This week we did an activity to demonstrate the difference between even and odd numbers. Each student received a handful of plastic tiles/chips and then made two rows of their pieces. Some students noticed that all of their pieces had a partner (that is, they were able to put two chips side-by-side with none leftover) and some noticed that they had one leftover at the end (all but one tile had a partner). We then made a chart of the total number of chips each child had in two columns- one with numbers in which all tiles had a partner (in the "partner" column) and one with numbers that had a leftover (the "leftover" column). After we'd completed the chart, we looked for patterns in the numbers and students discussed that all of evens ended in a 0, 2, 4, 6, or 8 and all odds ended with 1, 3, 5, 7, or 9. We also reviewed that if all of the chips had "a dancing partner," they were considered even. The group that had one "lonely" tile with "no dancing partner" were called odd. See example below: This was review for most students, however, it helped students to conceptually understand even and odd numbers better than just memorizing what even and odd numbers end in (or that all even numbers are divisible by two evenly and odd numbers always have a remainder of 1 if divided by two). The conceptual understanding of even and odd numbers will help students greatly as we move on to prime and composite numbers as one of the biggest misconceptions about prime/composite numbers is that all odd numbers are prime and all evens are composite- not true!!! In order for students to see the difference between these two types of number classifications, a conceptual understanding is extremely important. Prime/Composite Numbers This week we will be working to discover the difference between prime and composite numbers and then will compare them to even and odd numbers. Through a class activity, students will discover that prime numbers only have two factors (factors are numbers you can multiply together to get another number)- one and itself, that composite numbers have three or more factors, and the number 1 only has one factor (1) so it is neither prime nor composite. In order to understand what this looks like, students will make arrays to figure out all of the different factors a number has. Those numbers that only have one array (1 x itself) are prime. Here are a couple examples. 3- In order to figure out if this number is prime or composite, we think of all the numbers we can multiply times each other to get 3. We then make arrays to model the multiplication problems, like so: The only two numbers (factors) that can be multiplied times each other to make 3 are 1 and 3, because 1x3=3. Therefore, I know that 3 is prime because it has exactly two factors- 1 and itself (3). 6- In order to figure out if this number is prime or composite, we think of all the numbers we can multiply times each other to get 6. We then make arrays to model the multiplication problems, like so. I start with the factor 1. Next, I think of the next number that is a factor of 6 after 1 and know that 2 is a factor that can be multiplied times 3 to get 6 (so both 2 and 3 are factors). After 3, the next factor is 6, which I've already included, so I know that I can stop. Once you reach a factor you've already found, it means that you don't have to keep going because you've found them all. Therefore, the number 6 has 4 factors: 1, 2, 3, and 6. Since it has three or more factors, it is composite. 1- In order to figure out if this number is prime or composite, we think of all the numbers we can multiply times each other to get 1. We then make arrays to model the multiplication problems, like so. The only factor that can be multiplied times 1 to get 1 IS 1, so I really only have 1 factor for 1. Therefore, 1 is NEITHER prime nor composite because it doesn't even have two factors (which are needed to be prime-remember, prime numbers have exactly two factors and composite numbers have three or more factors). Last week, students colored in a hundreds chart, coloring in each multiple of 2, 3, 5, and 7. In the end, all of the composite numbers were colored in and the primes (those with only 2 factors) were left! Here is a video that talks about what we did:
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