Grade 4 · Session 04

Factors Multiples And Prime Numbers

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 4 — Factors, multiples, and prime numbers

Grade 4 · Math for Young Minds Total time: ~22 minutes Common Core: 4.OA.B.4 Today's idea: Every number has a shape — the rectangles you can build from it tell you its factors.

What students will be able to do

By the end of this session, the student can:

List all the factors of a whole number up to 100.
List the first several multiples of a number.
Tell if a number is prime — only two factors, 1 and itself.

Materials

Small square tiles (about 30 per student) — or grid paper
Worksheet (one per student)
Pencil

Substitution: No tiles? Grid paper works perfectly. Students shade in rectangles instead of building them. Pennies, beans, or paper squares are fine too.

New words

Word	Meaning we use in class
factor	A number that divides evenly into another number.
multiple	The result of multiplying a number by 1, 2, 3, …
prime number	A number with exactly two factors — 1 and itself.
composite number	A number with more than two factors.

Heads-up — common confusions

Factors vs. multiples gets tangled fast. Say it out loud: factors divide into a number; multiples come out of a number.
Students often miss the obvious factors — 1 and the number itself. Remind them: every number has those two for free.
Some students will say 1 is prime. It's not — primes have exactly two factors, and 1 only has one.

Plan

1 · Hello & today's idea — 2 min

"Today we're going to build rectangles out of squares — and what we find out is that every number has its own little family of rectangles."

Hold up 12 tiles (or draw 12 squares on the board).

Ask: "Can I arrange these 12 tiles into a neat rectangle? How many different ways?"

Let a few students guess. Don't confirm yet — just listen.

2 · Hands-on explore — 6 min

Give each student (or pair) about 12 tiles or a piece of grid paper.

Prompt: "Build every rectangle you can with exactly 12 tiles. No gaps, no leftovers. Sketch each one."

Let them work. Listen for:

Are they finding 1 × 12, 2 × 6, 3 × 4?
Are they trying 5 and noticing it doesn't work?
Are they flipping rectangles and calling them new? (That's okay — gently say 2 × 6 and 6 × 2 are the same pair.)

After a few minutes, gather answers on the board:

1 × 12     2 × 6     3 × 4

"Every number that fits into 12 evenly is called a factor of 12."

3 · Connect to the math — 4 min

Write on the board:

Factors of 12:  1, 2, 3, 4, 6, 12

"Factors divide into the number. Now let's flip it around."

Write underneath:

Multiples of 12:  12, 24, 36, 48, 60, ...

"Multiples come out of the number when you multiply it by 1, 2, 3, and so on."

Then introduce the special case:

"What if a number only makes ONE rectangle — a long skinny strip of 1 × something? Then it has only two factors. We call that a prime number."

Quick example: 7 tiles only make a 1 × 7 strip. Factors: 1 and 7. That's prime.

If more than two factors? Composite.

"One small thing — the number 1 is not prime. Primes need exactly two different factors, and 1 only has itself."

4 · Practice with support — 8 min

Pass out the worksheet. Work in order.

Problem 1 — together: List all the factors of 12. Use rectangles if it helps. Walk through it on the board. Answer: 1, 2, 3, 4, 6, 12.

Problem 2 — solo: List the first 6 multiples of 7. Remind: start at 7 × 1. Answer: 7, 14, 21, 28, 35, 42.

Problem 3 — solo: Is 13 a prime number? Why or why not? Answer: Yes — its only factors are 1 and 13.

Problem 4 — stretch: Find all prime numbers between 2 and 20. Encourage tile-checking or listing factors. Answer: 2, 3, 5, 7, 11, 13, 17, 19.

Circulate. If a student is stuck, ask: "Can you build a rectangle? How many ways?"

5 · What we did + Try at home — 2 min

"Today you learned that factors divide into a number, multiples come out of a number, and a prime number has only two factors — 1 and itself."

Send home:

"Pick a number between 10 and 30 — your age, the day of the month, your house number, a page number. Find all its factors. Is it prime or composite?"

