My Favorite Lesson Many teachers dread teaching the order of operations because of its heavy procedural focus. How do we help students make sense of this seemingly arbitrary "order" and why does it hold true?

In this Make 10! Challenge, we have students explore the order of operations by using different operations to make the friendly number, 10.

The linchpin of the lesson hinges on using the meanings of the operations and representing them in different orders to show why we need to perform the operations in a specific order. Look at the counters on the right - what expression do you see? How does the representation show which order makes sense?

Using two-colored counters to show the order of operations

Two-colored counters show the different outcomes when completing the multiplication and addition in different orders in the expression 3 x 2 + 4.


Steve Wyborney has a great resource for developing number sense through his SPLAT! activities. Activities range from subitizing, adding and subtracting, to representing and writing multi-step equations!

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Base 10 Block Challenge

Understanding place value in base 10 and the relationship between adjacent place values by representing a two-digit number with the Base 10 blocks. Student need to represent a number between 40-49 using the Base 10 Blocks in at least 6 different ways. This requires them to redefine the “whole," meaning the small unit cube cannot represent 1 for the 6th representation.

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A Role for Rational Numbers

While fair sharing activities are a great way to introduce fractions, we need students to see that rational numbers are everywhere and they can be very useful! In this complex instruction tasks, teams of students work together to determine if they think the electoral college is "fair" and then defend their thinking and reasoning to the class.

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Counting Cubes

Adapted from NCTM's Principles to Actions Toolkit, this Counting Cubes Task incorporates the complex instruction structures like group roles.

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Linear vs Quadratic

This task builds off of one presented by Jo Boaler on page 65 of Mathematical Mindsets. First students build and analyze the given sequence of blocks to figure out how many blocks the nth position of the pattern, but then they have to create their own patterns: one with a linear growth and one with a quadratic growth.

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Ten Black Dots

This task starts off deceptively easy, asking students to figure out how many dots they would need to make their own Ten Black Dots book. But then they are challenged to create a book with 100 black dots and then n black dots! Students are unknowingly summing the first 10 whole numbers, then the first 100 whole numbers, and finding patterns to find the sum of the first n whole numbers!

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