# Lesson 10

Here Comes the Sum

## Warm-up: Number Talk: Adding Fractions (10 minutes)

### Narrative

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.

### Launch

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

### Activity

• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Find the value of each expression mentally.

• $$\frac{2}{12}+\frac{1}{6}$$
• $$\frac{2}{6}+\frac{1}{2}$$
• $$\frac{1}{3}+\frac{1}{2}$$
• $$\frac{1}{3}+\frac{3}{2}$$

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “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.)

## Activity 1: Greatest Sum (15 minutes)

### Narrative

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
MLR8 Discussion Supports. Prior to solving the problems, invite students to make sense of the situations and take turns sharing their understanding with their partner. Listen for and clarify any questions about the context.
Engagement: Provide Access by Recruiting Interest. Leverage choice around perceived challenge. Invite students to select the order of problems in which they complete. Invite students to explain why they found which sum before others.
Supports accessibility for: Organization, Attention, Social-emotional skills

### Required Materials

Materials to Gather

### Required Preparation

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

### Launch

• 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
• Give students paper clips.
• “Now you will play 4 rounds of the Greatest Sum with your partner.”

### Activity

• 10–12 minutes: partner work time

### Student Facing

Use the directions to play Greatest Sum with a partner.

1. Spin the spinner.
2. Each player writes the number that was spun in an empty box for Round 1. Be sure your partner cannot see your paper.
3. Once a number is written down, it cannot be changed.
4. Continue spinning and writing numbers in the empty boxes until all 4 boxes have been filled.
5. Find the sum.
6. The person with the greater sum wins the round.
7. After all 4 rounds, the player who won the most rounds wins the game.
8. If there is a tie, players add the sums from all 4 rounds and the highest total sum wins the game.

Round 1

$$\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}} \,+ \,\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, =$$

Round 2

$$\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}} \,+ \, \frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, =$$

Round 3

$$\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, + \, \frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, =$$

Round 4

$$\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, + \, \frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, =$$

Total sum of all 4 rounds:

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “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.)

## Activity 2: Smallest Sum (20 minutes)

### Narrative

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).

### Required Materials

Materials to Gather

### Required Preparation

• Each group of 2 needs a paper clip.

### Launch

• 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.”

### Activity

• 10–15 minutes: partner work time

### Student Facing

Use the directions to play Smallest Sum with a partner.

1. Spin the spinner.
2. Each player writes the number that was spun in an empty box for Round 1. Be sure your partner cannot see your paper.
3. Once a number is written down, it cannot be changed.
4. Continue spinning and writing numbers in the empty boxes until all 4 boxes have been filled.
5. Find the sum.
6. The person with the lesser sum wins the round.
7. After all 4 rounds, the player who won the most rounds wins the game.
8. If there is a tie, players add the sums from all 4 rounds and the lesser total sum wins the game.

Round 1

$$\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, + \, \frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, =$$

Round 2

$$\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\,+\, \frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, =$$

Round 3

$$\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\,+\, \frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, =$$

Round 4

$$\frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}}\, +\, \frac{\boxed{\phantom{111\frac{1}{1}}}}{\boxed{\phantom{111\frac{1}{1}}}} \,=$$

Total sum of all 4 rounds:

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “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.)

## Lesson Synthesis

### Lesson Synthesis

“Today, we played some games that helped us practice adding fractions. How did the games help you think about adding fractions?” (I had to add the fractions that I made from the numbers I got with the spinner. The fractions in the sums had small denominators so it was not hard to find a common denominator.)

## Cool-down: Reflect on Fraction Addition (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.