Lesson 11
Which One Doesn’t Belong?
Warmup: Which One Doesn’t Belong: Strings of Numbers (10 minutes)
Narrative
This warmup prompts students to compare four strings of numbers. To identify a string that doesn’t belong, students may use what they know about properties and kinds of numbers—factors and multiples, odd and even numbers, numbers in base ten, and so on.
This warmup also prepares students for a series of design activities that prepare students to create their own Which One Doesn’t Belong activity.
Launch
 Groups of 2
 Display the image.
Activity
 “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
 1 minute: quiet think time
 2–3 minutes: partner discussion
 Record responses.
Student Facing
Which one doesn’t belong?
 0, 4, 8, 12, 16
 3, 6, 9, 12, 15
 5, 105, 205, 305, 405
 6, 60, 600, 6,000, 60,000
Student Response
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Activity Synthesis
 “Let’s find at least one reason why each one doesn’t belong.”
 “What did you look for when deciding which one doesn’t belong, or when finding a reason why each one doesn’t belong?”
 “What did the writer of this activity have to consider when designing this activity?” (Sample responses: All items must have something in common, but each item must have a feature that the other three don’t have.)
Activity 1: Add One That Doesn’t Belong (20 minutes)
Narrative
In this activity, students use their knowledge of numbers in base ten and of geometric figures to complete two Which One Doesn’t Belong sets. Students first study the attributes of the given items. They articulate why the items all belong to a set and why each one has a reason not to belong. Next, they propose a new item that shares a feature with others in the set but also has a unique feature that excludes it from the set.
Advances: Speaking, Conversing.
Supports accessibility for: Language, Attention, Memory
Launch
 Groups of 3–4
 7–8 minutes: smallgroup work time on the first set
Activity
 Pause for a wholeclass discussion. Select a group to share their reasoning and new item. Record their responses.
 After their explanation, ask if others:
 reasoned the same way but created a different fourth item. Invite them to share their addition.
 saw other reasons why the given items belong in a set and why each one doesn’t.
 4 minutes: independent work time on the second set
 4 minutes: smallgroup discussion on the second set
Student Facing
Here are two incomplete Which One Doesn’t Belong sets, each with one item missing. For each set:
 Find at least one reason that all items belong in the set.
 Find at least one reason that each item doesn’t belong.
 Add an item to complete each set. Make sure there is at least one reason it belongs and one reason it doesn’t belong.

Set 1

A, C, and D all belong because . . .

A doesn't belong because . . .
C doesn't belong because . . .
D doesn't belong because . . .

Add a new item B. It belongs because . . .
It doesn't belong because . . .


Set 2

A, B, and D all belong because . . .

A doesn't belong because . . .
B doesn't belong because . . .
D doesn't belong because . . .

Add a new item C. It belongs because . . .
It doesn't belong because . . .

Student Response
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Activity Synthesis
 Select another group to share their responses, reasoning, and new item for the second set. Record their responses.
 Ask others in the class if they reasoned about the properties of the given figures the same way as the presenting group but produced a different item to complete the set. Invite them to share their thinking and creation.
Activity 2: Add Two That Don’t Belong (15 minutes)
Narrative
In the second round of analysis and design, students use their knowledge of operations and expressions to complete a Which One Doesn’t Belong set with two missing items. Students first study the attributes of the given items. They articulate why the items all belong to a set and why each one has a reason not to belong. Next, they propose a new item that shares a feature with others in the set but also has a unique feature that excludes it from the set.
Launch
 Groups of 2
 5 minutes: independent work time
Activity
 “Work with your partner to make sure each new item added to the set has a reason to belong and not to belong.”
 5 minutes: partner work time
Student Facing
Here is an incomplete Which One Doesn’t Belong set. It has two missing items.
 Find at least one reason that the first two items, A and B, belong in the set.

Add two items to complete the set. Make sure there is at least one reason that each new item belongs and at least one reason it doesn’t belong.
 C and D both belong because . . .
 C doesn't belong because . . .
 D doesn't belong because . . .
 After you’ve completed the set, check items A and B. Does each one still have a reason not to belong? If not, adjust your new items so that A and B are each still unique in some way.
Student Response
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Activity Synthesis
 Invite students to share their analyses and new items.
 “Why do both A and B belong to the set?”
 “What were some features of the expressions that you looked at or experimented with to complete your set?” (The kind of numbers used, how many numbers are used, the order of the numbers, the symbols, the value of the expression.)
 If no students considered the value of the expression, ask them about it.
 “After adding C and D, did A and B still have a reason not to belong in your set? Did you have to revise your items?”
Activity 3: Add Three That Don’t Belong [OPTIONAL] (30 minutes)
Narrative
In this optional third round of analysis and design activity, students are given only one item showing multidigit multiplication using an algorithm with partial products. Students apply their understanding of operations on multidigit numbers and algorithms to add three new items that would complete a Which One Doesn’t Belong set.
As before, students begin by examining what’s given, but because only one item is shown, they now have considerably more freedom to define the attributes of other items in the set. Expect the increased openness to be a greater cognitive lift for students and to yield more varied sets. For instance, students might add to the set an area diagram, a calculation in standard algorithm, and a division algorithm.
For the activity synthesis, ask each group to test their set by presenting it to another group, and then to make note of one or more ways to improve their set based on their peers’ feedback.
Launch
 Groups of 3–4
 “Look at the only item in the given Which One Doesn’t Belong set. What do you notice? What do you wonder?”
Activity
 1 minute: quiet think time
 2 minutes: Invite students to share as many observations as they can. Record their responses.
 “Work with your group to add three more items to make a Which One Doesn’t Belong set. Just like before, each item has to have at least one reason to belong and one reason not to.”
 12–15 minutes: group work time
 2–3 minutes: Record the completed set on poster paper.
Student Facing
Here is an incomplete Which One Doesn’t Belong set. It has three missing items.
Add three items to complete the set. Make sure there is at least one reason that all items belong and at least one reason each item doesn’t belong.
 They all belong in the set because . . .
 A doesn't belong because . . .
 B doesn't belong because . . .
 C doesn't belong because . . .
 D doesn't belong because . . .
Student Response
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Activity Synthesis
 “Partner with another group and take turns presenting your set. Give your audience 1 minute of quiet think time and 2 minutes to discuss their observations. Record their responses.”
 “Based on your peers’ feedback, make a note of changes your group could make to improve the set.”
 “What were some mathematical features you paid attention to when creating and checking the new items?” (Sample responses: the operation, number of digits, algorithm used, odd or evennumbered result, whether carrying was involved, whether the numbers represent certain quantities)
Lesson Synthesis
Lesson Synthesis
“Today (or the past couple of days) you’ve used your mathematical understanding to complete and improve several Which One Doesn’t Belong sets. You’ve also created an original set.“
“As you studied more and more sets, did you find yourself getting better at identifying reasons that items belong or do not belong together? If so, in what ways? If not, what were some challenges?”
“What did you pay attention to at the end that you hadn’t in the beginning?”
Cooldown: Reflection (5 minutes)
CoolDown
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