For this activity, no instructions are provided. Instead, students will use examples of what imaginary players have done to figure out how to play the game. This lesson gives students the opportunity to practice the four arts of computational thinking (decomposition, pattern matching, abstraction, and algorithms) in one cohesive activity.
Getting Started - 15 minutes
Activity: Computational Thinking - 25 minutes
Wrap-up - 10 minutes
Assessment - 5 minutes
- Analyze information to draw conclusions
- Match identical portions of similar phrases to match patterns
- Identify differences in similar phrases and abstract them out
Materials, Resources and Prep
For the Student
- One die per group
- One Computational Thinking Kit per group
- Pens, Pencils, & Scissors
- Computational Thinking Assessment for each student
For the Teacher
Getting Started (15 min)
This lesson has four new and important words:
Algorithm - Say it with me: Al-go-ri-thm
A list of steps that you can follow to finish a task
Decompose - Say it with me: De-com-pose
Break a problem down into smaller pieces
Abstraction - Say it with me: Ab-strac-shun
Pulling out specific differences to make one solution work for multiple problems
Pattern Matching - Say it with me: Pat-ern Matching
Finding similarities between things
- Tell your students that you want them to sum up all of the numbers between 1 & 200.
- Use your body language to indicate that this is not a "serious" or graded exercise.
- Now, let them know that they must do it all in their heads.
- Add the time constraint of thirty seconds.
- They may feel overwhelmed. This is intentional. You can indicate with your tone and demeanor that you might be crazy asking this of them, but begin timing with a resounding: "Starting NOW".
- Use your body language to indicate that this is not a "serious" or graded exercise.
- Watch the class as you keep time. How many are lost in thought?
- When time is up, ask if anyone was able to get the total.
- Ask if there is anyone who thought the problem was so hard that they didn't even attempt it.
- Did anyone attempt it and just not finish?
- What did they try?
- Guide students toward thinking a little smaller.
- If we break the problem up into smaller pieces, it becomes easier to manage.
- Let's start at the two ends. What is 200 + 1?
- What is 199 + 2?
- What is 198 + 3?
- See a pattern?
- How many of these pairs will we have?
- What is the last pair we will find? 100 + 101
- That means that we have 100 total pairs.
- If we have 100 total pairs of sums of 201, how do we find the final total?
- What is 100 * 201?
- Now, what if we wanted to find the trick to do this with other numbers?
- Can we do it easily with 2,000?
- How about 20,000?
- What stays the same? What is different?
- If we use abstractions to make our end goal something that can change (say we name it "blank") then we can make an algorithm that will work for any number
- Work through the problem until you ultimately get ? = ("blank"/2) * ("blank"+1)
- Do a few simple examples to show that the algorithm is correct for blanks= 2, 3, 4, & 5.
"This is all to show that if you use the tools of Computational Thinking (decomposition, pattern matching, abstraction, and algorithms), then you can figure out how to solve problems that no one has already taught you how to solve...just like we did here! This will be an extremely powerful skill for the rest of your life!"
Activities: (25 min)
This lesson is all about a "Game with No Instructions." Students will be charged with figuring out how to play the game as a small group. The small details of their final algorithm are unimportant. What is important is that they were able to take a huge task like "figuring out how to play a game on their own" and take small steps toward achieving the goal.
Students will be guided toward discovering the rules using the steps of computational thinking. Resist the temptation to point the students toward "doing it right" and allow them just to do it on their own. If they feel stumped or confused, encourage the students to look at the information that has been given to them, or if they must, ask a classmate.
1) Divide students into groups of 2-4.
2) Have the groups read over user experiences to get an idea of how other students have played the “Game with No Instructions.”
3) Encourage them to pattern match between each experience by circling the sections of words that are identical from player to player.
4) Next, have them abstract away differences from each experience by underlining words that change from player to player.
5) Using pattern matching and abstraction, have them make a script template for game play by writing up the circled parts of the other students’ experiences, and leaving the underlined sections as blanks. For example:
6) Give students a blank sheet of paper to write a list of instructions for how they think this game should be played based on the user experiences that they just read. This will be their algorithm.
7) Have students play the game using the algorithm that they just made. Each player should get at least two turns.
Wrap-up (5 min)
- What should you try to do when you're asked to do something and you don't know how?
- If a problem is too hard, what should you try to do?
- If you find similarities in lots of solutions to different problems, what does that probably tell you?
- If you have a problem that is just a little different from a problem that you have a solution for, what would you do?
Flash Chat questions are intended to spark big-picture thinking about how the lesson relates to the greater world and the students' greater future. Use your knowledge of your classroom to decide if you want to discuss these as a class, in groups, or with an elbow partner.
- Which one of these definitions did we learn a word for today?
"Bringing two pieces together"
"Breaking a problem down into smaller pieces"
"An educated guess"
...and what is the word that we learned?
Assessment (5 min)
- Hand out the assessment worksheet and allow students to complete the activity independently after the instructions have been well explained.
- This should feel familiar, thanks to the previous activities.
Connections and Background Information
ISTE Standards (formerly NETS)
- 1.a - Apply existing knowledge to generate new ideas, products, or processes.
- 1.c - Use models and simulation to explore complex systems and issues.
- 2.d - Contribute to project teams to solve problems.
- 4.b - Plan and manage activities to develop a solution or complete a project.
- 4.d - Use multiple processes and diverse perspectives to explore alternative solutions.
CSTA K-12 Computer Science Standards
- CPP.L1:6-05. Construct a program as a set of step-by-step instructions to be acted out.
- CT.L1:6-02. Develop a simple understanding of an algorithm using computer-free exercises.
- CT.L2-01. Use the basic steps in algorithmic problem solving to design solutions.
- CT.L2-06. Describe and analyze a sequence of instructions being followed.
- CT.L2-08. Use visual representations of problem states, structures, and data.
- CT.L2-12. Use abstraction to decompose a problem into sub problems.
- CT.L2-14. Examine connections between elements of mathematics and computer science including binary numbers, logic, sets, and functions.
NGSS Science and Engineering Practices
- 3-5-ETS1-2. Generate and compare multiple possible solutions to a problem based on how well each is likely to meet the criteria and constraints of the problem.
Common Core Mathematical Practices
- 1. Make sense of problems and persevere in solving them.
- 2. Reason abstractly and quantitatively.
- 3. Construct viable arguments and critique the reasoning of others.
- 6. Attend to precision.
- 7. Look for and make use of structure.
- 8. Look for and express regularity in repeated reasoning.
Common Core Math Standards
- 3.OA.3 - Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.
- 4.NBT.B.4 - Fluently add and subtract multi-digit whole numbers using the standard algorithm.
- 5.NBT.B.5 - Fluently multiply multi-digit whole numbers using the standard algorithm.
Common Core Language Arts Standards
- SL.3.1 - Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 3 topics and texts, building on others' ideas and expressing their own clearly.
- SL.3.3 - Ask and answer questions about information from a speaker, offering appropriate elaboration and detail.
- L.3.6 - Acquire and use accurately grade-appropriate conversational, general academic, and domain-specific words and phrases, including those that signal spatial and temporal relationships.
- SL.4.1 - Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 4 topics and texts, building on others' ideas and expressing their own clearly.
- L.4.6 - Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal precise actions, emotions, or states of being and that are basic to a particular topic.
- SL.5.1 - Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others' ideas and expressing their own clearly.
- L.5.6 - Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal contrast, addition, and other logical relationships