Grade 4 · Session 03

Long Division Intro

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

📄 This page has 4 sections — jump to one:

📋 Session plan (for teachers)

Session 3 — Long division (intro)

Grade 4 · Math for Young Minds Total time: ~24 minutes Common Core: 4.NBT.B.6 Today's idea: Long division is how we share a big pile into equal groups — one step at a time.

What students will be able to do

By the end of this session, the student can:

Divide a 2-digit number by a 1-digit number, with or without a remainder.
Use the four steps of long division: divide, multiply, subtract, bring down.
Explain what a remainder means in a real situation.

Materials

Graph paper (one sheet per student)
Worksheet (one per student)
Pencil

Substitution: No graph paper? Have students draw their own column lines on lined paper, or turn lined paper sideways. The grid just keeps digits stacked neatly.

New words

Word	Meaning we use in class
quotient	The answer to a division problem.
remainder	What's left when something doesn't divide evenly.
dividend	The number being split up.
divisor	The size of each group, or the number of groups.

Heads-up — common confusions

Long division has four steps that repeat. Skipping one (especially "subtract") is the #1 way students get lost. Say the steps out loud each time.
Students often shrug off the remainder. In real life, the leftover usually matters — 5 leftover stickers is 5 kids who didn't get one.
Which number goes inside the bracket vs outside? The dividend (the big pile) goes inside. The divisor (the number of groups) goes outside.

Plan

1 · Hello & today's idea — 2 min

"Today we're going to learn the grown-up way to divide. It's called long division. It looks fancy, but it's just four little steps you repeat."

Write on the board:

divide → multiply → subtract → bring down

"Say those four words with me."

Say them together twice. Then:

"We use this when we share a pile of stuff into equal groups."

2 · Hands-on explore — 6 min

Hand out graph paper and pencils.

Problem 1 — together: "We have 48 stickers. We want to share them with 4 friends. How many does each friend get?"

Write on the board, using the graph paper grid:

      ____
   4 ) 48

"48 is the dividend — the pile. 4 is the divisor — the number of friends. The answer we're finding is the quotient."

Walk through the steps out loud, writing each one:

Divide: "How many 4s in 4? One." Write 1 above the 4.
Multiply: "1 times 4 is 4." Write 4 under the 4.
Subtract: "4 minus 4 is 0."
Bring down: "Bring down the 8."
Divide again: "How many 4s in 8? Two." Write 2 above the 8.
Multiply, subtract: "2 times 4 is 8. 8 minus 8 is 0."

"Quotient is 12. Each friend gets 12 stickers. Zero left over."

3 · Connect to the math — 4 min

Point at the four-step list on the board.

"Every time. Divide. Multiply. Subtract. Bring down. Then start over with the next digit."

Name the parts again, pointing at the board:

"Inside the bracket — the dividend, the pile. Outside — the divisor, the groups. On top — the quotient, the answer."

"And sometimes — not always — there's a remainder. That's the leftover. We'll see one in a minute."

4 · Practice with support — 9 min

Students work on graph paper. Circulate.

Problem 2 (solo): 85 ÷ 5 = ? → Quotient is 17. No remainder.

Look for: Are they writing all four steps? Or skipping "subtract"?

Problem 3 (solo, with remainder): 73 ÷ 3 = ? → Quotient is 24, remainder 1.

When a student finishes, ask: "What's the leftover? Where did it come from?"

Problem 4 (stretch): "A teacher has 95 stickers for 6 students. How many does each get? What does the remainder mean?" → 15 each, with 5 stickers left over.

Ask the stretch question out loud:

"5 left over. What does that mean? Can the teacher just split a sticker in half?"

Listen for: "5 kids could get an extra one," or "the teacher keeps them," or "someone misses out." All good answers. The point is — the remainder matters.

5 · What we did + Try at home — 2 min

"Today you learned long division. Four steps: divide, multiply, subtract, bring down. And you learned that the leftover — the remainder — often matters in real life."

Hand out the take-home:

"Tonight, find a small pile of something at home — grapes, cards, marbles, cookies, your allowance over a few weeks. Share it equally with a small number of people. Write down the quotient and the remainder. Does the remainder matter? Bring your answer next time."

