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* *Reflection: Developing a Conceptual Understanding
Crossing Over 100 - Section 2: Teaching the Lesson

Students had no trouble counting by tens, but trying to switch back to counting by ones for the stepping stones had some children confused. I went around and asked students about the numbers they were using for stepping stones. One of the children wrote 181 on one side of the river and 191 on the other side of the river (around her 180). I asked her which number was one more and she knew that 181 was 1 more than 180. I asked her if 191 was one less. She said yes.. no.. and then shook her head. She erased the 191 and then wrote 171. Again, I asked her if that was one less than 180. I had her count on her number line. Oh its.. and then she paused. It was clear that she was not able to think of one less than a 3 digit number. I covered the one hundred and said ok lets think. If I had 80 and wanted 1 more I would get to 81, like your 180, 181, but what comes before 80? She said 79 and then said, "OH, 179!" and she smiled.

Connecting to the reasoning she applies to working with 2 digit numbers helped her when working with 3 digit numbers.

The Common Core standards expect students to count by 10s to 1000, so working with hundreds and correcting misconceptions, is important before students begin to add and subtract with 3 digit numbers.

*Correcting Misunderstandings*

*Developing a Conceptual Understanding: Correcting Misunderstandings*

# Crossing Over 100

Lesson 12 of 14

## Objective: SWBAT count across decades and centuries when working with numbers between 100 and 1000

#### Warm up

*10 min*

Students have counted by 1s, 5s and 10s within one hundred. We practice this again in a game form to review counting skills. Students stand in a circle and pass a ball, randomly, around the circle. As each child gets the ball they say the next number.

Children must listen and track the count because they don’t know when the ball will come to them. (I help those who may struggle with counting across decades and centuries by providing support for them in the form of hints and questions, such as the person before you said 39, you know what comes after 3 so after 39 comes what....and hopefully they can say 40).

We practice with 1’s, 5’s and 10’s going to 300 by 10s. Counting continues to be important practice in second grade, as it is a critical skill for addition and subtraction. How students count is important as well, because if they always start in the same place and don't practice counting backwards as often (if not more) as counting up, counting won't become an addition/subtraction skill.

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#### Teaching the Lesson

*30 min*

I want children to think about what happens when they count across decades and centuries. I am helping them to visualize a structure for counting across decades (MP7) I put the number 130 on the board and say if we are counting by 10 what would come next? After a student says 140, I write 140 below 130. I ask students to help me continue. I place the numbers under one another, curving them into a river shape. Next I draw a line along each side of the numbers, making a river. I tell students that they will be making their own rivers for us to cross. I give each child a large paper and ask them to start at 150 and counting by tens, writing the numbers to make their own rivers. I ask them to make sure that they get at least to 250. I circulate around to see how students are doing in counting by tens across the decades, and from 200 to 300. When everyone is done, I ask them to trace along the edges of their numbers to make a river. Next I ask them to color their rivers with colored pencil so they can still see the river.

Next I hand each child a small piece of origami paper to make a canoe. We work together to fold the canoe. (directions can be found at origaminstructions.com). The origami is fun but takes time and patience (especially if you are not familiar with origami yourself, make the canoe a few times so you are comfortable with it.) If you'd rather not take the time for this, give students a small piece of paper and let them quickly draw and cut out a small canoe.

Now I tell students that we are going to cross our tens river with our canoes and as we do we are going to put in the stepping stones that help us cross the river. On my river I put 129 on one side of 130 and 131 on the other side. I circle each one and say these are my stepping stones to launch my canoe across the tens river. I ask them if they can put the stepping stones on their rivers. Again, we are looking at the structure of number patterns and also modeling with math as we gain a clearer understanding of how numbers work (MP4).

When we all have the stepping stones, we talk about launching our canoe to cross at a particular number (such as 180) if we step off the left (lower) side what number do we launch on. What if we step off on the right (higher) side. We launch our canoes in several places. I ask a student to pick a stepping stone to launch from. He/she can ask a friend what numbers they cross.

I ask students to look at the lower side of the river. What number is always in the ones place? (the 9). "The nine is our cue that we are about to cross the tens river. It means we are moving to a new group of tens when we are counting up. Be sure to be on the lookout for that 9 clue when you are counting up! Remember it is a warning sign that we are entering the river !" What number is always in the ones place on the higher side? (1) The one tells us we are safely on the other side of the tens river and can rest for a little while.

I tell students when we cross the river across a zero number, the nine is always the last number before we cross to a new tens if we are going up, but the zero is the last number before we go down to a new tens.

This activity helps students to concretely see what is happening when they need to count up or down. It is a skill they worked on in Kindergarten and First Grade but may still not have a strong understanding of what is really happening when they cross a decade. Students use counting up and down to become more fluent with adding and subtracting, so this understanding is important.

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#### Extension

*15 min*

For students who are ready, this same activity could be done with hundreds. The hundreds could also be done on a different day, or once children have a clear understanding of the tens. The idea is to reinforce counting skills that will help with later addition and subtraction strategies. Counting should be fluent and the changes that reflect place value changes (across decades and centuries) are skills worth taking time to reinforce before moving on to applications.

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##### Similar Lessons

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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

- LESSON 1: Getting Paid for our Work
- LESSON 2: Making Change
- LESSON 3: More Dimes and Dollars
- LESSON 4: It Is About TIme
- LESSON 5: Smiley Face Number Friends
- LESSON 6: Subtracting with Partners of 100
- LESSON 7: Making Change using Partners of One Hundred
- LESSON 8: Comparing Temperatures
- LESSON 9: Smoothing out subtraction
- LESSON 10: Missing Number Equations
- LESSON 11: Time and Money
- LESSON 12: Crossing Over 100
- LESSON 13: Moving Into Thousands
- LESSON 14: Unit 3 Assessment