Grade 4 · Session 02

Multi Digit Multiplication

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 2 — Multi-digit multiplication

Grade 4 · Math for Young Minds Total time: ~23 minutes Common Core: 4.NBT.B.5 Today's idea: Big multiplication gets easier when you break numbers apart and draw them as a rectangle.

What students will be able to do

By the end of this session, the student can:

Multiply a 2-digit number by a 1-digit number (like 47 × 6).
Multiply two 2-digit numbers using an area model (like 23 × 14).
Break a number apart by place value to make the math easier.

Materials

Graph paper (one sheet per pair)
Ruler (one per pair)
Worksheet (one per student)
Pencils

Substitution: If you don't have graph paper, plain paper works — just have students sketch rectangles freehand. The rectangle doesn't have to be to scale; it has to show the parts.

New words

Word	Meaning we use in class
partial product	One piece of a bigger multiplication problem.
area model	A rectangle drawing that shows multiplication as area.

Heads-up — common confusions

Some students forget to multiply all the partial products. Point at each box in the rectangle as you add.
Watch for misplaced zeros when multiplying by tens. 20 × 4 is 80, not 8.
When adding partial products, line up the columns. A quick check: does the sum look about the right size?

Plan

1 · Hello & today's idea — 2 min

"Today the numbers get bigger. We're going to multiply numbers like 23 and 47 — too big to count on your fingers. The trick is to break them apart."

Draw a rectangle on the board. Say:

"A rectangle's area is length times width. We're going to use that idea to multiply any two numbers."

2 · Hands-on explore — 6 min

Hand each pair graph paper and a ruler.

Prompt: "Draw a rectangle that is 23 squares long and 4 squares tall. Don't count every square one by one — find a faster way."

Let them work. Listen for:

Are they splitting the rectangle into a 20-part and a 3-part?
Are they counting one row at a time?

After about 3 minutes, pause everyone.

"Show me where the 20 is in your rectangle. Show me where the 3 is."

Have one pair share. You're listening for "I split it into a big piece and a little piece."

3 · Connect to the math — 5 min

Now name what just happened.

"You just made an area model. You broke 23 into 20 + 3. Each piece of the rectangle is a partial product — one piece of the answer."

Draw this on the board for Problem 1 — together: 23 × 4:

        20            3
     +-------+      +---+
   4 |  80   |      | 12|
     +-------+      +---+

   20 × 4 = 80   ← partial product
    3 × 4 = 12   ← partial product
       80 + 12 = 92

Read it out loud:

"20 times 4 is 80. 3 times 4 is 12. Add the partial products: 92."

"Every box gets multiplied. Every box gets added. Don't leave any out."

4 · Practice with support — 8 min

Pass out the worksheet. Students work alone or with a partner.

Problem 2 (solo): 47 × 6 = ? Nudge: "Break 47 into 40 + 7. Two partial products." → 282

Problem 3 (solo): 23 × 14 = ? Use an area model. Nudge: "Break both numbers. 23 = 20 + 3. 14 = 10 + 4. Your rectangle has four boxes now." → 322

        20         3
     +------+   +-----+
  10 | 200  |   |  30 |
     +------+   +-----+
   4 |  80  |   |  12 |
     +------+   +-----+
   200 + 30 + 80 + 12 = 322

Problem 4 (stretch): A movie theater has 24 rows with 18 seats each. How many seats total? Invite them to draw it first. Break 24 into 20 + 4 and 18 into 10 + 8. → 432

Circulate. If a student gets stuck, point to one box at a time: "What goes here?"

5 · What we did + Try at home — 2 min

"Today you learned to multiply big numbers by breaking them apart. The rectangle — the area model — shows every piece, every partial product."

Wave the take-home:

"Tonight, find a multiplication problem at home. Maybe windows times panes. Maybe books on a shelf times shelves. Maybe minutes per workout times workouts per week. Draw the rectangle. Solve it."

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	Needs reminders to break the number by place value. May forget a partial product, or misplace a zero.
Using	Draws the area model, fills in every box, adds the partial products, gets the right total.
Extending	Sees that `23 × 14` and `14 × 23` give the same answer. Or solves the stretch problem without drawing.

