Extending Place Value to Millions and DecimalsActivities & Teaching Strategies
Students need to physically move digits and build numbers to see how position changes value in large numbers and decimals. Moving from concrete to abstract, students need to shift digits left and right, observe the multiplicative pattern, and articulate the difference between whole and fractional values.
Learning Objectives
- 1Identify the place value of digits up to the millions place and to the thousandths place in a given number.
- 2Compare and order numbers with up to seven digits and three decimal places.
- 3Explain how the position of a digit affects its value in numbers up to millions and with decimal places.
- 4Partition numbers up to millions and with three decimal places into their expanded form.
- 5Calculate the value of a digit in any position within a number up to millions and with three decimal places.
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Manipulative Build: Million and Decimal Towers
Provide base-10 blocks and decimal paper strips. Students build a given number up to millions, then adjust one digit to see value change. In small groups, they create and trade numbers for partners to read aloud and partition.
Prepare & details
How does the position of a digit influence its value in a large number?
Facilitation Tip: During Manipulative Build, circulate and ask students to verbalise the place value of each digit they place on the tower before adding the next block.
Setup: Tables with large paper, or wall space
Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map
Place Value Chart Race: Digit Shifts
Set up large place value charts from millionths to millions. Pairs race to insert digit cards for target numbers, then shift one digit left or right and calculate the new value. Discuss patterns observed.
Prepare & details
Compare the value of a digit in the thousands place versus the thousandths place.
Facilitation Tip: In Place Value Chart Race, have students call out the new value of a shifted digit before recording it to reinforce rapid place-value calculation.
Setup: Tables with large paper, or wall space
Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map
Decimal Money Shop: Whole Class Simulation
Create a class shop with price tags using dollars and cents to three decimal places. Students take turns as shoppers and cashiers, writing receipts and making change while naming place values aloud.
Prepare & details
Explain how place value is crucial for understanding financial transactions.
Facilitation Tip: In Decimal Money Shop, intentionally give a price requiring regrouping across the decimal point to expose gaps in decimal addition.
Setup: Tables with large paper, or wall space
Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map
Number Line Compare: Individual Challenges
Students plot pairs of numbers on personal number lines spanning millions and decimals. They label digit places and explain which is larger, focusing on key digit comparisons.
Prepare & details
How does the position of a digit influence its value in a large number?
Setup: Tables with large paper, or wall space
Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map
Teaching This Topic
Use the concrete-to-representational-to-abstract sequence: first build with blocks, then draw and label charts, finally write expanded and word forms. Avoid rushing to symbols; students need repeated physical shifts to internalise the 10× change rule. Research shows that students who manipulate digits on charts or with cards develop stronger understanding than those who only write numbers.
What to Expect
Students will confidently name, compare, and partition numbers to millions with three decimal places. They will explain why a digit’s value changes when moved across the decimal point and use place value language to justify their reasoning.
These activities are a starting point. A full mission is the experience.
- Complete facilitation script with teacher dialogue
- Printable student materials, ready for class
- Differentiation strategies for every learner
Watch Out for These Misconceptions
Common MisconceptionDuring Manipulative Build, watch for students who treat each block position as additive rather than multiplicative, stacking identical blocks for millions and thousandths.
What to Teach Instead
Pause the tower construction and ask students to compare the height or volume of one million block to one unit block, then ask them to predict the size of a hundred-thousand block before building it.
Common MisconceptionDuring Place Value Chart Race, watch for students who shift digits without changing their value, e.g., moving a 4 from thousands to hundreds without dividing by 10.
What to Teach Instead
Ask students to write the new number after each shift and underline the digit that moved, then ask them to state the place value change in words before continuing the race.
Common MisconceptionDuring Decimal Money Shop, watch for students who add money as if there were no decimal point, e.g., treating $3.45 + $2.60 as 345 + 260.
What to Teach Instead
Hand students play money and ask them to count out the cents separately, then combine whole dollars and cents to reinforce the role of the decimal as a separator of units and parts.
Assessment Ideas
After Manipulative Build, present 7,890,123.456 and ask students to write the value of the digit '9' and the digit '4' in expanded notation, then write the number in words.
After Place Value Chart Race, give students 3,456,789 and 3,789,456 and ask them to write one sentence comparing the value of the digit '7' in both numbers, then order the numbers from smallest to largest.
During Decimal Money Shop, pose the question: 'Explain why understanding place value to the thousandths is important when discussing a country's national debt versus a personal savings account balance.' Facilitate a class discussion where students share their reasoning.
Extensions & Scaffolding
- Challenge students to create a 10-digit number with exactly two 5s, then write it in three different forms (standard, expanded, word) and justify their place-value choices.
- Scaffolding: provide pre-printed place-value charts with movable digit cards and a glossary of place-value terms for students to reference during tasks.
- Deeper: invite students to research a real-world dataset (e.g., national debt figures) and present how changing a single digit affects the total amount.
Key Vocabulary
| Place Value | The value of a digit based on its position within a number. Each position represents a power of 10. |
| Millions Place | The position in a whole number that represents one million (1,000,000) times the digit in that place. |
| Thousandths Place | The position in a decimal number that represents one-thousandth (1/1000) of a whole. |
| Expanded Form | Writing a number as the sum of the value of each digit. For example, 5,432.1 is 5000 + 400 + 30 + 2 + 0.1. |
Suggested Methodologies
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