Teach 3rd grade place value by moving from a model to a place-value chart, then to numbers and words. Ask students to explain what each digit represents and how ten units in one place can be exchanged for one unit in the next place.
This guide gives Texas teachers, tutors, and homeschool families a lesson sequence for TEKS 3.2A and 3.2B, a worked example, common misconceptions, and an exit ticket with answers.
Want lesson pages to use alongside the guide? Get the free Grade 3 place-value and number-forms sample. Preview two Mathtastico lessons in a 56-page PDF, with no email or purchase required.
What do the Grade 3 place-value TEKS cover?
- TEKS 3.2A: Build and break apart whole numbers up to 100,000 with objects, pictures, and numerical representations, including expanded notation when appropriate.
- TEKS 3.2B: Explain relationships in the base-10 system through the hundred thousands place.
Source: Texas Education Agency Grade 3 TEKS, mathematics section. Keep core examples within the stated range. Any larger numbers in supplemental materials can be treated as extension work.
A place-value lesson you can teach step by step
Materials: paper, pencils, a place-value chart, and base-ten blocks or paper counters labeled 1, 10, 100, 1,000, and 10,000. Start with smaller numbers if students need support, then build toward the example below.
1. Build and trade before naming places
Show 10 ones and exchange them for 1 ten. Repeat with 10 tens for 1 hundred and 10 hundreds for 1 thousand. Ask, “Did the amount change, or did we organize it differently?” Students should explain that the total stays the same.
For larger numbers, use labeled counters or drawings so students do not need thousands of individual blocks. Continue the pattern: 10 thousands make 1 ten thousand; 10 ten thousands make 1 hundred thousand.
2. Build 46,205 and name each digit’s value
Place 4 ten-thousand counters, 6 thousand counters, 2 hundred counters, no ten counters, and 5 one counters on the chart. Ask students to connect each group to its digit.
| Place | Digit | Value |
|---|---|---|
| Ten thousands | 4 | 40,000 |
| Thousands | 6 | 6,000 |
| Hundreds | 2 | 200 |
| Tens | 0 | 0 |
| Ones | 5 | 5 |
Ask, “Why is there a zero between the 2 and the 5?” It records zero tens and keeps the other digits in their places. Removing it would produce 4,625, a different number.
3. Connect standard form, word form, and expanded notation
- Standard form: 46,205
- Word form: forty-six thousand, two hundred five
- Expanded form: 40,000 + 6,000 + 200 + 5
- Expanded notation showing place-value products: (4 × 10,000) + (6 × 1,000) + (2 × 100) + (0 × 10) + (5 × 1)
Have students point to the model while reading each representation. The zero term may be omitted from the sum because it adds nothing; the zero still belongs in the standard-form numeral.
4. Show the same number another way
Trade 1 thousand for 10 hundreds. The model now has 4 ten thousands, 5 thousands, 12 hundreds, and 5 ones:
46,205 = 40,000 + 5,000 + 1,200 + 5.
Ask students to explain why both decompositions represent the same total. This checks understanding beyond memorizing place names.
5. Explain the relationship between neighboring places
Compare the value of the digit 6 in 46,205 with its value in 40,625. In the first number, it represents 6,000; in the second, 600. Six thousand is ten times 600. Connect the explanation to the trade: each thousand can be exchanged for 10 hundreds.
Three place-value activities for practice
- Build, sketch, explain: Partners choose a number, build or draw it, and name the value of every digit. Include a number with a zero.
- Number-form match: Make matching cards for a numeral, word form, expanded form, and model. Ask students to justify each match.
- Trade without changing: Give partners a model and ask them to exchange one unit for ten smaller units. They record a second decomposition and prove that the total stayed the same.
For a music connection, watch Build a Number, the STEAMspirations place-value song, then have students build their own example and explain it.
Common mistakes and questions that help
- Confusing a digit with its value: If a student says the 6 is worth 6, ask, “Six of which unit?” Return to the labeled counters.
- Skipping a zero: Compare 46,205 and 4,625 in the chart. Ask which digit changed places and how its value changed.
- Thinking a trade changes the total: Place 1 thousand beside 10 hundreds. Have the student count both amounts and describe their equivalence.
A three-question exit ticket with answers
- In 37,408, what is the value of the digit 7?
- Write 52,060 in expanded form and explain the zero in the hundreds place.
- Complete the trade: 8 thousands = ___ hundreds. Explain why.
Answers: 1. 7,000. 2. 50,000 + 2,000 + 60; the zero in the hundreds place records zero hundreds. 3. 80 hundreds, because each thousand is 10 hundreds, and 8 × 10 = 80.
If students identify values but struggle with trades, revisit the models. If they trade correctly but lose zeros when writing numbers, use the chart to connect each place to the numeral.
Continue with the free sample or Grade 3 curriculum
Open the free Grade 3 math sample for place-value and number-forms lesson pages. Then explore Mathtastico Grade 3 Unit 1: Whole Numbers, including the student workbook and matching teacher edition, sold separately in PDF and print formats.
For other units and topics, browse the 3rd-grade math curriculum collection. Check the included units and edition on each product before choosing.
Questions teachers and families ask
Can I use this for small-group intervention?
Yes. Begin with a number students can model confidently. Practice one trade and one explanation, then increase the number of places as their understanding grows.
Does this support Grade 3 STAAR math preparation?
Use it as focused practice in composing numbers and explaining place-value relationships. Pair it with instruction and review of the other Grade 3 math skills; this guide and the two-lesson sample are not a complete STAAR review program.
How far should Grade 3 place-value practice go?
Use whole numbers up to 100,000 for the composing and decomposing work here. Include the relationship that 10 ten thousands make 100,000 so students connect the hundred thousands place to the base-10 pattern.