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* *Reflection: Student Ownership
More than 100 - Section 3: Recognizing Patterns

We talked about patterns in numbers all day today. Students noted the patterns they were finding. They shared these patterns with each other. All of a sudden, near the end of class one student raised her hand excitedly. I called on her and she said, "did you know the numbers in the tens place go 4,4,4,4,4,5,5,5,5,5,6,6,6,6,6 but in the ones place they go 2,4,6,8,0 ?" She had been part of the discussion all during math, but suddenly she discovered the pattern on her own, almost oblivious to all that people had been discussing around her.

Sometimes we think that what we are saying is helping kids to figure things out. We explain and they "get it". But that is often not the case. Just because we teach something, students don't always understand it. They have to be developmentally ready to take in what we are sharing, and they need to make a connection to their own learning. We are helping students all the time to scaffold new learning onto old (Vygotsky's theory of learning), but we can't make it stick. Students have to discover things on their own. I had built many place value bridges, but today, this child finished the bridge for herself and saw something new about patterns of numbers.

*You have to find it yourself*

*Student Ownership: You have to find it yourself*

# More than 100

Lesson 1 of 5

## Objective: SWBAT identify patterns in numbers above 100.

#### Warm Up

*15 min*

Today I begin by reviewing skip counting with numbers between 100 and 999. I work with both even and odd numbers.

I begin with asking all children to come to the circle and stand in their spots. I have a small ball. I tell students that we will pass the ball around the circle and when they get the ball they need to say the next number. We will start by counting by 10s starting on the number 146. I say 146 and pass the ball to the person next to me. They say 156 and pass the ball on. There are 19 children in the class so we will pass over the next hundred as we count on by tens.

When I get the ball back I tell students that we will pass the ball the other way and count by 5s. This time we will start with 755. We follow the same procedure as above.

When I get the ball back I tell students that we will count by 2s this time starting on an odd number. This will make it a little harder. I say we will start with 801. Remember that counting by 2s is skip counting. I pass the ball in the direction of our first pass.

When the ball gets back to me I ask if students are ready for a challenge? This time we will count backwards. We will count by 1s starting at 999. We will go around the circle 2 times.I ask for a thumbs up if they think they can do it?

I help students whenever they are having trouble. I provide the number before and remind them what we are counting by. I help them count up or down to get to the next number. I try to help them notice the pattern that we are working with.

I ask students to return to their seats. I note anyone who struggled with any of the different counting patterns.

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I have noted student's abilities to count by 1,2,5,and 10 within 1,000. Now I want to extend this for students who are ready. I tell students we are going to revisit a game that they have played in the past, but this time with larger numbers. I tell students that I am going to hand them a blank road with the first number filled in. They are going to number the blocks of the road, counting by 1s or 2s, depending on what I write at the top of their paper.

I have a student hand out papers while I quickly go around and put a number between 100 and 5,000 at the top of the paper and fill in "counting by ________" (1, or 2 - starting with an odd number for more of a challenge). By filling in the numbers now, I can use the information I gathered in the warm up to individualize their learning. For most students I give them a starting number that will require them to count across the century (into the next hundred) because this is the area that is most difficult for students, but for a few students who are still not proficient with just counting on, I set it up so they count across several decades instead.

I ask students to number their papers and then they may decorate around their roads until everyone is ready for the game.

When everyone is ready, I partner students up so that those with numbers in the thousands are working together, and those with lower numbers are working together. I tell students that they will think of a number and then their partner will try to guess the number by asking is it greater than___, is it less than _______. Students use colored chips to cover the numbers that it can no longer be.

I demonstrate using a road that I have drawn on the board and crossing out the numbers but explaining that students will cover their numbers.

Example: If my board is numbered from 561 - 601, my partner might ask if it is greater than 591. If my number is 583 I would say not it is not greater than 591 and I would cover all numbers above 591. Next my partner might ask is it less than 577. I would say no it is not less than 577 and I would cover all numbers below 577. The game continues until the partner guesses the number, and then partners switch roles.

I circulate around the room and observe how the students are playing the game.

#### Resources

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#### Recognizing Patterns

*10 min*

In this section I want students to notice any patterns that emerge when they are counting larger numbers.

I ask them to find at least 2 patterns on their roads. I tell them to use a colored pencil to mark a pattern and then use a second color to mark the second pattern. They need to write on the side of the road what the patterns are.

I tell them to look carefully at the numbers and see what they notice. They might notice something about the ones place, the tens place, the hundreds place, or if they used thousands, the thousands place. It might be the way the numbers change, repeat or stay the same.

After about 5 minutes I ask for students to turn and talk to a partner and tell about the patterns they have found.

Finally I ask for 2 - 3 volunteers to share their patterns with the whole class. Although the students are counting by 1s and 2s, they are able to see changes in the tens place such as 179, 180, 181, 182…190, 191 so the tens place is going 7,8,9.. They notice that the hundreds place may go from 2 to 4. They notice that when counting by 2s the ones place had 0,2,4,6,8,0. etc.

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- UNIT 1: What and Where is Math?
- UNIT 2: Adding and Subtracting the Basics
- UNIT 3: Sensible Numbers
- UNIT 4: Sensible Numbers
- UNIT 5: Everything In Its Place
- UNIT 6: Everything in Its Place
- UNIT 7: Place Value
- UNIT 8: Numbers Have Patterns
- UNIT 9: Fractions
- UNIT 10: Money
- UNIT 11: The Numbers Are Getting Bigger
- UNIT 12: More Complex Numbers and Operations
- UNIT 13: Area, Perimeter and More Measurement
- UNIT 14: Length
- UNIT 15: Geometry
- UNIT 16: Getting Ready to Multiply
- UNIT 17: Getting Better at Addition and Subtraction
- UNIT 18: Strategies That Work