How Big Is One Thousand
Lesson 7 of 10
Objective: SWBAT use expanded notation to write and compare numbers to 1,000.
I begin today by asking students to take out their math journals. I tell them I am going to say a number and they are going to write the number that is 10 more. I give time between each number for students to write their number, but not to count. I am looking for students to demonstrate a fluent use of place value.
My numbers are 46, 87, 134, 265 and 876. We check the numbers together.
Next I ask students to write the number that is 10 less. My numbers are 86, 52, 980, 357, 663. We repeat the checking process.
(I have avoided numbers that take students into the next hundred for this part of the warm up because conceptually adding and subtracting 10 is something they have done within a given century. Some students could easily go across the century, but because this is a warm up, I am looking for all students to be successful.)
Now I ask students to write numbers that are 100 more. I use the same process for 100 more and 100 less.
My numbers are 245, 698, 57, 774, 186 and for 100 less I use 987, 164, 433, 278, 801.
Finally we count by 100s starting from 188. I ask everyone to stand. I point to the first person and say 188, what is 100 more? After that student, I continue around the room pointing to each student and asking them what is 100 more. This will take us across 1,000 so I offer support, especially to the student who has to go across 1,000 by scaffolding for them with we are in the 900s, what comes after 900? (1,000) Ok so if we are at 988, what do you think might come next? (1088). If they say 1,888 I remind them that we can only go up one hundred but 1,888 would mean I went up way more than 100. I write it on the board if needed so they can see the change and where they need to add and change.
Review of Expanded Notation
I invite students to come to the rug. I put "459 =" on the board. I ask for students to raise their hands and tell me how many hundreds are in the number (4). I write 4 hundreds or 400 + Now I ask how many tens? (5) 5 tens or 50 + How many ones? 9 so I write 9. 459 = 4 hundreds or 400 + 5 tens or 50 + 9.
I repeat the process for several other 3-digit numbers leaving off the words and just writing it as a number sentence. For example, 812 = 800 + 10 + 2.
Once I feel that students are confident with this process of expanded form (and I do tell them that this is what it is called), I put up a 4 digit number. We go through the same process with several 4 digit numbers.
Now I erase the board and write 716 (leave a big space) 617.
I ask someone to come up and write under the numbers the expanded form for each number.
Now I ask students if they remember the hungry alligator who eats the bigger number or closes his mouth if 2 numbers are the same. ( <, >, = signs). Can someone come up and look at the expanded notation and add the correct alligator mouth? We check together to make sure that they are correct.
I put up several other examples for the class to do together.
Building Larger Numbers
I tell students that today they will start by working with a partner to build base 10 buildings. They can not just pile up their blocks, but must have some blocks standing vertically when their partner says stop. Each pair will have 9 ones, 9 tens and 9 hundreds blocks to build with. I want them to work on the expanded form and not have to trade to find their answers so I limit them to 9 blocks for each place. I want students to look for the structure of 3 digit numbers and to use that to record the number they have built (MP7 - look for and make use of structure). This will also be important as they determine <> = later in the lesson. They should begin to look at the hundreds place first and then move to the tens and then the ones. This is where they are looking at the structure of the number and using it to determine which is larger.
I tell students that one partner will count to 60 while the other builds with blocks. When the partner says stop, the builder must stop and record their numbers, first in expanded form and then as one number. They will record these by taking a piece of paper and folding it in half the long (hot dog roll) way. They will write their number and the expanded form on the one side of the fold. Their partner will write their numbers next to it on the other side of the fold
I demonstrate building while they count to 60. When they stop I count my hundreds and write _00 + next I count my tens and write __0 and my ones __ = _ _ _. I tell students that next my partner will build while I count. I pick one student to build while I count. When I say stop I ask them to write their numbers beside mine on the other sides of the fold line.
When they are done I tell students that now they must put in the alligator mouth or the greater than, less than or equal sign. I let a student fill this in.
I remind students to fold the large paper in half and each write on one side of the paper and put the <, >, or = sign on the fold.
I give students about 15 minutes to play the game while I circulate around the room to check for understanding.
I ask students to return to their desks. I give each student a blank piece of paper. I ask them to write the numbers I say in expanded form and put an alligator mouth in the middle.
1. 357 573
2. 865 658
3. 748 847
I collect the student work as a formative assessment.