Millions Place Value

Overview

Students build on their understanding of place value and powers of ten to read, write, and represent whole numbers through 999,999,999. They use periods, place-value charts, expanded form, and mathematical discussion to connect standard, word, and expanded forms.

Learning intentions

Students will be able to:

• Read and write whole numbers through the millions period.
• Identify the value of each digit in a multi-digit number.
• Represent numbers in standard, word, and expanded form.
• Explain how each place is ten times the value of the place to its right.

Success criteria

• I can group digits into ones, thousands, and millions periods.
• I can read and write a number in word form.
• I can write a number in expanded form, including zero-value places correctly.
• I can explain how I know my answer is accurate.

Curriculum links

• South Carolina Mathematics: read and write whole numbers through the millions period in word, standard, and expanded forms.
• Common Core: read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.
• Common Core: use place-value understanding to compare the relative value of digits in multi-digit numbers.
• Mathematical Practice: reason quantitatively, use representations, and explain thinking clearly.

Lesson structure (45 minutes)

1. 0–10 min · Fluency warm-up. Teacher displays the fluency prompts in the fluency and place-value slides and asks students to solve six quick problems on whiteboards, including rewriting the relationship as (20 = 10 \times __). Students show answers simultaneously, explain the pattern, and complete examples such as “1 ten and 7 ones” and “9 tens and 1 one.”

• Expected answers include 17 and 91. Emphasize that one place is ten times the value of the place immediately to its right.

2. 10–14 min · Launch and connect. Teacher plays the short place-value launch video from the prepared deck, then asks: “What do the commas tell us?” and “How does a digit’s value change when it moves one place left?” Students turn and talk, then share that digits are organized in groups of three called periods: ones, thousands, and millions.

3. 14–22 min · Teacher model. Teacher uses the place-value chart on page 31 of the Big Book and the modeled place-value slides to represent 32,270,364 with dots. Model placing each digit in the correct column, reading the number, and writing:

• Standard form: 32,270,364
• Word form: thirty-two million, two hundred seventy thousand, three hundred sixty-four
• Expanded form: 30,000,000 + 2,000,000 + 200,000 + 70,000 + 300 + 60 + 4 Students copy the chart and explain why the zero in the ten-thousands place does not produce a term in expanded form.

4. 22–28 min · Guided practice. Teacher displays 421,056,230 and guides students to draw dots or place digits in a chart. Prompt: “Which periods contain a zero? Which values must still be named in word form?” Students work independently first, compare with a partner, and record standard, word, and expanded forms. Check the response before revealing the model.

• Expanded form: 400,000,000 + 20,000,000 + 1,000,000 + 50,000 + 6,000 + 200 + 30.

5. 28–35 min · Reasoning discussion. Teacher presents the discussion comparing Shen’s and Carla’s representations from the Big Book, using the discussion and error-analysis slides. Ask: “Who is correct?” “Where did the representations differ?” and “How can the place-value chart prove your answer?” Students discuss with a partner, defend a conclusion, and revise their work if needed. Highlight that commas separate periods but do not change the value of the digits.

6. 35–42 min · Independent application. Teacher completes problem 3, 291,583,015, with the class, pausing for students to suggest each digit’s value. Students then solve problem 4, 752,620,409, independently using the place-value practice and study guide. Require all three forms and a place-value chart or labeled reasoning. Students turn and talk to compare answers before the class reviews problem 4 using the answer-check and discussion slides.

7. 42–45 min · Plenary and homework. Teacher asks students to state one strategy for avoiding errors with zeros and one relationship between neighboring places. Students share with a partner, then the teacher distributes the practice quiz/study guide for homework, directing students to pages 45–46 of the EM2SC materials. Students complete the assigned pages and mark one question they would like reviewed.

Resources

• Whiteboards, markers, and erasers
• Big Book, page 31
• Place-value chart display or copies
• the complete fluency, launch, modeling, discussion, and review deck
• the place-value practice and study guide
• EM2SC practice quiz/study guide, pages 45–46
• Prepared place-value launch video
• Document camera or interactive display

Assessment

• Use whiteboard responses during fluency to check understanding of ten times relationships and basic place-value notation.
• During modeling and guided practice, listen for correct use of period names and question students about zero-value places.
• Collect or scan the independent work. Check that problem 4 includes accurate standard, word, and expanded forms; use homework responses to plan the next review.

Differentiation

• Support students with a color-coded place-value chart, period labels, comma cues, and a sentence frame: “The digit ___ is in the ___ place, so its value is ___.”
• Allow students who need additional processing time to build numbers with place-value disks or write one period at a time before combining the forms.
• Provide word-form vocabulary and partner rehearsal for multilingual learners, including “million,” “thousand,” “hundred,” and “period.”
• Challenge students who finish early to create a nine-digit number containing at least three zeros, write all three forms, and explain why no zero-value terms appear in expanded form.