Skip Counting Patterns

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Objective

SWBAT identify patterns in multiples of 2, 5, 10 and 100

Big Idea

Are there repeating patterns in number counting? Recording skip counts may help reveal patterns that can be used in solving later math problems.

Warm Up

15 minutes

I begin with a review today to connect to prior knowledge. Students are familiar with skip counting by 2, 5, 10 and 100. All of the children stand up and as I point to each child, they say the next number in the sequence. As we review today I am looking to see if students can attend to the structure of the skip counting we are doing and use it to help them find the next number. (MP7)

I begin with, "we are counting by 2s. I will begin with 2. As I point to you, you will say the next number." We go around the room twice. There are 19 children in the class so we get to 76.

Next we repeat the process starting at 3. Counting by 2s with odd numbers is much more difficult for students. They often want to revert back to the evens. I provide support as needed to remind students to skip one and go to the next number.

Next I say, "this time I will start with 100 and we will still count by 2s." I want students to realize that counting by 2s in the hundreds is the same sequence as counting in the ones. 

I next begin with 5 and ask children to count by 5s. We begin with the number 85. I want to  make suer that we have a chance here to cross over the 100 mark. 

We count this time in unison by 10s beginning at 320. Again I want students to get experience with crossing over the into the next hundred.  By counting in unison we are giving the students who struggle a chance to hear and participate without feeling singled out. 

We count by 100s beginning at 100, and then at 230. Here students should see that we are changing only the digit in the hundred's place. We will cross into the thousands here. We count in unison. 

I listen carefully to how students count across decades and centuries. I provide support as needed. It is challenging for students to make the change, especially across the hundreds. They often get to the 90s and then forget how to change into the next hundred even though they can count by hundreds starting at 100. It is harder to remember that I am at 690 counting by tens and I need to go to 700. They know that it is not 6hundred 100, but they have to stop and count up  in their heads 500, 600, 700 to know what they need to do. 

Looking for Patterns

30 minutes

I hand each student a blank sentence strip with a single line drawn lengthwise down the center. The sentence strip is 24 inches long.  I ask students to mark the line every inch with a small mark. (They should be able to mark from 200 to 240 on the sentence strip). I give them each a ruler to mark the inches with. Next I ask the students to write the number 200 on the first mark. Now I ask them to look at the inch marks they have made. I want them to write the numbers starting at 200 and counting by 2s along the number line.  This gives me a chance to check for understanding of their ability to count by 2s in the hundreds. I provide support for students who are struggling by providing them with a number line marked from 0 - 25. I ask them to think about what they are writing and see if they can find the pattern by using the lower numbered line. I point to how the pattern is the same but we have a 2 for the 2 hundreds in front of each number. 

Students fill in 202, 204, 206, 208, 210, 212, 214… Now I ask them to look at the numbers in the hundred's place, what do they notice? What about the tens place? What about the ones place? Are there any patterns that they might notice?  I want them to see that the number in the hundreds place does not change often, the number in the tens place goes up 0,1,2, etc. and the number in the ones place repeats 0,2,4,6,8,0..

I ask students to turn the sheet over and mark it again in inch marks. Now I ask them to begin with the number 145. I ask them to number the marks counting by 10s. Again we will share any patterns we see in the numbers in the hundreds, tens and ones place. This time they will see that there are more changes over 100 and no changes in the ones place because we are changing the tens and it is going up 4,5,6,7,8,9,,0,1,2,3,4,5, while the 5 in the ones place does not change at all, and the hundreds place stays the same for 10 numbers in a row.

I ask students  to turn back to the first side. I ask them to start at the number 204 and to remember that they are counting by 2s. How many more to get to 226? Could anyone make a number sentence using 204, 226 and the difference?  I repeat this with several other sets of numbers and then ask students to keep these number lines in their math suitcases for future use as a tool for adding or subtracting larger numbers. 

Independent Practice with Patterns

30 minutes

I want students to look for more patterns in tens and hundreds. I give students a large piece of plain paper. I ask them to draw a road on the paper. Now I ask them to mark the road into squares that are about the size of 2 fingers. I tell them the road should be curvy so they can get about 30 squares or more on their road.  Next I ask them to write a number between 100 and 900 that has a 3 in the tens place. Now I ask them to number the squares counting by 10. (See video below) Their road might be 231, 241, 251, 261, 271, 281, 291, 301, 311 321. etc.

I ask each student to take out colored pencils. They will use different colors to mark the squares in a pattern they notice in the ten's place (such as all numbers with a 1 in the tens place will be red, all with a 2 in the tens place will be yellow…) .

As students are working, I circulate around and ask them to explain the patterns they have identified.  I also check for understanding of counting by 10s.

For some students this task may be too easy or too difficult. I will go and give them a starting number that will make the task easier, such as starting at 50 and counting up by tens, or make the task harder by giving them a number that will roll over into the thousands such as starting with 978.

Students use the roads to play a number guessing game. I explain to them that they will need to ask place value clues to find out what number their partner is thinking of. I bring students to the rug to demonstrate the game. I think of a number and ask students to ask questions about the numbers using place value questions such as, " Is there a 2 in the ten's place?", "Is the number greater than 426?", etc.

After students ask a question, I cover the numbers it can't be (such as all numbers with a 2 in the ten's place) with a counter. I take more questions and cover numbers until students guess the number.

I check that students understand the game and then partner them up to play for about 10 minutes. I circulate around during the game to make sure students are asking place value questions.  Using Place Value Understanding

Closing

10 minutes

We will play a closing game of counting by 10s and 100s. I gather students in a circle. I tell them that we will play a game where every time a student calls out a number with a digit 2 in it, he or she must sit down. We start with the number 138. We count by 10s. Students hitting the 200s will realize that they all need to sit down.