Measurement & Data

4.I.1Convert units01/04

Convert larger units to smaller (within system).

Step01of 04

Within a measurement system (customary or metric), conversions all follow the same recipe: MULTIPLY when going from larger to smaller units, DIVIDE when going from smaller to larger.

4.I.1 — Convert larger units to smaller (within system).

Step 01 of 04

Within a measurement system (customary or metric), conversions all follow the same recipe: MULTIPLY when going from larger to smaller units, DIVIDE when going from smaller to larger.

Step 02 of 04

Customary conversions to memorize.

1 ft = 12 in	→feet → inches: × 12
1 yd = 3 ft = 36 in	→yards → feet: × 3
1 mile = 5,280 ft	→miles → feet: × 5,280
1 lb = 16 oz	→pounds → ounces: × 16
1 gal = 4 qt = 8 pt = 16 cups	→gallons → quarts: × 4
1 hour = 60 min, 1 min = 60 sec	→time

Step 03 of 04

Worked example. Convert 5 yards to inches.

5 yards × 3 ft/yard = 15 ft. 15 ft × 12 in/ft = 180 in. Or in one go: 5 × 36 = 180 inches.

5 yd = 180 in

Step 04 of 04

Metric conversions. All powers of 10 — easy.

1 m = 100 cm = 1,000 mm	→meters → mm: × 1,000
1 km = 1,000 m	→km → m: × 1,000
1 kg = 1,000 g	→kg → g: × 1,000
1 L = 1,000 mL	→L → mL: × 1,000

Example: 4.5 km = 4,500 m. Just multiply by 1,000 (move decimal 3 places right).

Key insight

Larger → smaller: MULTIPLY by the conversion factor. Smaller → larger: DIVIDE. Memorize the common conversions; metric is all powers of 10.

4.I.2 — Measurement word problems.

Step 01 of 04

Two parts: (1) convert all measurements to the same unit if needed, (2) perform the operation the question asks (add, subtract, multiply, etc.).

Step 02 of 04

Time example. A movie starts at 2:15 PM and lasts 1 hour 50 minutes. When does it end?

2:15 + 1 hour = 3:15. + 50 min: 3:15 + 50 min = 4:05 PM.

Step 03 of 04

Money example. A book costs $14.75. You give the cashier $20. How much change?

$20.00 - $14.75 = $5.25

Step 04 of 04

Distance example. A runner does 3 laps of 1/4 mile each. Total distance?

3 \times \frac{1}{4} = \frac{3}{4} mile

Always include UNITS in the answer. "5.25" is incomplete; "$5.25" or "5.25 miles" is a real answer.

Key insight

Pick a common unit, convert all measurements to it, do the arithmetic, answer with units. Time problems often need to think in hours and minutes separately.

4.I.3 — Area and perimeter of rectangles.

Step 01 of 04

Perimeter = total distance around the outside. Area = amount of surface inside.

Rectangle perimeter	→ $P = 2 l + 2 w$ (or $2 (l + w)$ )
Rectangle area	→ $A = l \times w$
Square perimeter	→ $P = 4 s$
Square area	→ $A = s^{2}$

Step 02 of 04

Worked example. Rectangle 8 ft long, 5 ft wide.

P = 2 (8) + 2 (5) = 16 + 10 = 26 ft

A = 8 \times 5 = 40 sq ft

Perimeter is in linear units (ft); area in square units (sq ft).

Step 03 of 04

Find a missing dimension. A rectangle has area 48 sq cm and length 8 cm. What's the width?

A = l \times w \Rightarrow 48 = 8 \times w \Rightarrow w = 6 cm

Step 04 of 04

Square shortcut. All four sides equal, so:

P = 4 s, A = s^{2}

For a 9 cm square: $P = 36$ cm, $A = 81$ sq cm.

Key insight

Perimeter (linear units):

2 l + 2 w

. Area (square units):

l \times w

. Squares are special rectangles where all sides are equal.

4.I.4 — Line plots with fractions.

Step 01 of 04

A line plot displays measurement data as marks above a number line. Each mark represents one data point at that value.

In grade 4, the values are usually fractions (1/8 inch increments, 1/4 cups, etc.).

Step 02 of 04

Make a line plot. Class plant lengths in inches: $2 \frac{1}{4}$ , $2 \frac{1}{2}$ , $2 \frac{1}{4}$ , $3$ , $2 \frac{3}{4}$ , $2 \frac{1}{2}$ .

Draw a number line from 2 to 3 with quarter-inch tick marks. Place an X above each value for each measurement.

Step 03 of 04

Read questions from a line plot.

"How many measurements?"	→count all the X marks
"What is the most common value?"	→tallest column = mode
"Range?"	→biggest value − smallest value
"Total / sum?"	→add up all values (use repeated addition for repeats)

Step 04 of 04

Worked question. From the plant data above: total length of all plants?

2 \frac{1}{4} + 2 \frac{1}{4} + 2 \frac{1}{2} + 2 \frac{1}{2} + 2 \frac{3}{4} + 3 = 15 \frac{1}{4} inches

Key insight

Line plots show data on a number line, one X per measurement. Read counts directly; compute range, mode, total from the marks. Fractional values mean fraction-arithmetic for sums.

Free diagnostic

Test your understanding: 10 questions, ~10 min.

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4.I.1 – 4.I.4 · CCSS 4.MD.A / 4.MD.B · Full curriculum →