Grade 2 · Session 01

Place Value To 1 000

Part of the Math for Young Minds curriculum — designed for neurodivergent students, grounded in real-world examples.

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📋 Session plan (for teachers)

Session 1 — Place value to 1,000

Grade 2 · Math for Young Minds Total time: ~20 minutes Common Core: 2.NBT.A.1 Today's idea: A 3-digit number is made of hundreds, tens, and ones.

What students will be able to do

By the end of this session, the student can:

Show a 3-digit number as hundreds, tens, and ones using blocks.
Read a 3-digit number correctly out loud.
Write the standard form of a number when given its expanded form.

Materials

Base-10 blocks per pair (hundreds flats, tens rods, ones cubes)
Place-value mat (one per pair)
Worksheet (one per student)
Pencil

Substitution: No base-10 blocks? Use stacks of dimes and pennies (dime = 10, penny = 1) plus a dollar bill or a labeled paper square for 100. Bundled craft sticks also work — 10 single sticks, a rubber-banded bundle of 10, and a bigger bundle of 100.

New words

Word	Meaning we use in class
hundreds	The digit telling how many groups of 100 there are.
expanded form	A number written as the sum of its place values (e.g., 245 = 200 + 40 + 5).

Heads-up — common confusions

Some students will read 207 as "twenty seven" or "two hundred seventy." Slow down. Touch each digit and name its place.
In numbers like 305, students may forget the zero. Say it out loud: "three hundred five." Every place still counts, even when it's zero.
The tens and hundreds columns get swapped. Keep the place-value mat in front of them.

Plan

1 · Hello & today's idea — 2 min

"Today we're going to look at big numbers — the kind you see on house doors, in books, and on price tags — and break them into pieces."

Hold up a hundreds flat, a tens rod, and a ones cube.

"This is 100. This is 10. This is 1. Today we build numbers out of these."

2 · Hands-on explore — 6 min

Hand each pair a place-value mat and a pile of base-10 blocks.

Problem 1 (together): "Show 245 with blocks. How many hundreds, tens, and ones?"

Walk them through it on the mat:

Put 2 hundreds flats in the hundreds column.
Put 4 tens rods in the tens column.
Put 5 ones cubes in the ones column.

Read it out loud together: "two hundred forty-five."

"2 hundreds, 4 tens, 5 ones. That's 245."

Listen for: Are they putting blocks in the right columns? Are they saying "two hundred forty-five" — not "twenty forty-five"?

Try one more together — point at the blocks and ask: "What number did we just build?"

3 · Connect to the math — 4 min

Now name what's happening.

Write on the board:

   2     4     5
   ↑     ↑     ↑
hundreds tens ones

  245  =  200  +  40  +  5

"When we write a number as the sum of its parts, that's called expanded form. 245 in expanded form is 200 + 40 + 5."

Try one tricky one together. Write 305 on the board.

"Read this with me: three hundred five. Three hundreds, zero tens, five ones. The zero matters — it holds the tens place."

4 · Practice with support — 6 min

Pass out the worksheet. Students can use blocks if they need to.

Problem 2 (solo): Write 700 + 30 + 6 in standard form. → 736

Problem 3 (solo): What is the value of the 4 in 142? In 412? In 421? → 40, 400, 4

"Same digit, different place, different value. Point to where the 4 sits each time."

Problem 4 (stretch): Write the biggest and smallest 3-digit numbers. Show each in expanded form. → 999 = 900 + 90 + 9 and 100 = 100 + 0 + 0

Circulate. If a student is stuck, hand them blocks and say: "Build it first."

5 · What we did + Try at home — 2 min

"Today you learned that every 3-digit number is made of hundreds, tens, and ones. You can write it the short way (245) or the long way — that's expanded form — 200 + 40 + 5."

Hand out the take-home note:

"Tonight, find a 3-digit number at home. A house number. A page in a book. A price on a receipt. The year a book was published. Say its hundreds, tens, and ones out loud."

Observation rubric — what to notice in this session

Use this during the session, not as a test. One observation per student is plenty.

