Alg1 Lesson 4.1: Counting Binary Strings

Roles:
Facilitator
Scribe
Resourcer
Includer

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas and prior info
● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools to
communicate your mathematics, reasons, and connections.

• Be ready to join the teacher for a huddle.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may arise.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the teacher.

● Check off tasks & skills on calendar.

● Select skills to work on.

● Work on Deltamath.

Remember to work on the following too…

Part 1: Exploring Binary

Strings

Binary Strings

Computers transmit and store information using a permutation of
digits with only two choices per spot. A popular way to do this is using a permutation of 0s and 1s, but information can be coded in other ways, too. For example, some hard disk drives use magnetic positives and negatives. DVDs use laser light that either is or is not reflected back. All of these systems are binary, since there are only two options per space. A sequence of symbols that uses only 0s and 1s is called a binary string.

1, 2, 4, 8, 16, 32, 64, 128, 256 …

All Permutations of Four 0’s and 1’s

In the common
decimal system,
these binary
numbers represent
numbers 0 through
15.

Bytes and Bits

A byte is a unit of storage in a computer
which contains 8-bits (8 binary digits or
length-8 strings) and can store 256
different values: 0 to 255. A bit is the
smallest unit of data in a computer.

Part 2: Creating a Formula

for Binary Strings

A table of
values for
the length

of the

strings, n,

and the

total

number of

binary

strings, b.

Part 3: Exploring Ternary

Strings

Handout 4.1: Video Game

Cheat Codes

Counting Formulas

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin the
wheel as a class and spend a minute or so
discussing our answers.