Third Grade: Fractions Word Problems

In this post, you will find a series of lessons on how to draw models for third-grade fractions word problems. Comment on this post with any questions or feedback. I’m getting a new mic, so I apologize for any fuzz. Sound level is fine.


Parent University: Singapore Math Models for Addition & Subtraction

This is a video of  the first half of a Parent University at Aspen Academy in Colorado. The video includes a short introduction to Singapore Math Models as well as sample problems for addition and subtraction word problems. Includes solutions for solving a variety of multi-step word problems and some amusing banter from the audience! Enjoy.

Read more about how parents learn about Singapore Math all over the world!

Metric Measurement Model

Simple Long Division Explained

Long division is very hard to teach. Students have to practice the process for a long period to ensure that they will recall at any given time. Introduce long division with the “why” and “how” and you will have better success.

Below are two videos explaining how to teach long division to your student(s). The first video explains 100 divided by 2 and the next is for 125 divided by 5.

The theory and language behind this method is based in Singapore Math instruction, assuming your student can mentally calculate, knows the concept of multiplication and division and uses visual models and language to solve math equations.

Teachers & parents, please comment on your experience with explaining long division! If you want to check homework, visit Long Division Calculator, but don’t tell the kids!

Don’t Let the Ship Down!

There are many examples of classroom games for practicing math facts with speed. But here’s a version that keeps students active, yet is simple enough for teachers to assess everyone individually. The kids call it Rocket Math, though different from the curriculum published  by D. Crawford. This is a game.

Students get in two lines. Head each line with a chair for the “pilots”.  Reveal a flash card to the pilots and have them call out the answer. The student who first calls out the correct answer gets to take the other pilot to their “wing”. The next two are up. Eventually, the rocket will become unbalanced and be taken down by the winning team!

I’ve noticed that students aren’t over-competitive with this game because they come up to challenge a different person most of the time. If anything, they get a general sense of whether they need to practice their facts in comparison to others in class. Years ago, I had a girl who struggled in math and was initially defeated in each play of Rocket Math only to come back after a long weekend with every fact down pat and ready to show it. Memorizing math facts is a task that is more representative of perseverance or “book smarts” than the ability to solve higher-order algorithms.

After watching the 3-minute video, you can see that teacher has a strong grasp on a few typical assessments:
1. Which students can state multiples of 2, 1 and 0 with automaticity?
2. Which students know their facts, but struggle under pressure?
3. Which students count their multiples to get an answer?
4. Which students struggle with confidence?
5. Which students watch the pilots while waiting in line to get extra exposure?
6. Which students miss the same fact repeatedly?

I have used “Jumping Calculator” and “Rocket Math” as primary practice of facts in the classroom. The result is total buy-in from students, as well as kinesthetic, visual and auditory presentation. Most important, the games are quick and free up time in the classroom to teach math as a language and subject. It’s nice to not spend 1/3 of the year on memorizing basic facts!

Challenge Comparison Model: Division

“Jumping Calculator” Build Muscles & Brain Cells in Math Class

To know math facts with automaticity and accuracy, students must be able to recall an answer without thinking twice. In fact, a true recall is a smooth as looking at someone’s face and knowing their name immediately. It takes practice and without that, you see kids counting up, guessing wrong and fatefully stalling out in math.

I created a multiplication fact memorization rewards program out of necessity and a need for parent buy in. I rolled my 1980’s jazzercise trampoline into the classroom and told the kids that they needed to memorize their multiples of 3 through 12. I explained that they wouldn’t “pass” unless they could say their multiples aloud in between each jump on the trampoline they were marveling at. Students immediately bought into the idea, but thought it was going to be too easy.


I decided to tie in a rewards program similar to most martial arts systems, where you “test” for a belt. A parent of one student owns a JuJutsu Academy and bought me 16 feet of every color belt they use at their academy. Next, a sweet grandparent volunteered to cut, sew and grommet each student a keychain-size belt that they can earn by jumping their multiples. The endless hours of sewing and promoting this program were worth it when the students were given their first testing day in math class last week.

To put anxieties aside, I let students “try” the tramp while jumping to their multiples of 2. They got the feel for speaking while jumping, timing each multiple as their feet hit the ground, and some humility. I set the groundrules for the program:

  1. No laughing. (unless someone falls off a 4-foot diameter trampoline)
  2. Hold all applause to the end. (passive agressive way to tell them to clap.)
  3. You can “try out” during math class or after school. (if you prefer a smaller audience)
  4. You have to say each multiple (through 12) before your feet hit the tramp.
  5. No gloating.
  6. Keep your keychain of belts in a safe place. (not easily replaced)
  7. Practice on the ground. That’s easier than the tramp.
  8. Milk your parents for all sorts of gratitude once you get your black belt!

The first “try outs” were a huge success. Some stumbled, but their confidence did not. The room was buzzing with studens practicing for their white belts (3’s). Next, they cheered eachother on as they earned their belt and set goals for the next one. Some were promising a black belt by Thanksgiving. Others were talking about whether their jumbo trampoline at home would be an advantage or disadvantage. Only one week in and the buy-in is huge.

So, the obvious question is…How will memorizing multiples help students learn their multiplication facts? First, students will look at a multiplication problem and automatically narrow their answer choices down to the 12 numbers called out while jumping. They will slowly narrow product choices to those within a reasonable range. When a student is asked 6×8 and they incorrectly answer 68, you can simply remind the student that 68 was NEVER a multiple they called out during their whole trampoline experience. Ruling out impossible answers helps students to grasp the reality of how many facts they really need to memorize.

  • white: 3’s
  • yellow: 4’s
  • orange: 5’s (easy motivator)
  • green: 6’s
  • blue: 7’s
  • purple: 8’s
  • brown:9’s
  • black: 12’s
  • Keep an inventory of which facts your student knows. Use many informal routes for quizzing throughout the day. If they are stumped, have them jump the multiples. See if that helps. It should. But if not, consider this: Their hearts are healthier, confidence is up and they have trained their brain to think quickly.