Using a Factor Pair Calculator to Check Factor Pairs from 51-100
Lesson 4 of 12
Objective: SWBAT find the missing factor using prior strategies learned and an online factor pair calculator for finding factor pairs from 51 to 100.
Warm Up: Timed Tests ap
Using the iPad ap, Timed Tests, students practiced their math facts. They needed to do two tests and try to beat their recorded scores. They are set at differentiated levels so that the student can master their level and develop confidence and fluency at the same time. If you don't have iPads for aps, paper and pencil timed tests are a good way to check up math fact fluency. Another resource we have used in the past is Rocket Math. This suggests 80 problems at 4 minutes. I have used this as my guideline when setting goals.. It is a manageable time and on average, students can be fairly successful at that rate.
Today I introduced Prime, Composite and Square Numbers on the whiteboard and we discussed the meaning as students wrote down the definitions in their notebooks. After a brief discussion as I pointed out examples of each on the cards we used in yesterday's lesson, I brought up this Learnzillion lesson* to introduce the idea that the Commutative Pair ( The Commutative Pair is the factor pairs that are the factor pairs that are the example of the Commutative Property within the factor pairs: i.e. 4x8 and 8x4.) needs to be considered when figuring out how many different ways we can make groups for a given whole number. I used this as another resource that will set them up for solving some word problems in a later lesson. I want them to understand that listing factor pairs is another way of considering groups of things. I want the to consider what the expression means: i.e 4 groups of 8 or 8 groups of 4.
I continued the lesson by asking my students these questions: We have been listing just the factor pairs up to the Commutative Pair. How does that limit our ability to show how many ways we can group things? When should we be considering all the ways we can make factor pairs?
I used the question to front load what I wanted them to think about as the Learnzillion lesson played. I told them that the Learnzillion lesson would show them a different way of thinking about grouping. That sometimes we need to consider the commutative pair because of what it means.
I started the video. I stopped at 12 to show them how to list factors again. I taught them that sometimes we are asked to just consider the factors of a product and not think about the pair part. They took notes in their journals.
We watched one more story problem involving the product 16 and we discussed how the doubles function.
I reviewed again:
1. When we are asked to simply list factor pairs or factors we do not include the commutative pair?
2. If we are talking about how many different ways we can group something, we use factor pairs to help us and include the commutative pairs. There is a distinct difference in what we are considering.
I told them that we would study this more deeply later when we solve multiplication word problems and that they needed to keep their notes handy for recall.
* If the Learnzillion resource wants you to register, just click on the "I am a student tab" to view the video.
I told my students that we needed to finish up the factor pair cards from our lesson yesterday.
They set to work quite quickly by partnering up with their buddies from yesterday until all of them were finished and then hung on the wall. The lesson from yesterday will need to be finished up the next day depending on how students work together and the speed in which they find their factor pairs.
Some students finished their factor pair cards sooner than others, so I decided to show each pair of students who were ready this handy factor pair calculator. This Factor Pair Calculator is great, but does not list the factor pairs in the manner we list them. It simply lists it as factors, which I had to explain in my instruction. But it is a really cool tool to use because it serves as a support tool after students use the strategies they have learned to check their accuracy. It is showing the use of Math Practice 5 because they use it after the thinking and listing process as a support tool.
The standard says that they must be able to list factor pairs to 100 and so the task is a bit more complicated as the numbers progress. I told each pair of students that they needed to list Factor Pairs in notebooks as they had in their lesson from the day before, but that they would be starting with 51 and moving forward.
I intended for them to just practice in today's lesson and that they could use this calculator to check, but they must use their divisibility rules that they had learned, arrays, and/or the listing strategy I had taught them. ( 1x51, 2x? 3x17, etc.) . As each group finished, soon all were playing with the calculator and working on listing factor pairs in their notebooks.
In the future, I use this strategy and lesson in warm ups of other lessons as it needs to be continually practiced toward mastery of this standard.
What did you notice?
I stopped my students after about 10 minutes. I had planned for them to practice longer, but the factor pair cards take longer to do than you think if some students are weak in their facts or have trouble figuring out the missing factor. That's what happened today.
I asked them: What did you notice? Was there anything different about these factor pairs that are greater than fifty?
One student noticed that there were prime numbers, but she thought 51 would be prime, so the calculator surprised her when it showed the factors! Another student noticed that aren't more factor pairs just because the number increases. Another student said that she thought is was more fun than she expected.
These remarks show the type of thinking that Common Core demands. Math Practice Standard 8 expects us to teach students to look for that repeated reasoning. This exercise supports most of the Math Practice Standards in general, but I think that looking for that repeated reasoning of using divisibility and logic for the missing factor is really stressed here. It gets them to think about comparison on a higher level now, and not just memorizing math facts by rote. The factor pair calculator serves as a check for them as they strive for accuracy. I noticed that they are thrilled when they discover they have found all of the factor pairs using just their strategies. They are enjoying that the calculator affirms they are absolutely right rather than they are wrong or forgetting some of the factor pairs.