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 factors and multiples. Misses 1 or the number itself. Needs tiles to find any factor pair.
Using	Lists all factors of 12. Writes multiples of 7 in order. Explains why 13 is prime in their own words.
Extending	Spots primes without building rectangles. Notices that even numbers (except 2) are never prime. Finds all primes under 20 on their own.

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

What's next (Session 5)

Building on this, Session 5 — Equivalent fractions and comparing revisits fractions. We find equivalent ones and compare tricky pairs like 3/4 vs 5/6 — using the same "look for the pattern" thinking we used today.

✏️ Worksheet (for students)

Math for Young Minds · Grade 4

Session 4 — Factors, multiples, and prime numbers

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

Today's big idea

Every whole number is built from smaller numbers called factors.

A factor divides evenly into a number. A multiple comes out when you multiply.

Factors go IN → Multiples come OUT.

Example we did together

We made rectangles for 6 using square tiles:

  1 × 6                     2 × 3
  ■ ■ ■ ■ ■ ■               ■ ■ ■
                            ■ ■ ■

Each rectangle shows a factor pair. So the factors of 6 are:

1, 2, 3, 6

6 has more than two factors, so 6 is a composite number.

Problem 1 — together

List all the factors of 12. Use rectangles if it helps.

Draw rectangles of tiles for 12 here. Try every shape you can.

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

The factors of 12 are:

____, ____, ____, ____, ____, ____

Problem 2 — on your own

List the first 6 multiples of 7.

Remember: multiples come from 7 × 1, 7 × 2, 7 × 3, …

Work it out here:

┌─────────────────────────────────────────────────────────┐
│                                                         │
│   7 × 1 =                                               │
│                                                         │
│   7 × 2 =                                               │
│                                                         │
│   7 × 3 =                                               │
│                                                         │
│                                                         │
└─────────────────────────────────────────────────────────┘

The first 6 multiples of 7 are:

____, ____, ____, ____, ____, ____

Problem 3 — on your own

Is 13 a prime number? Why or why not?

Try to draw rectangles for 13 tiles:

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

The factors of 13 are: ____, ____

Is 13 prime? ____ Because: ________________________________

Problem 4 — stretch

Find all the prime numbers between 2 and 20.

Cross out every number that has more than two factors. Circle the primes.

   2    3    4    5    6    7    8    9    10

   11   12   13   14   15   16   17   18   19   20

The prime numbers between 2 and 20 are:

____, ____, ____, ____, ____, ____, ____, ____

Careful: 1 is NOT prime — a prime needs exactly TWO factors.

Today's words

Word	What it means
factor	A number that divides evenly into another number
multiple	The result of multiplying a number by 1, 2, 3, …
prime number	A number with exactly two factors — 1 and itself
composite number	A number with more than two factors

Try at home tonight (1 minute)

Pick a number between 10 and 30. Find all its factors. Is it prime or composite?

Ideas for picking your number:

Your age
The day of the month
The last 2 digits of your house number
A page number from a book
Your favorite number

  My number: ____

  Its factors: ____________________________________

  Prime or composite?  ____________

Show a grown-up tomorrow morning.

🏠 Family guide (for parents)

Math for Young Minds · Grade 4 · Session 4

A note for grown-ups: today we explored factors, multiples, and prime numbers

What your child did today

In class today, we looked at numbers from the inside out.

The big idea: every whole number is built from smaller numbers multiplied together. We used square tiles to build rectangles — each rectangle shows a factor pair. A 2-by-6 rectangle of tiles shows that 2 and 6 are factors of 12.

Some numbers, like 13, can only be built as a single long strip. Those are prime numbers. Others, like 12, can be built lots of ways — those are composite numbers.

Your child practiced listing factors of 12, listing multiples of 7, and deciding whether 13 is prime.

