# 3.5 - Add and Subtract Fractions

The student will

• solve practical problems that involve addition and subtraction with proper fractions having like denominators of 12 or less.

### BIG IDEAS

• So that I can modify different amounts in order to create a product (e.g. doubling a recipe, creating a craft, etc.)

• So that I can combine distances to find a total (e.g. distances students ran, lengths on a ruler, etc.)

### UNDERSTANDING THE STANDARD

• Proper fractions, improper fractions, and mixed numbers are terms often used to describe fractions.  A proper fraction is a fraction whose numerator is less than the denominator.  An improper fraction is a fraction whose numerator is equal to or greater than the denominator.  An improper fraction may be expressed as a mixed number. A mixed number is written with two parts:  a whole number and a proper fraction (e.g., 3 5/8).
• When adding or subtracting fractions, an answer greater than one can be expressed as an improper fraction or the equivalent mixed number (e.g.,  3/5 + 4/5 = 7/5 = 1 2/5 ).
• When adding and subtracting fractions the fractions must represent like size units (e.g., one-fifth added to three-fifths is four-fifths). This understanding builds the foundation for why common denominators are necessary in future work with adding unlike fractions and for work in algebra when adding polynomial expressions.
• Reasonable answers to problems involving addition and subtraction of fractions can be established by using benchmarks such as 0, 1/2 , and 1. For example, 3/5 and  4/5 are each greater than 1/2, so their sum is greater than 1.
• Concrete materials and pictorial models representing area/regions (e.g., circles, squares, and rectangles), length/measurements (fraction bars and strips), and sets (counters) can be used to add and subtract fractions having like denominators of 12 or less.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

• Solve practical problems that involve addition and subtraction with proper fractions having like denominators of 12 or less, using concrete and pictorial models representing area/regions (e.g., circles, squares, and rectangles), length/measurements (e.g., fraction bars and strips), and sets (e.g., counters).

### KEY VOCABULARY

Updated: Aug 22, 2018