‘Mystery’ Warm-Ups, plus: Starting our Unit on Patterns


We found on our second quiz that many students were still struggling with word problems.  (Correct student quiz answers here.)  So we adapted some of  Steve Wyborney’s “Esti-mysteries”  to continue reviewing word problems, and students seem to enjoy these ‘mysteries’ and look forward to them.

Try these engaging warm-ups:

Important:  Take TIME when you show these. We try to slow down the process as much as possible (without totally ruining the tension!), in order to allow more students to spend the time they need thinking through the problems. Number 3 can be used as a “Number Talk’ to see how many ways students can see the problem 7 x 13.

On #1 and #2, students will need a small  100 chart  to cross out values as they solve.



Mental Math: On the next warm ups, we don’t allow pencils! We find that this increases student engagement, and they can’t ‘hide behind their pencils’.




Sharky (#6 and #7) is a popular addition to the warm ups!




We humans love patterns. We reproduce them in art, music and literature, we seek them out in nature, in daily life and even in the behavior of others. They allow us to make assumptions, develop strategies and navigate uncertainty. Patterns provide a sense of order – a comforting predictability in an otherwise mysterious universe.

The study of patterns should be central to our learning of mathematics. Luckily, children find them enticing, and enjoy observing and describing predictable changes in growth.

Day 1  – Square Numbers

Investigation:  We ask students to lay out one tile. Is it a square? What’s its area? Could  it be called 1-squared? Now lay out new tiles to show 2-squared, 3-squared and 4 squared. What do you notice?


Hmmm … do you want to change the colors of the tiles to show what you’re noticing?

3. Then students start on their classwork, which increases in difficulty as they go through it. Some students will need the whole time to complete 2 pages, while others will complete the whole 4 pages. This allows for differentiation by speed, which is the only difference we find matters in math. Speed (or lack of it!) is not necessarily an indicator of math ability. Many students who need time to process concepts end up being strong math thinkers in high school and beyond!


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