Help your learners create new connections between fractional parts and angle measurements! In the early elementary years, Montessori learners explore various names to describe angles: an acute angle is smaller than 90°, a right angle is 90°, an obtuse angle is more than 90° but less than 180°, a 180-degree angle is a straight angle, while an angle between 180° and 360° is a reflex angle, and finally, a 360° angle is a complete angle.
These concepts are usually presented using the Geometric Stick Material and reinforced using the Classified Geometry Nomenclature Cards. Our new set, Fractions with Degrees Activity Set, invites learners to work with concrete materials to observe and use cognitive reasoning to make the connections between separate skills they have previously acquired. The set contains a wooden graduated circle, labeled fractional parts from 1 to 1/10, and activity cards on all four arithmetic operations. The activity cards are divided into four sections, each covering one arithmetic process: addition, subtraction, multiplication, and division.
The activity cards require learners to add, subtract, multiply, or divide a given amount of fractional parts (1/8 + 1/8 =___) and to measure the angle of the fractional parts involved in the end process. Learners observe that 1/8 equals 45°. If they add two 1/8 fractional parts, they have 90° angles. Finally, they are asked to recall the names of the angles they have at the end of the process. Using visuals and concrete materials really helps learners appreciate the consistency of math. If we keep adding 1/8, we keep adding 45 degrees, which leads to 360° when eight 1/8 parts are combined. Each section of our activity cards is illustrated and explained in this post to let you appreciate the ingenuity of our exclusively designed material.
Materials
Fractions with Degrees Activity Set
or Fractions with Degrees & Fractions with Degrees Curriculum
Fractions with Degree Activity Cards
Section 1 – Adding Fractional Parts
Learners add fractional parts to form larger angles from acute to reflex angles in this section. The activity cards contain three commands, adding fractions with a common denominator (1/8 + 1/8), adding the same parts using degree values (90° + 90°), and providing the geometric term for the final angle formed by adding fractional parts (90° = right angle).
Section 2 – Subtracting Fractional Parts
The second section requires more attention. Learners work with fractional parts with uncommon denominators. For instance, they are provided 1/2, and they must subtract 3/8. By applying the subtrahend inside the graduated circle, learners can superimpose the fractional parts that serve as minuend (3/8 or 1/8 + 1/8 + 1/8) over the subtrahend to see the difference. It appears to be 1/8. They can verify this by looking at the degrees. 1/2 is 180°. When 45° x 3 is subtracted, it is left a fractional part space of 45°, which is 1/8.
Section 3 – Multiplying Fractional Parts
Section three reinforces the fact that multiplication is similar to addition. Learners select a fractional part (1/6 in our example to the right) that they take as many times as the multiplier indicates (4). They simply connect the parts in the circle to observe and read how many degrees the product would give. They observe that 1/6 equals 60°. They read on the circle that a total of four 1/6 is 240° (as in 4 x 6 = 24). Such an angle is called a reflex angle.
Section 4 – Dividing Fractional Parts
In the last section, learners must build whole angles using specific fractional parts (six 1/6, for instance). They are asked to divide the whole into specific parts (divided by 3, for instance). Finally, they must place the quotient in the graduated circle to measure the angle of the quotient and name the angle. This practice reinforces the difference between adding, subtracting, multiplying, or dividing, which are used through other concepts such as fractions or decimal numbers.
This unique method of fractional parts and degrees allows learners to work with higher thinking processes and create new mathematical connections that only experience and self-discovery can trigger. Along with this experience, learners are implicitly memorizing the angle value of many benchmark fractions, which will help with more complex learning processes in the future! For more Montessori materials and new support materials, regularly visit our website at www.alisonsmontessori.com.
