📋 Session plan (for teachers)

Session 1 — Place value with decimals

Grade 5 · Math for Young Minds Total time: ~25 minutes Common Core: 5.NBT.A.3 Today's idea: Every place to the right is one-tenth as much as the place before it.

What students will be able to do

By the end of this session, the student can:

• Read and write decimals out to the thousandths place.
• Explain that each place is 1/10 of the place to its left.
• Compare two decimals using place value.

Materials

• Place-value chart (one per pair) — columns from thousands down to thousandths
• Worksheet (one per student)
• Pencil

Substitution: If you don't have a printed chart, draw one on the board with these headers: thousands · hundreds · tens · ones · . · tenths · hundredths · thousandths. Students can copy it onto scratch paper.

New words

Heads-up — common confusions

• Some students will say 0.45 > 0.5 because 45 looks bigger than 5. Pause and line them up by place.
• Tenths and hundredths get mixed up. Point to the chart every time.
• 0.7 and 0.70 are the same number. Say this out loud more than once.

Plan

1 · Hello & today's idea — 2 min

"Today we're working with decimals — the numbers grown-ups actually use. Prices. Race times. Rainfall. We're going to read them, write them, and figure out which is bigger."

Hold up the place-value chart.

"This chart goes from thousands all the way down to thousandths. Every step to the right, the number gets ten times smaller."

Point across the chart, left to right, as you say it.

2 · Hands-on explore — 7 min

Hand each pair a place-value chart.

Prompt: "Write the digits of 2.345 in the chart — one digit per column. Then tell your partner what each digit is worth."

Let them work for 2 minutes. Walk around. Listen for:

• Are they putting the 2 in the ones column?
• Do they know 5 is in the thousandths column?
• Are they saying "five thousandths" out loud?

Then ask the whole group:

"What's the 3 worth? What's the 4 worth? What's the 5 worth?"

Take answers. Write them on the board:

2.345
2 ones · 3 tenths · 4 hundredths · 5 thousandths

Now the big idea:

"Look at tenths, then hundredths, then thousandths. Each one is one-tenth as much as the one before it. Ten hundredths make one tenth. Ten thousandths make one hundredth."

3 · Connect to the math — 4 min

Write on the board:

   tens · ones  .  tenths · hundredths · thousandths
              ↓     ↓          ↓             ↓
            each place is 1/10 of the one to its left

Now the tricky one. Write 0.7 and 0.70 side by side.

"Are these the same or different?"

Take a couple of answers. Then put both into the chart:

0.7   → 7 in tenths, nothing else
0.70  → 7 in tenths, 0 in hundredths

"Same number. A zero on the end doesn't change the value. That'll matter in a minute."

4 · Practice with support — 9 min

Pass out the worksheet.

Do problem 1 together out loud.

"Write four hundred eighty-three thousandths as a decimal."

Walk through it: the word "thousandths" tells us the last digit lands in the thousandths column. So we need three digits after the point. Answer: 0.483.

Now let students try the rest on their own or with a partner. Circulate.

• Problem 2: What is the value of the 2 in 4.027? → 2 hundredths, or 0.02. If a student says "tenths," point to the chart and count over from the decimal point together.
• Problem 3: Compare 0.9 and 0.89. Which is bigger? → 0.9. If a student picks 0.89, have them rewrite 0.9 as 0.90 and stack them. Now it's obvious.
• Problem 4 (stretch): Write three decimals between 0.5 and 0.6. → Any answers like 0.51, 0.55, 0.59 work. If a student is stuck, suggest they think of 0.5 as 0.50 and 0.6 as 0.60, then fill in.

5 · What we did + Try at home — 2 min

"Today you read and wrote decimals out to thousandths. You learned every place to the right is one-tenth as much. And you compared decimals by lining up the places."

Hand out the take-home:

"Find a decimal at home with more than one digit after the point. A race time. A scale reading. A rainfall number — like 1.25 inches. Bring it in and tell me what each digit is worth."

