Ms. Jackson has given the class some outlines to fill in with pattern blocks. She asks the class if they have any ideas about what would be the fastest way to fill the outlines with the fewest pattern blocks. Rob demonstrates that the way to use the fewest pattern blocks is to always try and use the yellow hexagons first, because they take up the most space.
During a math lesson involving 2-digit + 2-digit problems, Ms. Dodson asks the class if anyone can explain how they solved the problem 26 + 15. When Rea says, "I grouped by tens. 5 + 5 is 10; +20 is 30; +1 is 31," Ms. Dodson asks Rea to explain why she thinks that was the best way to solve the problem. Rea says, "It was quicker than counting on from 26 and faster than drawing 26 dots and 15 dots and counting them all."
The class is given a 3-D model of a dinosaur to assemble. Sandy recognizes that the model is a new kind of puzzle. She can tell from the picture of the completed model that the pieces of the dinosaur's backbone are all shaped the same, but are different sizes. Sandy separates all the pieces that form the dinosaur's backbone, using the same strategy that helps her solve jigsaw puzzles. She explains that her sorting the pieces first was better than starting the puzzle without sorting the pieces, because it's faster than looking for each pieces as you need it.
During an integrated lesson, collaborative groups are building models of four layers of the earth's crust. The available materials are cotton batting, play dough, plastic grass, Styrofoam peanuts, coffee grounds, and dried beans. Amy explains that they chose not to use the plastic grass because it would be crushed under the weight of any other material, and they didn't use the coffee grounds because they would mix with the other layers. Amy also explains that there were other solutions to the problem that worked, but that the one they chose worked best because of the density of the materials.

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