This algebra module has been designed to introduce kindergarten students to basic concepts of algebra and to enhance their problem solving skills. Each of the six sections of problems focuses on a key algebraic thinking strategy. Within each section, problems are sequenced by difficulty
This module may be used to complement the existing instructional program. It is particularly useful to reinforce concepts of number (counting, quantifying and comparing) and measurement (weight comparisons), as well as to develop problem solving skills.
The Key Algebraic Concepts
Equality/Inequality: In this module, students explore equal and unequal relationships by interpreting and reasoning about pictures of teeter totters with animals, one at each end of each teeter totter. Their job is to determine which animal is heavier, heaviest, lighter, lightest, or if the animals have the same weight.
Proportional Reasoning: A major reasoning method for solving algebraic problems is by reasoning proportionally. Proportional reasoning is sometimes called “multiplicative reasoning,” because it requires application of multiplication. In this module, students are introduced to proportional relationships when they “fill” glasses with straws (2 or 5 straws per glass), and count by 2s or 5s to figure out the total number of straws.
Interpret Representations: Mathematical relationships can be displayed in a variety of ways including with words, tables, graphs, diagrams and symbols. Having students interpret these types of displays and use the data in the displays to solve problems is critical to success with the study of algebra. In this module, students interpret pan balances, picture graphs, towers of numbers, letter patterns, and pictures of T-shirts with geometric shapes.
Reason Deductively: Students compare pictures to clues in order to figure out the one picture that fits all of the clues. They then describe the matching picture. For all problems, four pictures are presented. Given number towers with some numbers missing, students supply the missing numbers.
Reason Inductively: Presented with three rows of letters of a pattern, students identify the pattern and continue it by supplying the next two rows of letters.
The Problem Solving Five-Step Model
The model that we recommend to help students in all grades move through the solution problems has five steps. At the Pre-Kindergarten level, the focus is on Describe, Solve and Check.
Describe focuses students’ attention on the information in the problem display. In some cases, the display is a diagram. Other times it is a pictograph or model. Having students tell what they see will help them interpret the problem and figure out what to do to solve the problem.
My Job helps students focus on the task by having them tell what they have to do, that is, rephrase the problem in their own words.
Plan requires identification of the steps to follow to solve the problem and helps students focus on the first step. Knowing where to start is often the most difficult part of the solution process.
Solve is putting the plan to work and showing the steps.
Check is used to verify the answer.
We recommend that you “model” these steps in your instruction and that you encourage your students to follow the steps when solving the problems in this module and when describing their solution processes to others.