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

What's next (Session 3)

Building on this, Session 3 — Long division goes the other way: we take a big number and split it into equal groups, step by step.

✏️ Worksheet (for students)

Math for Young Minds · Grade 4

Session 2 — Multi-digit multiplication

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

Today's big idea

Big numbers get easier when you break them apart.

An area model is a rectangle that shows multiplication as area. Each piece inside is a partial product — one piece of the bigger problem.

Example we did together

To solve 13 × 5, break 13 into 10 + 3:

            10            3
        ┌─────────┬──────────┐
    5   │   50    │    15    │
        └─────────┴──────────┘

   50  +  15  =  65        so   13 × 5 = 65

Two partial products: 50 and 15. Add them up!

Problem 1 — together

Solve 23 × 4 using an area model. Break 23 into 20 + 3.

              20              3
        ┌───────────┬─────────────┐
   4    │           │             │
        │  20 × 4 = │   3 × 4 =   │
        │   _____   │    _____    │
        └───────────┴─────────────┘

Add the partial products:

  ______  +  ______  =  ______

So 23 × 4 = ______.

Problem 2 — on your own

47 × 6 = ? Use a strategy. Break 47 into 40 + 7.

Draw your area model here:

┌─────────────────────────────────────────────────────────┐
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
└─────────────────────────────────────────────────────────┘

Partial products:

  40 × 6 = ______        7 × 6 = ______

  ______  +  ______  =  ______

Watch out: don't lose the zero when multiplying by 40!

Problem 3 — on your own

23 × 14 = ? Use an area model. Break 23 into 20 + 3 and 14 into 10 + 4.

Draw your area model here (4 boxes inside!):

┌─────────────────────────────────────────────────────────┐
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
└─────────────────────────────────────────────────────────┘

Fill in your four partial products:

  20 × 10 = ______      3 × 10 = ______

  20 ×  4 = ______      3 ×  4 = ______

Add them all:

  ______ + ______ + ______ + ______  =  ______

Don't forget — you need ALL four partial products.

Problem 4 — stretch

A movie theater has 24 rows with 18 seats each.

How many seats in total?

              ___           ___
        ┌───────────┬─────────────┐
  ___   │           │             │
        │           │             │
        ├───────────┼─────────────┤
  ___   │           │             │
        │           │             │
        └───────────┴─────────────┘

Your four partial products:

  ______ + ______ + ______ + ______  =  ______ seats

Today's words

Word	What it means
partial product	One piece of a bigger multiplication problem
area model	A rectangle drawing that shows multiplication as area

Try at home tonight (1 minute)

Find a multiplication problem somewhere at home. Examples:

Windows × panes in each window
Books on a shelf × shelves in a bookcase
Weeks × days in a week
Cans × packs of soda
Minutes per workout × workouts per week

Draw an area model and solve it:

  ______  ×  ______  =  ______

Bring it tomorrow! Next time → Session 3: Long division — we go the other way and split big numbers into equal groups.

🏠 Family guide (for parents)

Math for Young Minds · Grade 4 · Session 2

A note for grown-ups: today we multiplied bigger numbers

What your child did today

In class today, we worked on multi-digit multiplication — problems like 47 × 6 and 23 × 14.

The big idea: you can break a big number into smaller, friendlier pieces, multiply each piece, and add the answers back together.

We drew rectangles on graph paper and split them into parts — for example, 23 × 4 became a rectangle split into 20 × 4 and 3 × 4. Then we added the two pieces: 80 + 12 = 92. Same answer, easier pieces.

By the end, your child was using this same idea to multiply two 2-digit numbers, like 23 × 14.

Why this matters

This is the year math gets bigger. Your child is moving from single-digit facts to numbers that don't fit in their head all at once. Breaking numbers apart isn't a trick — it's how mathematicians actually think. We're building understanding before speed. The standard algorithm comes later, and it lands better when the picture underneath it makes sense first.

No timed tests. No pressure. Speed comes later on its own.