Observation rubric — what to notice in this session

Use this during the session. One observation per student is plenty.

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

What's next (Session 2)

Building on this, Session 2 — Adding & subtracting decimals uses the same place-value thinking. We line up the decimal points and add or subtract just like whole numbers. Today's idea — that each place has its own value — is what makes that work.

✏️ Worksheet (for students)

Math for Young Minds · Grade 5

Session 1 — Place value with decimals

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

Today's big idea

Each place to the right is one-tenth as much as the place on its left.

That goes for whole numbers AND decimals. Past the decimal point we get: tenths, hundredths, thousandths.

Example we did together

  thousands  hundreds  tens  ones  .  tenths  hundredths  thousandths
      —         —       —    3    .    1        4            2

  Read it: "three and one hundred forty-two thousandths"
  Write it:  3.142

Each step right is 10× smaller. Each step left is 10× bigger.

  1   →   0.1   →   0.01   →   0.001
   (÷10)   (÷10)    (÷10)

Problem 1 — together

Write four hundred eighty-three thousandths as a decimal.

Fill in the chart, then write the number:

┌─────────────────────────────────────────────────────────┐
│   ones   .   tenths   hundredths   thousandths          │
│   ____   .   _____    _________    __________           │
│                                                         │
│                                                         │
│   Decimal:  0. ____  ____  ____                         │
│                                                         │
│                                                         │
│   Say it out loud:                                      │
│   "______________________________________________"      │
│                                                         │
└─────────────────────────────────────────────────────────┘

Problem 2 — on your own

What is the value of the 2 in 4.027?

Build the chart and circle the 2:

┌─────────────────────────────────────────────────────────┐
│   ones   .   tenths   hundredths   thousandths          │
│   ____   .   _____    _________    __________           │
│                                                         │
│                                                         │
│   The 2 is in the ________________ place.               │
│                                                         │
│                                                         │
│   Its value is  ____________  (also written 0.____)     │
│                                                         │
└─────────────────────────────────────────────────────────┘

Problem 3 — on your own

Compare: 0.9 and 0.89. Which is bigger?

Careful — more digits doesn't mean bigger!

Line them up by place value:

┌─────────────────────────────────────────────────────────┐
│            ones  .  tenths   hundredths                 │
│   0.9  →   ____  .  _____    _________                  │
│   0.89 →   ____  .  _____    _________                  │
│                                                         │
│                                                         │
│   Hint: rewrite 0.9 as 0.____ so they match.            │
│                                                         │
│                                                         │
│   The bigger number is  ________                        │
│                                                         │
└─────────────────────────────────────────────────────────┘

Answer in a sentence:

____________ is bigger because ____________________________.

Problem 4 — stretch

Write three decimals that are between 0.5 and 0.6.

  0.5  <  _______  <  _______  <  _______  <  0.6

Use the chart to test your answers:

┌─────────────────────────────────────────────────────────┐
│   ones   .   tenths   hundredths   thousandths          │
│   ____   .   _____    _________    __________           │
│   ____   .   _____    _________    __________           │
│   ____   .   _____    _________    __________           │
│                                                         │
│                                                         │
│   Could you find a decimal that uses THOUSANDTHS too?   │
│   Try one:   0. ____  ____  ____                        │
│                                                         │
└─────────────────────────────────────────────────────────┘

Reminder: 0.7 and 0.70 are the same number — extra zeros at the end don't change the value.

Today's words

Try at home tonight (1 minute)

Find a decimal at home with more than one digit after the point. Write it down and name each place value.

Where to look:

• A track-and-field or swim race time (like 12.47 seconds)
• A precise scale reading (your weight, or food on a kitchen scale)
• A long bill total (like $24.36)
• Rainfall on a weather app (like 1.25 inches)
• A measuring cup or ruler in millimeters
• A sports stat (batting average like 0.312)

  My decimal:  __________________________

  ones  .  tenths   hundredths   thousandths
  ____  .  _____    _________    __________

Show a grown-up tomorrow morning.

