Thursday, September 10, 2020

Helping Kids Write Their Own Math Problems

In Third Grade, Waldorf embarks upon a study of the Maths of Practical Life: Clocks & Calendars, Temperature, Mass & Volume, and Linear Measurement.

I think it's nice to do real-life math problems starting in Second Grade as well, when you get past the First Grade work with the math gnomes and the gems and on into Column Algorithms and borrowing and carrying. We do this with the Montessori materials, since I find them most intuitive for this level.

Jamie York has a handout, by the way, about Word Problems throughout the grades: Word Problems in Grades 1-8 (PDF)

Actually, while I'm on the subject, Jamie York has a HUGE AMOUNT of free resources on his site including sample math MLB pages for grades 1-11, and lesson plans and assessments for grades 1-5, 6, 7, 8, 9, 10, 11, and 12.

If you're teaching your child math this year, you need to check out his site!

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So, I thought in September it would be fun to do our math review in terms of real-life subjects, by creating math problems that my students are interested in. This ranges from the Timeline of Life, to the Planets and Outer Space, to what lives in the Layers of the Ocean, to the sinking of the Titanic.

Below are a few of the books that I put in tote bags, along with some sample math problems. But I also encouraged each family to continue to come up with their own math problems based on things that their child is interested in. Here are some thoughts around that:

A calculator is fine, if your child is really interested in something and the math is past his/her current level (such as decimals). The idea first and foremost is for your child to have a sense of what operation a problem is: addition, subtraction, multiplication, division, or some combination of these.

If your child is struggling, try swapping out littler numbers into the problem and see what operation it would take. Sometimes they get bogged down in how big the numbers are.

For example, what if you are finding out how much larger the surface area of our Sun is than Jupiter? The Sun has an area of 2,351,362,145,523 square miles. Jupiter has an area of 23,710,000,000 square miles. You say to your child, do we add / subtract / multiply / divide? And they are thrilled to read these large numbers but stuck past that. You say, if the Sun was 130 square miles and Jupiter was 4 square miles and we wanted to find out how much bigger the Sun was, what would we do?

After figuring out the operation, if the math is something your child can do (especially with the support of the Montessori hands-on materials), go for it. If it's just out of reach, you can solve it and tell them the answer. You can solve part of the problem, and let them do part. Or you can show them how to use a calculator. Sometimes conversion calculators are really handy too!

For example, I wanted one student to walk out the length of the Titanic so that she could see how long it really was. But downloading an app to track how many feet she's walked as she trots along seems like a lot of extra work. Guess what I found?

Conversions: Feet ⇔ Miles ⇔ Steps – The Step-Counting Calculator

Simply convert 883 feet to steps
(and it gives you an option for different length of your steps)

    Average step length for people with a height of
    • 4'11" - 5'7"
    • 5'7" - 6'3"
    • Enter exact step length

Then it tells you how much to walk. For her, it would be 450 steps! You can also do this with the length of a really big dinosaur, which would be fun.

The thing that matters with a calculator is that they have to know what they are typing in and why (it goes back to the question of what operation is this). If that connection isn't made then the learning is lost. So the calculator can't replace the thinking-it-through part of the problem. It can, however, replace the computation if that's helpful scaffolding for your child. We don't want to stop them from asking questions that are too hard for them to solve. The more questions, the better!

You can also round numbers so that they are easier for your child to manipulate. For example, the Titanic was actually 882.75 feet long.

The Titanic: Lost... and Found

by Judy Donnelly

    How long ago did the Titanic sink?

Bizarre Dinosaurs: Some Very Strange Creatures and Why We Think They Got That Way

by Christopher Sloan

    How much longer was the Parasaurolophus than the Tuojiangosaurus?

    If a top hat is 8 inches high, how tall would a Dracorex wearing a top hat be? (Notice that you have to convert feet to inches first.)
    I don't know if this really counts as a real-life situation, but it would be awfully fun to draw in the MLB.

Coral Reefs: A Journey Through an Aquatic World Full of Wonder

by Jason Chin

    If it is 104 miles from Carbondale to St. Louis, is this longer or shorter than the length of the Belize barrier reef? How much longer or shorter?

Grand Canyon

by Jason Chin

    If it is 104 miles from Carbondale to St. Louis, is this longer or shorter than the length of the Grand Canyon? How much longer or shorter?

    If the Grand Canyon formed 5 million years ago, how much older is it than you? Than your dad?


by Jason Chin

    How much does a moose weigh? How does it compare to the huge masses of ferns found in one redwood tree mentioned in Redwoods?

Astronomy for Kids: How to Explore Outer Space with Binoculars, a Telescope, or Just Your Eyes!

by Bruce Betts

    On page 143 of Astronomy for Kids, it says that ancient Chinese astronomers observed a supernova in 1054. How long ago was that?

Gross as a Snot Otter: Discovering the World's Most Disgusting Animals

by Jess Keating

    How much longer is a herring than a parrotfish (in cm)?

Cute as an Axolotl: Discovering the World's Most Adorable Animals

by Jess Keating

    How many bare-hearted glass frogs would it take to equal the length of a dwarf flying squirrel?

What Makes a Monster?: Discovering the World's Scariest Creatures

by Jess Keating

    The float of the Portuguese man-of-war is one foot long. This is the same as how many tyrant leech kings? (Notice that you have to convert feet to inches first.)

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