Visualizing Subtraction
Visualizing Subtraction - Related Videos
09:40
Novel Sequence Discovery by Subtractive Genomics
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Cited by 7 •
2019
The purpose of this protocol is to use a combination of computational and bench research to find novel sequences that cannot be easily separated from a co-purifying sequence, which may be only partially known.
09:43
Measuring Reaction Time and Donders' Method of Subtraction
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2023
Source: Laboratory of Jonathan Flombaum—Johns Hopkins University The ambition of experimental psychology is to characterize the mental events that support the human ability to solve problems, perceive the world, and turn thoughts into words and sentences. But people cannot see or feel those mental events; they cannot be weighed, combined in test tubes, or grown in a dish. Wanting to study mental life, nonetheless, Franciscus Donders, a Dutch ophthalmologist in the early 1800s, came up with a...
08:57
Improving Infrared Spectroscopy Characterization of Soil Organic Matter with Spectral Subtractions
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Cited by 19 •
2019
SOM underlies many soil functions and processes, but its characterization by FTIR spectroscopy is often challenged by mineral interferences. The described method can increase the utility of SOM analysis by FTIR spectroscopy by subtracting mineral interferences in soil spectra using empirically obtained mineral reference spectra.
01:22
Detection of Internal Carotid Artery Narrowing Using Digital Subtraction Angiography
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2025
Position a human patient with internal carotid stenosis, a condition characterized by narrowing of the internal carotid artery, on the imaging table for digital subtraction angiography (DSA). Insert an angiocatheter into the common carotid artery at the fourth cervical vertebra level. Capture a pre-contrast X-ray image to record background structures like bones and soft tissues using X-ray irradiation. Administer an iodine-based contrast medium into the carotid artery. The contrast medium...
12:19
Rapid Subtractive Patterning of Live Cell Layers with a Microfluidic Probe
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Cited by 2 •
2016
We present a protocol to perform subtractive patterning of live cell monolayers on a surface. This is achieved by local and selective lysis of adherent cells using a microfluidic probe (MFP). The cell lysate retrieved from local regions can be used for downstream analysis, enabling molecular profiling studies.
FAQs
The visual model preserves the relationship among the starting quantity, the quantity removed or compared, and the resulting difference. A learner can first inspect the quantities in a drawing, object arrangement, bar model, or number-line movement, then match those relationships to an equation. This connection helps explain why the symbolic calculation represents the situation rather than treating it as an isolated procedure.
These models describe different relationships that can produce a subtraction equation. A take-away model emphasizes what remains after removing a quantity. A comparison model focuses on the distance or difference between two amounts. An unknown-part model shows a whole and a known part while requiring the missing part to be found. Choosing the relationship clarifies what the subtraction represents.
Place-value representations show how quantities are organized into units of different sizes, allowing learners to reason about each part of a multidigit number. When regrouping is needed, the model makes the change in unit structure visible instead of hiding it in written notation. This supports more accurate subtraction and helps learners explain the logic behind each step.
A leftward movement on a number line represents reducing a starting amount by a specified distance. Its length shows how much is subtracted, while the landing point shows the result. This model makes the directional relationship between the starting quantity and the difference visible, giving learners a way to connect numerical change with the corresponding subtraction equation.
Counters, bar models, and number lines provide complementary ways to represent subtraction. Counters support direct actions with quantities, bars emphasize the relationship between a whole and its parts, and number lines show movement or distance. A teacher or learner can select the representation that best matches the problem, then connect the visual result to symbolic notation.
Begin by identifying the quantities and the relationship being described. Represent the starting amount with counters, a bar model, or a number line, then remove, compare, or mark the unknown part as appropriate. Determine the remaining or missing quantity, and finally record the matching equation. This sequence keeps the visual reasoning connected to the written calculation.
A model gives learners something to inspect after calculating. They can check whether the represented remainder, comparison distance, or unknown part matches the quantities in the problem. If the picture and equation disagree, the mismatch signals that the reasoning should be revisited. This supports accuracy while encouraging explanations based on relationships rather than answers alone.