Next time: Session 2 — we'll add and subtract decimals by lining up the decimal points.

🏠 Family guide (for parents)

Math for Young Minds · Grade 5 · Session 1

A note for grown-ups: today we worked with decimals and place value

What your child did today

In class today, we looked at a place-value chart that stretches from the thousands all the way down to the thousandths.

The big idea: each place to the right is one-tenth as much as the place to its left. Ten ones make a ten. Ten tenths make a one. Ten hundredths make a tenth. The pattern keeps going.

We read and wrote decimals like 0.483, figured out what each digit is actually worth, and compared decimals like 0.9 and 0.89 by lining up the place values.

Why this matters

This is where math starts to look like the math grown-ups actually use — race times, rainfall, scale readings, money. Decimals aren't a new kind of number. They're the same place-value system, extended to the right. Getting comfortable here makes adding, subtracting, and comparing decimals feel obvious later. Understanding first. Speed comes later, on its own.

🏠 Try this tonight (1 minute)

Find one decimal somewhere at home that has more than one digit after the point. Read it together. Then ask your child to name the place value of each digit after the decimal.

Easy places to look:

A short script:

• "What digit is in the tenths place?"
• "What digit is in the hundredths place?"
• "So what is that 4 actually worth?" (Four hundredths, or 0.04.)

That's it. One number. One minute.

Words your child is learning

• Thousandths — the third digit after the decimal point. One out of 1,000.
• One-tenth as much — each place to the right is 10 times smaller than the place to its left.

If your child says…

"This is easy." Good. Try this: which is bigger, 0.9 or 0.89? Many kids say 0.89 because it has more digits. It's actually 0.9 (the same as 0.90). If they get it, ask them to explain why — that's where the real understanding shows.

"This is hard." Also good. Slow down and draw a tiny place-value chart on paper: ones, decimal point, tenths, hundredths, thousandths. Write the number with one digit in each box. Once the digits have a home, the meaning gets easier. We're not in a rush.

"I don't want to." Fair. Keep it to one number. Point at the weather or a receipt, ask one question, and move on. These small noticings add up more than a long sit-down ever could.

What's next

In our next session, we'll start adding and subtracting decimals. The trick is simple: line up the decimal points, then add or subtract like whole numbers. 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)

🔢 Each place is 10× smaller

Picture 1 — The place-value chart

  thousands hundreds  tens   ones  •  tenths  hundredths  thousandths
    1000      100      10      1         1/10    1/100      1/1000

      ┌─────────────────────────────────────────────────────────┐
      │   3      0      5      2   •    4         8         3   │
      └─────────────────────────────────────────────────────────┘
                                  ↑
                          decimal point

Each step → is one-tenth as much. ← Each step is 10× bigger.

Picture 2 — Read this decimal

       0  •  4     8     3
              ↑     ↑     ↑
           tenths  hundr. thousandths
           4/10   8/100   3/1000

Say it: "four hundred eighty-three thousandths" = 0.483

Picture 3 — What is the 2 worth?

       4  •  0     2     7
       ↑     ↑     ↑     ↑
      ones tenths  ↑   thousandths
                hundredths
                 = 0.02

➤ The 2 in 4.027 = 2 hundredths = 0.02

How to compare: line up the point!

       0.9  0    ←  add a 0 to match places
       0.8  9
       ───────
        ↑    ↑
      tenths  hundredths

     9 tenths  >  8 tenths   →   0.9 > 0.89

✨ 0.7 = 0.70 = 0.700 — extra zeros on the right don't change the value.

When is one decimal bigger? ✅ / ❌

Start at the tenths. If tied, go to hundredths. Then thousandths.

Try this in your head

   Name THREE decimals between 0.5 and 0.6

   0.5  •••••••••  0.6
        ↑   ↑   ↑
        ?   ?   ?

➤ ____ , ____ , ____

Answer: 0.51, 0.55, 0.59 (any three with tenths = 5 and hundredths 1–9)