Session 10, Grades K-2, Part C:
More Problems That Illustrate Algebraic Thinking (45 minutes)

In This Part: Strips and Balancing Blocks | Shape Machines | Number Machines
Mystery Machines | Two-Steppers

At the K-2 grade level, there are many problems that prepare students for their later work in algebra. Experiences with these problems can also build bridges between arithmetic and algebra, while increasing the students' chances for success in future mathematics. Note 6

In this section we'll analyze problems at the K-2 level for their algebraic content. For each K-2 problem, find a mathematical solution, then answer questions (a)-(f) listed below. If it is helpful, print this page and refer to the questions as you work on each problem.

 a. What algebraic content is in the problems? b. What content does it prepare students for later? c. How does this content relate to the mathematical ideas in this course? d. How would your students approach this problem? e. What are other questions that might extend students' thinking about the problem? f. Does your current program in mathematics at your school include problems of this type?

Problem C1

Draw two strips with this pattern

 a. How many X's are in the two strips all together? b. How many +'s are in the two strips all together? c. Predict how many O's will be in four strips all together. d. How do you know? e. Draw the strips to check.
 Now draw four strips with this pattern:

 a. How many X's are in the four strips all together? b. How many O's are in the four strips all together? c. Predict how many X's will be in six strips all together. d. How do you know? e. Draw the strips to check.

Problem C2

For each scale, determine which weighs more -- the cube, the cylinder, or the sphere -- and explain how you know.

Which scale has the heavier blocks? Explain how you know.

 Problems adapted from Groundworks: Algebraic Thinking, Grade 1 and Grade 2, by Carole Greenes and Carol Findell (New York: Creative Publications, Wright Group/McGraw-Hill, 1998). The above materials may not be reproduced without the written permission of Wright Group/McGraw-Hill.
 Session 10, Grades K-2: Index | Notes | Solutions | Video