# Laying the foundation for lifelong success in mathematics.

**The ***Tutoring 4 Less *approach to Elementary Math

*Tutoring 4 Less*approach to Elementary Math

At Tutoring 4 Less, our tutors help their students learn elementary math in a way that will serve them throughout their academic careers and their lives. They provide individualized instruction that focuses on building the foundation in key areas that will help unlock each student’s inherent reasoning and analytical skills.

At Tutoring 4 Less we recognize that each student has a different learning style and academic need. In order to address each student’s academic need accurately, we set each student’s individual learning goals by using our assessment tools along with school and parent feedback.

We aim to challenge all of our students by requiring them to use higher-order thinking to make connections between elementary math concepts and real world applications. We help our students develop the ability to apply the processes of mathematics in everyday life and to acquire a positive attitude towards math.

Elementary math structures, operations, and language provide students with the framework and tools for reasoning, justifying choices, and expressing ideas clearly. As students identify relationships between mathematical concepts and everyday situations they develop the ability to use math to extend and apply their knowledge in other academic areas such as art, science, history, language arts, and music. At *Tutoring 4 Less *we teach our students how to build bridges between math and the real world.

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**Elementary Math Overview**

Studies have shown that strong numeracy and literacy skills are essential in achieving a lifetime of success. Because of our technology-driven society successful individuals are required to think critically about problems and complex issues. Modern day students must be able to analyze and adapt to new situations, solve problems, and communicate their thinking clearly and effectively.

Elementary Math identifies specific areas of study within curriculum. The specific areas covered in elementary math are: Number Sense, Measurement, Geometry and Spatial Sense, Patterning, Algebra, Data Management and Probability.

**Below is a more detailed description of the topics we cover in elementary math:**

**Number Sense:**

Number sense refers to a general understanding of number and operations. It focuses on the ability to develop useful strategies for solving problems. Students are expected to understand the relationships amongst numbers and make connections in different ways to represent them. They learn how to count in various ways and develop an understanding of the four basic operations (adding, subtracting, multiplying and dividing). Number sense also influences effective computing skills.

**Measurement:**

The ability to understand measurements directly connects to the world in which we live. Many of these concepts are also directly connected to other subject areas such as science, social studies, architecture, and engineering. By studying the math of measurements students learn about different objects, their standard units, and the measuring tools and processes involved in measuring quantities such as density, length, area, volume, mass, temperature, and capacity.

They will learn about and use the standard units (kilograms, liters, and meters) to calculate the magnitude of different objects. They also deal with measurements of time and rate. Students also learn about the important relationships between a variety of shapes and figures, and how to calculate the perimeters, areas, volumes, surface area, and circumference of those shapes.

**Geometry and Spatial Sense:**

Spatial sense is the intuitive awareness of one’s surroundings and the objects in them. Geometry helps us represent and describe objects and their correlation to space and time. A strong sense of spatial relationships also reinforces a students understanding of numbers and measurement. Spatial sense is necessary for understanding and appreciating the many geometric aspects of our world.

Insights and intuitions about the characteristics of two-dimensional shapes and three-dimensional figures, the interrelationships of shapes, and the effects of changes to shapes are important aspects of spatial sense. Students develop their spatial sense by visualizing, drawing, and comparing shapes and figures in various positions. Mathematical concepts and skills related to location and movement are also addressed in this area of study.

**Patterning and Algebra:**

One of the central themes in elementary mathematics is the study of patterns and relationships. This area not only requires students to recognize, describe, and generalize patterns, it requires them to build mathematical models to discern observable patterns in the real world. Elementary students identify patterns in shapes, designs, and movements, as well as in sets of numbers. They study both repeating patterns as well as growing and shrinking patterns and develop ways to extend them.

Students also use graphs, tables, and verbal descriptions to represent relationships that generate patterns. Through activities and investigations students examine how patterns change in order to develop an understanding of variables as changing quantities. In the intermediate grades, students represent patterns algebraically and use these representations to make predictions.

A second focus of this subject area is on the concept of equality. Students look at different ways of using numbers to represent equal quantities. Variables are introduced as “unknowns”, and techniques for solving equations are developed. Problem solving provides students with opportunities to develop their ability to make generalizations and to deepen their understanding of the relationship between patterning and algebra.

**Data Management and Probability:**

The ability to understand and interpret data is essential in today’s technological society. This section focuses on teaching students to organize data, make sense of variables and patterns, and judge the logical validity of any claims and interpretations made. Even elementary students are expected to count objects and communicate their findings with charts and graphs.

Students should be able to collect, display, and interpret data to answer specific questions. They must also construct and analyze arguments that involve data and its illustration. All students need to understand the role probability plays in data collection and decision-making.