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Activities

Mathematical activities and discussions serve as the major component of the Measuring Up Project.  These projects use various manipulatives, such as pattern blocks in the Planet Cafe problem, that help students discover patterns and relationships.   Other activities involve drawing and cutting out paper.   An exercise in enlarging a picture on grid paper, for example, evolved into a lesson on area and proportions.   An activity requiring cutting circles into 2 or more congruent pieces led to a discussion of fractions.  The teachers participating in this development project successfully implemented at least one of the activities presented during the sessions into their own classrooms.

Experiencing algebraic thinking:  The Planet Cafe Problem . . . 

The following describes the arrangement of tables and chairs in Uncle Bill's Cafe:

The tables are square in shape and orange colored.
The chairs are green and triangular in shape.
Uncle Bill always prefers to push the tables next to each other in a linear fashion for the different groups of customers as shown in the diagram.

The students diagram this model using pattern blocks and then explore the patterns and relationships between arrangements with one table, two tables, three tables, etc . . This problem also allows students to predict how many tables Uncle Bill would need if a party of, say 37, people were to arrive for lunch.

This problem extends into discussions about perimeter and algebraic expressions.  It also allows students to discover multiple ways to think and represent patterns and relationships, as well as realize other real life applications.

Investigating growth situations:  A focus on area measures and proportions . . .

This activity gives students an excellent opportunity to discover how an enlargement of a shape affects its area.  Depending on the grade level, the enlarged object can range from a simple shape, such as a rectangle, to a more challenging design, such as the sailboat pictured below.  After understanding how doubling the dimensions of an object affects its area, students can extend the problem and predict how the area of an object will be effected by tripling the dimensions.  Students may also think about how this applies to real life, such as enlarging a photograph on a copying machine.

Exploring fraction and proportion situations . . . 

This activity is an excellent way for students to discover how fractional pieces of a whole relate to each other.  The project has students create their own fraction circle kit by cutting circular pieces of paper into congruent slices.  Using the kit, students can then discover and see relationships between fractions, including size and arithmetic operations involving fractions.  The pieces are ideal for helping students solve word problems such as the following:

Linda's brownies recipe requires one-fourth cup of chocolate.
Linda has five-eighths cup of chocolate.
How many recipes could Linda prepare with all the chocolate that she had, if she had enough of all the other ingredients?
Please explain.

Using the fraction circle kits, the students work together to represent and solve the problem.  Finally, the students must be able to explain their solutions. 

Sample of Discussed Readings

Bay-Williams, J. M.  (2001).  What is algebra in elementary school?  Teaching Children Mathematics 8(4), 196-200.

Fouche, K.  (1997).  Algebra for everyone:  Start early.  Mathematics Teaching in the Middle School 2(4), 226-229.

Kieran, C.  (1991).  Helping to make the transition to algebra.  Arithmetic Teacher 38, 49-51.