Discover Place-Value Relationships

Overview

In this first lesson of the four-part unit “Place-Value Power Moves,” students investigate how a digit’s value changes from one place to the next. They build on prior place-value knowledge by connecting whole-number and decimal positions through a factor-of-10 relationship.

Learning intentions

• Students will be able to identify the place and value of an underlined digit.
• Students will be able to explain that moving one place left makes a digit’s value 10 times greater.
• Students will be able to explain that moving one place right makes a digit’s value one-tenth as great.
• Students will be able to describe these relationships in whole numbers and decimals.

Success criteria

• I can identify the place of a digit.
• I can state the value of a digit.
• I can explain whether moving left makes the value 10 times greater or moving right makes it one-tenth as great.
• I can answer at least 4 of 5 place-value relationship questions correctly.

Curriculum links

• Number and Operations in Base Ten: relationships between the values of digits in adjacent places.
• Number and Operations in Base Ten: patterns when multiplying or dividing decimals by powers of 10.
• Number and Operations in Base Ten: reading and writing decimals through thousandths.
• Mathematical Practice: explain reasoning, use place-value models, and communicate precisely.

Lesson structure (30 minutes)

1. 0–2 min · Hook. Display the sequence 5 → 50 → 500 using the opening number sequence and ask, “What changed, and what stayed the same?” Students turn and talk, then share that the value became 10 times greater each time the digit moved one place left.

2. 2–7 min · I Do: model whole numbers. Use the whole-number place-value model and draw a chart with ones, tens, hundreds, and thousands; model the 5 in 5, 50, and 500, emphasizing that the digit remains 5 while its value changes from 5 to 50 to 500. Students track the digit’s place and repeat the language: “Moving left makes the value 10 times greater.”

Then model the reverse relationship: in 500, the 5 has a value of 500; moving it one place right gives 50, which is one-tenth as much. Clarify that “10 times greater” describes the value relationship, not a change in the digit itself.

3. 7–15 min · We Do: connect whole numbers and decimals. Display the color-coded chart in the decimal place-value model and place 3 in the ones, tenths, and hundredths positions: 3, 0.3, and 0.03. Use arrows to show that moving right divides the value by 10 and moving left multiplies it by 10. Students respond with fingers, pointing, verbal answers, or place-value disks as the teacher asks:

• “Which is 10 times as much as 0.4?”
• “What is one-tenth of 6?”
• “In 2.75, what is the value of the 7?”

Check understanding after each example and correct language immediately. Invite students to explain using the frame, “The digit is in the ___ place, so its value is ___. Moving ___ makes it ___ times as much.”

4. 15–25 min · You Do: independent practice. Distribute the underlined-digit practice worksheet. Students identify the place and value of each underlined digit, then describe how the value changes when the digit moves one place left or right. Include five items mixing whole numbers and decimals through hundredths, such as 4,000, 360, 7.2, 0.56, and 8.04. Students complete the first item with the teacher, then work independently. Circulate and ask, “What place is the digit in?” and “What is the value one place to the left?” Students may use a chart or disks.

5. 25–30 min · Exit ticket and close. Display the exit prompts on the exit-ticket and reflection slide. Students answer on paper:

• In 6.4, what is the value of 4?
• What is 10 times the value of 4?
• Explain what happens when a digit moves one place to the right.

Collect responses and invite one student to restate the key relationship: each place to the left is 10 times the value, and each place to the right is one-tenth the value.

Resources

• the Place-Value Power Moves slide deck
• the underlined-digit practice worksheet
• Large whole-number and decimal place-value chart
• Place-value disks
• Color-coded place columns and arrows
• Whiteboard and markers
• Pencils
• Optional individual place-value charts for student desks

Assessment

• During the hook and guided practice, listen for whether students distinguish the digit from its value and correctly use “10 times” and “one-tenth.”
• During independent work, check that students identify the place, state the digit’s value, and describe the direction of change.
• Use the exit ticket to identify students who need additional modeling or practice before Lesson 2. The target is at least 4 correct responses out of 5 opportunities across the worksheet and discussion.

Differentiation

• Provide a large, color-coded place-value chart, place-value disks, arrows, reduced problem sets, and immediate feedback for students who need support.
• Read directions aloud, give one direction at a time, allow generous wait time, and accept verbal, pointing, or choice responses.
• Use dyslexia-friendly materials: clear sans-serif font, large spacing, uncluttered number cards, strong color contrast, and one problem per line. Allow students to respond orally or with manipulatives.
• For English learners, preteach “place,” “value,” “left,” “right,” “greater,” and “one-tenth,” using gestures and the sentence frame: “The digit is in the ___ place, so its value is ___.”
• Students ready for challenge explain relationships across multiple places, including tenths and hundredths, and create their own number examples that demonstrate a 10-times or one-tenth relationship.

Extension

• Create a number in which the same digit appears in three places, then explain the relationship among all three values.
• Write and solve a partner challenge involving a digit moving across two or more places, including a decimal place.