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Extending to Symbols

6-8
In Parts I and II of this investigation, students learn about the notion of equivalence in concrete and numerical settings. As students begin to use symbolic representations they use variables as place holders or unknowns. This part of the i-Math investigation illustrates the continued transition from the concrete balance view of equivalence to a more abstract view.

Modeling Multiplication With Streets and Avenues

3-5
This lesson encourages students to explore the array model of multiplication, a model that lays an important foundation for the later study of area. The lesson focuses on the factors 4 and 6. Students will also explore products with 0 or 1 as a factors. First students make arrays with counters, and then they create a second concrete example of the array model using toothpicks. They also write problems which involve multiplication.

Big Math and Fries

6-8
We are lucky to live in an age where there is a lot of nutrition information available for the food we eat. The problem is that much of the data is expressed in percents and some of those percents can be misleading. This lesson is designed to enlighten students about how to calculate percent of calories from fat, carbohydrates, and protein. The calculations are made to determine if a person can follow the Zone Diet with only McDonald's food items.

Pan Balance – Shapes

3-5, 6-8
Use this tool to build up to algebraic thinking by exploring how to balance shapes of unknown weight.

Balancing Shapes

6-8
Students will balance shapes on the pan balance applet to study equality, essential to understanding algebra. Equivalent relationships will be recognized when the pans balance, demonstrating the properties of equality.

Balancing Act

Pre-K-2
Problems such as those in this activity help develop what students already know in preparation for writing equations and learning ways to solve for variables. Students use mathematical models to explore quantitative relationships. When presented with pictures of pan balances with one or more objects in each pan, they communicate relationships between the weights of the objects by comparing the balanced and unbalanced pans.

Pan Balance – Numbers

3-5, 6-8
Use this tool to strengthen understanding and computation of numerical expressions and equality using a balance scale.

Everything Balances Out in the End

6-8
Use a pan balance to study equality, order of operations, numerical and variable expressions, and other key algebraic concepts.

Exploring Equations Further

9-12
Starting from the concrete notion of weights and balance and moving to symbolic expressions and representations of functions, this i-Math investigation has focused on some of the issues that arise along the way. In this part, this connection is extended to functions. More sophisticated tools allow for a greater diversity of investigations.

Mouse=Mouse: Using a Book to Explore Variable and Equality

Pre-K-2
In the book Balancing Act by Ellen Stoll Walsh, two mice find a teeter-totter and have a fun time balancing each other. When more animal friends come along to join them, they find their teeter-totter unbalanced. This hands-on lesson uses the book as an introduction to the concept that both sides of an equation need to be equal and balanced in order to use the "equal to" symbol; otherwise the "not equal to" symbol must be used. In addition, students use pictures and symbolic letters to represent variables in an equation.