🏠 Try this tonight (1 minute)

Find one multiplication problem already living in your home and solve it together. That's it.

Try one of these:

Thing	What to multiply
Windows × panes in each	e.g., 5 × 4
Books on a shelf × shelves	e.g., 12 × 3
Days in a week × weeks	e.g., 7 × 4
Cans × packs	e.g., 6 × 5
Minutes per workout × workouts per week	e.g., 20 × 3

A short script:

"How many groups are there?"
"How many in each group?"
"Can we break the big number into easier pieces?"

If they want to draw a rectangle and split it, great. If they want to do it in their head, also great. The goal is just one real problem, one real answer.

Words your child is learning

Partial product — one piece of a bigger multiplication problem
Area model — a rectangle drawing that shows multiplication as area

If your child says…

"This is easy." Wonderful. Hand them a harder one — like 36 × 24 — and ask them to draw the rectangle and show you all the pieces. Ask: did you remember to multiply every part?

"This is hard." Also fine. Slow down. Start with a smaller problem, like 13 × 4. Draw the rectangle. Split the 13 into 10 and 3. Multiply each piece. Add. The picture does the heavy lifting — let them lean on it as long as they need.

"I don't want to." Skip the worksheet feeling. Just find one real thing — eggs, windows, cans — and ask the question out loud while you're doing something else. One minute. No pencil required.

A heads-up on common mix-ups

These are normal at this stage, not a problem:

Forgetting to multiply all the pieces of the rectangle
Losing track of zeros when multiplying by tens (like 20 × 4)
Lining up the partial products in the wrong column when adding

If you see one of these, just point at the rectangle and ask, "did we get every part?"

What's next

In our next session, we go the other way. Session 3 is long division — splitting bigger numbers into equal groups, step by step. Multiplication and division are two sides of the same coin, and your child is ready for it.

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

— Math for Young Minds

🔑 Cheat sheet (visual)

🔑 Big multiplication = break it apart

Picture 1 — Area model: 23 × 4

            20             3
        ┌────────────┬─────────┐
        │            │         │
    4   │   20 × 4   │  3 × 4  │
        │    = 80    │  = 12   │
        └────────────┴─────────┘

           80   +   12   =   92
           ▲         ▲
           └─────────┴──── partial products

23 × 4 = 92 ✨

Picture 2 — 47 × 6 (break 47 → 40 + 7)

            40             7
        ┌────────────┬─────────┐
        │            │         │
    6   │   40 × 6   │  7 × 6  │
        │   = 240    │  = 42   │
        └────────────┴─────────┘

          240   +   42   =   282

47 × 6 = 282

Picture 3 — 23 × 14 (both numbers split!)

            20             3
        ┌────────────┬─────────┐
        │            │         │
   10   │  20 × 10   │ 3 × 10  │
        │   = 200    │  = 30   │
        ├────────────┼─────────┤
        │            │         │
    4   │   20 × 4   │  3 × 4  │
        │    = 80    │  = 12   │
        └────────────┴─────────┘

      200 + 30 + 80 + 12  =  322
       ▲    ▲   ▲    ▲
       └────┴───┴────┴──── 4 partial products

23 × 14 = 322

How to read the area model

              ┌──── break this number into tens + ones
              │
        2 3   ×   1 4    =    322
        │              │
        │              └─── total area
        └──── break this one too

   Each little box = one partial product.
   Add ALL the boxes to get the answer.

When does the area model fit?

✅ Use it when...	❌ Don't need it when...
`47 × 6` — bigger numbers	`7 × 6` — basic fact
`23 × 14` — two 2-digit numbers	`10 × 5` — easy in your head
You want to see every piece	You already know the answer

Break numbers into tens + ones. Multiply each piece. Add them all up.

Try this in your head

   🎬  A theater: 24 rows  ×  18 seats each

            20             4
        ┌────────────┬─────────┐
   10   │    200     │   40    │
        ├────────────┼─────────┤
    8   │    160     │   32    │
        └────────────┴─────────┘

➤ 200 + 40 + 160 + 32 = ____ seats

Answer: 24 × 18 = 432

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