Where the student is	What you'd see
Developing	Mixes up tens and hundreds columns. Reads 207 as "twenty seven." Needs blocks to find each place.
Using	Builds a 3-digit number on the mat correctly. Reads it out loud the right way. Writes 700 + 30 + 6 as 736.
Extending	Explains that the 4 in 421 is worth 400 without counting. Notices that 999 is the biggest 3-digit number on their own.

No fail state. "Developing" today is "using" next week.

What's next (Session 2)

Building on this, Session 2 — Adding & subtracting within 100 uses what we know about tens and ones to add and subtract bigger numbers. Sometimes we'll need to regroup — trade 10 ones for a ten, or a ten for 10 ones.

✏️ Worksheet (for students)

Math for Young Minds · Grade 2

Session 1 — Place value to 1,000

[ Hello ]  →  [ Explore ]  →  [ Connect ]  →  [ Practice ← we are here ]  →  [ Try at home ]

Today's big idea

Every digit in a number has a place. The place tells you its value.

In a 3-digit number, we have hundreds, tens, and ones.

   2     4     5
   |     |     |
hundreds tens ones

We say it: "two hundred forty-five." (Not "twenty forty-five!")

Example we did together

   ▓▓▓        ||||        •  •
   ▓▓▓        ||||        •  •
              ||||           •
              ||||
   2 flats    4 rods       5 cubes
  = 200       = 40         = 5

      200  +  40  +  5  =  245

This is called expanded form: 245 = 200 + 40 + 5.

Problem 1 — together

Show 245 with your blocks on the place-value mat.

Hundreds	Tens	Ones

Draw the blocks you used:

┌─────────────────────────────────────────────────────────┐
│                                                         │
│   Hundreds        │     Tens      │      Ones           │
│                   │               │                     │
│                   │               │                     │
│                   │               │                     │
│                   │               │                     │
│                   │               │                     │
│                                                         │
└─────────────────────────────────────────────────────────┘

Fill in the blanks:

____ hundreds, ____ tens, ____ ones

Problem 2 — on your own

Write 700 + 30 + 6 in standard form.

Draw the blocks for this number:

┌─────────────────────────────────────────────────────────┐
│                                                         │
│   Hundreds        │     Tens      │      Ones           │
│                   │               │                     │
│                   │               │                     │
│                   │               │                     │
│                   │               │                     │
│                   │               │                     │
│                                                         │
└─────────────────────────────────────────────────────────┘

Standard form: ________

Say it out loud: "seven hundred ______-six."

Problem 3 — on your own

What is the value of the digit 4 in each number?

Watch out — the same digit can mean very different things!

┌─────────────────────────────────────────────────────────┐
│                                                         │
│    1  4  2     →   the 4 is worth  ________            │
│                                                         │
│                                                         │
│    4  1  2     →   the 4 is worth  ________            │
│                                                         │
│                                                         │
│    4  2  1     →   the 4 is worth  ________            │
│                                                         │
│                                                         │
└─────────────────────────────────────────────────────────┘

Problem 4 — stretch

Write the biggest and smallest 3-digit numbers.

Hint: the smallest one still needs three digits!

Biggest 3-digit number: ________

Expanded form: ______ + ______ + ______

Smallest 3-digit number: ________

Expanded form: ______ + ______ + ______

Careful — don't forget the zeros. Every place still counts!

Today's words

Word	What it means
hundreds	The digit telling how many groups of 100 there are
expanded form	A number written as the sum of its place values (e.g., 245 = 200 + 40 + 5)

Try at home tonight (1 minute)

Find a 3-digit number somewhere at home. Examples:

The house number on your front door
A page number in a book you're reading
A price on a grocery receipt
The year a book was published
The number on a license plate
A channel number on the TV

Write your number here: ________

Say its hundreds, tens, and ones out loud:

____ hundreds, ____ tens, ____ ones

Show a grown-up tomorrow morning.

Next time: we'll add and subtract bigger numbers — and learn a trick called regrouping!

🏠 Family guide (for parents)

Math for Young Minds · Grade 2 · Session 1

A note for grown-ups: today we started place value to 1,000

What your child did today

In class today, we explored place value in three-digit numbers.

The big idea: the spot a digit sits in tells you what it's worth. The 2 in 245 isn't just "two" — it's two hundreds.

