Unit 5 — Addition and Subtraction Strategies

Welcome back!

Now that you understand place value, you are ready to solve larger addition and subtraction problems.

Instead of simply memorizing steps, you will learn why the methods work.

Understanding the numbers helps you become a confident mathematician.

Using Place Value

Place value helps us organize numbers.

Example:

246

+

132

Think about each place separately.

Hundreds:

200 + 100 = 300

Tens:

40 + 30 = 70

Ones:

6 + 2 = 8

Now combine them.

300 + 70 + 8 = 378

Adding Larger Numbers

Sometimes we add numbers without regrouping.

Example:

321

+

256

Add the ones.

1 + 6 = 7

Add the tens.

2 + 5 = 7

Add the hundreds.

3 + 2 = 5

Answer:

577

Regrouping

Sometimes the ones add to more than 9.

Example:

248

+

175

Ones:

8 + 5 = 13

Write 3 ones.

Regroup 1 ten.

Then add the tens and hundreds.

Regrouping helps us keep the correct place value.

Subtracting Larger Numbers

Subtraction also uses place value.

Example:

654

−

231

Subtract:

Hundreds:

6 − 2 = 4

Tens:

5 − 3 = 2

Ones:

4 − 1 = 3

Answer:

423

Regrouping in Subtraction

Sometimes there are not enough ones to subtract.

Example:

402

−

185

We regroup from the next place value.

This gives us enough ones to complete the subtraction correctly.

Regrouping is another way of exchanging one larger unit for smaller units.

Estimating Answers

Before solving a problem, it is often helpful to estimate.

Example:

398 + 201

Round to:

400 + 200

Estimate:

600

Your exact answer should be close to your estimate.

Estimating helps us notice mistakes.

Solving Word Problems

Read carefully.

Ask yourself:

• What information is given?
• What is the question?
• Should I add or subtract?
• Does my answer make sense?

Understanding the story is just as important as doing the math.

Activity

Solve these problems.

356 + 221

487 + 164

725 − 302

640 − 218

Estimate each answer before solving.

Then compare your estimate with the exact answer.

Practice

Answer these questions.

Why is place value important?

When do we regroup while adding?

When do we regroup while subtracting?

Why do mathematicians estimate answers?

What should you do after solving every problem?

Review

Today you learned:

• place value makes larger calculations easier
• regrouping helps when digits are too large or too small
• estimating helps check answers
• word problems require careful reading
• understanding is more important than memorizing steps

Strong addition and subtraction skills prepare you for multiplication, division, and more advanced mathematics.

Looking Ahead

Next we will discover multiplication.

You will learn that multiplication is a fast way to add equal groups.