📋 Session plan (for teachers)

Session 7 — Decimals: tenths and hundredths

Grade 4 · Math for Young Minds Total time: ~22 minutes Common Core: 4.NF.C.6, 4.NF.C.7 Today's idea: A decimal is just a fraction in disguise — tenths and hundredths of a whole.

What students will be able to do

By the end of this session, the student can:

• Read and write decimals like 0.3 (= 3/10) and 0.47 (= 47/100).
• Place a decimal on a number line from 0 to 1.
• Compare two decimals and say which is bigger.

Materials

• Graph paper showing 10×10 grids (one or two per student)
• Worksheet (one per student)
• Pencils

Substitution: If you don't have 10×10 grid paper, draw a square on the board and split it into 10 columns. That's tenths. Split each column into 10 again — that's hundredths.

New words

Heads-up — common confusions

• Some students will say 0.4 < 0.39 because "39 is bigger than 4." Slow down here. Show that 0.4 = 0.40. Then compare.
• 0.07 is seven hundredths, not "seven." Say it out loud the long way the first few times.
• The fraction 1/4 and the decimal 0.25 are the same number. Worth pointing out when it comes up.

Plan

1 · Hello & today's idea — 2 min

"Today we're going to talk about numbers that live between the whole numbers. Like the price on a receipt — $3.45. That .45 part. What does it really mean?"

Draw a number line from 0 to 1 on the board.

Ask: "What number lives halfway between 0 and 1?"

Take a few answers. Don't correct yet — just listen.

2 · Hands-on explore — 6 min

Hand each student a 10×10 grid.

Prompt: "This whole grid is 1. The whole thing. Now shade in 3 columns."

Wait. Let them shade.

"You just shaded 3 out of 10 columns. That's 3/10. We can also write it as 0.3. Read it: 'three tenths.'"

Now:

"Shade 7 more little squares — not columns, just single squares."

"Those single squares are hundredths. There are 100 little squares in the whole grid. You shaded 7 more, so now you have 3 tenths and 7 hundredths shaded. That's 0.37."

Listen for: Are they seeing that one column = 10 little squares = 1 tenth = 10 hundredths?

3 · Connect to the math — 4 min

Write on the board:

   0 . 3 7
       ↑ ↑
       │ └── hundredths (out of 100)
       └──── tenths     (out of 10)

Say it out loud: "Zero point three seven. Three tenths and seven hundredths. Thirty-seven hundredths."

Now draw the number line again:

  0 ─┬─┬─┬─┬─┬─┬─┬─┬─┬─┬─ 1
     0.1   0.3       0.7

"Each little tick is one tenth. So 0.3 lives 3 ticks past 0."

Quick check — point and ask:

"Where would 0.5 go? Where would 0.9 go?"

Then the key idea for comparing:

"0.4 is the same as 0.40. We can add a zero on the end without changing the value. That trick helps us compare decimals."

4 · Practice with support — 7 min

Pass out the worksheet. Work through these in order.

Problem 1 — together:

"Write 7/10 as a decimal."

Do this one out loud. Answer: 0.7. Say it: "seven tenths."

Problem 2 — solo:

"Write 0.83 as a fraction."

Let students try on their own. Answer: 83/100. Read it: "eighty-three hundredths."

Problem 3 — solo:

"Compare 0.6 and 0.45. Which is bigger?"

This is the tricky one. If a student says 0.45, ask them to write 0.6 as 0.60. Answer: 0.6 is bigger, because 0.60 > 0.45.

Problem 4 — stretch:

"How many cents is $0.75? And what fraction is that of a dollar?"

Invite them to think about a dollar as 100 pennies. Answer: 75 cents = 75/100 = 3/4 of a dollar.

Circulate. Look for students writing the fraction form next to the decimal — that's the connection clicking.

5 · What we did + Try at home — 2 min

"Today you learned that decimals are fractions in disguise. The first digit after the dot is tenths. The second digit is hundredths."

"Tonight, find a decimal out in the world — on a receipt, a thermometer, a food label, or a gas pump. Read it out loud the long way. Like $3.45 is 'three and forty-five hundredths.'"

Observation rubric — what to notice in this session

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

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

What's next (Session 8)

Next time, Session 8 — Angles, lines, symmetry closes out Grade 4 with geometry. We'll look at angles, parallel lines, and mirror symmetry — a different kind of "math gets bigger" to end the year on.

