Translations

Code	Language		Translator	Run

Credits

weelookang@gmail.com; Francisco Esquembre; Felix J. Garcia Clemente

Main Themes:

1. Introduction to Measurement using Non-Standard Units: Both resources implicitly and explicitly address the foundational concept of measuring objects using units that are not part of a standard system (e.g., paper clips). This approach is particularly relevant for early learners as it helps develop an intuitive understanding of length and the process of measurement before introducing standard units like centimeters or inches.
2. Interactive Learning and Exploration: The "How to measure length..." resource highlights the use of a JavaScript HTML5 applet simulation model to facilitate interactive learning. This model allows users to actively engage in the process of measuring objects (specifically a pencil in the described example) using virtual paper clips.
3. Importance of Consistent and End-to-End Placement of Units: The material emphasizes the crucial principles of accurate measurement, even with non-standard units. This includes using the same unit throughout the measurement and placing them end-to-end without gaps or overlaps.
4. Development of Measurement Vocabulary: The resources touch upon the introduction and use of relevant vocabulary associated with measurement, such as "unit," "long," "longer," "longest," "short," "shorter," and "shortest."
5. Alignment with Primary Education Goals: The "For Teachers" section of the interactive model explicitly links its use to "Primary 1: Length_Interactive board using non-standard units to measure the length of object," outlining specific learning goals for this age group.

Most Important Ideas and Facts:

• Non-Standard Units as a Foundation: The primary focus is on using non-standard units (illustrated by virtual paper clips) to introduce the concept of length measurement. The interactive model allows students to "measure some objects using the virtual paper clips as non-standard units."
• Randomized Lengths for Practice: The simulation includes a feature where "each reset randomly set a new length from 5 to 10 units," providing varied practice opportunities for students.
• Automated Alignment for Ease of Use: The interactive includes "automatic" left alignment, and the "yellow left alignment will automatically snap to the left of the pencil or object," simplifying the initial setup for measurement.
• Hands-on Simulation: Users can "drag on the paper clips and position them in a straight line to count the number of units of length is required to measure the length of the pencil." This interactive element encourages active participation.
• Reinforcement through Input and Playback: The model allows users to "try to input the correct answer on the input field" and includes a "play" button to "play the movement of the paper clips," potentially demonstrating the correct placement.
• Key Principles for Accurate Measurement: The "What have you learned about length?" section directly addresses essential measurement principles:
• "I must use the same non-standard units when comparing the length of objects."
• "When measuring length, the units must be placed end-to-end without gaps or overlaps (can accept 'space')."
• Estimation Skills: The interactive encourages students to "explore to estimate the length of different objects using the paper clips," fostering estimation skills before precise measurement.
• Context within a Broader Educational Resource: The "Breadcrumbs" section places this specific tool within a larger context of "Open Educational Resources / Open Source Physics @ Singapore," indicating a commitment to freely available educational materials covering various science and mathematics topics.
• Attribution and Licensing: Both sources provide clear attribution to the authors (weelookang@gmail.com; Francisco Esquembre; Felix J. Garcia Clemente) and specify the licensing terms under which the materials are released ("Creative Commons Attribution-Share Alike 4.0 Singapore License" for the content, with a separate license for commercial use of the EasyJavaScriptSimulations Library).

Quotes from the Original Sources:

• "This interactive supports the exploration of measurement of a pencil using paper clips."
• "Each reset randomly set a new length from 5 to 10 units"
• "You can drag on the paper clips and position them in a straight line to count the number of units of length is required to measure the length of the pencil"
• "I must use the ___________ non-standard units when comparing the length of objects." (with suggested answer: "same")
• "When measuring length, the units must be placed end-to-end without __________________." (with suggested answer: "gaps or overlaps")
• "Note: The objects used here are for illustration only, it is not the actual size of the object."
• "This email address is being protected from spambots. You need JavaScript enabled to view it. ; Francisco Esquembre; Felix J. Garcia Clemente" (referring to credits for the interactive model).

Conclusion:

The provided resources offer a valuable introduction to the concept of measurement, particularly length, for young learners. The interactive simulation model provides a hands-on, exploratory environment where students can grasp fundamental principles of measurement using non-standard units. The emphasis on consistent unit usage, end-to-end placement, and the development of measurement vocabulary aligns with key pedagogical goals in early mathematics education. The open educational resource nature of the material makes it accessible for educators seeking engaging and effective tools to teach foundational measurement concepts.

