# Base-Ten Blocks

Canonical: https://manipulatives.org/manipulatives/base-ten-blocks/

Units, rods, flats, and larger blocks that represent the grouping structure of base-ten numbers.

![Blue unit cubes, a ten rod, and a hundred flat](https://manipulatives.org/_astro/base-ten-blocks.B8XVdvc5.svg)

Published: 2026-10-09
Reviewed: 2026-10-10

Topics: place-value, operations, number-sense

## What they teach

### Place value

Compare one unit, a group of ten units, and a group of one hundred units.

### Regrouping

Exchange ten of one piece for one of the next size while preserving the amount.

### Operations

Build quantities, join or separate them, and record what the exchanges mean.

## How to use them

1. **Agree on the unit.** Start with a small cube as one. Line up ten cubes alongside a rod and ten rods alongside a flat.

2. **Build a number.** Model 34 using three rods and four cubes. Read the quantity as three tens and four ones.

3. **Trade and explain.** Exchange one rod for ten cubes. Describe why two tens and fourteen ones still make 34.

## Try an activity: Show 42 three ways

Build 42 using tens and ones. Exchange one ten, then another, to create three representations. Write a matching addition expression for each arrangement.

## An exchange changes the pieces, not the value

The key question is not how many objects are on the table. It is how much each object represents. Three rods and four cubes are seven pieces, but they represent 34 when a rod is worth ten and a cube is worth one.

For 27 + 16, build both quantities, combine the ones, then exchange ten of the thirteen ones for a ten. The result is four tens and three ones. Write the equation alongside the model so the physical exchange has a written counterpart.

When using the blocks for decimals, explicitly redefine the unit. If a flat represents one whole, a rod is one tenth and a small cube is one hundredth. Avoid switching between this convention and whole-number values mid-task without naming the change.

For another way to show grouping, compare a model with [linking cubes](https://manipulatives.org/manipulatives/linking-cubes/), which learners can actually connect into tens.

The app preview shows grouping in [Math Bars](https://manipulatives.org/manipulatives/math-bars/). Its number bars offer a way to work with ones, tens, and groups of a hundred on screen. A physical base-ten set has different pieces and dimensions, so choose the model that makes your lesson's exchange or measurement visible.

## Choose your toolkit

Choose pieces with consistent ten-to-one proportions. Check the numbers of unit cubes and tens rods, not just whether a large thousand cube is included.

- [hand2mind Place Value Frame with Base Ten Blocks](https://www.amazon.com/dp/B0DQDV5G9P) — Organize ones, tens, and hundreds in separate compartments. Includes a frame, 10 unit cubes, 10 tens rods, 10 hundreds flats, and a Getting Started Guide. Add extra unit pieces for examples such as 27 + 16.

- [Simply Magic Base Ten Blocks (131 pieces)](https://www.amazon.com/dp/B08795FXXM) — Model place value and regrouping with 100 unit cubes, 20 tens rods, 10 hundreds flats, and one thousand cube.

### Manipulatives app

The preview shows tens and ones in Math Bars. This is a grouping model; physical base-ten blocks also let learners compare the lengths, areas, and volumes of their pieces.

[Explore the app](https://apps.apple.com/us/app/manipulatives-hands-on-math/id6780701668)

## Related tools

- [Math Bars](https://manipulatives.org/manipulatives/math-bars/)
- [Cuisenaire Rods](https://manipulatives.org/manipulatives/cuisenaire-rods/)
- [Linking Cubes](https://manipulatives.org/manipulatives/linking-cubes/)
- [Hundred Charts](https://manipulatives.org/manipulatives/hundred-charts/)
- [Number Lines](https://manipulatives.org/manipulatives/number-lines/)