The purpose of this activity is for students to recognize that different strategies can be used to find common denominators. The two strategies highlighted in this activity are those with which students have worked throughout the last several lessons.

• Use the product of the two denominators.
• Use a smaller, recognizable, common multiple of the two denominators.
• Both strategies are valuable, and students can consider using these strategies in the next activity when they practice finding a variety of sums and differences.

When students evaluate the students’ claims about common denominators, they critique the reasoning of others (MP3).

• Invite previously selected students to share.
• “How do you know that 18 will not work as a common denominator?” (It is not a multiple of 8.)
• “How do you know that 24 will work as a common denominator?” (It is a multiple of 6 and 8.)
• “How do you know that 48 will work as a common denominator?” ( )
• “Which denominator do you prefer to use and why?” (I like 24 because it’s smaller, so the arithmetic is easier. I like 48 because I know right away which multiples to use to get the common denominator.)
• Invite students to share other common denominators that they found.
• “Would you use any of these denominators to find the sum? Why or why not?” (No, it makes the numbers bigger, and I need to figure out which multiple to use to get these common denominators.)

The purpose of this activity is for students to consider which common denominators will be most helpful to add and subtract fractions. The numbers for each problem are chosen to highlight different strategies. The first problem has different denominators, with one a multiple of the other. Students likely will recognize that they can use one of them as a common denominator, reducing the number of computations needed. The second problem does not have one denominator that is a multiple of the other. The numbers are small and their product is a good choice for a common denominator. The other problems have greater denominators that share common factors. For these problems, some students may prefer to find a smaller common denominator as it can make the arithmetic simpler. Other students may prefer taking the product of the denominators because they don’t need to work to find a common multiple of the two denominators.

• Display expression: 
• Invite students to share the denominators they used to find the value of the expression.
• “Why are there different choices for a common denominator?” (Any number that is a multiple of both 9 and 12 works.)
• Display expression:
• “Which common denominator did you use for these fractions?” (50 or 100, because I could see that they are common multiples and know what factors to multiply by 10 and by 25 to get those numbers.)
• “Which strategy do you prefer to use to find a common denominator?” (Using the product always works, but the multiplication can be challenging sometimes. Finding a smaller common denominator can be helpful because I might not have to multiply large numbers, but it can be time consuming.)