📋 Session plan (for teachers)

Session 6 — Adding & subtracting fractions

Grade 4 · Math for Young Minds Total time: ~22 minutes Common Core: 4.NF.B.3 Today's idea: When the pieces are the same size, fractions add and subtract just like counting.

What students will be able to do

By the end of this session, the student can:

• Add fractions with the same denominator (like 3/8 + 2/8 = 5/8).
• Subtract fractions with the same denominator.
• Notice when an answer becomes one whole or more than one whole.

Materials

• Fraction strips per pair (eighths and sixths)
• Worksheet (one per student)
• Pencil

Substitution: If you don't have fraction strips, draw two long bars on paper — one split into 8 equal pieces, one split into 6. Students can shade pieces with a pencil.

New words

Heads-up — common confusions

• Many students will add the bottoms too: 3/8 + 2/8 = 5/16. It's a fair guess. Slow down and show with strips — the piece size doesn't change.
• Some will forget to simplify. 4/8 is correct, and it equals 1/2. Both are fine; name the simpler one.
• Watch for kids flipping + and − signs when they're moving fast. Point to the sign before they start.

Plan

1 · Hello & today's idea — 2 min

"Today we're going to add and subtract fractions. The trick? Look at the bottom number first."

Hold up two eighth-strips. Line them up so the pieces match.

Ask: "If each piece is the same size, what happens when I put 3 pieces and 2 pieces together?"

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

2 · Hands-on explore — 6 min

Hand each pair their fraction strips (eighths and sixths).

Prompt: "Lay out the eighths strip. Color or cover 3 pieces. Now add 2 more pieces. How many eighths in all?"

Let them work. Listen for:

• Are they keeping the pieces the same size?
• Are they counting pieces, or trying to change the bottom number?

After about 2 minutes, pause everyone.

"What did you get? What happened to the bottom number?"

Take 2–3 responses. You're listening for "It's still eighths — the pieces didn't change size."

3 · Connect to the math — 4 min

Now name it.

"When two fractions have the same bottom — the same size pieces — we call them like denominators. We just add the tops. The bottom stays the same."

Write on the board:

   3/8   +   2/8   =   5/8
    ↑         ↑         ↑
  pieces   more pieces  total pieces
                       (same size!)

"The bottom tells us the size of the piece. The size doesn't change when we add more pieces."

Show with strips:

[■][■][■][ ][ ][ ][ ][ ]   3/8
        +
[■][■][ ][ ][ ][ ][ ][ ]   2/8
        =
[■][■][■][■][■][ ][ ][ ]   5/8

4 · Practice with support — 8 min

Pass out the worksheet.

Problem 1 — together: Add 3/8 + 2/8. Use the fraction strips. Walk through it on the board. Answer: 5/8.

Then let students try problems 2 and 3 on their own. Circulate.

• Problem 2 (solo): 5/6 − 1/6. Watch the minus sign. Answer: 4/6, which simplifies to 2/3.
• Problem 3 (solo): 1/4 + 2/4 + 1/4. Ask: "Does the answer simplify?" Answer: 4/4 = 1 whole. This is the "more than counting pieces" moment — name it.

Problem 4 — stretch: A pie is cut in 8 slices. You eat 3, your sibling eats 2. How much is left?

If a student is stuck, invite them to draw the pie first. Answer: 3/8 left.

5 · What we did + Try at home — 2 min

"Today you learned that fractions with like denominators are easy — same-size pieces, just count them. Add the tops. The bottom stays the same."

Wave the take-home note:

"Tonight, find something at home you can split into equal parts — a pizza in 8, a chocolate bar in 6, an orange in 10, graham crackers. Take some. Leave some. Write the fraction left."

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 7)

Building on this, Session 7 — Decimals — tenths and hundredths shows that decimals can do the same job as fractions — and connect straight to money. Fractions are nice; decimals open another door.

✏️ Worksheet (for students)

Math for Young Minds · Grade 4

Session 6 — Adding & subtracting fractions

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

Today's big idea

When fractions have the same bottom number, the pieces are the same size — so you can just add or subtract the tops.

We call these like denominators.

Only add the tops (numerators). The bottom stays the same!

Example we did together

Fraction strips, all eighths:

  ▓ ▓ ▓ . . . . .      3/8
  ▓ ▓ . . . . . .      2/8
  ───────────────
  ▓ ▓ ▓ ▓ ▓ . . .      5/8

    3     2     5
   ─── + ─── = ───
    8     8     8

The bottom stays 8. We only added 3 + 2 on top.

Problem 1 — together

Add 3/8 + 2/8. Use your fraction strips to check.

Shade the strips:

┌─────────────────────────────────────────────────────────┐
│   ┌───┬───┬───┬───┬───┬───┬───┬───┐                     │
│   │   │   │   │   │   │   │   │   │   3/8               │
│   └───┴───┴───┴───┴───┴───┴───┴───┘                     │
│                                                         │
│   ┌───┬───┬───┬───┬───┬───┬───┬───┐                     │
│   │   │   │   │   │   │   │   │   │   2/8               │
│   └───┴───┴───┴───┴───┴───┴───┴───┘                     │
│                                                         │
│   ┌───┬───┬───┬───┬───┬───┬───┬───┐                     │
│   │   │   │   │   │   │   │   │   │   total             │
│   └───┴───┴───┴───┴───┴───┴───┴───┘                     │
│                                                         │
└─────────────────────────────────────────────────────────┘

   3       2         ____
  ─── + ─── =  ─────
   8       8         ____

Problem 2 — on your own

Subtract 5/6 − 1/6.

Draw 6 equal pieces. Shade 5. Then cross out 1. How many are left?

