Our Understanding of Numbers

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SWBAT demonstrate an understanding of place value to 100 and an understanding of the terms greater than and less than.

Big Idea

This lesson is an informal assessment of student understanding of the base ten system, a critical area in the Common Core.

Warm Up

15 minutes

Students are presented with a problem that uses some of the terms we have been talking about for the last couple of weeks: I am greater than 50. I have a 2 in the ones place. I have the digit 9 in my number. I am less than 108. I am a 2 digit number. What number am I?

I read the clues to the students to insure that lower readers have equal opportunity to solve the problem as higher readers. Processing language may also be difficult for some students so I write as I talk, I am greater than 50 (write >50, I have a 2 in the ones place (HTO - my students know this stands for Hundreds Tens Ones - you could also write out the words as you say them), I have the digit 9 in my number - write a 9 above the HTO. I am less than 108 write <108. I am a two digit number, erase the H from HTO) 

I give students time to work on the problem independently while I circulate around the room supporting students and checking on progress with the problem. Next I ask for volunteers to explain how they arrived at an answer. 

When I first presented the problem several students looked at the problem and began to whine, "It is too hard." (These are the students who usually find math easy because they can complete computation equations.) We talked about at least trying and maybe finding part of the answer. I pointed out the individual parts of the clues to students and asked them if they could possibly identify one of the digits, or know how many digits were in the number? This helped them to feel that they could be somewhat successful. 

I presented a second similar problem after we talked through the first problem and students felt more willing to try. 

The Common Core standards are directed at helping students to become thinkers in math. It moves away from rote repetition towards deeper understanding. This exercise encouraged deeper thinking, which required perseverance to solve (MP1).


15 minutes

The students are introduced to a new game to practice, Partners of Ten. I invite students to walk to the rug while they count to 30. I have them sit so everyone can see an then I demonstrate by playing part of a round with one student as my partner, while the remaining students watch.

I take a deck of cards with only the cards 0 - 9 (I use a math deck, but if you have regular cards you will use 1 - 9). We deal so that each of us has 5 cards. The remainder of the cards are placed face down in the center. I tell students that the game is like Go Fish except that this time they will be looking for the Ten's partner for the card in their hand. I refer to the Ten's Rhyme on the board and tell them they can use it to help them remember what partner they are looking for.

I ask my partner for a 7 (I am holding a three). He says Go Fish and then he asks me for a 6 (he has the 4). I hand him my 6. Play continues until all the cards are used up. 

Students may pick up a card from the draw pile if they run out of cards in their hand.

I am looking for students to use precision when thinking about partners of 10. They need to remember which numbers go together to get to 10. They need to figure out the exact number for each card they have by counting up to ten, using the number line or number grid posted on the wall, using the number grids on their desks, or by using their fingers. Attending to precision to really learn the partners of ten is important here. (MP6)

Informal Assessment

20 minutes

This is an informal assessment of the student's understanding of the concepts of digit, greater than, less than and using blank number lines and building with base 10 blocks. Here is the sensible numbers assessment. These are the concepts that provide a foundation of the concept of number that will lead to fluency with adding and subtracting using place value later on. 

I hand out the paper and pencil sheet that has both base 10 numbers problems and blank number line problems. I also put out base 10 blocks and number lines for students to use. Together we read the problems and then I ask students to fill in what they believe to be the best way to solve the problem. 

I allow students time to solve the problems on their own (to make sense of the problems and persevere in solving them (MP1). I circulate around the room to provide support to students who are struggling. I work with small groups of students who need help counting on the number line- Struggling Students.  At the end of the time I collect the student work so I can evaluate it and determine next steps. Students who finish early are encouraged to use the IPADs to practice math facts. There may also be students who do not finish before the math period is over but this too provides me with formative information about what they need to work on.