Comparing Fractions and Decimals

Students sometimes have a difficult time understanding how fractions and decimals are related and how they can be compared.  As always, providing a visual is essential for student understanding.  Once students have a strong understanding on how to compare fractions, you can add decimals to the mix.

Begin by having students put together their fraction tiles.  Give students 2 fractions to compare using one of the 5 strategies for Comparing Fractions.  For example, 2/5 and 2/8.  Have a discussion on how 2/5 is larger because both fractions have 2 pieces and fifths are larger than eighths.

Ask, how would the decimal 0.3 compare to those two fractions?  Students should realize that 0.3 is 3/10 and therefore would fall between the two fractions.

Finally, ask students “where would the decimal 0.35 fall?”  Discuss with students who this decimal is half way between 0.3 and 0.4.

This is a common misconception for students and providing that visual is a great way to strengthen student understanding of fractions and decimals.  Have students try several similar problems to strengthen their understanding of how decimals and fractions compare.

What strategies do you have for comparing fractions and decimals?

Using Algebra Tiles

Algebra tiles are a great way to make an abstract concept like Algebra, visual.  You will be amazed at the difference this tool will make for students.  Today I will first explain what the tiles represent.    Then, over the next few days I will be posting some lessons you can do using the Algebra Tiles.  The Algebra tiles I use can be purchased “>here, or you can download a free version here.

The small squares represent units.  The yellow side means to add and the red side means to subtract (or add a negative).  Therefore, to represent adding 5, I would use 5 yellow tiles.

To represent subtracting 3, I would use three red tiles.

The long tiles represent an unknown quantity, your variable.  The green side is for positive variables and the red side is for negative variables.  Therefore, to represent 3n, I would use three of the long green tiles.

To represent subtracting 2y or -2y, I would use two long red tiles.

Last, are the large square tiles.  These represent your variable squared, n².  Just like when using an area model to understand multiplication, you can see that n x n = n², our large square.

So, to represent 2w² you would use two large blue squares.

To represent subtracting g², or-g² you would use one large red square.

This is what the expression n² + 4n – 5 would look like.

Have your students practice representing simple expressions with the tiles so they fully understand how they work before moving forward with another lesson.

Comment below if you have used algebra tiles in your classroom or if you have any questions!