Solving Measurement Word Problems

Grade 4 Measurement and Data: 4.MD.A.2

In this lesson:

• Choose the right operation from the story, not the numbers
• Convert units before combining or comparing measurements
• Show every solution on a labeled number line

Learning Objectives for This Lesson

By the end of today, you can:

1. Solve measurement word problems with all four operations
2. Convert a larger unit to a smaller one first
3. Solve measurement problems with fractions or decimals
4. Show solutions on a labeled number line
5. Decide which operation a story requires

A Hiker Walks Two Distances

A hiker walks 3 km in the morning and 5 km in the afternoon.

How far does she walk in all?

Quick Check: Fifteen Minutes Later

What time is it 15 minutes after 11:45?

Notice that the answer crosses into the next hour.

Predict: How Long Is Recess?

Recess starts at 11:45 a.m. and ends at 12:15 p.m.

Try to find the length of recess before the next slide reveals a strategy.

Counting Forward Beats Straight Subtraction

• Two hops of 15 minutes: recess is 30 minutes
• 1115 − 1045 = 70 is not 70 minutes — clock time resets at 60

Three Quick Single-Step Measurement Checks

• Fish tank has 20 L, loses 3 L: 20 − 3 = 17 L
• 8 bags of flour at 2 kg each: 8 × 2 = 16 kg
• $20 bill for a $12 book, change: 20 − 12 = 8 dollars

How Many Times as Heavy?

A bag of potatoes has a mass of 10 kg. A bag of onions has a mass of 2 kg.

How many times as heavy is the potatoes compared to the onions?

One Number Line, Four Structures

• Combine or separate: add or subtract along the scale
• Equal groups: multiply or divide by a group size
• Comparison: divide to find "how many times"
• Every measurement is a point or a hop on a labeled scale

Your Turn: Solve and Label

For each problem: (a) name the operation, (b) sketch a number line with a
scale, (c) solve and label the unit.

Problems span distance, time, liquid volume, mass, and money.

Two Ropes, Two Different Units

A rope is 3 yards long. Another rope is 5 feet long.

What is the total length of the two ropes?

Try:

Convert the Units, Then Combine

Step 1: Convert 3 yards to feet.

Step 2: Now both measurements are in feet: add.

Smaller Unit Means Bigger Number

Before every conversion, ask: should my answer be bigger or smaller than
the number I started with?

Converting to a smaller unit always makes the number bigger — so
multiply, never divide.

Hallway or Rug: How Much Wider?

72 − 54 = 18 inches

Two More Conversions, Same Routine

• Piano: 1 hr 20 min, then 50 more:

• Punch: 3 L of juice, 500 mL of sparkling water:

When the Divisor Has Two Digits

Tyler has $4. Stickers cost 60 cents each. How many can he buy?

Convert: $4 = 400 cents. Build up groups of 60:

Your Turn: The Chef's Cheese

A chef has 2 kg of cheese. She uses 800 g for one recipe and 450 g for
another.

How many grams of cheese are left? This one needs a conversion and two
operations.

The Rule for Mixed Units

Whenever a problem gives two different units, convert first.

Always convert the larger unit into the smaller one, so the arithmetic stays
in whole numbers.

Real Measurements Aren't Always Whole

You've been solving with whole numbers so far.

But real measurements are often half a mile, a quarter of an hour, or
$3.50 — not whole numbers at all.

Walking in Fourths of a Mile

3/4 + 1/4 = 1 mile

A Fraction of a Conversion Factor

A recipe calls for 1/2 pound of butter. How many ounces is that?

Since 1 lb = 16 oz:

Decimals in Money and Volume

• 3 markers at $1.25 each: 3 × 1.25 = $3.75
• A bottle holds 1.5 liters: 1.5 × 1,000 = 1,500 mL

Why the Number Line Is Required

A number line isn't optional here — it's what makes fraction and decimal
sizes visible.

3/4 of a mile looks like three of four equal segments. $1.25 sits one
quarter of the way from $1.00 to $2.00.

Ribbon: No Scaffolding This Time

• Lily has a 2-foot ribbon
• Cuts off 1/4 foot, then splits the rest into 3 equal pieces

Four Mistakes to Watch Out For

Different units can't combine directly — always convert first
Smaller unit, bigger number — multiply to go smaller, never divide
An answer without a unit isn't finished — always label it
Clock time isn't base-10 — count forward, don't subtract the numbers

Key Takeaways From Today's Lesson

✓ The story tells you the operation, not the size of the numbers
✓ Different units must be converted before you operate
✓ Fractions and decimals follow the exact same routines
✓ A labeled number line shows the scale behind every answer

Coming Up Next: Area and Perimeter

You can now solve measurement word problems across five contexts, with
conversions, fractions, and decimals.

Next lesson turns this same toolkit toward area and perimeter, where the
operations act on the sides of a rectangle instead of a single scale.