Common Core standards for number sense rely heavily on the understanding of place value. Today's lesson provides several ways to reinforce that understanding. Students are counting by hundreds to see that changes only take place in the hundred's place, and they are making numbers based on the place value of the digits. Each of these reinforces the basic understanding of place value that can be used later when adding and subtracting numbers within 1000 which is expected by the Common Core to be mastered by the end of the year.
I begin today with oral skip counting by 100. Together the class counts from 0 to 1,000. Next I ask the girls to count by 100s and then the boys so that I can get a better picture of who is easily counting, and who is following the lead of classmates.
I want students to begin to understand that when adding 100 to a number they are changing only the hundred's digit. The rest of the digits stay the same. When I start students at 135 and we count by hundreds students should recognize that only the 1 will change. The 35 will stay the same.
Next we all count back by 100 from 900 to 100.
Counting backwards should be incorporated into counting lessons whenever possible. Students are familiar with counting forward, but backwards is what they really need for subtraction. If you are timing students, count backwards instead of forwards. If you are lining students up, do it in reverse alphabetical/number order. Use counting backwards whenever you get a chance.
Next I ask students what would happen if I started at 150 and wanted to count by 100s. I let students suggest what would come next and I record it on the board. I continue asking students for what comes next. After I have recorded from 150 to 750 I ask students what they notice. We discuss that the digits in the tens and ones place have stayed the same, but the digit in the hundreds place has changed.
To end the warm ups I put the beginning of the pattern 125,225 __, __, __, ___, ___, ___, 925 and ask students to complete the pattern in their math journals.
Again, I am hoping that students will see that they do not need to count 100 each time, but can merely manipulate the hundred's digit.
As a result of the assessment from the last unit, I know that I have several students who still do not understand the idea of digits representing ones, tens and hundreds. During this lesson they will be looking at written numbers and building those numbers with base ten blocks, choosing the correct type of block to represent each digit. I want these students to be able to recognize that a number such as 385 represents 3 hundreds, 8 tens and 5 ones.
After students show competency with building numbers, they will draw 3 cards, form a 3 digit number and then build that number while their partner does the same. After both students have completed their number, they can compare the two numbers and see who has the larger number.
For the other students they will practice making, and modeling their numbers playing a Largest Number game.
Together we will practice the game so students know what to do. See the practice page and directions.
Once the student has completed the independent practice, they will join a partner. Each one will roll the dice 3 times and record the digits they roll. Then the students form the largest number they can and compare it with their partner's number. The largest number receives a tally mark.
I will give a slip of paper with the words 1 group of 100, 2 groups of 100, etc. to each group of students. They will find a way to model that number for the rest of the class to refer to. An example might be if a group has 2 groups of 100, they might make sets of 10 candies, until they reach 200. They will label their picture with the slip of paper.
These models will be used for later math problems.
Each group will show their representation of groups of 100. I set this up as a mini-museum. Each group set their representation on their desks. Students were then able to walks around the room and look at the representations. Some groups had used 3 dimensional objects so the museum format made sharing easier. Set your ground rules for walking around, such as no touching, walking in a particular direction, no more than 4 people at one representation at one time, only 5 minutes for viewing all, etc. This will reduce the chance of chaos or off task behaviors.