Session 5: Model Lesson (U5L5)
50 minutes
lesson exploration
Purpose
This model lesson is intended to introduce participants to the binary number system while modeling classroom practices related to learning in context and differentiation.
Objectives
- Participants are exposed to the essential content knowledge necessary to plan and implement Lesson 5 of Unit 5.
- Participants observe a plan for early finishers that focuses on going deeper into the content instead of faster or further.
- Participants identify strategies for incorporating a variety of student perspectives into the classroom.
Supplies & Prep
Room Setup:
- Participants seated in pods
Facilitator Supplies:
Teacher Supplies:
- Printed copies of the “Representing Numbers 2021” - Activity Guide
- Printed copies of number cards (Alternatively use post-it notes)
- Scissors (if the cards are not precut)
Agenda
Warm Up (5 minutes)
Activity (35 minutes)
Wrap Up (10 minutes)
Facilitation Guide
Warm Up (5 minutes)
(5 minutes) Numerical Data
The “ideas to get you started” prompts below are taken directly from the curriculum. This is an opportunity to model modifying the lesson plan to be more personally relevant for the people in the room. Think about stores or businesses popular in your area or maybe a local weather issue that involves data collection in the form of numbers that could be substituted here.
Prompt: Create a list of all the information you might want to represent to a computer as a number. Here are some ideas to get you started
- An online store (what kinds of numbers does a store keep track of?)
- A social media profile (what things about you or your friends are numbers?)
Discussion Goal
In this and the following lessons students will be learning a new system to represent numbers using on-off signals. Motivate this activity by thinking back to the kinds of information students eventually will want to represent with this system. If students need help brainstorming give them a couple examples, e.g. age, their height, their birthday, the number of friends they have, the cost of items, an item's rating, etc.
Think - Pair - Share: Allow students a minute to think silently before having them share with their tables and then the group as a whole.
- (1 minute) Think: individual reflection
- (1 minutes) Pair: discuss with a partner
- (3 minutes) Share: share and discuss with the whole group
Remarks
Numbers are a really useful and important way to represent all kinds of information. If we want to represent numbers to a computer, we're going to have to learn a new system that allows us to do that. The “Question of the Day” is What system do computers use to represent numbers?
Activity (35 minutes)
(5 minutes) Model
Complete an example problem as a whole group. Ask students to arrange cards face up and face down so that exactly thirteen dots are showing. (It is important that each group uses only one set of cards.) After some trial and error, students should see that the 8, 4, and 1 cards should be face up, and the 2 card should be face down. (U U D U)
(10 minutes) Practice
Facilitator Tip
The number cards will need to be cut. This can be done by the facilitator before the workshop or by the participants during the workshop. If the plan is for the participants to cut out the cards during the workshop, scissors will need to be available for participant use. You might also consider having participants create the number cards using post-its to eliminate the need for printing and cutting.
Distribute: Give each pair a copy of the activity guide and a set of number cards.
Facilitator Tip
As participants are working, circulate the room and spot check for correct answers on the activity guide. Some answers will vary (numbers 1 - 4 on page 1 and numbers 5 and 6 in “Decoding Multiple Numbers” on page 2). Use the following guide to check for accuracy: 
Allow students to complete the rest of the first page in pairs. Ask them to raise their hand when they complete the first page to receive further instructions.
Part of what you are modeling here is how to differentiate to meet the unique learning needs within the room. Part of the is having a plan for early finishers. The goal is to have these students go deeper, not faster or further. Avoid having students move on to the second page of the activity guide. Instead, you might extend the learning for these students by challenging them to create a binary representation for a larger number requiring more than 4 bits (pick a number between 16 and 31).
(5 minutes) Discuss
In this discussion, you are modeling incorporating multiple voices into the room. Before calling on people that have not volunteered, give students the opportunity to discuss with a partner or table. When you call on someone, ask them to share what they discussed as a group. In general, it is less threatening to share a group answer than an individual answer.
When all students have finished the page, ask them to come back together as a class and share their answers.
Discussion Goal
After some discussion, students should note that there is only one way to represent any particular number in this system. This is an important point to bring out because it would be confusing if two patterns meant the same thing.
Prompt: Was there more than one possible answer for any of the problems?
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(2 minutes) Table talk: Participants share responses to the prompt. One participant gathers a couple of ideas that will be shared with the whole group during the share out.
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(2 minutes) Share out: The facilitator selects a participant from each group to share different responses from others at the table. The facilitator then asks if any groups in the room disagree with the response that was shared. The discussion should continue until all participants agree and understand why there can only be one way to represent any particular number in this system.
Remarks
With these cards, we've created a binary system to represent numbers. Because we used a pattern that we can follow as our numbers get bigger, our system can work for as high as we can count. Of course, our cards will eventually run out of space to put the dots, so we're going to look at a tool that will help us to use binary numbers in the hundreds.
(10 minutes) Binary Number Widget
Students complete the top section on the back of the activity guide to create a Binary Profile. Once completed, partners trade activity guides and use the Binary Number Widget on Code Studio to decode the binary profile.
As pairs finish encoding and decoding their Binary profiles, they trade back to verify the answers are correct. Challenge students to create a new question they can trade with another student, until all pairs are finished.
(5 minutes) Discuss
Discussion Goal
Students should recognize that the patterns of the numbers and the rules that they follow can help them determine the next numbers in the sequence. For an 8-bit number, starting from the left, the pattern goes 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1.
Prompt: The last question on this activity guide uses an 8-bit number, even though we haven't talked about how to represent these numbers yet. Do you think we can figure out what numbers are needed for 8-bit numbers? How?
- (2 minutes) Table Talk: Participants share responses to the prompt. One participant gathers a couple of ideas that will be shared with the whole group during the share out.
- (3 minutes) Share: The facilitator selects a participant from each group to share different responses from others at the table. The facilitator then asks if any groups in the room disagree with the response that was shared.
Wrap Up (10 minutes)
(10 minutes) Discuss
Remarks
With these cards, we've created a binary system to represent numbers. Because we used a pattern that we can follow as our numbers get bigger, our system can work for as high as we can count. Those are all types of data that need to be represented in binary. We're going to watch a video that explains a little bit more about how this works.
- Refer to the questions to consider with the video.
- Show the video, “Binary and Data” to the group.
- Invite a couple of participants to respond to the questions to consider with the video.
Discussion Goal
The goal of this discussion is to have students think more deeply about the purpose of binary.
- For the first question, they may want to return to their ASCII character sheets and see how the computer would interpret the same binary sequence as a number. For their image representation, they may wonder whether it is even useful to interpret the binary sequences as numbers. In the end, the purpose of defining all data as numbers is less about the "reality" of what the ones and zeros represent, and more about how binary is traditionally interpreted.
- For the second question, allow students to think of different ways that the computer would distinguish between different types of data. While it's not necessary for students to come up with any specific answer, challenge them in any ways that involve human interpretation of context, such as knowing that a name is most likely text and age is most likely a number. Assure them that they will look at the problem again in a couple of
Questions to consider with the video:
- Why are all the types of data on the computer stored as numbers?
- If everything is stored as a number, how do you think the computer tells the difference between numbers, letters, images, and sound?