📋 Session plan (for teachers)

Session 3 — Mental-math strategies

Grade 2 · Math for Young Minds Total time: ~20 minutes Common Core: 2.NBT.B.9 Today's idea: Your head and your fingers can do big math — if you pick a smart strategy.

What students will be able to do

By the end of this session, the student can:

• Add by breaking numbers into tens and ones (like 47 + 25 → 40 + 20 + 7 + 5).
• Subtract by counting up (like 52 − 38 → from 38 to 52 is 14).
• Pick a strategy that fits the numbers in front of them.

Materials

• Small whiteboard or scratch paper (one per pair)
• Marker or pencil
• Worksheet (one per student)

Substitution: No whiteboards? Any scrap paper works. The point is a place to jot the parts so they don't get lost in your head.

New words

Heads-up — common confusions

• Some kids try to use one strategy for everything. Different numbers like different tricks.
• When breaking a number apart, kids can lose track of the parts. Write the parts down.
• After breaking, kids sometimes forget to put it back together at the end.

Plan

1 · Hello & today's idea — 2 min

"Today we're not going to write big stacked-up problems. We're going to do math in our heads — at the store, walking home, anywhere. The trick is picking a smart way. We call that a strategy."

Write the word strategy on the board.

"A strategy is just a way of solving a problem. Some strategies are faster for some numbers."

2 · Hands-on explore — 6 min

Give each pair a whiteboard and marker.

Write on the board: 47 + 25

"Don't stack it. Don't carry. I want you to break these numbers apart. What's the tens part of 47? What's the ones part?"

Let them talk. Listen for 40 and 7, 20 and 5.

Now guide them:

"Add the tens together. Then add the ones together. Then put them back."

On the board, build it with them:

   47  +  25
   ↓       ↓
  40+7   20+5

  40 + 20 = 60
   7 +  5 = 12
  60 + 12 = 72

"That's our first strategy — break into tens and ones."

Now introduce the second idea:

"Sometimes a number is almost a friendly number — like 10, 20, 50, or 100. Friendly numbers are easy."

Write 39 + 8.

"39 is almost 40. What if we gave it 1 more first?"

3 · Connect to the math — 3 min

Name the two strategies on the board:

Strategy 1: Break into tens and ones
Strategy 2: Jump to a friendly number
Strategy 3: Count up (for subtraction)

"For subtraction, instead of taking away, you can count up from the small number to the big one."

Show on the board:

  52 − 38
  38 → 40   (that's 2)
  40 → 52   (that's 12)
  2 + 12 = 14

"Same answer. Easier in your head."

4 · Practice with support — 7 min

Pass out the worksheet. Work through these in order.

Problem 1 — together: Add 47 + 25 by breaking into tens and ones. Walk through it again out loud: 40 + 20 = 60, 7 + 5 = 12, 60 + 12 = 72. Write each part.

Problem 2 — solo: Add 39 + 8. Add 1 first to make a friendly 40, then add 7. Answer: 39 + 1 = 40, then 40 + 7 = 47.

Problem 3 — solo: Subtract 50 − 27 by counting up. Prompt: "27 to 30 is 3. 30 to 50 is 20. Add them." Answer: 23.

Problem 4 — stretch: "Which strategy would you use for 28 + 32? Try it." Answers vary — many work. A common smart one: take 2 from 32, give it to 28 → 30 + 30 = 60.

Circulate. If a student is losing the parts, point at the whiteboard and say: "Write the parts down. Don't hold them all in your head."

5 · What we did + Try at home — 2 min

"Today you learned three strategies: break into tens and ones, jump to a friendly number, and count up. Smart math people pick the one that fits the numbers."

Hand out the take-home:

"This week, try a mental-math problem while you're walking or in the car. Maybe two prices in a store. Maybe minutes until lunch. Maybe your age plus your sibling's age. Then tell a grown-up which strategy you used."

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 4)

Building on this, Session 4 — Adding & subtracting within 1,000 uses the same regrouping idea, but with bigger numbers. We move up to hundreds — and the strategies you learned today still work.

✏️ Worksheet (for students)

Math for Young Minds · Grade 2

Session 3 — Mental-math strategies

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

Today's big idea

You can solve math in your head by picking a smart strategy.

Break numbers into tens and ones, or jump to a friendly number like 10, 20, or 50.

Example we did together

We added 47 + 25 by breaking into tens and ones:

   47   +   25
   │         │
  40+7     20+5

  Tens:  40 + 20 = 60
  Ones:   7 +  5 = 12
  Total: 60 + 12 = 72

We say it: "Break it apart, add the parts, put it back together."

Problem 1 — together

Add 47 + 25 by breaking into tens and ones.

┌─────────────────────────────────────────────────────────┐
│                                                         │
│   Tens:   40  +  20  =  ____                            │
│                                                         │
│   Ones:    7  +   5  =  ____                            │
│                                                         │
│   Add them:  ____ + ____ = ____                         │
│                                                         │
│                                                         │
└─────────────────────────────────────────────────────────┘

So 47 + 25 = ____

Problem 2 — on your own

Add 39 + 8. First add 1 to make a friendly 40. Then add the rest.

