Great Inheritance Mathematics Term A · Independent learning

Volume and Capacity — Part 1

Learning target: Convert between cm³ and mL and between appropriate metric volume units.

Begin with the exact prerequisite checkpoint below. Afterward, explain why your strategy works, not merely which procedure to use.

Opening task

Explore · volume capacity conversion

A container holds 1,875 cm³ of liquid. Express this capacity in milliliters and liters.

Show answer and worked explanation

Answer: 1,875 mL = 15/8 L

How it works: 1 cm³ = 1 mL, so 1,875 cm³ = 1,875 mL. Divide by 1,000 mL/L: 1,875/1,000=15/8 L.

Lesson-specific prerequisite checkpoint

Do this without a worked example. If you cannot explain it, review the earlier skill before continuing.

Convert 1000 mL into liters.

Show answer and worked explanation

Answer: 1 L

How it works: 1,000 mL = 1 L; 1 cm³ = 1 mL.

Understand the idea

Convert between cm³ and mL and between appropriate metric volume units.

A cubic centimeter has exactly the capacity of one milliliter. One thousand milliliters make a liter, so 1,000 cm³ equals 1 L. A volume number in cm³ transfers directly to the same numerical number in mL but not in L.

Vocabulary focus: unit cube, cuboid, cubic units, capacity. Make a small labeled model, work through the arithmetic, and explain the result in words.

Watch for: Assuming 1 cm³ equals 1 L.

Model to study: 1 cm cube to 1 mL container illustration.

Worked examples

Worked examples 1 · volume capacity conversion

A container holds 4,625 cm³ of liquid. Express this capacity in milliliters and liters.

Solution: 4,625 mL = 37/8 L

Why: 1 cm³ = 1 mL, so 4,625 cm³ = 4,625 mL. Divide by 1,000 mL/L: 4,625/1,000=37/8 L.

Worked examples 2 · volume capacity conversion

A container holds 3,000 cm³ of liquid. Express this capacity in milliliters and liters.

Solution: 3,000 mL = 3 L

Why: 1 cm³ = 1 mL, so 3,000 cm³ = 3,000 mL. Divide by 1,000 mL/L: 3,000/1,000=3 L.

Worked examples 3 · volume capacity conversion

A container holds 3,125 cm³ of liquid. Express this capacity in milliliters and liters.

Solution: 3,125 mL = 25/8 L

Why: 1 cm³ = 1 mL, so 3,125 cm³ = 3,125 mL. Divide by 1,000 mL/L: 3,125/1,000=25/8 L.

Check understanding

Check understanding 1 · volume capacity conversion

A container holds 5,625 cm³ of liquid. Express this capacity in milliliters and liters.

Show answer and worked explanation

Answer: 5,625 mL = 45/8 L

How it works: 1 cm³ = 1 mL, so 5,625 cm³ = 5,625 mL. Divide by 1,000 mL/L: 5,625/1,000=45/8 L.

Check understanding 2 · volume capacity conversion

A container holds 4,125 cm³ of liquid. Express this capacity in milliliters and liters.

Show answer and worked explanation

Answer: 4,125 mL = 33/8 L

How it works: 1 cm³ = 1 mL, so 4,125 cm³ = 4,125 mL. Divide by 1,000 mL/L: 4,125/1,000=33/8 L.

Guided practice

Guided practice 1 · volume capacity conversion

A container holds 1,500 cm³ of liquid. Express this capacity in milliliters and liters.

Show answer and worked explanation

Answer: 1,500 mL = 3/2 L

How it works: 1 cm³ = 1 mL, so 1,500 cm³ = 1,500 mL. Divide by 1,000 mL/L: 1,500/1,000=3/2 L.

Guided practice 2 · volume capacity conversion

A container holds 5,000 cm³ of liquid. Express this capacity in milliliters and liters.

Show answer and worked explanation

Answer: 5,000 mL = 5 L

How it works: 1 cm³ = 1 mL, so 5,000 cm³ = 5,000 mL. Divide by 1,000 mL/L: 5,000/1,000=5 L.

Guided practice 3 · volume capacity conversion

A container holds 3,750 cm³ of liquid. Express this capacity in milliliters and liters.

