Modeling Situations
Students can model situations using algebraic thinking before they are ready to think in terms of formulas and equations with variables. 'Doing" algebra is taking a situation, looking at its parts, and putting the parts into a 'whole' that makes sense. This analysis and synthesis process is the key to algebraic thinking. Students at 4th and 5th grade can use and develop these skills by creating models for situations, and describing them with sketches, words and numbers, moving into formulas and variables as they are ready.
We might begin by asking students to use toothpicks to model a rectangle that is twice as long as it is wide. The models might take on the following appearances (remember that there are many ways to think about these situations)...
Students might assign numerical lengths to these models, like 1x2, 3x6, etc...
Now, we ask students to determine the length of the long side if the short side measures100 linear units. The models could be used in this manner:
All of these models answer the question "What is the length of a rectangle whose length is twice its width, and whose width is 100 linear units?"
What if the width is 82 linear units? 75 linear units? Use a model to think about the rectangle and answer the questions.
We can use models for number puzzles, too. Suppose these lengths of straws represent 100 linear units and 1 linear unit:
What would the following collection of straw pieces represent?
Now let's solve some puzzle problems...
This straw represents a
secret number: 
Use straw pieces to model the following
situations...
Now, suppose my secret number is 50. What are the mystery numbers? Use your models to think about these numbers might be.
Here are some other situations to model and think about. What are some possible numbers that could 'fit' each situation?
Now that you've had some practice with simple models, let's go to Applying Models!