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

   5       1         ____
  ─── − ─── =  ─────
   6       6         ____

Problem 3 — on your own

Add 1/4 + 2/4 + 1/4.

Draw a strip cut into 4 equal pieces. Shade 1, then 2 more, then 1 more.

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

   1       2       1         ____
  ─── + ─── + ─── =  ─────
   4       4       4         ____

Does the answer simplify? ____ / ____ = ____ whole

Problem 4 — stretch

A pie is cut into 8 slices. You eat 3 slices. Your sibling eats 2 slices.

       🥧 🥧 🥧 🥧
       🥧 🥧 🥧 🥧
     (8 slices total)

• Slices eaten in all: ____ + ____ = ____
• Slices left: 8 − ____ = ____
• Write the fraction left: ____ / ____

Hint: the bottom number stays 8 — the pieces are all the same size.

Today's words

Try at home tonight (1 minute)

Find something you can split into equal parts. Take some, leave some. Write the fraction left.

• A pizza cut in 8 slices
• A chocolate bar with 6 pieces
• An orange in 10 slices
• A pack of graham crackers
• A muffin tin with 12 spots

   I had  ____ / ____
   I took ____ / ____
   Left:  ____ / ____

Show a grown-up tomorrow morning.

Next time: Decimals — tenths and hundredths. Fractions are nice, but decimals can do the same job — and they connect to money!

🏠 Family guide (for parents)

Math for Young Minds · Grade 4 · Session 6

A note for grown-ups: today we added and subtracted fractions

What your child did today

In class today, we worked with fractions that have the same bottom number.

The big idea: when the pieces are the same size, you can add or subtract them just by counting pieces. So 3/8 + 2/8 is just "three eighth-pieces plus two eighth-pieces" — five eighth-pieces, or 5/8.

We used fraction strips that lined up side by side. Same denominator means same-size pieces. Your child added eighths, subtracted sixths, and noticed when the answer made a whole — like 1/4 + 2/4 + 1/4 = 4/4, which is just 1.

Why this matters

Fractions are where a lot of older students lose their footing. We're going slowly on purpose. If your child understands why 3/8 + 2/8 is 5/8 and not 5/16, the rules will stick. Understanding first. Speed comes later, on its own. No timed tests, no rush.

🏠 Try this tonight (1 minute)

Find something at home that's already split into equal parts. Take some, leave some. Ask your child to write the fraction that's left.

Easy starters:

A short script:

• "How many pieces total?" (that's the bottom number)
• "How many are left?" (that's the top number)
• "So what fraction is left?"

If they want to go further: "How many did we eat? Can you write that as a fraction too?"

Words your child is learning

• Like denominators — fractions whose bottoms are the same. The pieces are the same size, so you can count them together.

If your child says…

"This is easy." Good. Ask them: "What's 3/8 + 4/8?" Then: "What about 5/8 + 5/8?" See if they notice when the answer is more than one whole. That's the next layer.

"This is hard." Also good. Slow down. Draw a pizza or a chocolate bar on paper and shade the pieces. Counting shaded pieces is the same as adding fractions — just with a picture. The picture is the math.

"I don't want to." Fine. Skip it tonight. Try again tomorrow with something they actually want to split — a snack, a deck of cards, a row of crackers. Math sticks better when there's something real on the table.

What's next

In our next session, your child will meet decimals — tenths and hundredths. Fractions are nice, but decimals can do the same job — and they connect straight to money, which makes them feel real fast.

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

— Math for Young Minds

🔑 Cheat sheet (visual)

🍕 Same-size pieces add up

Picture 1 — Strips line up (eighths)

   3/8                  2/8
 ┌──┬──┬──┐         ┌──┬──┐
 │▓▓│▓▓│▓▓│   +     │▓▓│▓▓│
 └──┴──┴──┘         └──┴──┘

           =

 ┌──┬──┬──┬──┬──┐
 │▓▓│▓▓│▓▓│▓▓│▓▓│   =  5/8
 └──┴──┴──┴──┴──┘

Same-size pieces → just count them. ✨

Picture 2 — Taking away (sixths)

  5/6                              4/6
 ┌──┬──┬──┬──┬──┐                ┌──┬──┬──┬──┐
 │▓▓│▓▓│▓▓│▓▓│▓▓│  −  1/6   =   │▓▓│▓▓│▓▓│▓▓│
 └──┴──┴──┴──┴──┘                └──┴──┴──┴──┘

     5/6 − 1/6 = 4/6   (= 2/3)

Picture 3 — Filling a whole (fourths)

 ┌──┐     ┌──┬──┐     ┌──┐         ┌──┬──┬──┬──┐
 │▓▓│  +  │▓▓│▓▓│  +  │▓▓│    =    │▓▓│▓▓│▓▓│▓▓│
 └──┘     └──┴──┘     └──┘         └──┴──┴──┴──┘

   1/4   +   2/4    +   1/4   =   4/4   =  1 whole 🎉

How to read the sign

            ┌──── add the TOPS
            │
        3       2          5
        ─   +   ─    =     ─
        8       8          8
            │              │
            │              └── bottom stays the same
            └──── bottoms match → like denominators

Say it: "3 eighths plus 2 eighths equals 5 eighths."

When can I add/subtract straight across?

Like denominators = bottoms are the same = pieces are the same size.

Try this in your head 🥧

 🍕 cut in 8 slices
 ┌──┬──┬──┬──┬──┬──┬──┬──┐
 │YOU│YOU│YOU│SIB│SIB│  │  │  │
 └──┴──┴──┴──┴──┴──┴──┴──┘
   You ate 3/8     Sibling ate 2/8

➤ 8/8 − 3/8 − 2/8 = ____ left

Answer: 3/8 left 🍕