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 which number goes inside the bracket. Skips a step (often "subtract"). Forgets the remainder.
Using	Walks through all four steps in order. Gets the quotient. Names the remainder when there is one.
Extending	Explains in their own words what the remainder means in the sticker problem. Sees that the remainder is always smaller than the divisor.

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

What's next (Session 4)

Building on this, Session 4 — Factors, multiples, prime numbers looks at the building blocks of multiplication — and finds the special numbers that only have themselves and 1 as factors.

✏️ Worksheet (for students)

Math for Young Minds · Grade 4

Session 3 — Long division (intro)

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

Today's big idea

Long division splits a big pile into equal groups, one digit at a time.

The steps repeat: divide, multiply, subtract, bring down.

The number inside the bracket is the dividend (the pile). The number outside is the divisor (how many groups). The answer on top is the quotient.

Example we did together

We shared 48 marbles into 4 equal groups.

        1  2     ← quotient
      ┌──────
    4 │ 4  8
        4         (4 × 1 = 4, subtract)
        ─
        0  8     (bring down the 8)
           8     (4 × 2 = 8, subtract)
        ───
           0     ← no remainder!

So 48 ÷ 4 = 12. Each group gets 12 marbles.

Problem 1 — together

Divide 48 ÷ 4 using long division. Follow the steps with your teacher: divide, multiply, subtract, bring down.

┌─────────────────────────────────────────────────────────┐
│                                                         │
│         ┌──────                                         │
│       4 │ 4  8                                          │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
└─────────────────────────────────────────────────────────┘

Quotient: ____ Remainder: ____

Problem 2 — on your own

85 ÷ 5 = ?

Set it up in the box. Show every step.

┌─────────────────────────────────────────────────────────┐
│                                                         │
│         ┌──────                                         │
│       5 │ 8  5                                          │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
└─────────────────────────────────────────────────────────┘

Quotient: ____ Remainder: ____

Problem 3 — on your own

73 ÷ 3 = ?

Heads up: this one has a remainder. That's okay!

┌─────────────────────────────────────────────────────────┐
│                                                         │
│         ┌──────                                         │
│       3 │ 7  3                                          │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
└─────────────────────────────────────────────────────────┘

Quotient: ____ Remainder: ____

So 73 ÷ 3 = ____ R ____

Problem 4 — stretch

A teacher has 95 stickers for 6 students. She wants each student to get the same number.

   🧒  🧒  🧒  🧒  🧒  🧒        ⭐ × 95
   6 students                    95 stickers

Do the long division:

┌─────────────────────────────────────────────────────────┐
│                                                         │
│         ┌──────                                         │
│       6 │ 9  5                                          │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
└─────────────────────────────────────────────────────────┘

Each student gets ____ stickers.
There are ____ stickers left over.
What does the remainder mean here? (write a sentence)

______________________________________________________
______________________________________________________

Today's words

Word	What it means
quotient	The answer to a division problem
remainder	What's left when something doesn't divide evenly
dividend	The number being split (goes inside the bracket)
divisor	The size of each group, or how many groups (goes outside)

Try at home tonight (1 minute)

Find a small pile at home and a small number of people. Divide. Is there a remainder? Does it matter?

Share grapes among your siblings 🍇
Split a deck of cards among players 🃏
Share marbles into equal piles
Divide cookies onto plates 🍪
Share an allowance over a few weeks 💰

  Total: ____    ÷    People: ____    =    Each: ____   R  ____

Next time: Session 4 — factors, multiples, and prime numbers. The building blocks of multiplication!

🏠 Family guide (for parents)

Math for Young Minds · Grade 4 · Session 3

A note for grown-ups: today we started long division

What your child did today

In class today, we started long division — sharing a pile of objects into equal groups.

The big idea: when numbers get bigger, we need a step-by-step method to share them out. We learned the four moves: divide, multiply, subtract, bring down. Repeat.

We worked through 48 ÷ 4 = 12 together on a long-division grid, then your child tried a few on their own, including one with a leftover. We also talked about what those leftovers mean in real life.

Why this matters

Division is how we make sense of sharing, splitting, and grouping — and it shows up everywhere later, in fractions, in measurement, in money. Long division looks like a lot of steps, but each one is small. We're not racing through it. Understanding first. Speed comes later, on its own. No timed tests here.

