It is important to learn to classify numbers because it helps us understand the different types of numbers and how they are related to each other. For example, if children are solving a math problem, they need to know what type of number they are working with in order to choose the correct operation.
Understanding the different types of numbers becomes increasingly important as learners progress through math. For instance, in algebra, students need to be able to differentiate between rational and irrational numbers in order to solve equations. In geometry, students need to be able to differentiate between integers and rational numbers in order to calculate areas and volumes. Therefore, our team at Alison’s Montessori created a new innovative material to help children keep working on such important foundational knowledge. Our material consists of an informed chart, a working chart, and number-printed cards. In this post, we emphasize the importance of working with numbers and suggest a way to introduce the materials.
Background Information about Numbers
As Montessori guides, we know that providing our learners with a strong foundation in mathematics is important. This includes teaching them about integers, whole, rational, irrational, and natural numbers. These different types of numbers are essential for understanding and solving many real-world problems.
For example, upper elementary learners work with integers on a number line, which are any whole numbers and their opposites (1, 2, 3, 4, -1, -2, -3, -4…). Later, learners learn to define rational numbers, which can be expressed as a fraction of two integers (2/10, -3/4…). Rational numbers are essential for understanding many concepts, such as money, time, and measurement. Learners learn that a rational number is a number that can be written as a/b where a and b are integers and where b is different from zero. This definition does not make much sense without a good understanding of the nature of numbers.
On the other hand, irrational numbers cannot be expressed as a fraction of two integers. They are less common than rational numbers in everyday life, but they are still important in many areas of mathematics, such as geometry and trigonometry. Irrational numbers are non-terminating (terminating decimals such as 0.25) and non-repeating decimals (repeating decimals such as 0.434343), such as pi and the square root of 2.
Teaching learners about rational, irrational, and natural numbers will prepare them for more advanced mathematical concepts, such as algebra, geometry, and calculus. Our simple yet powerful chart with cards will ensure independent access and repetitive experience to this foundational knowledge.
You will find below a brief description of how to organize our new material on Rational and Irrational Numbers Charts with Cards.
Materials
Rational and Irrational Numbers Charts with Cards
First, present the informed chart to your learners: “What is a natural number?” “Can you name some?” “What is not a natural number?” “What is a whole number?” “What about integers?” “What is the difference between whole numbers and integers?” Keep on providing support.
Next, place the mute chart with the columns and the cards in front of your learners. You can begin by modeling the process. Intentionally select natural and whole numbers. Place them in their respective categories. Proceed the same way with integers. Ask your learners to tell you the difference between whole numbers and integers.
Once every card is placed on the chart, you may discuss why some numbers may have fit into many categories. For instance, 5 is a real number, a whole number, a natural number, and an integer.
Finally, remove the cards from the chart and invite your learners to practice sorting the numbers on their own. Your learners may put the informed chart away if they want to practice without help. They may check the informed chart afterward.
We recommend you create a section in your math area for concept development materials, which are key foundational skills (see list below.) For more Montessori materials, visit our website at www.alisonsmontessori.com.
- Wooden Time Fractions
- Seven Triangles of Reality Matrix Control and Mute Charts
- Wooden Multiplication Wheel with Control Charts
- Fraction Classifications – Cloth Charts and Tiles
- Decimal Ruler
- Fraction Ruler
- Metric Ruler
