Numbers Have Patterns

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Objective

SWBAT identify the patterns of numbers to 100 on a hundreds chart and use words to describe the pattern they see.

Big Idea

Mathematics is known as the science of patterns. When students are able to see that numbers are predictable, it is easier for them to grasp what the digits in numbers stand for.

Getting Started

10 minutes

Yesterday students explored the greater than, less than, and equal symbols. In the last 2 lessons they have also explored putting digits together to make numbers. This activity can be scaffolded for students by using pre-prepared sentence strips, that guide the placement of the numbers I dictate and  <>= symbol.

Today, as a warm up, I dictate two numbers by saying, "Write a number with a digit 4 in the ten's place, and a digit 7 in the one's place. Now leave a space next to it for an "alligator mouth" - the symbol used to show which number is larger <>=. Then write another number with a digit 8 in the ten's place and a digit 2 in the one's place. Now add the "alligator mouth" and remember...he is very hungry."

After giving students time to think and write, I ask, "Can anyone read the number sentence you just wrote?" 

I try to get students to use their mathematical language of greater than, less than terms as they read the number sentence 47 is less than 82. I write it on the board for students to see and check their own work.

I do 3 - 4 additional problems, adding numbers in the hundreds and numbers with a 0 in one of the places. 

I give students a quick stretch as they come to the rug. (I often tell students to do 5 hops, or 6 jumping jacks on the way to the circle so they are ready to listen when they sit down.)

Teaching the Lesson

15 minutes

On the SmartBoard I bring up the image of a hundreds chart. 

If you do not have a way to project a grid, you can purchase a hundreds chart poster, even a white board configured with a hundreds chart, to use in your classroom. You can also purchase or create individual grids that are laminated so students can use them during the year. I find that it is a valuable resource to have in my classroom especially at the beginning of the year. Many students will begin to add and subtract larger numbers, and to count to ten using the number grid tool. The grid provides a structure that students can attend to as they clarify the differences between numbers such as 23 and 32. (MP7)

I ask students to look at the grid and tell me what they notice about it. I take comments from four or five students and may highlight, or point, to visually reference what they are saying (such as all the numbers in the last row end in 0, or the numbers in the tens place go up by one in each row.)

Next I highlight the numbers 5, 10, 15, 20, 25.... and ask students what they see. I am asking students to attend to the structure of the hundreds grid as they gain a clearer understanding of how it works. (MP7) I give students wait time and will not take any responses - indicating hands down - so that students who need more time to think aren't discouraged from putting in the effort. I am looking for students to recognize the repeating 5, 0 pattern, and that all the 5's are in a row, etc. 

I highlight the column of 3, 13, 23, 33, 43, etc. and again, ask what they notice. 

After we have had a class discussion, I tell students that today they will be working with number grids. There will be three groups. One group will be using the individual student grids and finding numbers, then finding the number that is one more, one less, ten more, ten less. The second group will be making their own number grid. (Here I put in the first number so that children who grasp the number grid can be working with larger numbers.) The last group will be finding groups of tens and ones on the number grid by matching base 10 block structures to the numbers on the grid and identifying how many tens and ones in the number and what the digits in the number are. In this last activity students are modeling their understanding using the base 10 blocks (MP4).

I divide the students into their work groups and send each group to a center. (I differentiate by providing larger or smaller numbers at the various centers to meet the needs of all students.)

Practice

30 minutes

During this part of the lesson the students will work for 10 minutes at one of the centers and then move to the next center. 

If I have parent support, I will be free to move from center to center supporting student learning while the volunteers assist with the management of the centers. If I have no volunteers for this lesson, I will work with the students identifying the digits, building the number with base ten blocks, and seeing how the position on the number chart is related to the size of the number. 

Closure

5 minutes

After all of the students have visited each center I will have them return to their seats. It is time for them to write one thing they have learned about the number grid today in their Math Journal. This will serve as an informal assessment of student understanding of the number grid and how it is arranged.