Show answer and worked explanation

Answer: 3,750 mL = 15/4 L

How it works: 1 cm³ = 1 mL, so 3,750 cm³ = 3,750 mL. Divide by 1,000 mL/L: 3,750/1,000=15/4 L.

Independent practice

Independent practice 1 · volume capacity conversion

A container holds 875 cm³ of liquid. Express this capacity in milliliters and liters.

Show answer and worked explanation

Answer: 875 mL = 7/8 L

How it works: 1 cm³ = 1 mL, so 875 cm³ = 875 mL. Divide by 1,000 mL/L: 875/1,000=7/8 L.

Independent practice 2 · volume capacity conversion

A container holds 3,500 cm³ of liquid. Express this capacity in milliliters and liters.

Show answer and worked explanation

Answer: 3,500 mL = 7/2 L

How it works: 1 cm³ = 1 mL, so 3,500 cm³ = 3,500 mL. Divide by 1,000 mL/L: 3,500/1,000=7/2 L.

Independent practice 3 · volume capacity conversion

A container holds 5,375 cm³ of liquid. Express this capacity in milliliters and liters.

Show answer and worked explanation

Answer: 5,375 mL = 43/8 L

How it works: 1 cm³ = 1 mL, so 5,375 cm³ = 5,375 mL. Divide by 1,000 mL/L: 5,375/1,000=43/8 L.

Independent practice 4 · volume capacity conversion

A container holds 1,625 cm³ of liquid. Express this capacity in milliliters and liters.

Show answer and worked explanation

Answer: 1,625 mL = 13/8 L

How it works: 1 cm³ = 1 mL, so 1,625 cm³ = 1,625 mL. Divide by 1,000 mL/L: 1,625/1,000=13/8 L.

Independent practice 5 · volume capacity conversion

A container holds 2,000 cm³ of liquid. Express this capacity in milliliters and liters.

Show answer and worked explanation

Answer: 2,000 mL = 2 L

How it works: 1 cm³ = 1 mL, so 2,000 cm³ = 2,000 mL. Divide by 1,000 mL/L: 2,000/1,000=2 L.

Challenge and error analysis

Challenge and error analysis 1 · worked-error diagnosis

Error-analysis notebook: Learner notebook (LESSON): “5875 cm³ = 5875 L; I treated a milliliter as a liter.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: A container holds 5,875 cm³ of liquid. Express this capacity in milliliters and liters.

Show answer and worked explanation

Answer: 5,875 mL = 47/8 L

How it works: Wrong step/assumption: Learner notebook (LESSON): “5875 cm³ = 5875 L; I treated a milliliter as a liter.” Diagnosis: Count full three-dimensional layers, use three perpendicular Course and cubic units; use cm³=mL only for capacity conversion. Correct computation: 1 cm³ = 1 mL, so 5,875 cm³ = 5,875 mL. Divide by 1,000 mL/L: 5,875/1,000=47/8 L.

Challenge and error analysis 2 · reasoning transfer

Reasoning and transfer: Solve, then explain a different way to check your answer (inverse operation, estimate, model, or units as appropriate). A container holds 2,625 cm³ of liquid. Express this capacity in milliliters and liters.

Show answer and worked explanation

Answer: 2,625 mL = 21/8 L

How it works: 1 cm³ = 1 mL, so 2,625 cm³ = 2,625 mL. Divide by 1,000 mL/L: 2,625/1,000=21/8 L. Verification: show why the answer has a reasonable magnitude and matches the operation, referent and unit.

Exit check

Exit check 1 · volume capacity conversion

A container holds 3,625 cm³ of liquid. Express this capacity in milliliters and liters.

Show answer and worked explanation

Answer: 3,625 mL = 29/8 L

How it works: 1 cm³ = 1 mL, so 3,625 cm³ = 3,625 mL. Divide by 1,000 mL/L: 3,625/1,000=29/8 L.

Exit check 2 · volume capacity conversion

A container holds 2,500 cm³ of liquid. Express this capacity in milliliters and liters.

Show answer and worked explanation

Answer: 2,500 mL = 5/2 L

How it works: 1 cm³ = 1 mL, so 2,500 cm³ = 2,500 mL. Divide by 1,000 mL/L: 2,500/1,000=5/2 L.

Target for independent mastery: all exit-check problems correct plus a justified explanation. A instructor may reteach the concept if calculations are correct without meaningful reasoning.