The concept of Least Common Denominator (LCD) is key to being able to add and subtract with fractions that have unlike denominators or compare the size of different fractions. It's essential for students to thoroughly grasp the idea, and until they do so, they can't move forward with fractions.
Modeling with LEGO bricks is the perfect way to teach students how to find the least common denominator. This method from Brick Math, called the "Fraction Train," starts with concrete representation of the math problem using bricks, to teach students exactly where the idea of a common denominator comes from.
1. Start by explaining that the process for finding Least Common Denominator with bricks is called the "Fraction Train." Have students build brick models of 2/3 and 3/4. Label them Fraction 1 and Fraction 2.
2. Discuss the value of the numerators and the denominators of 2/3 and 3/4. Ask students if the wholes are the same, and if not, which whole is larger? Explain that you will be finding the Least Common Denominator so you can compare the fractions.
3. Place one 1x3 brick on the baseplate, showing the denominator of Fraction 1, and under that, a 1x4 brick showing the denominator of Fraction 2.
Now it's time to start building your "fraction train." You'll be building out a train of bricks that makes a rectangle.
Add enough 1x3 bricks to the top row, and enough 1x4 bricks to the bottom row, until both rows are the same length and the bricks form a rectangle. Count the studs in each row (12) to find the Least Common Denominator—the smallest number that both denominators can divide into evenly.
Discuss the fact that 12 is also the equivalent whole for both fractions 2/3 and 3/4.
4. Now it's time to build the equivalent fractions for 2/3 and 3/4, using the Least Common Denominator of 12.
Place two 1x12 bricks on the baseplate to represent the LCD of 12 for each fraction.
5. Look at the fraction train again. There are 4 bricks in the top row of the fraction train. This shows the number of 1x2 bricks (from the numerator of Fraction 1) that will model the numerator of the equivalent fraction. Count the studs in the numerator (8) and the denominator (12) . This shows that the equivalent fraction for 2/3 is 8/12.
6. Repeat the process for Fraction 2. Count the studs on the model of the numerator (9) and on the denominator (12). The equivalent fraction for 3/4 is 9/12.
7. Now the equivalent fractions can be compared, since they both have the same denominator. Have students look at the numerators of each fraction and determine which fraction is larger, based on having the larger number of studs in the numerator. Extend the learning by having students draw their models. Have them write a math sentence that compares the two fractions (2/3 <3/4 because 8/12 < 9/12).