Just what is algebraic thinking

Students decompose numbers at this level by using objects or drawings. They should record each decomposition by drawing a picture. If students write an equation, they must also share a pictorial representation or show using manipulatives. There are 7 pencils in the package. How many pencils are missing? Kindergarten students solve problems fluently, which means efficiently, accurately, and flexibly.

Accuracy means getting a correct answer, efficiently means solving a problem in a reasonable amount of steps, and flexibly means using strategies such as make ten, counting on, using doubles, using the commutative property, using fact families, etc.

Fluency does not mean knowing the answer instantly. First grade students identify, describe, and apply number patterns and properties in order to develop strategies for basic facts NCTM, Students in first grade solve addition and subtraction word problems with At this level, do not use letters for the unknown symbols; instead use a box, picture, or a question mark.

In first grade, students are learning to mathematize as they model addition and subtraction with objects, fingers, and drawings. This is foundational to algebraic thinking and problem solving. It is critical that students understand the problem situation and represent the problem. You can select the operation, the problem type, the unknown variable, and how many problems to generate.

As students solve word problems, it is critical that they not rely on keywords. Algebraic thinking includes recognizing and analyzing patterns, studying and representing relationships, making generalizations, and analyzing how things change. Of course, facility in using algebraic symbols is an integral part of becoming proficient in applying algebra to solve problems.

But trying to understand abstract symbolism without a foundation in thinking algebraically is likely to lead to frustration and failure. Algebraic thinking can begin when students begin their study of mathematics.

At the earliest grades, young children work with patterns. At an early age, children have a natural love of mathematics, and their curiosity is a strong motivator as they try to describe and extend patterns of shapes, colors, sounds, and eventually letters and numbers. And at a young age, children can begin to make generalizations about patterns that seem to be the same or different.

This kind of categorizing and generalizing is an important developmental step on the journey toward algebraic thinking. Throughout the elementary grades, patterns are not only an object of study but a tool as well. As students develop their understanding of numbers, they can use patterns in arrays of dots or objects to help them recognize what 6 is or whether 2 is larger than 3.

As they explore and understand addition, subtraction, multiplication, and division, they can look for patterns that help them learn procedures and facts. Subtract your original number again. Add Quadruple that! Tell me your result… Aha! Double that!

Your answer is your original number! Add 5. Subtract 1. Your answer is 9! It is certainly possible to make up tricks without the restrictions given here, but they are not suitable for most students in elementary school. The algebra is not harder, but the pictures and arithmetic can be harder.

How it works Click here to learn how to do this trick and to understand how it works. Related posts. Read more. Puzzles: Mobile Puzzles Read more. Puzzles: Logic Puzzles Read more. Teachers who help students to understand the specific procedures of arithmetic in ways conceptually consistent with the generalized procedures of algebra give students networks of connections that they can draw upon when they begin the formal study of algebra.

It involves properly using properties of the number system. It requires the ability to read, write, and manipulate both numbers and symbolic representations in formulas, expressions, equations, and inequalities.

In short, being fluent in the language of algebra requires both understanding the meaning of its vocabulary i. Functions and mathematical modelling represent forums for the application of algebraic ideas. Related documents. Algebraic Expressions. We believe the learning of mathematics takes place when students.