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* *Reflection:
Bigger or Smaller - Section 2: Practice

It is time to begin to differentiate math instruction within the classroom. I have had time to identify the children who are struggling and children who are getting bored because the work is too easy. I have been keeping track of student progress using a simple checklist (see resources), so I have a running record of those who are having some difficulty and those who are catching on to everything. I also am aware that there are students who are catching on to most things, but have some gaps in their understanding.

Differentiation is an important part of teaching in any subject area. It is important to remember that every student comes with different background, strengths and weaknesses. We need to use formative assessments to measure where students are at so we can provide them with appropriate learning experiences.

Today, I took 2 groups for about 10 minutes each. The first group was the enrichment group. I presented students with a problem to solve that involved using larger numbers and ordering the numbers to show which towns around us have a larger population. I chose five towns and looked up their populations online. I presented the population to these students, asking them to order the towns by population size from greatest to least. This lesson extended the terms greater than and less than, to greatest and least, as well as student use of larger numbers.

The second group was students struggling with the comparison of two numbers. They had trouble understanding that 81 and 18 were different numbers. We worked with base 10 blocks to build the numbers and compare them.

For both groups the work was appropriate and I felt that I was meeting their needs more effectively with these lessons.

I did not take a third group today, but they too (those who are understanding the concepts with some practice) need special time to work on a project that is challenging and appropriate for them.

*Individualizing*

*Individualizing*

# Bigger or Smaller

Lesson 1 of 6

## Objective: SWBAT compare numbers from 0 to 999 using greater than and less than terminology and symbols.

## Big Idea: Second grade students are asked to apply two complementary processes: counting and grouping. The conceptual understanding of the place value of a number and combining/separating numbers using place value, are critical aspects of mathematical thinking.

*45 minutes*

#### Getting Started

*20 min*

Today's lesson will work on modeling with mathematics. (MP4). I want students to think about a number and what it represents and to see the model of that number as they grasp the difference between 3, 30 and 300. All have the digit 3 in them, but it represents something very different in each number. By building a model here, students can see how different those three numbers really are.

To reinforce that students recognize what each digit in a number represents, I hold up 3 100-base-10 blocks. I ask students to write the number this represents in their math journals.

Once students have had time to think and write, a volunteer writes the numeral on the board. Students are asked to show, with a thumbs up or down, if they agree with this answer. We are critiquing the reasoning of another student (MP3) in a very basic way here.

After we have discussed and agreed on the correct response, I hold up other combinations of 100's, 10's and 1's and repeat the process, giving students time to think and write. During this time, I circulate around the room noting any child who is struggling with this task.

Next I bring the students to the rug. I allow them a 2 minute transition/talk and stretch break. When students are settled, I put two sets of blocks on the rug. I ask 2 students to write the amounts on the white boards beside the piles. I ask students which pile has more? How do they know? We build several numbers together and write and compare them.

Next, we build numbers and review the students’ understanding and use of the term "digit". To do this I ask students to write a digit by describing its place value, e.g., "Can you put the digit 3 in the one's place, the digit 5 in the ten's place and the digit 7 in the hundred's place?"

When students are successful with this task, I bring out a "Very Hungry (very greedy) Alligator". I tell the students that he likes to eat the biggest pile he can find. He opens his mouth to chomp the greatest - biggest - amount.

I ask for student help in pointing his mouth to the greatest amount. I note that the smaller - less - amount is by the smallest part of his mouth (his mouth is like an angle when wide open - a greater than/less than sign which I draw in black on the green alligator).

I show students the Very Hungry Alligator video clip to reinforce what we have been sharing.

We experiment now with making new numbers and feeding them to the Hungry Alligator.

Eventually I have them build 2 numbers that are equal - the same amount. I tell them that when the alligator sees this, it becomes confused and shuts his mouth. I show them the shut mouth (2 parallel lines) on the board and ask them what math symbol it looks like. They quickly identify the equal sign. I tell them that when the two piles are the same the alligator doesn't eat either one because they are equal, so instead we use the equal sign.

I hand students paper alligators to use with their work today and have students return to their seats.

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#### Practice

*20 min*

Students have watched me guide them through building numbers and feeding the alligators. Now they need to have some guided practice. I ask students to work with the child sitting next to them. I ask each child to build a number less than 999 (all the blocks they have together) and then to feed the alligator. I allow about 5 minutes for group practice while I walk around and help those who are having difficulty.

I stop students with my quiet signal (ringing of the bell) and ask them to turn to the board. I show them how I can "draw the alligator" when I don't have one. I tell them that today they will do a practice page where they will "draw the alligator". I also tell students to color any digit in the ten's place blue today. I do one demonstration problem on the board, and then let students work on their page.

It is time for me to think about individualizing the lessons for math. I have been mostly doing the same lesson for the whole class, but some children are quick to grasp the concept of number, and others are still confused. While students are working independently, I will work with two groups for enrichment/extra practice. I will also provide students with iPads that have several math fact apps. Students who finish, but who are not part of one of the two groups, may have time practicing math facts. Automaticity with math facts is a good foundation for later math work.

Enrichment: Working with larger numbers. (See reflection for activity.)

Extra practice: Using number cards to identify each digit and what number it represents.

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#### Closing

*5 min*

For the closing today I ask all students to return to their desks. I ask them if anyone can tell me what the mathematical terms are for the big and little sides of the alligator mouth. I hold the alligator between 2 numbers on the board and see if anyone can recall the term greater than. I write a new problem and we try to find the term less than. Finally I show them the confused alligator with the closed mouth and ask them the term for that symbol (equal). I ask them to write two numbers in their math journals and to put the greater than, less than or equal symbol between the numbers and to write the correct term so they can have it to refer to later on.

*expand content*

- 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