┌─────────────────────────────────────────────────────────┐
│                                                         │
│   Step 1:   39  +  1  =  ____                           │
│                                                         │
│   Step 2:   ____  +  7  =  ____                         │
│                                                         │
│   (We used 1 of the 8, so 7 is left.)                   │
│                                                         │
│                                                         │
│                                                         │
└─────────────────────────────────────────────────────────┘

So 39 + 8 = ____

Problem 3 — on your own

Subtract 50 − 27 by counting up from 27 to 50.

┌─────────────────────────────────────────────────────────┐
│                                                         │
│       +____           +____                             │
│   27 ──────► 30 ──────────► 50                          │
│                                                         │
│   Jump 1:  27 to 30 is  ____                            │
│                                                         │
│   Jump 2:  30 to 50 is  ____                            │
│                                                         │
│   Add the jumps:  ____ + ____ = ____                    │
│                                                         │
└─────────────────────────────────────────────────────────┘

So 50 − 27 = ____

Problem 4 — stretch

Which strategy would you use for 28 + 32? Try it!

Hint: Is there a friendly number hiding nearby? What if you moved 2 from 32 over to 28?

┌─────────────────────────────────────────────────────────┐
│                                                         │
│   My strategy: ____________________________________     │
│                                                         │
│   My work:                                              │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│   28 + 32 = ____                                        │
└─────────────────────────────────────────────────────────┘

Today's words

Try at home tonight (1 minute)

Try a mental-math addition while you're walking or in the car. Tell a grown-up your strategy.

• Adding two prices at the store
• Minutes until lunch
• How much you'd save if your weekly allowance doubled
• Your age plus your sibling's age

  My problem:   ____  +  ____  =  ____

  My strategy:  __________________________________

Next time: Session 4 — adding & subtracting with bigger numbers, up to 1,000!

🏠 Family guide (for parents)

Math for Young Minds · Grade 2 · Session 3

A note for grown-ups: today we did math in our heads

What your child did today

In class today, we worked on mental-math strategies — ways to solve problems without writing every step.

The big idea: good math is flexible. Different numbers want different approaches.

We practiced two strategies. One: break numbers into tens and ones (47 + 25 becomes 40 + 20 and 7 + 5, then put it together → 72). Two: count up to subtract (52 − 38 → from 38 to 52 is 14). Your child also tried problems like 39 + 8 by jumping to a friendly number first (39 + 1 = 40, then add 7).

Why this matters

Mental math isn't a trick — it's a sign your child understands how numbers work. When kids can break a number apart and put it back together, they're building the same thinking that powers regrouping, multiplication, and fractions later. We're not in a rush. Understanding first. Speed comes later, on its own.

🏠 Try this tonight (1 minute)

While you're walking somewhere or riding in the car, give your child a small addition or subtraction problem to do in their head. Then ask: "What strategy did you use?"

The strategy is the whole point — more than the answer.

A short script:

• "Try this one in your head."
• "How did you do it?"
• "Did you break it into tens and ones, or count up, or something else?"

If they get stuck, that's fine — let them grab a finger or two, or talk it out loud. There's no timer.

Words your child is learning

• Strategy — a way of solving a problem, like a method
• Friendly number — a round number like 10, 20, 50, or 100 that's easy to work with

If your child says…

"This is easy." Wonderful. Ask them to solve it a different way. If they broke it into tens and ones, can they count up instead? Flexibility is the real skill.

"This is hard." Also fine. Slow down. Let them use fingers or a piece of paper — that's not cheating, that's thinking. Try smaller numbers first. The strategies will click with practice, and there's no rush.

"I don't want to." Okay. Try once more with something they care about — the cost of two snacks, the minutes until a show starts. If it's still a no, leave it. One minute another day is plenty.

What's next

In our next session, we'll stretch the same ideas to bigger numbers — adding and subtracting within 1,000. Same thinking, just moving up to hundreds.

Thanks for taking a minute tonight. These small everyday moments are where math lives.

— Math for Young Minds

🔑 Cheat sheet (visual)

🧠 Mental math = pick a smart way

Picture 1 — Break into tens and ones

        47   +   25

       ╱  ╲    ╱  ╲
      40   7  20   5

      40 + 20  =  60     ← tens
       7 +  5  =  12     ← ones
      60 + 12  =  72  ✨

Split → add the parts → put back together.

Picture 2 — Make a friendly number

        39  +  8

   ┌─ borrow 1 from the 8 ─┐
   ▼                       ▼
   39 + 1 = 40        ← friendly!
   40 + 7 = 47  ✨

   38   39   [40]   41 ... 47
    •    •    ★      •      •
              ↑
         friendly number

Picture 3 — Count up to subtract

        50  −  27   =   ?

    27 ─────► 30 ─────────────► 50
        +3           +20

         3   +   20   =   23  ✨

Hop to a friendly number first, then hop the rest.

How to pick a strategy

              ┌──── look at the numbers
              │
       28  +  32
              │
              └──── close to tens? → make friendly!

       28 + 2 = 30
       32 − 2 = 30
       30 + 30 = 60  ✨

Which strategy fits?

✅ Many strategies can work. ❌ Don't force one way for every problem.

Don't lose your parts!

   40 + 20 = 60          ┐
                         ├──  keep BOTH,
    7 +  5 = 12          ┘    then add: 60 + 12

   ⚠️  60 alone is NOT the answer.

Try this in your head

        36  +  9   =   ?

➤ Make it friendly: 36 + ___ = 40, then add the rest.

Answer: 36 + 4 = 40, 40 + 5 = 45