Place Value Patterns

Overview

In this first lesson of the five-lesson Whole Number Operations unit, the student reviews how digits represent different amounts according to their positions. The lesson connects place value to expanded form, even and odd numbers, and increasing or decreasing patterns by tens, hundreds, and thousands.

Learning intentions

Students will be able to:

• Identify the value of a digit in a whole number.
• Write whole numbers in standard and expanded form.
• Classify whole numbers as even or odd.
• Complete and explain increasing and decreasing counting patterns.
• Explain how a digit’s value changes when it moves one place left or right.

Success criteria

• I can name the place and value of any digit in a whole number.
• I can write a number in expanded form and build a number from expanded form.
• I can classify a number as even or odd and explain how I know.
• I can complete a pattern and describe the rule, including patterns by tens, hundreds, or thousands.

Curriculum links

• Number and Operations in Base Ten — place-value relationships in multi-digit numbers.
• Number and Operations in Base Ten — patterns when multiplying by powers of 10.
• Number and Operations in Base Ten — reading, writing, and expanding numbers using place value.
• Number and Operations in Base Ten — mathematical reasoning and explanation.

Lesson structure (45 minutes)

1. 0–5 min · Hook and retrieval. Open the place-value hook slides and display the question, “Which is greater: a 6 in 6,000 or a 6 in 60? How do you know?” Ask the student to respond verbally and record a quick estimate, then review the terms digit, place, and value.

2. 5–13 min · Direct teach: place value. Use the place-value teaching slides to build 4,725 on a place-value chart and model that each place to the left is 10 times the place to its right. The student labels each digit’s place and value, then explains why the 7 represents 700 rather than 7.

3. 13–21 min · Expanded form and even/odd review. Model 4,725 as 4,000 + 700 + 20 + 5, then use the expanded-form practice slides for guided examples such as 8,304 and 6,090. The student writes two numbers in expanded form, builds one standard-form number from expanded form, and classifies each number as even or odd using the ones digit.

4. 21–32 min · Number-pattern investigation. Display the pattern directions in the pattern investigation slides. Give the student these sequences: 2,400, 2,500, 2,600, ___, ___; 7,350, 7,250, 7,150, ___, ___; and 9,000, 8,000, 7,000, ___, ___. The student completes each sequence, identifies the rule, and explains which place changes. Ask, “What stays the same? What changes?” and “How does the value change when we add or subtract 10, 100, or 1,000?”

5. 32–40 min · Independent application. Distribute the place-value and number-pattern worksheet. The student completes tasks identifying digit values, writing expanded forms, classifying numbers as even or odd, and completing increasing and decreasing sequences. Prompt the student to show a place-value drawing or equation when an answer is uncertain; provide feedback after each short section rather than waiting until the end.

6. 40–45 min · Plenary and exit check. Return to the review and exit-question slides and ask the student to explain one completed pattern. For the exit ticket, the student answers: “In 5,555, how many times greater is the value of the first 5 than the value of the second 5?” and “Complete 3,200, 3,300, 3,400, ___ and state the rule.” Review the responses aloud and note any misconception for Lesson 2.

Resources

• the complete place-value and number-pattern slide deck
• the place-value and number-pattern worksheet
• Place-value chart
• Base-ten blocks or place-value disks
• Whiteboard and marker
• Pencil and eraser
• Optional number cards for creating additional examples

Assessment

• During direct teaching, ask the student to identify the place and value of selected digits and explain the 10-times relationship.
• Listen for accurate explanations of pattern rules, checking whether the student identifies the changing place rather than only giving the next number.
• Use the exit ticket to assess place-value relationships and counting patterns. Reteach with a place-value chart if the student confuses a digit with its value or reverses increasing and decreasing patterns.

Differentiation

• For support, use a labeled place-value chart, base-ten blocks, color-coded digits, and sentence frames such as “The ___ is in the ___ place, so its value is ___.”
• Reduce the size of numbers temporarily, then return to numbers through the thousands. Read each sequence aloud while the student tracks the changing place.
• For a student who needs additional challenge, ask them to create a pattern using a change of 10, 100, or 1,000 and explain how the same rule would appear when multiplying by a power of 10.
• Because the class has one student, adjust the pace immediately, provide frequent opportunities to explain thinking, and use verbal response, drawing, or manipulatives before requiring written explanations. For EAL or language support, preteach digit, place, value, increase, decrease, and rule with visual examples.