Solving Word Problems

Addition and Subtraction Within 20

In this lesson:

• Learn four types of word problems
• Find unknowns in different positions
• Use objects, drawings, and equations

Learning Objectives

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

1. Solve "add to" and "take from" problems with result unknown
2. Solve "put together" and "take apart" problems with unknown parts
3. Use a symbol like ☐ or ? to show the unknown in an equation
4. Identify where the unknown is - result, change, or start
5. Use strategies to solve problems up to 20

Quick Review

You already know:

• Addition means putting together or adding to
• Subtraction means taking apart or taking from
• Problems like "3 + 4 = ?" within 10

Today:
We'll solve problems up to 20 with unknowns in different spots

Four Problem Types

1. Add to - something gets added
2. Take from - something gets removed
3. Put together / Take apart - two parts make a whole
4. Compare - how much more or less

Each type tells a different story, so focus on what is happening

Add-To Problem

Story: There are 9 crayons in the box. Maria puts in 4 more. How many crayons are in the box now?

• Start: 9 crayons
• Change: add 4 more
• Result: how many now?

Writing the Equation

Story: 9 crayons, Maria puts in 4 more, how many now?

Equation:

• 9 is what we started with
• 4 is what we added
• ☐ is what we're trying to find

Answer: crayons

Take-From Problem

Story: There are 13 grapes on the plate. Jayden eats 5. How many grapes are left?

• Start: 13 grapes
• Change: take away 5
• Result: how many left?

Writing the Equation

Story: 13 grapes, Jayden eats 5, how many left?

Equation:

• 13 is what we started with
• 5 is what we took away
• ☐ is what's left

Answer: grapes

Quick Check

Solve this problem:

8 birds are on a fence. 6 more land. How many birds are on the fence now?

What equation would you write?
What strategy will you use to solve it?

Quick Check - Answer

Problem: 8 birds, 6 more land, how many now?

Equation:

Strategy ideas:

• Count on from 8: "9, 10, 11, 12, 13, 14"
• Make 10:

Answer: 14 birds

The Part-Part-Whole Mat

Three sections:

• Whole - the total amount
• Part - one piece
• Part - another piece

Put-Together Problem

Story: There are 14 animals at the farm. 6 are cows and the rest are chickens. How many are chickens?

• Whole: 14 animals (total)
• Part 1: 6 cows
• Part 2: ? chickens

Writing It Two Ways

Problem: 14 animals, 6 cows, rest are chickens

Addition way:

Subtraction way:

Both equations describe the same problem!

Unknowns in Different Positions

The unknown (☐) can be:

• Result unknown: - most common
• Change unknown: - harder
• Start unknown: - hardest

The mat works for all three!

Change-Unknown Problem

Story: Aisha has 7 stickers. She earns some more at school. Now she has 12. How many did she earn?

• Start: 7 stickers
• Change: ? earned
• Result: 12 now

Use counters: Start with 7, add more until you reach 12, then count what you added

Writing the Equation

Problem: Aisha has 7, earns some, now has 12

Equation:

• 7 is the start
• ☐ is the change (what we're finding)
• 12 is the result

Answer: She earned 5 stickers

Your Turn: Start-Unknown

Story: Some birds were in a tree. 6 more flew in. Now there are 11. How many were there at the start?

Think about:

• What is the whole?
• What is one part you know?
• What part are you finding?

Try using your part-part-whole mat

Your Turn - Answer

Problem: Some birds in tree, 6 flew in, now 11

Part-part-whole mat:

• Whole: 11 birds (total now)
• Part 1: ? birds (start)
• Part 2: 6 birds (flew in)

Equation:

Answer: 5 birds were there at the start

Quick Check

Find the unknown:

What strategy will you use?

Quick Check - Answer

Equation:

Strategies:

• Count on from 9 until you reach 15
• Think: "What plus 9 makes 15?"
• Use part-part-whole: 15 is whole, 9 is one part, ? is other part

Answer: 6

Comparison Problems

Comparison is different:

• Not adding or removing anything
• Just looking at two groups
• Finding the difference

Story: Leo has 12 marbles. Sara has 5 marbles. How many more marbles does Leo have than Sara?

Side-by-Side Model

Match up the marbles one-to-one - the unmatched ones show the difference

Writing the Equation

Problem: Leo has 12, Sara has 5, how many more?

Equation:

Or you can think of it as:

Both work - the difference is 7

Start-Unknown Problems

What it means: Finding what you started with

Story: Some children were in the classroom. 4 more walked in. Now there are 11. How many were there at the start?

This is like working backward - you know the total and one part, so find the other part

Solving Start-Unknown

Problem: Some children in room, 4 walked in, now 11

Part-part-whole mat:

• Whole: 11 children (total now)
• Part 1: ☐ children (were there at start)
• Part 2: 4 children (walked in)

Equation:

Answer: 7 children were there at the start

Your Turn: Start-Unknown

Story: Some students were on the bus. 3 more students got on. Now there are 10 students on the bus. How many students were on the bus at the start?

Write the equation with ☐ for the unknown
Try to solve before the next slide

Your Turn - Answer

Problem: ? on bus, 3 got on, now 10

Equation:

Solve:

• Whole: 10 (total now)
• One part: 3 (got on)
• Other part: ? (were there at start)

Answer: 7 students were on the bus at the start

Quick Check

Find the unknown:

What does the ? represent in this equation?

Quick Check - Answer

Equation:

The represents the start - what you had before adding 7

Solve:

• Think: "What plus 7 makes 15?"
• Or: "15 minus 7 equals ?"

Answer: 8

Key Takeaways

✓ Four problem types: add to, take from, put together/take apart, compare
✓ Unknowns can be result, change, or start
✓ Use ☐ or ? to show the unknown in equations
✓ Part-part-whole mat works for all problem types

Watch out:
Don't use keywords - understand what's happening in the story
Unknown can be anywhere - not just at the end
Check: Is the big number the total or a part?
Comparison: Don't add or take away - just see the difference

Next Steps

Coming up next: Adding three whole numbers (1.OA.A.2)

Keep practicing:

• Use the part-part-whole mat for all types
• Write equations with unknowns in different positions
• Think about the story, not just keywords

You're ready!