Rebecca Zook - Math Tutoring Online

When I was growing up, I learned to do elapsed time problems by subtracting the start time from the end time (and when necessary, borrowing while keeping in mind that there are 60 minutes in a hour).

This technique always seemed convoluted, so when a fifth grade tutoring student of mine was working on elapsed time problems, I tried this visual way of solving them, which seemed to be much more intuitive for my student.

Let’s say you have a problem like this: A train departs at 2:55 and arrives at 5:18. How long is the train ride?

First, draw a timeline:

Draw in the beginning and ending times, marking the hours as you go:

Draw loops to count the hours:

Add up the hours:

Draw loops to count the minutes left at either end:

Add the minutes together:

Combine the hours and the minutes, and you’re done!

That’s it!

Once you do a few of these, there’s lots of different ways to draw the loops. For example, you could start at 2:55 and loop to 3:55 (1 hour), 4:55 (2 hours), and then from 4:55 to 5:18 (4:55 to 5:00 is 5 minutes; 5:00 to 5:18 is 18 minutes; 5 + 18 = 23 minutes) to get 2 hours and 23 minutes.

And after drawing some of these out, you can use the same process to do elapsed time problems mentally, too. Just think about counting from one time marker to another and adding up the different loops.

*Visiting from this week’s Carnival of Homescooling? Welcome, I’m glad to see you here! Below are some more posts you may enjoy.

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Growing up, I remember learning to remember the difference between the greater than and less than signs by imagining a hungry alligator with an open mouth getting ready to “eat” the bigger number.

I recently got to work on this concept in an online tutoring session with a student of mine who’s a fifth grader.

First we had a regular < sign and we talked about the "alligator" idea.

He drew in some pointy alligator teeth:

Then he spontaneously drew a whole alligator:

As we worked on different inequality problems, he took it further. He drew a picture of a bird and explained that the bird’s closed little beak is shaped like an inequality sign. The bird would go for the smaller meal, while the alligator would go for the bigger meal.

And he topped it off – with sound effects.

The smaller number, which the bird would eat, has a “peck peck” sound. The larger number, which the alligator would eat, has a “chomp chomp” sound. Oh my gosh, I love it!

I’d never seen the alligator metaphor pushed this far before, and I wanted to share my student’s creative ideas!

What’s your favorite way to remember (or teach) the difference between the two signs?

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Do you need a way to remember unit conversion effortlessly and forever? Or just a way to calculate how many cups there are in a gallon?

Here’s how to figure it out. Draw a gallon man!

First, draw a really big capital G. (This is the gallon.)

Inside the G, draw four big Qs. (These are the quarts.)

Inside each Q, draw two Ps. (These are the pints.)

Inside each P, draw two cs. (These are the cups.)

For the final flourish, draw an arrow to one of the cs and write “8 ounces.” (There are eight ounces in every cup.)

When one of my students, a fifth grader, taught me about Gallon Man, I thought, I wish I had learned about this in fifth grade! My entire life, I’ve had to look up each of the conversions and never really internalized how they all fit together.

Since I’ve been introduced to Gallon Man, I’ve gleefully shared him with a fourth grade tutoring student (online), a friend who is a professional organic farmer (in person), innocent bystanders (at a restaurant), and most recently, my Mom (over the phone…”first, draw a really big G…”)!

They’ve all found Gallon Man helpful. Responses have included: “Can I take that drawing home with me?”, “Oh…I get it!”, and “I’m going to hold onto this.”

Gallon Man is totally visual and works for many learning styles. You can SEE how many quarts are INSIDE a gallon. Gallon Man is intuitive for all grade levels (unlike dimensional analysis, you don’t have to worry about the numerators or denominators). Gallon Man is practical. You can use it in your kitchen or in the grocery store. Gallon Man is easy to remember. And Gallon Man is fun to draw!

Gallon Man has recently gotten some airtime from other math bloggers, including Sam J Shah, who pointed out that it really helped him to see someone drawing Gallon Man. Here’s Sam’s post and video.

Yay for mnemonic devices!

*Are you looking for an online math tutor who uses multisensory methods? I’d love to help! Give me a call at 617-888-0160 to discuss your situation.

*Visiting from the Math Teachers at Play Carnival (Adventure Edition)? Welcome, I’m glad to see you here! Below are a few other posts you might enjoy!

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