UK K12 GCSE/A-Level: Year 1 KS1 Mathematics - Measurement, Length, Weight, Capacity

Learning objectives

By the end of this topic, students will be able to: - Understand the concept of measurement and its importance in everyday life. - Define and explain the units of length, weight, and capacity. - Measure lengths, weights, and capacities using various tools and techniques. - Compare and order lengths, weights, and capacities. - Solve problems involving length, weight, and capacity.

Core concepts

Length

• Metre (m) is the unit of length in the metric system.
• A metre is equal to 100 centimetres (cm) or 1000 millimetres (mm).
• We use metres to measure the length of objects, such as a pencil or a book.
• To measure length, we use a ruler or a measuring tape.

Weight

• Gram (g) is the unit of weight in the metric system.
• A gram is equal to 1000 milligrams (mg).
• We use grams to measure the weight of objects, such as a pencil or a book.
• To measure weight, we use a balance or a scales.

Capacity

• Litre (L) is the unit of capacity in the metric system.
• A litre is equal to 1000 millilitres (mL) or 1000 cubic centimetres (cm³).
• We use litres to measure the capacity of containers, such as a cup or a bottle.
• To measure capacity, we use a measuring jug or a measuring cup.

Worked examples

Example 1: Measuring length

Tom has a pencil that is 15 cm long. He wants to measure the length of his pencil using a ruler. What will he see on the ruler?

Answer: Tom will see a line that is 15 cm long on the ruler.

Example 2: Measuring weight

A book weighs 250 g. What will the balance show if we place the book on it?

Answer: The balance will show 250 g.

Example 3: Measuring capacity

A cup can hold 250 mL of water. What will the measuring jug show if we pour 250 mL of water into it?

Answer: The measuring jug will show 250 mL.

Common misconceptions

• Students may confuse the units of length, weight, and capacity.
• Students may not understand that a metre is equal to 100 cm or 1000 mm.
• Students may not know how to use a ruler or a measuring tape correctly.
• Students may not understand that a gram is equal to 1000 mg.
• Students may not know how to use a balance or a scales correctly.

Exam tips

• Make sure to read the questions carefully and understand what is being asked.
• Use the correct units of measurement.
• Show your working and explain your answers.
• Use a ruler or a measuring tape to measure lengths.
• Use a balance or a scales to measure weights.
• Use a measuring jug or a measuring cup to measure capacities.

MCQs

MCQ 1 [F]

What is the unit of length in the metric system? A) Gram B) Metre C) Litre D) Kilogram

Correct answer: B) Metre Why the distractors fail: A) Gram is the unit of weight, C) Litre is the unit of capacity, and D) Kilogram is a unit of weight, but not length.

MCQ 2 [H]

A book weighs 250 g. What is its weight in kilograms? A) 0.25 kg B) 2.5 kg C) 25 kg D) 250 kg

Correct answer: A) 0.25 kg Why the distractors fail: B) 2.5 kg is too heavy, C) 25 kg is too heavy, and D) 250 kg is too heavy.

MCQ 3 [F]

A cup can hold 250 mL of water. What is its capacity in litres? A) 0.25 L B) 2.5 L C) 25 L D) 250 L

Correct answer: A) 0.25 L Why the distractors fail: B) 2.5 L is too large, C) 25 L is too large, and D) 250 L is too large.

MCQ 4 [H]

A pencil is 15 cm long. What is its length in metres? A) 0.0015 m B) 0.015 m C) 1.5 m D) 15 m

Correct answer: B) 0.015 m Why the distractors fail: A) 0.0015 m is too small, C) 1.5 m is too large, and D) 15 m is too large.

MCQ 5 [F]

A book weighs 250 g. What is its weight in milligrams? A) 250,000 mg B) 2,500,000 mg C) 25,000,000 mg D) 250,000,000 mg

Correct answer: A) 250,000 mg Why the distractors fail: B) 2,500,000 mg is too large, C) 25,000,000 mg is too large, and D) 250,000,000 mg is too large.

Short-answer questions

Question 1

Explain how to measure the length of an object using a ruler.

Answer: To measure the length of an object using a ruler, we place the object on the ruler and read the measurement from the ruler. We make sure that the object is straight and that the ruler is level.

Question 2

Explain how to measure the weight of an object using a balance.

Answer: To measure the weight of an object using a balance, we place the object on one side of the balance and a known weight on the other side. We adjust the known weight until the two sides are balanced, and then we read the weight of the object from the balance.

Question 3

Explain how to measure the capacity of a container using a measuring jug.

Answer: To measure the capacity of a container using a measuring jug, we fill the jug with the liquid until it reaches the desired level. We then read the measurement from the jug and record it.

Question 4

Compare and order the following lengths: 5 cm, 10 cm, 15 cm, 20 cm.

Answer: The lengths in order from smallest to largest are: 5 cm, 10 cm, 15 cm, 20 cm.

Question 5

Compare and order the following weights: 100 g, 200 g, 300 g, 400 g.

Answer: The weights in order from smallest to largest are: 100 g, 200 g, 300 g, 400 g.