Importance of Higher Order Thinking in Mathematics Education

Oct 13, 2025 by wbrum.org 4 views

Introduction

Higher order thinking is a critical component of mathematics education, as it enables students to analyze and evaluate complex mathematical concepts. In this article, we will explore the concept of equivalent fractions and use area models to demonstrate whether Fred's statement is correct. We will also discuss the importance of higher order thinking in mathematics education and provide two real-world examples of equivalent fractions.

What are Equivalent Fractions?

Equivalent fractions are fractions that have the same value, even though they may look different. For example, the fractions $$\frac{1}{2}$$ and $$\frac{2}{4}$$ are equivalent because they both represent the same amount of a whole. In this article, we will examine whether the fractions $$\frac{1}{2}$$ and $$\frac{7}{8}$$ are equivalent.

Drawing Area Models

To determine whether the fractions $$\frac{1}{2}$$ and $$\frac{7}{8}$$ are equivalent, we can draw area models to represent each fraction. An area model is a visual representation of a fraction, where the numerator represents the number of equal parts and the denominator represents the total number of parts.

Area Model for $$\frac{1}{2}$$

To draw an area model for $$\frac{1}{2}$$, we can divide a rectangle into two equal parts. The numerator, 1, represents the number of equal parts, and the denominator, 2, represents the total number of parts.

+--------+
|       |
|  1/2  |
|       |
+--------+

Area Model for $$\frac{7}{8}$$

To draw an area model for $$\frac{7}{8}$$, we can divide a rectangle into eight equal parts and shade seven of them. The numerator, 7, represents the number of shaded parts, and the denominator, 8, represents the total number of parts.

+--------+--------+--------+--------+--------+--------+--------+--------+
|  1    |  1    |  1    |  1    |  1    |  1    |  1    |  1    |
|  2    |  2    |  2    |  2    |  2    |  2    |  2    |  2    |
+--------+--------+--------+--------+--------+--------+--------+--------+

Are $$\frac{1}{2}$$ and $$\frac{7}{8}$$ Equivalent?

By examining the area models, we can see that $$\frac{1}{2}$$ and $$\frac{7}{8}$$ are not equivalent fractions. The area model for $$\frac{1}{2}$$ represents one half of a rectangle, while the area model for $$\frac{7}{8}$$ represents seven eighths of a rectangle. These two fractions have different values and are not equivalent.

Importance of Higher Order Thinking in Mathematics Education

Higher order thinking is a critical component of mathematics education, as it enables students to analyze and evaluate complex mathematical concepts. By using area models to represent fractions, students can develop a deeper understanding of equivalent fractions and improve their problem-solving skills.

Real-World Examples of Equivalent Fractions

Equivalent fractions are used in a variety of real-world applications, including cooking, measurement, and finance. Here are two examples:

Example 1: Cooking

When baking a cake, a recipe may call for $$\frac{1}{2}$$ cup of sugar. However, the baker may only have $$\frac{3}{4}$$ cup of sugar available. In this case, the baker can use an area model to determine that $$\frac{1}{2}$$ and $$\frac{3}{4}$$ are equivalent fractions, and use the available sugar to make the cake.

Example 2: Measurement

When measuring a room for carpeting, a homeowner may need to calculate the area of the room in square feet. If the room is 12 feet by 15 feet, the homeowner can use an area model to determine that the area of the room is $$\frac{3}{4}$$ of a square foot. This is equivalent to $$\frac{1}{2}$$ of a square foot, which is a more common unit of measurement.

Conclusion

In conclusion, higher order thinking is a critical component of mathematics education, and equivalent fractions are an important concept in mathematics. By using area models to represent fractions, students can develop a deeper understanding of equivalent fractions and improve their problem-solving skills. We hope that this article has provided a clear explanation of equivalent fractions and the importance of higher order thinking in mathematics education.

