Billiard Ball Problem

The Billiard Ball Problem is a beautiful exploration of a situation both natural and novel. Great for problem solving, with connections to ratio and proportion. Also check out this Billiard Ball simulator on Scratch.

Penny, Nickel, Dime

This version of Don’t Break the Bank is a hit with students, and also helps give a concrete meaning to place value by linking it to both money, addition, estimation, and multiplying by fives and tens. It takes very little time, so it can be used as a warmup, station activity, or in those five minutes before class ends. While …

Math Magic Trick

This trick is an extraordinary introduction to the power of algebraic thinking, and a reminder of what makes algebra so awe-inspiring. A video Launch for this lesson is available in two parts. PDF of the lesson is below the videos. Part 1. When using as a class launch, stop at 2:45 and let the class come up try to find …

Story Problem – The Kite

  Looking for more? Check out this student generated extra challenge question on this story. Remember that you can always ask students to come up with their own challenge problems if they finish early!


Story Problem – The Monster

For this long-form story problem, read the story to your class first, then give them the questions to answer, and the story as a reference. Optional artistic tie-in: draw a picture of the monster. Optional challenge: write another question about the story.

Pyramid Puzzles

Pyramid puzzles are a fun and deceptively tricky puzzle. Sometimes these can’t be done without some risk taking—encourage guessing and checking, and learning from the inevitable mistakes, especially on the harder puzzles. More on Pyramid Puzzles here.

What’s the biggest rectangle?

Math concepts: Area, perimeter, number patterns Materials: Graph paper, pencil Tags: 3.MD.7.a-b, 4.OA2, 4.OA.3, 4.OA.5, 4.OA.5, 5.OA.3, MP1, MP2, MP3, MP5, MP6, MP7. Of all the rectangles with a given perimeter, which one has the largest area? This simple question launches a fascinating exploration. The Launch Remind students of the definition of area and perimeter. Then pose the following question: …

Magic Squares

Topics: Addition, Subtraction, Logic Materials: Pencil and paper, Recommended Grades: 2, 3, 4 Common Core: Put the numbers 1-9 into a square so that every column, row, and diagonal adds to 15. Why We Love Magic Squares This is a truly historical problem, with roots in cultures around the world. The arithmetic looks fairly simple at first, but the problem …

The Calendar Problem

Topics: Multiplication, addition, Materials: Calendar, Hundreds chart, pencil and paper, calculator (optional) Common Core: 4.OA.1, 4.OA.3, 4.OA.5, 4.NBT.5, MP1, MP2, MP3, MP6, MP7, MP8 How can you add up these numbers so quickly? Why we love this lesson Simple to launch, instantly engaging and accessible, this puzzle is a beautiful demonstration of the usefulness of multiplication. Not only that, figuring …