Guided Lessons

# Expanded Form to Millions

Saying lengthy numbers doesn't have to be a challenge! Relate the digits in numbers to their place value to help students say the expanded form. Use this lesson on its own or use it as support to the lesson Many, Many Millions.
This lesson can be used as a pre-lesson for theMany, Many MillionsLesson plan.

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This lesson can be used as a pre-lesson for theMany, Many MillionsLesson plan.

Students will be able to write a seven-digit number in standard form, word form, and expanded form.

##### Language

Students will be able to discuss expanded form for numbers through the millions period using colour-coding and peer discussions.

(5 minutes)
• Display the first problem of the Expanded Form: Which One Doesn't Belong? worksheet. Have the students consider the options that exist for 30 seconds.
• Tell them to turn and talk to their partner about which number is out of place or does not belong with the other numbers.
• Remind students they need to have a reason for their answer. For example, "I think the number four doesn't belong because there are two fours and not one," or "I think the number five thousand is out of place because there is no value of five thousand in the largest number. It should be fifty-thousand instead."
• Listen for how students say the numbers and all the vocabulary they use to help guide the lesson and determine the amount of time to spend on vocabulary instruction.
(8 minutes)
• Refer to the number from the introduction section (i.e., 30,451,234) and say it aloud, using correct terms and pausing at each comma.
• Define the terms Value, place value,And Expanded form. Have students turn and repeat the definition of each word to their partner and then have the other partner do the same.
• Ask for volunteers to restate the definition or give an example for a key term of their choice. Allow students to write ideas on their vocabulary cards or glossary.
• Use the place value chart to write the number in the correct location, starting with the ones place and moving to the left. Alternatively, you can count the number of digits in the number and then count on the place value chart so you can start with the largest place value and work your way to the right on the chart.
• Emphasize that the PeriodsHave three numbers in between and they have a "title" to describe them (e.g., millions, thousands, ones).
• Model writing the expanded form of the number, referring to the place value chart. Tell them they should add the addition signs after each value is listed with the zero place holders. Use specific colors for the numbers in each period. (Tip: you can also place the value of all the digits on the chart to show how the zeros are placeholders for the other place values.)
• Have students use their whiteboards to copy your teacher markings and colour-code their numbers based on the period they belong to (see Place Value Chart: Millions worksheet).
(6 minutes)
• Play a snowball activity where the students form a large circle, write a six-digit number on half a piece of paper and their name on the back, crumple it up, and throw it into the middle of the circle.
• Number the students off and call on students based on terms related to their number (e.g., odd numbers, one digit numbers, etc.). When students' numbers are called, they need to pick up a paper, open it, and say the number aloud to someone near them. That person will listen to the number and help the speaker say the number correctly, if necessary.
• Tell students to throw the crumpled paper back into the circle if the students get it right, or hold onto it if they think they need help.
• Repeat the process a few times so each student gets at least two chances to say a number.
• Review the numbers that students need help with. (Note: encourage students to keep the papers whose numbers are not six digits and and those that were a challenge for them to say.)
(7 minutes)
• Model using one of the numbers written on the crumpled paper to state the value of one of the digits (e.g., "In the number 3,456,341, the value for the digit in the hundred thousands place is 400,000.")
• Play the same snowball activity again, but this time have students say the value of the place of your choice using the same crumpled numbers from the previous section. (Tip: you can have a set of index cards that have place values written (i.e., ten thousands) and hold them up after each set student (i.e., numbers) you call out to answer the question.)
• Tell students they will keep their assigned number and call on other students to pick up a crumpled sheet of paper (e.g., all numbers divisible by 3, etc.).
• Explain to students the place value they should focus on (e.g., hundred thousands place). When students open the "snowball" they should tell the value of the digit in the place value you chose to someone near them and show that person their paper.
• Tell students to throw the crumpled paper back into the circle if the students get it right, or hold onto it if they think they need help.
• Repeat the process a few times so each student gets at least two chances to say the value of the digit in the place value of your choice.
• Review the numbers that students need help with and solicit help from advanced students to act as student-teachers when it comes to saying the numbers and expanded forms.

Beginning

• Allow students to use their home language (L1) or their new language (L2) in all discussions. Provide bilingual reference materials to assist in their vocabulary word acquisition.
• Encourage them to use the vocabulary cards and terms in their conversations and writing. Allow them to draw pictures to support their understanding of the terms.
• Have students write the largest number from the Expanded Form: Which One Doesn't Belong? worksheet on their place value charts and then write the expanded form for that number as well. Referring to the place value chart can help them when they have to say the expanded form number.

• Pair students with mixed ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
• Ask them to share their numbers and expanded form first and offer sentence stems and ideas for other students.
(7 minutes)
• Distribute the Place Value Chart: Millions worksheet to each student and ask them to correctly write down the number you tell them. The numbers should be smaller than a billion (e.g., 5,786,234).
• Have them circle the digit in the place value of your choice after they have written at least three numbers down.
• End the assessment by asking the students to write the value of a circled number of their choice on the bottom of the place value chart. Allow them to use the headings on the chart to help with their expanded form.
• Allow students to say their numbers (i.e., the whole number and the value of the circled number) to their elbow partner.
(7 minutes)
• Choose volunteers to share their expanded form number aloud and have students write the number down on their whiteboards as they listen to it.
• Finish the Expanded Form: Which One Doesn't Belong? worksheet as a class and discuss the steps they can take to determine the expanded form of the largest number. For example: "I can write the largest number on the place value chart and circle the values of the numbers shown in the worksheet. If I cannot find the value that is given in the worksheet, then that may be the number that doesn't belong."