Perimeter is the distance around; area is the squares inside; volume is the cubes that fill a box. Tile it and count, then multiply: length × width for a rectangle, one layer times the number of layers for a box. Missing sides, L-shapes, two boxes stuck together, and the question every story problem hides — fence, carpet, or fill? Then converting length, mass, capacity and time inside one system, and why 2 hours 15 minutes is not 215 minutes. Study cards, hints, a practice quiz at three levels, and four workshop activities that check themselves.
A rectangle, 6 long and 2 wide. Two different questions can be asked about it.
Around is perimeter, counted in lengths. Covering is area, counted in squares. Filling is volume, counted in cubes. Underline which one the question wants before you touch a formula.
Two things people get wrong
⚠️People often think…
The perimeter of a 6 by 2 rectangle is 6 + 2 = 8.
A rectangle has FOUR sides, and you walk all of them: 6 + 2 + 6 + 2 = 16. Adding just two gives you half the fence and a yard full of loose dogs.
Trace it with your finger. Count every side you cross.
⚠️People often think…
48 inches is 576 feet, because you multiply by 12.
Going from a small unit to a big one means FEWER of them, so you divide: 48 ÷ 12 = 4 feet. 576 feet is longer than a football field, which is your signal that something went the wrong direction.
Bigger unit, smaller number. Always check if it sounds crazy.
Read the word before the numbers
1Watch one
What is the perimeter of a 6 by 2 rectangle?
Perimeter means all the way around.
Four sides: 6, 2, 6, 2.
Add them all: 16.
16 units of length — not squares.
2Do one with me
A box is 4 long, 3 wide and 2 tall. How much fits inside?
“Fits inside” means volume, so you add or multiply?
4 × 3 × 2 =
The units are square or cubic?
💬One sentence, then you move on
How do you tell whether a question wants perimeter or area?
3Try one
48 inches is how many feet?
I want a hint first
Twelve inches make one foot. You are going to the bigger unit, so there will be fewer — divide.
Where this goes
Where this lives
Fencing a yard is perimeter. Carpeting a room is area. Filling a cooler is volume. Buy the wrong one and you come home short.
What this feeds
Next unit is geometry and the coordinate plane — naming shapes by their rules, and finding places on a grid.
Name one thing you would measure around, and one you would measure across.
One card at a time — tap “Show me” to check yourself, then Next. Start at Foundation; when those feel easy, climb.
Helpful Hints
🤔 Which measure is it? — the routine
Read the problem and ask what the thing DOES → goes AROUND the edge (fence, frame, ribbon, a lap) → PERIMETER: add the sides → COVERS a flat surface (carpet, paint, tiles, seed) → AREA: length × width, square units → FILLS a box (water, sand, cubes, packing) → VOLUME: length × width × height, cubic units → write the number WITH its unit.
Measuring is COUNTING UNITS. Perimeter counts unit lengths laid end to end around the edge. Area counts unit squares laid side by side to cover the inside. Volume counts unit cubes stacked to fill a box. The formulas are just fast ways to count: 4 rows of 7 squares is 7 × 4; 2 layers of 12 cubes is 12 × 2. Converting units is counting the same thing with a different-sized unit — smaller unit, bigger count.
Lengths, squares, cubes — count them.
⚠️ Traps the test loves
Giving the area when the question asked for the perimeter, or the other way round. Underline the word first.
Adding only two sides for a perimeter: 6 + 2 = 8 for a 6 by 2 rectangle. It has FOUR sides: 16.
Adding the three edges of a box instead of multiplying: 4 + 3 + 2 = 9. Volume is 4 × 3 × 2 = 24.
Gluing units together: 2 h 15 min = 215 min, or 3 m 45 cm = 48 cm. Convert the big unit first, THEN add.
Converting the wrong direction: 48 inches = 576 feet. Small to big means fewer — divide.
Forgetting the unit or using the wrong one: writing 15 cm for an area. It is 15 cm² — square centimeters.
📏 Formulas and conversions — the chart
Measure
How to find it
Unit
Example
Perimeter
add all the sides, or 2 × (l + w)
units (cm, ft)
5 by 3 → 16 units
Area
l × w
square units (cm², ft²)
5 by 3 → 15 square units
Volume
l × w × h, or base area × height
cubic units (cm³, in³)
4 by 3 by 2 → 24 cubic units
Length
1 m = 100 cm · 1 cm = 10 mm · 1 km = 1000 m
1 ft = 12 in · 1 yd = 3 ft
3 m 45 cm = 345 cm
Mass / capacity
1 kg = 1000 g · 1 L = 1000 mL
1 lb = 16 oz · 1 gal = 4 qt
2 kg = 2000 g
Time
1 h = 60 min · 1 min = 60 s · 1 day = 24 h
—
2 h 15 min = 135 min
🎯 How the test will ask
A rectangle with two sides labeled — “find the perimeter” or “find the area.” Read which one; write the unit.
A rectangle with the area (or perimeter) given and one side — “find the missing side.” Divide for area; subtract two lengths and halve for perimeter.
An L-shaped floor — “find the area.” Cut it into rectangles and add, or box it in and subtract.
A box built from unit cubes, or three edge lengths — “find the volume.” One layer, times the number of layers.
Two boxes — “which holds more?” Multiply all three edges of each; never judge by the longest side.
A story — “fence, carpet, or fill?” Decide perimeter, area or volume before touching a number.
“3 m 45 cm = ? cm” or “2 h 15 min = ? min” — convert the big unit, then add the small part.
✅ Before the test, can you…
Find the perimeter AND the area of a 7 by 4 rectangle, with the right units on each?
Find the missing width when the area is 24 and the length is 6? When the perimeter is 20 and the length is 7?
Find the area of an L-shape by cutting it into two rectangles?
Find the volume of a 5 by 3 by 2 box, and explain it as layers of cubes?
Say which of two boxes holds more, using their volumes?
Convert 3 m 45 cm to cm, 48 in to ft, and 2 h 15 min to min — and say when to multiply and when to divide?
Tell, from a story, whether it is asking for perimeter, area or volume?
Pick your level
Look back at anything you missed — the hint that appeared is exactly what to reread tonight.
How sure did you feel?
Workshop
Work like a mathematician: cut a garden that is not a rectangle into rectangles you lay yourself, sort fences from carpets from fish tanks, put a unit conversion in order step by step, then settle an argument about which box holds more. Every activity checks itself, and hints are free.
Meet the three measures
Tap the object. The measure is the job it is asking for.
Fence, carpet, tank. Around, cover, fill. Same rule as the microscope: the object speaks first.
A job
Tap the empty frame, the tiled floor, or the box that holds water.
Names stay off until you ask. Job first.
Your practice never leaves this device. There is no account and no sign-in. Your work is saved in this browser only, and you can erase it whenever you want.
Your practice record — saved on this device
This is your record of the module on screen — it stays here and goes nowhere. Independent means you got it right on the first tap; supported means you got it after the explain-and-retry, or marked ‘I had it’ on a revealed answer. Both count, and neither is a grade. If your teacher asks, copy the row or show them this screen.
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The answer key is for a teacher: it prints only from here, for the unit on screen. Print the study packet prints the study pages and a blank quiz — never the answers.