 

Study Guide: Measurement with Non-Standard Units

Key Concepts

• Measurement: The process of determining the size, quantity, or degree of something, typically by comparing it with a standard unit. In this context, we are focusing on measuring length.
• Length: The distance between two points of an object, typically measured along a straight line.
• Non-standard Units: Units of measurement that are not universally agreed upon or standardized (e.g., paper clips, shoes, pencils).
• Standard Units: Universally accepted and defined units of measurement (e.g., meters, centimeters, inches). These are not the focus of the provided materials but are important to understand the context of non-standard units.
• Alignment: The act of placing objects in a straight line or in proper relative positions, crucial for accurate length measurement.
• Estimation: Making an approximate judgment or calculation of the length of an object.
• Comparison: Determining whether one object is longer, shorter, or the same length as another.
• Iteration: The process of repeatedly placing a non-standard unit end-to-end to measure the length of an object.
• Accuracy: How close a measurement is to the true value. When using non-standard units, accuracy depends on consistent unit size and careful placement.
• Units (as a word): In the context of early measurement, "unit" refers to a single instance of the chosen non-standard measuring tool (e.g., one paper clip is one unit).

Quiz

1. According to the materials, what is the primary non-standard unit used to demonstrate the measurement of length? Why is this unit effective for introducing the concept of measurement to young learners?
2. Describe the process of measuring the length of a pencil using paper clips as outlined in the provided text. What are the key steps involved in obtaining an accurate measurement with these non-standard units?
3. The "Sample Learning Goals" section mentions the importance of using "the word unit to measure length." Explain what this means in the context of using paper clips to measure a pencil. Provide an example.
4. What are the two crucial rules highlighted in the "What have you learned about length?" section regarding the use of non-standard units when measuring length? Why are these rules important for obtaining reliable measurements?
5. Explain the concept of "automatic alignment" as described in the context of the interactive tool. How does this feature aid in the measurement process?
6. The materials suggest that the lengths of the objects in the interactive tool are "for illustration only" and "not the actual size of the object." Why is this disclaimer important when using virtual non-standard units for learning about measurement?
7. How does the interactive tool encourage exploration and estimation of length using paper clips? Describe at least two features that support this learning approach.
8. For primary students learning about length, what is the benefit of starting with non-standard units like paper clips before introducing standard units of measurement?
9. The text mentions that the length of the pencil in the interactive resets randomly between 5 and 10 units. Why might this feature be beneficial for a student learning to measure length?
10. How do the suggested answers provided in the text reinforce the key learnings about measuring length with non-standard units? Give a specific example from the answers provided.

Quiz Answer Key

1. The primary non-standard unit used to demonstrate measurement of length is paper clips. Paper clips are effective for introducing measurement to young learners because they are familiar, tangible objects that can be easily manipulated and counted.
2. To measure the length of a pencil using paper clips, you need to take several paper clips and position them end-to-end in a straight line along the length of the pencil, ensuring no gaps or overlaps. Then, you count the total number of paper clips required to cover the entire length of the pencil, which gives you the length in "paper clip units."
3. Using "the word unit to measure length" means that when we measure using a non-standard item like a paper clip, we express the measurement as a number of those items. For example, if a pencil is as long as 7 paper clips placed end-to-end, we say the pencil is 7 units long, where one "unit" represents the length of one paper clip.
4. The two crucial rules are: 1) Use the same non-standard units when comparing lengths, and 2) Place the units end-to-end without gaps or overlaps. These rules are important because they ensure a consistent and accurate comparison of lengths. Using different-sized units or leaving gaps/overlaps would lead to unreliable measurements.
5. "Automatic alignment" refers to the interactive tool's feature where the yellow left alignment marker automatically snaps to the left edge of the pencil or object when it is repositioned. This feature helps ensure that the non-standard units are consistently aligned from the starting point of the object, promoting more accurate measurement.
6. The disclaimer that the object sizes are for illustration only is important because the virtual paper clips are not being compared to a real-world object of known, fixed size. The focus is on understanding the process of measurement using non-standard units, rather than obtaining an actual, standardized measurement of a real pencil or shoe.
7. The interactive tool encourages exploration by allowing students to drag and position the paper clips themselves to measure the length of different virtual objects. It promotes estimation by presenting objects with randomly set lengths (within a range) and providing an input field for students to guess the length in paper clip units before revealing the "correct" answer.
8. Starting with non-standard units helps primary students grasp the fundamental concept of measurement as a comparison against a chosen unit without the complexities of standardized scales and numerical conversions. It allows them to focus on the process of iteration, alignment, and counting before introducing the abstract idea of standard units.
9. The random resetting of the pencil's length between 5 and 10 units provides repeated opportunities for students to practice their measurement skills with different lengths. This variability prevents rote memorization and encourages them to actively engage in the measurement process each time.
10. The suggested answer for the first question, "I must use the same non-standard units when comparing the length of objects," directly reinforces the importance of consistency in measurement. It highlights that for a fair comparison, the size of the measuring tool must remain constant.

