Math Tools and Place Value

Overview

In Lesson 1 of the “Build, Model, Solve” unit, students use concrete and visual tools to review place value through 1,000,000. They read, write, compare, round, compose, and decompose numbers, then connect these ideas to the Grade 4 understanding that each place is ten times the value of the place to its right.

Learning intentions

Students will be able to:

• Read and write multi-digit whole numbers in standard, word, and expanded form.
• Build, compose, and decompose numbers using place-value tools.
• Compare and round whole numbers using place-value reasoning.
• Explain how the value of a digit changes from one place to the next.
• Use precise mathematical language during partner discussions.

Success criteria

• I can build and represent a number in more than one way.
• I can read, write, compare, and round numbers through 1,000,000.
• I can explain why a digit is worth ten times as much in the place to its left.
• I can use an equation, model, or place-value explanation to justify my thinking.

Curriculum links

• Number and Operations in Base Ten — recognizing the ten-times relationship between adjacent place values.
• Number and Operations in Base Ten — reading, writing, comparing, and representing multi-digit whole numbers.
• Number and Operations in Base Ten — rounding multi-digit whole numbers to any place.
• Number and Operations in Base Ten — using place value and models to support multiplication and division reasoning.

Lesson structure (60 minutes)

1. 0–5 min · Hook and activate. Display 4,000 and 40,000 in the opening comparison slide and ask, “How can the same digit have different values?” Students make a quick prediction, then share one idea with a partner.

2. 5–13 min · Diagnostic check. Distribute the place-value diagnostic and practice sheet and ask students to complete the first five questions independently: write 306,205 in words and expanded form, identify the value of the 6, compare 458,210 and 485,210, and round 72,649 to the nearest thousand. Students work silently while the teacher notes misconceptions and students who need immediate support; do not grade for completion.

3. 13–25 min · Model with tools. Open the place-value modeling slides and model 324,506 using a place-value chart, disks, and base-ten blocks. Teacher builds and decomposes the number, emphasizing that 1 hundred thousand equals 10 ten-thousands and that a digit’s value is ten times the value of the same digit one place right; students build the number with a partner and record two equations, such as 324,506 = 300,000 + 20,000 + 4,000 + 500 + 6.

4. 25–38 min · Partner tool task. Give each pair number cards, a place-value chart, place-value disks, and base-ten blocks. Teacher displays numbers from the build-and-represent task slides—such as 507,030; 680,405; and 999,999—and prompts pairs to draw a card, build the number, write it in standard, word, and expanded form, then compose or decompose it in a different way. Students take turns as Builder and Explainer, using the question-stem cards to support talk such as “The digit ___ has a value of ___ because…”

5. 38–50 min · Compare and round. Teacher models comparing numbers by examining the greatest place first, then rounds 468,275 to the nearest ten, thousand, and hundred thousand using a number line and place-value reasoning. Students complete the remaining problems on the comparison, rounding, and explanation tasks, including one challenge: “Create two six-digit numbers that round to 500,000.” Partners compare answers and must justify one response with a model, equation, or spoken explanation.

6. 50–56 min · Math talk and error analysis. Show the statements on the discussion and error-analysis slides: “In 70,000, the 7 is worth ten times the 7 in 7,000” and “52,499 rounds to 52,000 to the nearest thousand.” Students silently decide whether each statement is true, discuss their reasoning with a partner, and revise any incorrect statement. Invite several pairs to share; classmates listen for evidence based on place value.

7. 56–60 min · Exit check. Students complete the final section of the individual exit questions: write 604,090 in expanded form, compare 604,090 and 640,090, round 604,090 to the nearest ten thousand, and explain why the 6 in the hundred-thousands place is worth ten times the 6 in the ten-thousands place. Collect responses to group students for the next lesson.

Resources

• the complete place-value slide deck
• the place-value diagnostic and practice sheet
• Place-value disks, including disks through 1,000,000
• Base-ten blocks
• Large place-value charts
• Number cards with numbers through 1,000,000
• Pencils, crayons, and blank paper
• Projector or interactive display

Assessment

• Use the opening diagnostic to identify gaps in reading, writing, comparing, and rounding numbers.
• Listen during partner work for correct use of place-value language and check whether students connect models to equations.
• Use the individual exit questions to determine who can explain the ten-times relationship and who needs reteaching with concrete tools.

Differentiation

• Support students with a color-coded place-value chart, prewritten place names, smaller numbers first, and sentence frames: “I know ___ is greater because ___.” Allow students to build every number before recording it.
• For students needing additional support, pair a developing student with a patient peer and provide only the place values needed for the current number. Read number names aloud privately when decoding is a barrier.
• Support multilingual learners with gestures, labeled visuals, partner rehearsal, and the terms digit, value, place, expanded form, compare, and round displayed on the slides.
• Extend ready students by asking them to create a number that satisfies multiple conditions, such as “between 400,000 and 500,000, rounds to 450,000 to the nearest ten thousand, and contains two digits with a ten-times relationship.”