Place Value Relationships

Overview

This two-day sequence develops understanding of whole-number place value through ten times and one-tenth relationships, expanded form, and powers of 10. Students use models, equations, discussion, and written explanations to show how a digit’s value changes when it moves between places.

Learning intentions

Day 1

• Students will be able to identify the value of each digit in a whole number.
• Students will be able to explain how adjacent places are related by factors of 10.
• Students will be able to represent numbers in standard, word, and expanded form.

Day 2

• Students will be able to explain how multiplying or dividing by powers of 10 changes place value.
• Students will be able to use equations and place-value models to justify their thinking.
• Students will be able to solve and explain place-value problems independently.

Success criteria

Day 1

• I can name the value of every digit in a whole number.
• I can explain that each place is 10 times the place to its right.
• I can write a number in standard, word, and expanded form.
• I can explain my answer using place-value language.

Day 2

• I can explain what happens when a number is multiplied or divided by 10, 100, or 1,000.
• I can use a place-value chart or equation to show the change.
• I can check whether my answer is reasonable.
• I can clearly explain my strategy to a partner or group.

Curriculum links

• South Carolina Mathematics Standard 5.NR.1.2: understanding whole-number place value and relationships between places.
• Number and Operations in Base Ten: explaining patterns involving powers of 10.
• Number and Operations in Base Ten: reading, writing, and representing numbers using place value and expanded form.
• Mathematical practices: reasoning quantitatively, modeling, explaining, and attending to precision.

Lesson structure (Day 1 — 60 minutes)

1. 0–5 min · Hook and prior knowledge. Display 444,444 in the place-value introduction deck and ask, “How can the same digit have six different values?” Students turn and talk, then share observations.

2. 5–15 min · I Do—model place value. Use a large place-value chart in the place-value chart and teacher model to model 582,406, naming each digit’s place and value; students record one modeled example on the two-day place-value practice worksheet.

3. 15–25 min · We Do—build relationships. Guide the class through examples such as 6,000, 600, and 60, emphasizing that moving one place left makes a digit’s value 10 times greater; students explain the relationship using the sentence frame, “The ___ place is ___ times the ___ place.”

4. 25–38 min · Collaborative practice. In pairs, students complete the standard, word, and expanded-form tasks on the two-day place-value practice worksheet; partners must compare answers and justify one response.

5. 38–50 min · Small-group instruction. Meet with a teacher-led group needing support, using a place-value chart and numbers within 100,000. Other students complete the independent section of the two-day place-value practice worksheet and check work with a partner.

6. 50–56 min · Intervention and challenge. The intervention group receives targeted practice matching digits to values and correcting place-value errors. Students who are ready solve: “A digit has a value of 7,000 in one number and 700 in another. What changed, and why?”

7. 56–60 min · Closure. Revisit the hook in the discussion and closure slides. Students complete an oral or written response: “One place to the left is ___ times the place to the right because ___.”

Lesson structure (Day 2 — 60 minutes)

1. 0–7 min · Retrieval warm-up. Use the retrieval and review slides to display three numbers. Students identify a selected digit’s value and write one expanded-form representation on the two-day place-value practice worksheet.

2. 7–18 min · I Do—powers of 10. Model 43 × 10, 43 × 100, and 43 × 1,000 with a place-value chart and equations. Explain that multiplying by a power of 10 shifts each digit left the appropriate number of places; students annotate the model.

3. 18–28 min · We Do—reason and explain. Solve examples including 6,200 ÷ 10 and 8,000 ÷ 100. Ask, “What happens to the value of each digit?” Students use partner talk and explain why the number becomes greater or less.

4. 28–42 min · You Do—independent practice. Students complete multiplication, division, comparison, and explanation problems on the two-day place-value practice worksheet. Require a chart, equation, or written explanation for selected items.

5. 42–52 min · Small group and intervention. Teach a support group with a place-value chart, focusing on one-place shifts before moving to 10, 100, and 1,000. The intervention group corrects common errors, such as adding zeros without explaining the place-value change. Other students complete the challenge problems.

6. 52–57 min · Share and assess. Display two solutions in the strategy-sharing slides. Students identify which explanation is more precise and defend their choice using place-value vocabulary.

7. 57–60 min · Closure and exit check. Students respond to the final prompt in the plenary slide: “Explain why 3,500 ÷ 100 = 35.” Collect the completed worksheet for assessment.

Resources

• the two-day place-value introduction, modeling, practice, and closure deck
• the two-day place-value practice worksheet
• Large place-value chart
• Individual place-value charts
• Base-ten blocks or place-value disks
• Whiteboards and markers
• Pencils and highlighters
• Prepared small-group number cards

Assessment

• Listen for accurate use of “10 times greater,” “10 times as much,” “place,” and “value” during partner and group explanations.
• Check student models, equations, and expanded forms during guided and independent practice; record students needing reteaching.
• Use the Day 2 closure response to determine whether students understand the relationship between powers of 10 and digit values.

Differentiation

• Support multilingual learners and students with learning needs using color-coded place-value charts, manipulatives, labeled examples, repeated oral rehearsal, and sentence frames such as “The digit ___ is worth ___ because it is in the ___ place.”
• The intervention group works with smaller numbers and one place-value shift at a time before progressing to larger numbers and powers of 10.
• Provide partially completed charts, enlarged print, reduced problem sets, and frequent teacher checks for students needing additional processing or motor support.
• Advanced learners explain multiple methods, create a number that meets given place-value conditions, or investigate what changes when a digit moves two or three places.