Word Problems: Situation Types and Unknowns

Lesson 1 of 2

In this lesson:

• Identify five situation types in any word problem
• Solve problems with the unknown in the result, change, or start position
• Represent every problem with a tape diagram and matching equation

Learning Objectives

By the end of this lesson, you should be able to:

1. Identify the situation type — adding to, taking from, putting together, taking apart, or comparing
2. Solve one-step problems within 100 with the unknown in the result position
3. Solve one-step problems with the unknown in the change or start position, writing an equation with □ for the unknown
4. Represent any problem with a labeled tape diagram and a matching equation

You Already Know Word Problems

In Grade 1, you solved problems like:

"Lena had 8 apples. She got 5 more. How many does she have now?"

8 + 5 = □

This year: same five problem types, bigger numbers (up to 100), and the unknown can be anywhere.

Let's review all five types — with Grade 2 numbers.

Situation 1: Adding To

"There were 34 children on a playground. 21 more came out to play. How many children are on the playground now?"

• Something changes: a quantity grows
• Action: more come, are added, arrive

Equation: 34 + 21 = □

Situation 2: Taking From

"There were 55 children on the playground. 21 went inside for lunch. How many are still outside?"

• Something changes: a quantity shrinks
• Action: some leave, are used, are removed

Tape diagram: whole = 55, one part = 21, missing part = □

Equation: 55 − 21 = □

Same idea as add-to, but the direction is reversed

Situation 3: Putting Together

"A basket has 34 red apples and 21 green apples. How many apples are in the basket?"

• Nothing changes: two groups are already there
• No action: we just count them together

Tape diagram: part = 34, part = 21, total = □

Equation: 34 + 21 = □

Notice: The equation looks like add-to — but nothing changes here!

Situation 4: Taking Apart

"A basket has 55 apples. 34 are red. How many are green?"

• We know the whole: 55 total
• We know one part: 34 red
• We find the other part: ? green

Tape diagram: whole = 55, part = 34, missing part = □

Equation: 55 − 34 = □

The tape diagram tells you which to subtract — not the word order

Situation 5: Comparing (Preview)

"One box has 55 crayons. Another has 34. How many more crayons does the first box have?"

• Nothing changes: two groups already exist
• We ask: how much bigger is one compared to the other?

Two bars side by side — the longer bar shows the bigger amount; the bracket shows the difference

Equation: 55 − 34 = □

(We'll go much deeper on comparison in Deck 2)

Five Situation Types

Before you solve — identify the type and draw the diagram

Your Turn: Identify the Type

Read each story. Write the situation type — then draw the tape diagram.

1. "Mia had 47 stamps. She bought 28 more."
2. "A jar has 63 beads. 37 are blue. The rest are red."
3. "Leo has 72 cards. Ava has 54 cards. How many more does Leo have?"

Label the type before you solve!

Same Story — Three Questions

You can ask the same story three different ways:

• Result unknown: 34 + 21 = □ — we know both parts, find the total
• Change unknown: 34 + □ = 55 — we know one part and the total
• Start unknown: □ + 21 = 55 — we know the change and the total

The tape diagram stays the same — only the box moves to a different position

Result Unknown (Review)

"There were 34 children. 21 more came out. How many are there now?"

Equation: 34 + 21 = □ = 55

The box is at the top — we add to find the total

Change Unknown

"There were 34 children. Some more came out. Now there are 55. How many came out?"

Equation: 34 + □ = 55

Solve: 55 − 34 = □ = 21

The box moved to the middle — use the inverse operation

Start Unknown

"Some children were on the playground. 21 more came out. Now there are 55. How many were there at the start?"

Equation: □ + 21 = 55

Solve: 55 − 21 = □ = 34

The box moved to the beginning — use the inverse operation

Take-From: Three Versions

Same story, three questions:

Watch out: Start unknown + take-from → add to solve!

Strategy: Draw the Diagram First

For any unknown position:

1. Read the problem — identify start, change, and result
2. Draw the tape diagram — put □ where the unknown is
3. Write the equation — read it from the diagram
4. Solve using the inverse operation if the unknown is not at the end

The diagram is the bridge between the words and the equation

Your Turn

Draw the tape diagram, write the equation, and solve:

1. "There were 47 birds on a wire. Some flew away. Now there are 29. How many flew away?"

   → Identify: take-from, __________ unknown

2. "Some books were on a shelf. A librarian added 38. Now there are 75. How many were there at the start?"

   → Identify: add-to, __________ unknown

Draw the diagram first — then write the equation

Key Takeaways

✓ There are five situation types — identify the type before solving
✓ The unknown can be in the result, change, or start position
✓ Draw the tape diagram first — the equation follows from the diagram
✓ Inverse operations solve change-unknown and start-unknown problems

Keywords mislead: "more" in a problem ≠ always add
Word order misleads: the tape diagram tells you which to subtract
Put-together ≠ add-to: nothing changes in put-together

Next: Lesson 2

Coming up in Lesson 2:

• Comparison problems — all three sub-types with the comparison tape diagram
• Two-step problems — two equations, two unknowns, one story

Connection: the tape diagram skills from today are the foundation for Lesson 2

Get ready to compare and take two steps at a time!