References

[1] National Council of Teachers of Mathematics. (2013). Principles to Actions: Ensuring Mathematical Success for All.
[2] Mathematics Education Research Group of Australasia. (2015). Mathematics Education: A Guide for Teachers.
[3] National Center for Education Statistics. (2019). Mathematics Education in the United States.

Additional Resources

[1] Khan Academy. (n.d.). Equivalent Fractions.
[2] Math Open Reference. (n.d.). Equivalent Fractions.
[3] IXL. (n.d.). Equivalent Fractions.

Introduction

In our previous article, we explored the concept of equivalent fractions and used area models to demonstrate whether the fractions $$\frac{1}{2}$$ and $$\frac{7}{8}$$ are equivalent. We also discussed the importance of higher order thinking in mathematics education and provided two real-world examples of equivalent fractions. In this article, we will answer some frequently asked questions about equivalent fractions and provide additional resources for further learning.

Q&A

Q: What are equivalent fractions?

A: Equivalent fractions are fractions that have the same value, even though they may look different. For example, the fractions $$\frac{1}{2}$$ and $$\frac{2}{4}$$ are equivalent because they both represent the same amount of a whole.

Q: How can I determine if two fractions are equivalent?

A: To determine if two fractions are equivalent, you can use an area model to represent each fraction. If the area models are the same, then the fractions are equivalent.

Q: What are some real-world examples of equivalent fractions?

A: Equivalent fractions are used in a variety of real-world applications, including cooking, measurement, and finance. For example, when baking a cake, a recipe may call for $$\frac{1}{2}$$ cup of sugar. However, the baker may only have $$\frac{3}{4}$$ cup of sugar available. In this case, the baker can use an area model to determine that $$\frac{1}{2}$$ and $$\frac{3}{4}$$ are equivalent fractions.

Q: Why is it important to understand equivalent fractions?

A: Understanding equivalent fractions is important because it enables students to analyze and evaluate complex mathematical concepts. By using area models to represent fractions, students can develop a deeper understanding of equivalent fractions and improve their problem-solving skills.

Q: Can you provide some additional resources for further learning?

A: Yes, here are some additional resources for further learning:

[1] Khan Academy. (n.d.). Equivalent Fractions.
[2] Math Open Reference. (n.d.). Equivalent Fractions.
[3] IXL. (n.d.). Equivalent Fractions.
[4] National Council of Teachers of Mathematics. (2013). Principles to Actions: Ensuring Mathematical Success for All.
[5] Mathematics Education Research Group of Australasia. (2015). Mathematics Education: A Guide for Teachers.

Common Misconceptions

Misconception 1: Equivalent fractions are always the same.

A: Equivalent fractions are not always the same. For example, the fractions $$\frac{1}{2}$$ and $$\frac{3}{6}$$ are equivalent, but they are not the same.

Misconception 2: Equivalent fractions can only be found by simplifying fractions.

A: Equivalent fractions can be found by simplifying fractions, but they can also be found by using area models or other methods.

Misconception 3: Equivalent fractions are only used in simple math problems.

A: Equivalent fractions are used in a variety of math problems, including simple and complex problems.

Conclusion

In conclusion, equivalent fractions are an important concept in mathematics, and understanding them is crucial for students to develop a deeper understanding of mathematical concepts. By using area models to represent fractions, students can develop a deeper understanding of equivalent fractions and improve their problem-solving skills. We hope that this article has provided a clear explanation of equivalent fractions and the importance of higher order thinking in mathematics education.

References

[1] National Council of Teachers of Mathematics. (2013). Principles to Actions: Ensuring Mathematical Success for All.
[2] Mathematics Education Research Group of Australasia. (2015). Mathematics Education: A Guide for Teachers.
[3] National Center for Education Statistics. (2019). Mathematics Education in the United States.

Additional Resources

[1] Khan Academy. (n.d.). Equivalent Fractions.
[2] Math Open Reference. (n.d.). Equivalent Fractions.
[3] IXL. (n.d.). Equivalent Fractions.