Foundations of Mathematical Thinking · 1st Year · Number Sense and Place Value · Autumn Term

Measuring Length with Non-Standard Units

Comparing the size of objects using uniform non-standard units.

• NCCA Curriculum Specifications
• NCCA: Primary - Measurement

About This Topic

Weight and balance introduce students to the concept of mass. In the 1st Year curriculum, the focus is on 'heavier', 'lighter', and 'balances'. Students use their hands as 'human scales' to compare two objects before moving to formal balance scales. This helps them understand that weight is not always related to size, a small lead fishing weight can be heavier than a large balloon.

Students also explore the idea of 'conservation of mass', that the weight of an object stays the same even if its shape changes (like a ball of playdough being squashed). This topic comes alive when students can physically model the patterns of balance and use non-standard units (like marbles) to find the weight of common classroom objects.

Key Questions

1. Justify why we must use the same size unit when measuring two different things?
2. Analyze what happens if we leave gaps between our measuring tools?
3. Explain how we can compare the height of two things that are in different rooms?

Learning Objectives

• Compare the lengths of different classroom objects using a consistent non-standard unit.
• Explain why using the same size unit is crucial for accurate length measurement.
• Analyze the impact of gaps or overlaps on the measurement of an object's length.
• Demonstrate how to measure the height of objects located in different areas using a chosen non-standard unit.
• Justify the selection of a specific non-standard unit for a given measurement task.

Before You Start

Counting and Cardinality

Why: Students need to be able to count accurately to determine how many units make up a length.

Object Permanence

Why: Students must understand that objects continue to exist even when not directly observed, which is foundational for understanding measurement as a stable property.

Key Vocabulary

Non-standard unit	A measurement tool that is not part of a formal system, such as paperclips, blocks, or hands. It must be uniform in size for accurate measurement.
Length	The measurement of how long an object is, from one end to the other.
Measure	To find out the size, amount, or degree of something, especially by using an instrument or device marked in units.
Uniform	The same size, shape, or amount. When measuring, each unit must be identical to the others.

Watch Out for These Misconceptions

Common Misconception

Thinking that bigger objects are always heavier.

What to Teach Instead

This is the most common weight misconception. Provide 'conflicting' objects like a large balloon and a small apple. Let students hold both to feel the difference, then use a scale to prove that size does not equal mass.

Common Misconception

Believing the scale is 'broken' if it doesn't move immediately.

What to Teach Instead

Students often expect instant results. Teach them to wait for the scale to 'settle' and explain that small differences in weight might not tip a sturdy classroom scale, introducing the need for sensitive measurement.

Active Learning Ideas

Inquiry Circle: The Mystery Weight

Give each group a 'mystery' wrapped box and a set of wooden blocks. They must use a balance scale to find out exactly how many blocks it takes to make the scale level, recording their 'weight' in blocks.

25 min·Small Groups

Simulation Game: Human Scales

Students stand with arms out like a scale. A partner places a heavy book in one hand and a light pencil in the other. The 'scale' student must tilt their body to show which is heavier, while the class describes the movement.

15 min·Pairs

Think-Pair-Share: Big vs. Heavy

Show a large sponge and a small stone. Ask students to predict which is heavier. After testing on a scale, they discuss in pairs why the 'big' thing wasn't the 'heavy' thing.

15 min·Pairs

Real-World Connections

• Carpenters use non-standard units like their own hands or pencils to quickly estimate lengths when a formal ruler is not immediately available, especially for rough cuts or initial planning.
• Interior designers might use common objects like books or fabric swatches to compare the dimensions of furniture or wall spaces before committing to specific measurements, ensuring items fit aesthetically and physically.
• Early childhood educators use a variety of non-standard units, like linking cubes or craft sticks, to help young children grasp the concept of measurement before introducing formal rulers and meters.

Assessment Ideas

Quick Check

Provide students with a collection of uniform non-standard units (e.g., 10 identical blocks). Ask them to measure the length of a pencil and record the number of blocks. Then, ask them to measure the width of a book using the same blocks and record the number. Observe if they maintain consistent unit placement and count accurately.

Exit Ticket

Give each student a card with a picture of two objects of different lengths. Ask them to write one sentence explaining how they would compare the lengths using paperclips. Then, ask them to write one sentence explaining why it's important that all the paperclips are the same size.

Discussion Prompt

Present students with a scenario: 'Imagine you need to measure the height of your desk and your friend's desk, but your desks are in different classrooms. How could you use your shoes to compare their heights?' Facilitate a class discussion, guiding students to explain how they would measure each desk with shoes and then compare the number of shoes used.

Frequently Asked Questions

When do Irish students start using kilograms?

Kilograms and grams are typically introduced in 3rd Class. In 1st Year, the focus is entirely on non-standard units (cubes, marbles, beans) and the language of comparison to build a strong conceptual foundation.

How can active learning help students understand weight and balance?

Weight is a 'hidden' property that you can't see, only feel. Active learning strategies like 'Human Scales' allow students to feel the pull of gravity on different objects. By using balance scales in collaborative groups, students have to agree on when a scale is 'level', which requires careful observation and discussion. This hands-on testing is the only way to truly dismantle the 'big equals heavy' misconception.

What is a balance scale actually measuring?

A balance scale compares the mass of two objects by seeing which one is pulled more strongly by gravity. If the two sides are level, it means the mass is the same on both sides.

How can I practice weight at home without a scale?

Use a 'heavier or lighter' game with groceries. Give your child two items (like a tin of beans and a bag of crisps) and ask them to guess which is heavier just by feeling them in their hands.

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