Math activity
Place Value City
Build a city of towers using blocks! Each tower represents a number. Practice counting groups and discovering that bigger numbers need taller towers.
Materials and setup
- craft sticks or straws
- rubber bands
- beans or small counters
- cups
- paper
- pencil
How this changes by age
Pre-K (ages 3–4)
Build a city of towers using blocks! Each tower represents a number. Practice counting groups and discovering that bigger numbers need taller towers.
Steps
- Use blocks or Legos to build towers of different heights: 1 block, 3 blocks, 5 blocks, 7 blocks.
- Point to each tower and count the blocks together.
- Line them up from shortest to tallest. Which number is biggest? Smallest?
- Build a tower to match a number you call out: 'Build me a tower of 6!'
- Play 'Guess My Tower': parent builds a tower behind a book, child guesses how many blocks.
- Tell a grown-up one thing that surprised you.
Learning objectives
- Count objects up to 10 and build representations
- Order numbers from least to greatest using physical models
- Connect quantity to physical size (more blocks = taller tower)
Kindergarten (ages 5–6)
Build Place Value City where tens are tall buildings and ones are small houses. Construct numbers 11-99 using bundles of 10 and loose ones.
Steps
- Bundle 10 craft sticks or straws together with a rubber band. Make at least 5 bundles.
- Explain: 'In Place Value City, each bundle of 10 is a tall building. Each loose stick is a small house.'
- Build the number 34: lay out 3 bundles (3 tens = 30) and 4 loose sticks (4 ones = 4). 30 + 4 = 34!
- Practice building 6 different two-digit numbers. Write each number and draw its place value city.
- Challenge: 'What happens when you have 10 loose sticks? Bundle them into a new ten! Now you have one more building!'
- Tell a grown-up one thing that surprised you.
Learning objectives
- Represent two-digit numbers using tens and ones
- Understand that 10 ones can be regrouped into 1 ten
- Write two-digit numbers and explain the value of each digit
Early elementary (ages 6–8)
Expand Place Value City to include hundreds. Use base-10 blocks or homemade materials to build numbers up to 999 and explore expanded form, comparing, and rounding.
Steps
- Create place value materials: single beans = ones, cups of 10 beans = tens, bags of 100 beans = hundreds.
- Build 5 three-digit numbers and write each in standard form, expanded form (e.g., 400 + 50 + 3), and word form.
- Compare pairs of numbers using < > and =. Explain: 'Start by comparing the hundreds place first.'
- Round 8 three-digit numbers to the nearest 10 and the nearest 100.
- Play 'Place Value City Builder': roll a die 3 times. Arrange the digits to make the biggest possible number, then the smallest.
- Challenge: what is the largest three-digit number? The smallest? How many three-digit numbers exist?
- In one sentence, tell a parent or sibling what surprised you today.
Learning objectives
- Represent numbers to 999 using hundreds, tens, and ones
- Write numbers in standard, expanded, and word form
- Compare and round three-digit numbers
Upper elementary (ages 8–10)
Extend Place Value City to millions and decimals. Explore how each place is 10 times the one to the right, investigate powers of 10, and work with numbers in scientific notation.
Steps
- Create a giant place value chart from millions to thousandths. Label each place and its value.
- Write 5 numbers with 6+ digits in standard form, expanded form, and word form.
- Investigate the pattern: 1 x 10 = 10, 10 x 10 = 100, 100 x 10 = 1000. Each place is 10 times the place to its right. What about going left (dividing by 10)?
- Work with decimals: represent 3.456 on your chart. What does each digit represent?
- Multiply and divide by powers of 10: 4.5 x 100 = ?, 3200 / 10 = ?. What pattern do you notice in the decimal point movement?
- Research real-world large and small numbers (distance to the sun, width of a hair). Express 5 in scientific notation and explain what each part means.
- In one sentence, tell a parent or sibling what surprised you today.
Learning objectives
- Understand place value from millions through thousandths
- Apply powers of 10 to multiply and divide, recognizing decimal point patterns
- Express numbers in scientific notation and connect to real-world quantities
Safety and evidence note
Read the full activity before beginning. An adult should supervise tools, heat, food, outdoor work, movement, and experiments as appropriate. Completion records that the activity was done; the child’s explanation, work sample, photo, or demonstration is stronger evidence of learning than a completion check alone.
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