🏠 Try this tonight (1 minute)

Find a small pile of something at home, and a small number of people to share it with. Divide it up. See if anything is left over.

A short script:

"How many do we have in total?"
"How many people are sharing?"
"How many does each person get? Is anything left over?"
"Does the leftover matter here?"

Easy starters around the house:

Thing to share	Who shares it
Grapes	Among siblings
A deck of cards	Among players
Marbles	Among friends
Cookies	On plates
Allowance	Over a few weeks

The leftover is the interesting part. Sometimes it matters a lot (one extra cookie — who gets it?). Sometimes it doesn't (one extra card — set it aside).

Words your child is learning

Dividend — the number being split (the whole pile)
Divisor — the size of each group, or how many groups
Quotient — the answer to a division problem
Remainder — what's left when something doesn't divide evenly

If your child says…

"This is easy." Great. Hand them a bigger number, like 73 ÷ 3, and ask what the remainder means. Could you really split 73 cookies among 3 people evenly?

"This is hard." Also great. Long division has four steps for a reason — it's a lot to hold in your head. Slow down. Use graph paper so the columns line up. Walk through one step at a time: divide, multiply, subtract, bring down. Skipping a step is the most common slip, and it's fixable.

"I don't want to." Fine. Skip the worksheet feel. Just grab a small pile of something real on the kitchen table and share it out by hand. That is division. The pencil-and-paper version can wait until tomorrow.

What's next

In our next session, we look at factors, multiples, and prime numbers — the building blocks of multiplication. We'll find the numbers that only have themselves and 1 as factors.

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

— Math for Young Minds

🔑 Cheat sheet (visual)

🔑 Long division = sharing fairly

Picture 1 — Share 48 cookies, 4 plates

   🍪🍪🍪      🍪🍪🍪      🍪🍪🍪      🍪🍪🍪
   🍪🍪🍪      🍪🍪🍪      🍪🍪🍪      🍪🍪🍪
   🍪🍪🍪      🍪🍪🍪      🍪🍪🍪      🍪🍪🍪
   🍪🍪🍪      🍪🍪🍪      🍪🍪🍪      🍪🍪🍪

    plate 1     plate 2     plate 3     plate 4

       48 cookies  ÷  4 plates  =  12 each ✨

How to read the sign

                        ┌──── quotient (the answer)
                        │
                       12
                      ─────
       divisor ─►  4 ) 48   ◄── dividend
                      
       "outside" splits "inside"

➤ dividend = number being split ➤ divisor = number of groups ➤ quotient = answer

Picture 2 — The 4 steps (48 ÷ 4)

   Divide → Multiply → Subtract → Bring down

      1                 12              12
    ─────             ─────           ─────
   4)48              4)48            4)48
    -4 ↓              -4              -4
     ─                ──              ──
     0                 08              08
                                      -8
                                      ──
                                       0    ← done!  quotient = 12

Same dance every time. Don't skip a step. 🕺

Picture 3 — When it doesn't split evenly (73 ÷ 3)

        24  R 1
      ──────
   3 ) 73
      -6        ← 3 × 2
      ──
       13
      -12       ← 3 × 4
      ──
        1       ← remainder! left over

➤ remainder = what's left when it doesn't divide evenly.

When does the remainder matter?

✅ It matters when...	⚠️ Think about it when...
`95 stickers ÷ 6 kids = 15 R 5`	leftover stickers — give away? save?
`17 cookies ÷ 4 friends`	someone gets fewer, or you split one
`73 marbles ÷ 3 jars`	1 marble has no jar!

The remainder is real. Ask: what happens to the leftovers?

Which goes inside?

        BIG number (dividend) goes INSIDE
                    │
                   ▼
              ┌────────
       4   ) │   48
       ▲     └────────
       │
   small number (divisor) goes OUTSIDE

Try this in your head

   85 ÷ 5 = ?

        ? 
      ────
   5 ) 85

➤ quotient = ____ remainder = ____

Answer: 85 ÷ 5 = 17, no remainder. ✅

🔜 Next: factors, multiples, and prime numbers — the building blocks of multiplication.

← Back to Grade 4