Subject: Math
Grade: 5th Grade
Topic: Prime and Composite Numbers, Factors
Focus questions: What are the characteristics of prime and composite numbers? How do arrays help us to determine if a number is prime or composite?
Materials: set of slips of paper with random numbers, set of slips of paper with pictures of arrays, set of cards with numbers and tape
TEKS: §111.7. Mathematics, Grade 5.
5.3: Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve meaningful problems. The student is expected to: (D) identify common factors of a set of whole numbers, 5.5: Patterns, relationships and algebraic Thinking. The student makes generalizations based on observed patterns and relationships. The student is expected to: (B) identify prime and composite numbers using [concrete objects,] pictorial models, and patterns in factors pairs.
§117.19. Theatre, Grade 5
(a)(1): Students rely on their perceptions of the environment, developed through increasing visual awareness and sensitivity to surroundings, memory, imagination, and life experiences, as a source for creating artworks. They express their thoughts and ideas creatively, while challenging their imagination, fostering reflective thinking, and developing disciplined effort and problem-solving skills.
REVIEW (5 MIN)
Before we start our drama work, let’s review the material for today’s lesson. Write word Prime on the board. Who can raise their hand and quickly tell me what a prime number is? Do the same with composite and array. Make sure the students are bringing up Factors. Great! We are going to play a quick game to get our minds thinking about our math concepts.
BUZZ (10 MIN)
"This game is called Buzz and I need everyone to make a standing circle, finding a space on a piece of tape on the ground. These are the spots in the game. The way we play this game is we are going to go around the circle counting from 1-50. When you say your number, you have to send a bolt of energy to the next person in the circle. We want to keep the energy going around the circle without dropping it. Do you think we can do that? Great! Let’s try a first round." Students do first round. "For our next round, we are going to make it a little more challenging. We are still going to go around saying our numbers, BUT if it is your turn and your number is a multiple of 3, you are going to say buzz instead. So for example, if I say 2, then the next person would say" (pause for students to say buzz, if they don’t say it, then the facilitator does). "Great! Any questions? Yes, we will still send the bolt of energy, even if it’s your turn to say buzz. Okay, let’s try it!" Students do 2nd round. "Does anyone have any suggestions for our group on how to be more successful in this game? Do you think we can do it again, but with a different challenge added? This time, we are going to go around the circle at least twice, and if it is your turn and your number is a prime number, you will say buzz. We are only doing prime numbers this time. Just to review, what is a prime number? Great! Let’s try this third round. And let’s make sure that we are being respectful of our classmates. If someone says the number instead of buzz, we will keep playing and discuss it afterwards, okay? Alright let’s go!" Do third round.
Processing: So on a scale of 1-10, how do you think we played today? What did you feel were the ones that were the hardest to do? What did you have to remember to do well in this game?
Transition: So for our next activity, we are going to delve deeper into our understanding of these concepts. We are going to play a game that will help us talk about prime and composite numbers, and explain them.
TRUTH ABOUT ME (15 MIN):
"This is an activity called The Truth About Me. We are going to stay in our standing circles and for the first round of this game, I will hand each of you a piece of paper with either a number or a word on it. You are not to tell anyone else in the group what is on your paper. The person in the middle will begin by saying The Truth About Me is… and will then describe what is on their paper, without saying the exact word or number. Whoever else in the circle also shares that characteristic must change places and find a new place in the circle. At the same time, the person in the middle is also trying to get a spot. Does that make sense? So for example, if I had the number 18 (which none of you have,) I might say I am a multiple of 2. Anyone else who has a number that is a multiple of 2, will try and switch spots. Any questions? Great. So everyone take a few moments to look at their paper and try and determine every possible way this concept can be described." Allow students a minute or so, offering the option to ask the teacher for help.
"Are we ready?" Play first round of game for a few minutes. "Alright! So for our last round, I am going to give you new pieces of paper. These ones have arrays on them. We are going to play the same way but you will be describing your arrays. You can use the same factor, prime, or composite language, but you can also describe them by saying how many are across or up and down." Play 2nd round.
Processing: Students can sit in their spots during processing. What did you notice about yourself during this game? What did you find difficult? How did this game help you to understand the math concepts?
WHO AM I?/COVER THE SPACE/DATA PROCESSING (20 MIN)
"Our next activity will use all the skills we have worked on today. You will get a card with tape on the back. On this card will a number. But you will not know what the number is. I will place the card on your forehead without you seeing. The objective of this game, is to ask questions to the other people in the class to try and figure out what your number is. The most questions you can ask one person is 2. After your 2nd question, you have to move to another person. Everyone will have a number so while you are asking questions, you will also be answering someone else’s. When you ask a question, be sure to not ask “is my number…?”. Really think about the language we used in Truth About Me and how you can find out what your number is. For example, a better question might be “Am I divisible by 2?” or “Is there only one other factor other than myself?” What might some other good questions be?" Brainstorm possible questions with them and write them on the board for reference. Incorporate arrays into the questions (square vs rectangle, and the proportions of the sides).
"You are going to walk around the space (set the boundaries for the playing space) and ask/answer questions for a few minutes. As soon as you think you know what your number is, you are going to silently stand on this line. From this point to this point is a line and it goes from least to greatest. Let’s mark the middle point with this piece of tape." Put a piece of tape where the beginning, middle and end of the line would be. "All of the numbers are between 1 and 30, so the middle tape would be 15. Any questions? Okay, great, let’s begin! "
As soon as all the students are on their line, have them say out in order what they think their number is. They then take their cards off and see if they were correct. If they were not, have them move to their correct spot.
PROCESSING: What was easy or difficult about this exercise? What kinds of questions didn’t help you? What kinds of questions were the most useful? Did you see anything interesting that the other students were doing?
1(D): What did we do in our work together today? Anything else? (encourage students to describe what it was that we did without describing how we did it). What skills allowed you to be successful in our work?
2(A): How did these activities help you to think differently about our math concepts? Did you make any discoveries about them? Did anything become easier to know?
3(R): We are now going to work on some math exercises connected to these concepts. How did these activities help us prepare for our math exercises?
Possible extensions to Who Am I/Cover the Space/Date Processing: Have students then quickly get into different groups as delegated by the facilitator (Get into groups of same factors, prime and composite, if you have the same number of factors etc)