crops connect countries worldwide

(Click on the image to view full size)

The graphic and the article itself are published under a Creative Commons license, meaning it can be shared freely as long as the authors and original source are credited.

This could be used for so many ways in the homeschool — for geography, social studies, biology, math…

  • See what part of the world each component of lunch or dinner first came from.
  • See which common foods your family eats are not on the map and see if you can find out where they originally came from.
  • See which of the foods can now be grown in your area and which ones need a different climate.
  • See what part of the world has your favorite foods.
  • See what similarities you can find in foods from each region.
  • Categorize the foods into groups (fruits, grains, root vegetables, greens, etc.) and see if you can find patterns for the regions.
  • Which region has the most foods listed?
  • What percentage of the foods on the map are eaten at least once a month at your house?

The authors of the paper are:

Colin K. Khoury, Harold A. Achicanoy, Anne D. Bjorkman, Carlos Navarro-Racines, Luigi Guarino, Ximena Flores-Palacios, Johannes M. M. Engels, John H. Wiersema, Hannes Dempewolf, Steven Sotelo, Julian Ramírez-Villegas, Nora P. Castañeda-Álvarez, Cary Fowler, Andy Jarvis, Loren H. Rieseberg, Paul C. Struik
 .
Clearly they did a lot of work to assemble this.  Check out the paper itself for more graphics and a lot more information.

 

Save