✏️ Worksheet (for students)

Math for Young Minds · Grade 4

Session 7 — Decimals: tenths and hundredths

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

Today's big idea

A decimal is a number with a dot. The dot shows where the whole ends and the parts begin.

The first digit after the dot is tenths (out of 10). The second digit after the dot is hundredths (out of 100).

   0  .  4  7
         ↑  ↑
      tenths  hundredths

So 0.47 means 47 out of 100 = 47/100.

Example we did together

A number line from 0 to 1, split into 10 equal jumps:

  0     0.1   0.2   0.3   0.4   0.5   0.6   0.7   0.8   0.9    1
  |─────|─────|─────|─────|─────|─────|─────|─────|─────|─────|
                                       ★

The ★ is at 0.6 — that's 6 tenths, or 6/10.

We say it: "six tenths."

Problem 1 — together

Write 7/10 as a decimal.

Shade 7 out of 10 strips below:

┌─────────────────────────────────────────────────────────┐
│                                                         │
│   ┌──┬──┬──┬──┬──┬──┬──┬──┬──┬──┐                       │
│   │  │  │  │  │  │  │  │  │  │  │                       │
│   └──┴──┴──┴──┴──┴──┴──┴──┴──┴──┘                       │
│    1  2  3  4  5  6  7  8  9 10                         │
│                                                         │
│                                                         │
│   7/10  =  ______                                       │
│                                                         │
└─────────────────────────────────────────────────────────┘

We say it: "seven tenths."

Problem 2 — on your own

Write 0.83 as a fraction.

Shade 83 squares on the 10×10 grid:

┌─────────────────────────────────────────────────────────┐
│                                                         │
│    ┌─┬─┬─┬─┬─┬─┬─┬─┬─┬─┐                                │
│    ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤                                │
│    ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤                                │
│    ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤                                │
│    ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤                                │
│    ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤                                │
│    ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤                                │
│    ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤                                │
│    ├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤                                │
│    └─┴─┴─┴─┴─┴─┴─┴─┴─┴─┘                                │
│                                                         │
│    0.83  =  ______ / ______                             │
└─────────────────────────────────────────────────────────┘

Problem 3 — on your own

Compare 0.6 and 0.45. Which one is bigger?

Place both numbers on the number line below:

┌─────────────────────────────────────────────────────────┐
│                                                         │
│   0                    0.5                     1        │
│   |─────|─────|─────|─────|─────|─────|─────|─────|     │
│                                                         │
│                                                         │
│   Trick: write 0.6 as 0.60. Now compare 0.60 and 0.45.  │
│                                                         │
│                                                         │
│   Bigger number:  ______                                │
│                                                         │
└─────────────────────────────────────────────────────────┘

Watch out: 0.6 is NOT smaller than 0.45 just because "45 > 6". Line up the place values!

Problem 4 — stretch

You have a coin worth $0.75.

       ┌───────────────┐
       │   $ 0 . 7 5   │
       └───────────────┘

• How many cents is $0.75? ______ cents
• Write it as a fraction of a dollar: ______ / 100
• Can you simplify that fraction? ______ / ______

Hint: $0.25 is one quarter of a dollar. How many quarters are in $0.75?

Today's words

Try at home tonight (1 minute)

Find a decimal somewhere at home and read it out loud. Examples:

• A price on a receipt (like $3.45 → "three and forty-five hundredths")
• A thermometer reading
• A weight on a food label
• A gas pump price per gallon
• A number of miles on a road sign

Write down the decimal you found:

  ______ . ______

Say it out loud to a grown-up tomorrow morning.

Coming up next — Session 8: Angles, lines, and symmetry. We close Grade 4 with geometry!

🏠 Family guide (for parents)

Math for Young Minds · Grade 4 · Session 7

A note for grown-ups: today we started decimals

What your child did today

Today we met decimals — numbers that use a dot to show parts of a whole.

The big idea: a decimal is just another way to write a fraction. 0.3 is the same as 3/10. 0.47 is the same as 47/100.

We used a number line from 0 to 1, split first into 10 equal pieces (tenths), then into 100 (hundredths). We also used 10×10 grids on graph paper — shading 47 little squares out of 100 to see what 0.47 looks like.

Then we practiced placing decimals on the line and comparing two of them to see which is bigger.

Why this matters

Decimals are everywhere outside the classroom — money, weights, temperatures, gas pumps. This is the first time your child sees that fractions and decimals are two ways of saying the same thing. That connection comes back in Grade 5, in measurement, in percents later on. We're not rushing. Understanding first. Speed comes later, on its own.

