Prior to lesson:
I always check to see what domains students should have already mastered in order to be successful. My goal is for students to be able to count on from any number and say the next few numbers that come afterwards.
I begin by writing a given number on the board. I ask students, what are the next three numbers after 350? 351, 352, 353
Then, I ask them to if you were to count back from 350, what are the first three numbers that you would say? 349, 348, 347
At this point I’m just checking to see what they know so far, this is important because I need to make sure I am meeting them where they are in their learning process.
I repeat this pattern if needed using different strategies. This will help clear up any misconceptions so far. MP4- Model with mathematics.
I continue working with students using an interactive white board site (Smart-Board) until they are ready to move forward in their learning.
I keep in mind what students should be able to do by the end of this lesson, and I focus on the importance of this skill. Students should be able to count by 2s, 5s, and 10s and relate this concept to the multiplication process. However, I want them to explore the patterns of numbers when they skip count. For instances; when skip counting by 5s, the ones digit alternates between 5 and 0. When students skip count by 100s, the hundreds digit is the only digit that changes, and it increases by one number.
To start I want students to experience learning in a fun way. I use a tick method. To do this, I say, starting at the tick mark that has the number 12 under it; count on the next 2 tick marks after that.
What are the next to numbers after 2 if you are counting on the next 2 tick marks?
2, 4, 6
Various ways to learn:
Because there are various ways skip counting can be done, I differentiate my instructions by modeling how the number chart can also be used to determine the next number. Using the hundreds chart, I model beginning at the number 2 and continuing the same pattern (counting by 2’s) for the next two numbers. The students were floored when we came up with the same pattern shown in the first illustration.
Before continuing on to independent work, it is important to check on student understanding to see if further discussion is needed, or if the students can now determine the pattern on their own. It is a balance between ensuring students have the knowledge and skills to begin applying what they have learned, and having adequate time to practice and share out. It is critical to discuss what patterns students' discovered and how they knew it was a pattern, because by articulating they are solidifying their own thinking, and growing their peers.
Students seem to be working well with the concept of counting in a given pattern, so I allow them additional time to attend to precision.
I give students the “Skip Check”. If students do not master the given quiz by scoring an 80 percent or above, I use the data from the quiz to drive my instructions. If over 40 percent of the students struggle with this standard, I will re-teach it using small group instructions and spiral it out into homework assignments. I may also add a few problems for morning work!
We worked on the following mathematical practices:
MP.2. Reason abstractly and quantitatively.
MP.6. Attend to precision.
MP.7. Look for and make use of structure.
MP.8. Look for and express regularity in repeated reasoning.
(Students need many opportunities counting, up to 1000, from different starting points. They should also have many experiences skip counting by 5s, 10s, and 100s to develop the concept of place value.)
During this stage we go over problems 1 and 2 together. I want students to make the connections between what they learned and being able to represent repeated addition, as it relates to multiplication. Remember! It is okay if students do not make this connection on their own, however, if they don’t be sure to pull them into a small group setting and go back over the “teacher’s narrative” located at the beginning of this lesson.
(Be sure to re-introduce the multiple strategies that can be used to learn skip counting.)
I go over what I intend for students to gain from this lesson. For instance; I want them to understand that counting by 2s, 5s and 10s is counting groups of items by that amount.
Have the students to think about the given patterns of the model, and explain how they determined their answer. (MP8: Look for and express regularity in repeated reasoning).
As students are working, I circle the room to probe students. I want to see what they are thinking. Some students are able to describe and explain the concept of skip-counting. I check a couple of students to see if they could tell me how this skill can help them understand the multiplication process. However, not that many students made the connection. So, I will continue working with them in smaller groups until they have examine and explored enough to figure it out on their own. Student Work-Sample