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# Where Are Our Understandings

Lesson 1 of 10

## Objective: SWBAT show their understandings of numbers and operations.

## Big Idea: Before moving on, sometimes it is important to look back. What do my students know and what misunderstandings do I need to work with?

*55 minutes*

#### Warm Up

*10 min*

I start today with some decomposed numbers that I want students to put back together. I ask them to take out their math journals and write the numbers I am describing.

I say, "I have 2 hundreds, 4 tens and 3 ones. What number do I have?" I walk around to see if students are understanding what I am asking. I tell them we will do 5 and then we will check to see if we all agree.

I say, "I have 9 hundreds, no tens and 1 one. What number do I have?

I have no hundreds, 3 tens and 8 ones. What number do I have?

I have 2 thousands, 7 hundreds, 6 tens and no ones. What number do I have?"

I have been circulating around the room watching how students have been doing with this. Now I ask for volunteers to come up and write the numbers on the board so we can check our work.

(I am especially interested in how students dealt with the digit zero in these examples. I did purposefully say no tens, or no hundreds or no ones to see if they would realize that is where the zero place holder comes in. I did not try a number such as 8 hundreds 5 ones. This is something that I might do in the closing after students have practiced more with using zero as a place holder.)

If I feel that most of the students are secure with this skill I will move on. If it looks as if most students are missing this skill, I will spend more time here reviewing and working together to write the numbers. My assumption going in is that most of the students have mastered this, and are ready to move on, but part of the purpose of today's lesson is to identify those students who are not making progress with understanding place value concepts.

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#### Assessment of Prior Learning

*20 min*

Today I tell students that they will be working on their own to complete a short math packet. I tell them to read the directions and ask for help if they need it. I remind them that they have many math tools they can rely on in their math suitcases, but today we are not going to use the calculator. They may use their other tools such as number lines, number grids, base ten blocks, etc.

I hand out the papers. I have several challenge papers available for those who finish early.

I circulate around the room to support students who are struggling. I also make sure that students are explaining their thinking as the work.

#### Resources

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Today students will play a game that will require them to understand ones, tens and hundreds. They will play in groups of 3.

The first student in the group will turn over 3 single-digit cards and combine them to make a 3-digit number. The next student will draw from the "TO DO!" (said like Ta Da!) pile. The cards say + 1, - 1, +10, - 10 and +100, - 100. This student writes the new number on their mini white board. For instance, if the center cards say 345 and I draw + 10 I would write 355 on my board. The other 2 players also draw cards and write their numbers. The student with the smallest number of the 3 gets 1 point. All cards are returned to the TO DO pile!

The next player draws 3 new digit cards and makes a number. Play is repeated as before.

I want students to attend to the structure of the numbers as they add and subtract 1,10 or 100. This helps to reinforce MP7 (look for and make use of structure). Some students may need to use manipulative in order to add or subtract across centuries. For the other adding and subtracting of 1 and 100, students should be able to do this automatically. They should be able to look at the structure of the number and determine the ones, tens, hundred's place and then go up or down 1 group (of one or ten or 100) in order to find their new number.

During the game I circulate around to observe how students are applying place value strategies to make their numbers.

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#### Closing

*5 min*

I ask students to return to their desks. I say ok I am going to say a number and I want you to give me 100 more. I say 765 and point to a student to give the answer. Now I repeat the number 865 and say to another student give me 10 less. I repeat their answer and give the next child a different direction. I keep going until everyone has had a turn.

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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: Where Are Our Understandings
- LESSON 2: Students As Teachers
- LESSON 3: Students as Teachers Part II
- LESSON 4: Kindness Day Math
- LESSON 5: Manipulation Central
- LESSON 6: More Than One Way to Solve A Problem
- LESSON 7: How Big Is One Thousand
- LESSON 8: Let's Compare
- LESSON 9: Assessment
- LESSON 10: Missing Numbers in Japanese