Why this matters

Factors and multiples are the quiet building blocks behind a lot of what's coming — fractions, common denominators, division, and later algebra. We're not racing to memorize prime numbers. We're learning to see how numbers fit together. That seeing pays off for years. No timed tests here. Understanding first, speed comes later on its own.

🏠 Try this tonight (1 minute)

Pick a number between 10 and 30. Find all its factors together. Then ask: is it prime or composite?

Easy ways to pick a number:

Where to look	Example
Your child's age	10
Today's date	the 17th
Your house number	last 2 digits
A page in any book	page 24

A short script:

"What numbers divide evenly into it?"
"Don't forget 1 and the number itself."
"How many factors did we find? Just two? Then it's prime."

If grid paper or tiles are handy, try building rectangles. One long strip only? Prime. More than one rectangle? Composite.

Words your child is learning

Factor — a number that divides evenly into another number
Multiple — what you get when you multiply a number by 1, 2, 3, …
Prime number — a number with exactly two factors: 1 and itself
Composite number — a number with more than two factors

A helpful reminder: factors divide INTO a number; multiples come OUT of it.

If your child says…

"This is easy." Wonderful. Ask them to find a number between 30 and 50 with lots of factors. Or ask whether 1 is prime. (It isn't — primes have exactly two factors, and 1 only has one.)

"This is hard." Also fine. Pull out a small pile of objects — coins, beans, cereal pieces. Try to arrange 12 of them into equal rows. Then try 13. The hands-on part is where the understanding sticks.

"I don't want to." No problem. Skip the worksheet feel and just pick one number from the dinner table — the number of plates, the time on the clock. One number, one minute. That's enough for tonight.

What's next

In our next session, we revisit fractions — finding equivalent ones and comparing fractions like 3/4 and 5/6. The factor work from today will quietly help.

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

— Math for Young Minds

🔑 Cheat sheet (visual)

🔑 Factors, multiples, primes

Picture 1 — Factors of 12 are rectangles

  1 × 12               2 × 6              3 × 4

  ■■■■■■■■■■■■        ■■■■■■            ■■■■
                      ■■■■■■            ■■■■
                                        ■■■■

Factors of 12 → 1, 2, 3, 4, 6, 12 ✨

A factor divides evenly into a number.

Picture 2 — Multiples come OUT of a number

  7 ───►  ●         (7 × 1)
  7 ───►  ●●        (7 × 2)
  7 ───►  ●●●       (7 × 3)
  7 ───►  ●●●●      (7 × 4)
  7 ───►  ●●●●●     (7 × 5)
  7 ───►  ●●●●●●    (7 × 6)

  Multiples of 7:  7, 14, 21, 28, 35, 42

A multiple is what you get by multiplying.

Factors vs Multiples

            ┌──── factors go IN ────┐
            ▼                       ▼
       1, 2, 3, 4, 6  ─────►  [ 12 ]  ─────►  12, 24, 36, 48…
                                              ▲
                              multiples come OUT

Picture 3 — Prime = only 1 rectangle

   13 tiles → only one rectangle works:

   ■■■■■■■■■■■■■        1 × 13   ✅
                        2 × ?    ✗
                        3 × ?    ✗
                        4 × ?    ✗

   Factors of 13:  1, 13   →  PRIME ✨

A prime number has exactly two factors: 1 and itself. A composite number has more than two factors.

When is it prime?

✅ Prime	❌ Not prime
`13` → factors: 1, 13	`12` → factors: 1,2,3,4,6,12 (composite)
`7` → factors: 1, 7	`1` → only ONE factor (not prime!)
exactly 2 factors	fewer or more than 2

Primes from 2 to 20

   2   3   ·   5   ·   7   ·   ·   ·   11
   ·   13  ·   ·   ·   17  ·   19  ·   ·

   →  2, 3, 5, 7, 11, 13, 17, 19

Try this in your head

   Pick the number 15.
   What rectangles can you build?

   1 × 15      3 × 5

➤ Factors of 15 = ____ Prime or composite? ____

Answer: 1, 3, 5, 15 → composite (4 factors)

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