Place Value

One rule, applied over and over

Ten ones make one ten. Ten tens make one hundred. Ten hundreds make one thousand. Nothing new is learned at each step, which is why a child who understands the trade at 46 needs very little extra teaching for 4,600. Every digit therefore carries two facts: what it is, and where it sits. Reading 307 as three hundreds, no tens, and seven ones is the whole idea contained in one number.

English hides this from young children. Twenty-four says its tens first, but fourteen says its ones first, and eleven and twelve say nothing useful at all. Many first-grade reversals, such as writing 41 for fourteen, are a language problem rather than confusion about quantity. Say "one ten and four ones" alongside the ordinary word for a few weeks and the reversals usually stop on their own.

Bundling: the two weeks that do the work

Before any expanded-form page, spend two weeks physically bundling. The child has to be the one who counts the ten and puts the band on, because watching you do it teaches nothing at all. The aim is that a bundle stops being ten sticks and becomes one ten: a single object she counts as one, without opening it to check.

1. Count craft sticks or straws into tens, banding each ten as you reach it.
2. Say a number: "Build 34." She takes three bundles and four loose sticks.
3. Ask three questions about that same number: how many tens, how many ones, how many sticks altogether.
4. Hand her 34 unbundled sticks and ask her to find out how many without counting by ones.
5. Trade in both directions: a bundle for ten loose sticks, and ten loose sticks for a bundle.

What to use instead of base-ten blocks

Craft sticks and rubber bands, drinking straws, or pennies and dimes do everything commercial base-ten blocks do, and money is the most convincing of them because a child already believes a dime is worth ten pennies. A hundred chart shows what adding ten does: you drop straight down a row. Drawing is the bridge from objects to numerals, with a line for each ten and a dot for each one, quick enough to use on real problems.

You can hear it when she reads a number

Secure place value sounds like four tens and six, an instant answer to what is ten more than 46, and a comparison made by place rather than by counting up. She should also be able to describe 60 in two ways, as six tens and as sixty, and know without hesitating that the two descriptions are the same claim.

• She builds 34 as three sticks and four sticks.
• She writes 3007 for three hundred seven, or reads 307 as thirty-seven.
• She has to count on by ones to find ten more than 46.
• She compares 19 and 91 by the digits alone and calls them the same size.
• Her regrouping in addition is unreliable, or a two-digit answer gets written in the ones column.

The two places worth re-teaching

Stay inside two-digit numbers until the trade is automatic. Do not introduce hundreds to a child who cannot yet trade tens, because the rule does not become clearer at a larger size. Work below twenty for a week, since that is where the language fights the math, saying every number twice. Then move to numbers with a zero in the tens, such as 105, which is where most of the remaining trouble lives, and build them so the empty column is something she can see.

When tens, hundreds, and thousands each land

Tens and ones usually take from the middle of kindergarten to the end of first grade to become secure. Hundreds and the trades that go with them commonly take most of second grade. Numbers to a million, and the extension into decimals, run from third to fifth grade. Expect to return to it more than once: a child who was fine with two digits can look lost in the first week of three, and that is ordinary.

First, your child should already…

This skill builds directly on:

• Numbers and Counting — master this first.
• Addition — master this first.

What your child is learning

Place value is what lets children work with larger numbers. A 4 in the tens place means forty, not four; that idea powers regrouping, rounding, and multi-digit operations.

Signs your child is ready

• Can bundle ten ones as one ten
• Reads and writes two-digit numbers
• Can compare numbers by tens and ones

Practice this skill

Worksheets and decodable practice for Place Value are in the library.

• Kindergarten — Teen Number Place Value 80 worksheets
• Grade 5 — Place Value 92 worksheets
• Grade 1 — Place Value 20 worksheets
• Grade 2 — Place Value 24 worksheets
• Grade 3 — Place Value: Missing Digits 16 worksheets
• Grade 4 — Place Value 20 worksheets

Every set opens its first three worksheets to everyone; the rest are included with All Access.

How to know it’s mastered

The child builds, writes, expands, compares, and decomposes grade-level numbers using place value.