We have created a new set of task cards, Comparing Fractions, to help learners understand and manipulate fractions. Our set consists of 56 cards divided into five sections. Knowing how to compare fractions allows them to determine which bit is larger or smaller and to order them from least to most significant to least. Understanding fractions and their relationships is also essential in many daily activities, from cooking to time management to understanding measurements.
In real life, comparing fractions is helpful in many situations, such as when baking and following recipes, calculating scores in games or sports, and when converting between different units of measurement. Cognitively, learning how to compare fractions helps develop critical thinking and problem-solving skills, as well as logical reasoning and spatial awareness. It also allows children to strengthen their number sense and to identify and understand patterns. In this post, you will find a short description for each section to help you understand how the set has been scaffolded.
In this first section, learners use their visual perception to compare two fractions by using the lesser than and greater than signs. This practice allows them to work flexibly with fractions with different denominators. The answer is on the back of each card.
In the second section, learners can determine if two fractions are equivalent by using a process called “cross products.” The process consists of multiplying the numerator of one of the fractions, with the denominator of the other fraction, and repeating the process with the numerator of the second fraction with the first fraction. If the two product match, this proves that the fractions are equivalent. For instance, when comparing 3/6 and 4/8, one multiplies 3 x 8 and 4 x 6. Both products are 24 which mathematically proves that the two fractions are equivalent.
In the third section, learners are asked to compare two fractions by reducing them. They use the lesser than, greater than, or equal signs to solve the problem. A detailed answer can be found on the back of each card.
In section four, learners work with proper fractions. Proper fractions provide a clear visual representation of parts of a whole. They help develop a strong understanding of fractions as representing a portion or a part of a whole quantity. As an exercise, learners put together fractional parts to determine how many whole are formed, and how many fractional parts are left.
In the last section, learners are asked to bring fractional parts together and write down the proper fractions they form. This practice helps learners visualize both the concrete and written versions of a proper fraction. The answer is on the back, which makes the work independent work!
Our task cards are designed to support independent work and repetition in a Montessori learning environment. They follow through with presentations and do not prevent children from creating their own math problems. They are designed in a sequential manner that respects the order in which learning should be scaffolded.
For more Montessori math support materials, visit our website regularly at www.alisonsmontessori.com!
