Please click on the thumbnails to enlarge the photos. The work above shows some more interesting strategies for subtracting and for showing possible combinations. On a recent test, students were asked to subtract $25,000 from $712,000. Many students used the traditional algorithm with mixed results. Today, the class decided that decomposing the numbers, less the 0s, and using positive and negative values made solving the problem easier. Most students realize that using negative values is way easier than it first sounds. Look at the middle photo.
The possible combinations problem involved making sandwiches with three major ingredients, a bread (Wheat or Rye), a meat (turkey, ham, or chicken), and a cheese (Swiss or American). Most students as comfortable using a tree diagram to show the combinations, but many students fail to understand exactly what a combination is. In this case, a combination is a type of bread with one type of meat and one type of cheese. Once that became clear, students could easily see (via their tree diagrams) that each bread type could have six possible combinations of ingredients. Look at the top photo.
