Okay, I’ll admit that Legos are a cliche in math problems for kids but to my credit, the student I was talking to suggested that Legos are something we buy in different sized packages.

Here is the problem:

Sally wanted to buy 473 legos.  At the store they are sold in packages of 100, 20, 5, and 1.  Show all the ways you can find that she can buy the exact number of legos.

Use pictures, numbers, and words to prove your answer.


Traffic Jam

As I move through this journey as a mathematics coach I see the way I look at the world change.  I find problems in more places and I see math opportunities in every direction.  I feel confident that if you are just beginning to make changes in the way you teach that this will happen to you also.

Here is an example.

Chinese Traffic Jam


This traffic jam in China was caused by construction back in 2010.  The traffic jam was 1000 km in length.  The average car is 4 m long.

Estimate how many cars you think could have been caught in the traffic jam.  Show why your answer is reasonable or not reasonable.

As we travel through this journey of mathematics I hope you will begin to see math everywhere as I am beginning to do.

Derived Facts

When one encounters a problem such as the one above there are four main strategies for solving.

1. Counting All – Begin at the first object and count all.    Most children use this strategy as they learn to count.

2. Counting On -As students develop they will notice the first number and then count on from that number, using it as a starting point to count on from.

3. Known Facts – Sometimes we just know the fact because it has been committed to memory.

4. Derived Facts – Another strategy for solving problems is to manipulate the numbers in the problem to make them easier to manage.  Students who use this strategy might make a group of ten and then see that there are two and three left which makes five.  They might also see that the numbers are close to 7+7 and since that is one less, and the known double 14, the answer must be 15.

Knowing that this is how students approach problems is important but it wasn’t until I was reading Jo Boaler’s book, What’s Math Got to Do with It? did I realize just HOW important it was.

Here I used the Create A Graph tool from NCES to show the frequency with which students 8 and older use these strategies to solve addition problems.


I encourage you to pick up a copy of Jo Boaler’s book, What’s Math Got to Do with It?.

Carnegie Art Museum Visit


On my recent trip to the Carnegie Art Museum in Pittsburgh I came across this work or art by Mel Bochner.  The opportunity to connect mathematics and art are often missed and this presents a wonderful problem.

While there are many ways to use this in the classroom but I would simply present the work to small groups and ask them to interpret it and then create their own work of art.  They could also trade diagrams and allow other groups to create their work.

Are there other ways to make a diagram of a block structure?