We used base-10 blocks on a place-value mat. A flat is one hundred, a rod is ten, a small cube is one. Your child built numbers like 245 by grabbing 2 flats, 4 rods, and 5 cubes.

We also practiced reading numbers out loud the right way — "two hundred forty-five," not "twenty forty-five" — and writing numbers like 700 + 30 + 6 in their short form: 736.

Why this matters

Place value is the quiet engine behind almost all of arithmetic. Once a child sees that 245 is really 200 + 40 + 5, adding, subtracting, and later multiplying bigger numbers start to make sense instead of feeling like magic. We're not in a rush. Understanding first. Speed comes later, on its own.

🏠 Try this tonight (1 minute)

Find a three-digit number somewhere around you. Then ask your child to break it apart.

Easy places to look:

Where	Example
The house or apartment number	412
A page number in a book	207
A price on a receipt	$3.05 → 305
The year a book was published	1998 → try the last three

A short script:

"What's the hundreds digit?"
"What's the tens digit?"
"What's the ones digit?"
"Now say the whole number out loud."

If the number has a zero in the middle — like 305 — pause there. "Three hundred five." The zero still counts; it's holding the tens spot open.

Words your child is learning

Hundreds — the digit telling how many groups of 100 there are
Expanded form — a number written as the sum of its place values, like 245 = 200 + 40 + 5

If your child says…

"This is easy." Good. Try a sneaky one: 408, or 770, or 600. Ask them to say it out loud and tell you the value of each digit. The zeros are where the thinking lives.

"This is hard." Also good. Slow down and use real objects — pennies for ones, dimes for tens, dollar bills for hundreds. Build the number together on the table. Seeing it makes the digits feel real.

"I don't want to." Fine. Skip it tonight. Tomorrow, point at a house number on a walk and just ask, "How many hundreds in that?" One question counts. These don't have to be sit-down sessions.

What's next

In our next session, your child will start adding and subtracting within 100 — including the moment where we sometimes need to regroup (trade ten ones for a ten, or a ten for ten ones). Today's place-value work is what makes that click.

Thanks for taking a minute tonight. These small kitchen-table moments are where math lives.

— Math for Young Minds

🔑 Cheat sheet (visual)

🏠 Place value: hundreds, tens, ones

Picture 1 — Build 245 with blocks

   HUNDREDS    |    TENS     |   ONES
               |             |
   ▢▢▢▢▢       |             |
   ▢▢▢▢▢       |   ┃ ┃ ┃ ┃   |   ●  ●  ●
   ▢▢▢▢▢       |   ┃ ┃ ┃ ┃   |   ●  ●
   ▢▢▢▢▢       |   ┃ ┃ ┃ ┃   |
   ▢▢▢▢▢       |             |
               |             |
     2         |     4       |     5

2 hundreds + 4 tens + 5 ones = 245

Say it: "two hundred forty-five"

Picture 2 — Reading the sign

        2     4     5
        │     │     │
        │     │     └──  ones
        │     └────────  tens
        └──────────────  hundreds  ← new word!


       245  =  200  +  40  +  5
                └──── expanded form ────┘

Picture 3 — The same 4 in different spots

    1 4 2          4 1 2          4 2 1
      ↑            ↑                  ↑
     tens       hundreds            ones
   value = 40   value = 400      value = 4

The spot tells the value. ✨

Picture 4 — Don't lose the zero!

    3 0 5   →   3 hundreds + 0 tens + 5 ones

    Say:  "three hundred five"   ✅
    NOT:  "thirty-five"          ❌

Every place still counts — even a 0. 🔍

When is it expanded form?

✅ Expanded form	❌ Not expanded form
`700 + 30 + 6`	`7 + 3 + 6`
`200 + 40 + 5`	`2 + 4 + 5`
each piece shows its place value	digits without their value

To go back to standard form, add the pieces:

   700 + 30 + 6  =  736

Try this in your head

   What is the biggest 3-digit number?
   What is the smallest?

➤ biggest = ____ = ____ + ____ + ____ ➤ smallest = ____ = ____ + ____ + ____

Answer: 999 = 900 + 90 + 9 Answer: 100 = 100 + 0 + 0

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