🏠 Try this tonight (1 minute)

Find a decimal somewhere in the house or on the way somewhere. Ask your child to read it out loud the long way — not "point four seven" but "forty-seven hundredths."

Where to look:

A short script:

• "What's the number?"
• "How would you read it out loud?"
• "What's the part after the dot — tenths or hundredths?"

That's it. One number, read out loud, and you're done.

Words your child is learning

• Decimal — a number that uses a dot to show parts of a whole
• Tenths — the first digit after the decimal point; out of 10
• Hundredths — the second digit after the decimal point; out of 100

If your child says…

"This is easy." Good. Ask them a tricky one: which is bigger, 0.6 or 0.45? Many kids say 0.45 because 45 looks bigger than 6. But 0.6 is the same as 0.60 — which is more than 0.45. If they catch that, they've really got it.

"This is hard." Also good. Grab graph paper if you have it, or sketch a 10×10 grid. Shade in the decimal. 0.3 is 3 columns out of 10. 0.30 is 30 little squares out of 100 — same amount. Seeing it on the grid does most of the work.

"I don't want to." Fine. Skip the worksheet feeling and just read one number off a receipt together while you're doing something else. One number. Out loud. That counts.

A heads-up on two common mix-ups

• 0.07 is seven hundredths, not "seven." The zero matters.
• 1/4 and 0.25 are the same number. So are 3/4 and 0.75 — that's why 75 cents is three-quarters of a dollar.

These click with practice. No rush.

What's next

In Session 8 we close out Grade 4 with geometry — angles, parallel lines, and mirror symmetry. A different flavor of math, and a nice way to finish the year.

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

— Math for Young Minds

🔑 Cheat sheet (visual)

🔟 Decimals = parts of a whole

Picture 1 — The 10×10 grid

   0.3  =  3/10  (tenths)        0.47  =  47/100  (hundredths)

   ■ ■ ■ □ □ □ □ □ □ □            ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
   ■ ■ ■ □ □ □ □ □ □ □            ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
   ■ ■ ■ □ □ □ □ □ □ □            ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
   ■ ■ ■ □ □ □ □ □ □ □            ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
   ■ ■ ■ □ □ □ □ □ □ □            ■ ■ ■ ■ □ □ □ □ □ □
   ■ ■ ■ □ □ □ □ □ □ □            □ □ □ □ □ □ □ □ □ □
   ■ ■ ■ □ □ □ □ □ □ □            □ □ □ □ □ □ □ □ □ □
   ■ ■ ■ □ □ □ □ □ □ □            □ □ □ □ □ □ □ □ □ □
   ■ ■ ■ □ □ □ □ □ □ □            □ □ □ □ □ □ □ □ □ □
   ■ ■ ■ □ □ □ □ □ □ □            □ □ □ □ □ □ □ □ □ □

   3 columns of 10                4 full rows + 7 more
   = 30/100 = 3/10                = 47/100

Picture 2 — On the number line

   0                       0.5                       1
   ├───┬───┬───┬───┬───┬───┬───┬───┬───┬───┤
   0  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  1
                   ▲               ▲
                  0.3             0.6

   Zoom in between 0.4 and 0.5  (hundredths):

   0.4                                          0.5
   ├──┬──┬──┬──┬──┬──┬──┬──┬──┬──┤
  0.40                ▲                       0.50
                    0.45

How to read the dot

                ┌──── tenths  (out of 10)
                │ ┌── hundredths (out of 100)
                │ │
       0   .   4 7
       │
       └──── whole number part

   Say it:  "zero point four seven"
            = "forty-seven hundredths"
            = 47/100

Comparing decimals — line them up!

       0.6   vs   0.45
                                  ✅ same number of places
       0.60  vs   0.45               0.60 > 0.45
       ────       ────               so  0.6 > 0.45
       60/100     45/100

Money is decimals!

   $1.00  =  one whole dollar  =  100 cents

   $0.75  →   ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
              ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
              ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
              ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
              ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
              ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
              ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
              ■ ■ ■ ■ ■ ■ ■ ■ ■ ■   ← 75 of 100 squares
              □ □ □ □ □ □ □ □ □ □
              □ □ □ □ □ □ □ □ □ □

      75 cents  =  75/100  =  3/4 of a dollar 🪙

Try this in your head

   Write  7/10  as a decimal.

   ■ ■ ■ ■ ■ ■ ■ □ □ □     ← 7 out of 10

➤ 7/10 = 0. ___

Answer: 0.7 ("seven tenths")