Students need many ways to experience writing numbers. I begin this lesson by explaining that we will be using data charts to gather data on ten of our favorite states. We will later use this information to extend our place value skills. It is my intention for students to use place value skills to represent numbers in various ways. In particular, students will practice standard, written, and expanded form.
To review a bit, I place a place value chart on the board. I point to each column and ask students to read the title with me. I stop at the ones, tens, hundreds, thousands, ten-thousands, hundred- thousands, and millions to explain how to enter in the correct numbers accord to its value. For instance, I write 112,234 on the board. I ask students to tell me what number is in the hundreds place. They all note that 2 is in the hundreds place. How can I write two hundred in written, standard, and expanded form? Some students tend to struggle on the written part, so I scaffold them through by saying the number aloud, and then writing it. I practice this couple of more times to make sure students understand. After we are finished warming up, I tell students to get ready to explore.
MP.3. Construct viable arguments and critique the reasoning of others.
MP.4. Model with mathematics.
MP.6. Attend to precision.
MP.7. Look for and make use
MP. 8. Look for and express regularity in repeated reasoning.
Material: State Chart.docx
In this portion of the lesson, I pair students in groups of 5’s to gather population data on different states. I allow students to choose what states they gather information from. However, they must require data from at least 10 states. I give each group a chart that will allow them to enter their states and the population. I explain that they will be working indecently to write the populations in standard, written and expanded form. As students are researching the internet to gather the information, I reinforce their learning by asking the following questions: How do you write numbers in written form?, How do you write numbers in expanded form? How do you write the number in standard form? Does writing number in different ways change the value? Explain?
For struggling students, I demonstrate how to enter in the information on the chart to make sure they understand what they need to do. I remind students to only enter in the population information.
Now that students have researched and collected the data, I ask them to return to their assigned seats to begin working on their own. First, I want to test out just how comfortable they are with numbers. I ask students to compare the states on their chart to see which state has the greatest and the smallest populations. Then, I ask student volunteers to write the number for the state with the greatest population on an index card. I ask them to pass the card to the person on their right. After the card has been past, I ask the student to write the number in written form. I give the student a couple of minutes to write the number. As the student is working, I encourage him to invite other students to help him. Then, I ask him to pass the card to the student in front of him. Can anyone guess what I will ask next? You will ask us to write the number in expanded form. Exactly!
Once the students and I are finished writing the number in standard, expanded, and written form. I hand out twenty index cards, and ask students to write the stand and number with the lowest population. I take the cards and place them on a large table, and ask student volunteers to come up and put the numbers in order from least to greatest. Of course students are timed. After one group is finished, I rotate another group of volunteers until all students have had a chance arranging the numbers in order from least to greatest. I ask students how they know how to order the cards. As extra practice, students may repeat this activity using index cards in written and expanded form.
Material: State Chart.docx
In this portion of the lesson, I want to see what students can use the information they have gained so far.
As students are working, I circle the room to check for understanding. For instance, I may say what is the difference between standard and expanded form? Explain how a place value chart can help you determine the value of each digit. Can you show me?
Students are able to give explanations and illustration of expanded and standard form. Because it is equally important for students to use older concept to help them understand the structure of newer concepts, I ask them to explain how place value help them determine the amount of zeros used in expanded form. Students explain that a zero is added every time you move a number to the left. So, it is the same as ten times a number. I continue this process until students’ time is up. I use their responses to determine if additional practice is needed.