Essay Format Questions

1. Discuss the advantages and limitations of using non-standard units like paper clips to introduce the concept of length measurement to primary school students.
2. Explain how interactive simulations, such as the one described in the provided text, can enhance a student's understanding of measurement compared to traditional methods of instruction.
3. Analyze the role of alignment and iteration in obtaining accurate length measurements, whether using non-standard or standard units. Provide examples to support your analysis.
4. Consider the progression of teaching measurement in early grades. How do non-standard units serve as a foundational step towards understanding and using standard units of measurement effectively?
5. Evaluate the effectiveness of the "Sample Learning Goals" and "What have you learned about length?" questions in guiding student learning and assessing their understanding of basic measurement principles using non-standard units.

Glossary of Key Terms

• Alignment: The arrangement of objects in a straight line or in proper relative position.
• Estimate: To roughly calculate or judge the value, number, quantity, or extent of something.
• Iteration: The repetition of a process or procedure, in this context, repeatedly placing a measuring unit end-to-end.
• Length: The measurement of something from end to end; the longer or longest dimension.
• Measurement: The act or process of determining the size, amount, or degree of something.
• Non-standard Unit: A unit of measurement that is not officially recognized or standardized.
• Standard Unit: A unit of measurement defined by a recognized authority or system, ensuring uniformity.
• Unit: A standard quantity in terms of which other quantities are expressed. In the context of non-standard measurement, it refers to a single instance of the chosen measuring tool.

Sample Learning Goals

Measurement of Length

This interactive supports the exploration of measurement of a pencil using paper clips.

Each reset randomly set a new length from 5 to 10 units

The alignment is automatic and is on the left.

The pencil or object can be reposition and the yellow left alignment will automatically snap to the left of the pencil or object.

You can drag on the paper clips and position them in a straight line to count the number of units of length is required to measure the length of the pencil

Click play and the interactive play the movement of the paper clips

Finally, try to input the correct answer on the input field in the top right corner.

For Teachers

Primary 1: Length_Interactive board using non-standard units to measure the length of object

In this lesson, you will learn to
- measure some objects using the virtual paper clips as non-standard units.
- use the word unit to measure length
- estimate the length of objects with number of units


Before you use the interactive board to explore and measure objects using the paper clips,
please refer to the explanation below to understand how the different buttons work.

It's exploration Time!

After you have read the explanation of the different buttons, please explore to estimate the length of different objects using the paper clips.
Note: The objects used here are for illustration only, it is not the actual size of the object.

What have you learned about length?

1. I must use the ___________ non-standard units when comparing the length of objects.
2. I learn words like _____________ when comparing the lengths of objects.
3. When measuring length, the units must be placed end-to-end without __________________.

Suggested Answers

I must use the same non-standard units when comparing the length of objects.
2. I learn words like long/longer/longest/short/shorter/shortest (any reasonable answer) when comparing the lengths of objects.
3. When measuring length, the units must be placed end-to-end without gaps or overlaps (can accept 'space').

Research

[text]

Video

https://youtu.be/VHCL3kuIhKk 

 Version:

1. https://weelookang.blogspot.com/2020/04/how-to-measure-pencil-math-primary-1.html  

Other Resources