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Partner A: I think Dowon is right because there are two pieces of pizza. Both Dowon and Lisa will get a piece of pizza, so it seems fair to me.

Partner B: I agree with Lisa. The pizza is cut in two pieces, but they are not equal sizes. One person would get a smaller piece and the other would get a bigger piece. That doesn't seem fair.

Partner A: Oh, that makes sense! When we partition things in half, each part needs to be equal in size. I change my answer, I think Lisa is right.

Partner B: That's right! So the pizza is not partitioned in equal halves.

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Student Problem Using Paired Verbal Fluency 

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Student Problem Using Paired Verbal Fluency 

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Dowon and Lisa order a pizza to share. The pizza is cut into two pieces. Dowon thinks the pizza is correctly cut in half because there are two pieces. Lisa thinks the pizza is not cut correctly in half because the pieces are not equal. Who do you agree with? Why?

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1. What kinds of foods look like circles? (pizza, pie, tortilla/quesadilla, pancake/waffle)

When these foods are cut into pieces, this is called partitioning (part/partitioning).

Imagine you are sharing an apple pie after your Thanksgiving meal

Sharing with one other person - how would you partition this? (two equal halves)

Sharing with three other people - how would you partition this? (four equal fourths)

2. Folding pre-made circles in halves and fourths

In halves/fourths - what makes it halves/fourths? (two/four equal halves/fourths)

Examples of different orientation of the partitions (horizontal, vertical, oblique)

3. Non-examples

Show examples

Have students come up with examples, using circle worksheets (two examples, two non-examples)

4. Assessment - Paired Verbal Fluency (halves)

Display situation on the board, read through

Student on left is partner A; student on right is partner B

20 seconds for each partner to talk about answers

Share responses

5. Assessment - Exit Ticket (fourths)

Two examples and two non-examples provided (partner A version & partner B version)

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Reference List

Circle Worksheet

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appropriate & inappropriate applications of assessment

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appropriate & inappropriate applications of assessment

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Appropriate:

Useful in processing, organizing, and integrating information

When students have background knowledge of the subject

Can be used as a closure activity to summarize what they have learned

Can be used to activate prior knowledge before conducting a lesson

Allows students to practice oral language skills (eye contact, body language, summarization, asking for clarification)

Inappropriate:

When students have just been introduced to a topic and know little about it

When dealing with generalized topics; should be more specific in scope (should not address a whole unit but rather a subset of that unit)

May be difficult for English-language learners

May be difficult for students who have a hard time concentrating on listening or have small attention spans

High level of noise is generated as partners are talking, so it may be difficult for students to hear one another

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of Exit Ticket (Partner A)

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Terms/Ideas Addressed:

Partition

Halves

Fourths

Orientation of partition

Equal/Unequal parts

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Following a lesson on partitioning circles into halves and fourths, students will demonstrate their understanding by recognizing, on an exit ticket, two examples and two non-examples of circles.

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Paired Verbal Fluency (PVF) is a dialogue-centered strategy in which students summarize and reflect in an active verbal discussion. Students are paired with a partner and assigned a role as either partner A or B. The class will be provided with a prompt or a topic to discuss. Each partner will take turns discussing the given topic in timed rounds. The discussion rounds should be repeated two to three times to give students ample opportunity to construct meaning about a topic and learn from the ideas of others. When using this technique to access prior knowledge, it is recommended that the allotted discussion time should increase with each round. This gives students more time to think as they continue to access knowledge they already have. When using this technique to summarize learning, it is recommended that the allotted discussion time should decrease with each round. Because students are summarizing the learning, less time is required for each round as they and their partner have already covered the information. Students should be reminded to listen carefully to each other. After completion, the teacher can ask for a summary of what the students have discussed. Students can also record important key points they went over with their partner in a notebook to remember for a later time. Overall, this strategy is useful in having students display what they already know and build on their knowledge by listening to others in a short period of time.