Lesson 10

The purpose of this Number Talk is for students to demonstrate strategies they have for adding fractions with unlike denominators. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to add and subtract fractions with unlike denominators.

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “How do equivalent fractions help us add fractions with unlike denominators?” (It lets me find fractions with the same denominators and then I can just add the numerators.)
• “How do you decide on the denominator to use for your equivalent fractions?” (I either use a common multiple of the 2 denominators that I know or I can multiply the 2 denominators to find a common multiple.)

The purpose of this activity is for students to practice adding fractions with unlike denominators and to reason about how the size of the numerators and denominators impacts the value of a fraction (MP7). Monitor for students who:

• place any large numbers like 4, 5, and 6 in the numerator, if possible, and smaller numbers like 1, 2, and 3 in the denominator
• notice that there are many 1's and 2's on the spinner and try to wait for these and use them as denominators

• Each group of 2 needs 1 paper clip for their spinner.

• Groups of 2
• Display: \(\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, + \,\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\)

• Spin the spinner.
• Write the number in one of the four boxes.
• Repeat until all four boxes are filled.
• Ask students to compute the sum.
• “Is it possible to get a larger sum by placing the 4 digits in different boxes?”
• 1 minute: quiet think time
• Ask students to share.
• Give students paper clips.
• “Now you will play 4 rounds of the Greatest Sum with your partner.”

• 10–12 minutes: partner work time

• “What strategies were helpful as you played Greatest Sum?” (I tried to make fractions that have a larger numerator than denominator so they would be greater than one. I tried to make sure the ones and twos were in the denominator and put bigger numbers in the numerator.)
• “How did you add your fractions?” (My denominators were 1, 2, 3, and 4 so I used 12 as a common denominator for all of them.)

The purpose of this activity is for students to practice adding fractions with unlike denominators. Monitor for students who notice that the overall strategy in this game is the same as in the previous game except that the numbers that they placed in the numerator in the first game go in the denominator in this game and similarly the numbers that went in the denominator in the first game go in the numerator in this game (MP8).

• Each group of 2 needs a paper clip.

• Groups of 2
• “Take a minute to read over the directions for Smallest Sum.”
• 1 minute: quiet think time
• Give students paper clips.
• “Play Smallest Sum with your partner.”

• 10–15 minutes: partner work time

• “What strategies were helpful as you played Smallest Sum?” (I tried to make unit fractions with large denominators. I used the opposite strategy to the previous game, trying to put the smallest numbers in the numerator and the largest numbers in the denominator.)