Iteration: Unit Fraction Knowledge and the French Fry Tasks

2015 ◽  
Vol 22 (3) ◽  
pp. 148-157 ◽  
Author(s):  
Ron Tzur ◽  
Jessica Hunt
Keyword(s):  
French Fry ◽  
Unit Fractions ◽  
Unit Fraction

Using these tasks can help nurture children's multiplicative notions of unit fractions beyond part-whole understanding.

Unit Fractions as Superheroes for Instruction

2020 ◽  
Vol 113 (4) ◽  
pp. 278-286
Author(s):  
Susan Baker Empson ◽  
Victoria R. Jacobs ◽  
Naomi A. Jessup ◽  
Amy Hewitt ◽  
D'Anna Pynes ◽  
...  
Keyword(s):  
Unit Fractions ◽  
Unit Fraction ◽  
Children's Strategies

The complexity of understanding unit fractions is often underappreciated in instruction. We introduce a continuum of children's understanding of unit fractions to explore this complexity and to help teachers make sense of children's strategies and recognize milestones in the development of unit-fraction understanding. Suggestions for developing this understanding are provided.

scholarly journals Dynamic Windows Scheduling with Reallocation

2021 ◽  
Vol 26 ◽  
pp. 1-19
Author(s):  
Martín Farach-Colton ◽  
Katia Leal ◽  
Miguel A. Mosteiro ◽  
Christopher Thraves Caro
Keyword(s):  
Supply Chain ◽  
Bin Packing ◽  
Time Slot ◽  
Peak Load ◽  
Communication Channels ◽  
Current Load ◽  
Constant Amount ◽  
Unit Fractions ◽  
Consecutive Time ◽  
Multiple Variants

We consider the Windows Scheduling (WS) problem, which is a restricted version of Unit-Fractions Bin Packing, and it is also called Inventory Replenishment in the context of Supply Chain. In brief, WS problem is to schedule the use of communication channels to clients. Each client c i is characterized by an active cycle and a window w i . During the period of time that any given client c i is active, there must be at least one transmission from c i scheduled in any w i consecutive time slots, but at most one transmission can be carried out in each channel per time slot. The goal is to minimize the number of channels used. We extend previous online models, where decisions are permanent, assuming that clients may be reallocated at some cost. We assume that such cost is a constant amount paid per reallocation. That is, we aim to minimize also the number of reallocations. We present three online reallocation algorithms for Windows Scheduling. We evaluate experimentally multiple variants of these protocols showing that, in practice, all three achieve constant amortized reallocations with close to optimal channel usage. Our simulations also expose interesting tradeoffs between reallocations and channel usage. We introduce a new objective function for WS with reallocations that can be also applied to models where reallocations are not possible. We analyze this metric for one of the algorithms that, to the best of our knowledge, is the first online WS protocol with theoretical guarantees that applies to scenarios where clients may leave and the analysis is against current load rather than peak load. Using previous results, we also observe bounds on channel usage for one of the algorithms.

scholarly journals Monochromatic solutions to equations with unit fractions

1991 ◽  
Vol 43 (3) ◽  
pp. 387-392 ◽  
Author(s):  
Tom C. Brown ◽  
Voijtech Rödl
Keyword(s):  
Solutions To Equations ◽  
Unit Fractions ◽  
Image Position ◽  
Positive Integers

Our main result is that if G(x1, …, xn) = 0 is a system of homogeneous equations such that for every partition of the positive integers into finitely many classes there are distinct y1,…, yn in one class such that G(y1, …, yn) = 0, then, for every partition of the positive integers into finitely many classes there are distinct Z1, …, Zn in one class such thatIn particular, we show that if the positive integers are split into r classes, then for every n ≥ 2 there are distinct positive integers x1, x1, …, xn in one class such thatWe also show that if [1, n6 − (n2 − n)2] is partitioned into two classes, then some class contains x0, x1, …, xn such that(Here, x0, x2, …, xn are not necessarily distinct.)

scholarly journals An Application of the Box-Jenkins Approach to Forecasting the Cold Storage of French Fries

1980 ◽  
Vol 9 (2) ◽  
pp. 51-54 ◽  
Author(s):  
Richard P. Beilock ◽  
James W. Dunn
Keyword(s):  
Cold Storage ◽  
Important Determinant ◽  
French Fries ◽  
Price Expectations ◽  
French Fry ◽  
The Future ◽  
Stock Information ◽  
Market Strategies

Potatoes suitable for frozen french fries are harvested in the fall and then apportioned for the rest of the year by processors. This involves storage in either fresh or frozen form. Participants in both the fresh and french fry market consider the level of frozen french fry stocks to be an important determinant of activity in these markets and therefore use stock information to form price expectations [Phillips et al., 16–18]. The ability to forecast the future level of stocks with some accuracy would undoubtedly be an additional aid in developing market strategies. This paper provides one means of forecasting frozen french fry stocks.

scholarly journals A multi-site cutting device implements efficiently the divide-and-conquer strategy in tumor sampling

F1000Research ◽  
2016 ◽  
Vol 5 ◽  
pp. 1587 ◽  
Author(s):  
Jose I. Lopez ◽  
Jesus M. Cortes
Keyword(s):  
Synthetic Data ◽  
Daily Practice ◽  
Divide And Conquer ◽  
Intratumor Heterogeneity ◽  
Pathology Laboratory ◽  
Simple Method ◽  
French Fry ◽  
Histological Processing ◽  
Tumor Sampling ◽  
Selection Of

We recently showed that in order to detect intra-tumor heterogeneity a Divide-and-Conquer (DAC) strategy of tumor sampling outperforms current routine protocols. This paper is a continuation of this work, but here we focus on DAC implementation in the Pathology Laboratory. In particular, we describe a new simple method that makes use of a cutting grid device and is applied to clear cell renal cell carcinomas for DAC implementation. This method assures a thorough sampling of large surgical specimens, facilitates the demonstration of intratumor heterogeneity, and saves time to pathologists in the daily practice. The method involves the following steps: 1. Thin slicing of the tumor (by hand or machine), 2. Application of a cutting grid to the slices (e.g., a French fry cutter), resulting in multiple tissue cubes with fixed position within the slice, 3. Selection of tissue cubes for analysis, and finally, 4. Inclusion of selected cubes into a cassette for histological processing (with about eight tissue fragments within each cassette). Thus, using our approach in a 10 cm in-diameter-tumor we generate 80 tumor tissue fragments placed in 10 cassettes and, notably, in a tenth of time. Eighty samples obtained across all the regions of the tumor will assure a much higher performance in detecting intratumor heterogeneity, as proved recently with synthetic data.

scholarly journals The Effect of Field Heat Reduction Methods on Fresh and Processing Qualities of Red and Russet Potato Cultivars

2021 ◽  
Vol 6 (2) ◽  
pp. 345-355
Author(s):  
Sastry S. Jayanty ◽  
◽  
Esam Emragi ◽  
David G. Holm
Keyword(s):  
Weight Loss ◽  
Wound Healing ◽  
Reducing Sugars ◽  
Reduction Method ◽  
French Fries ◽  
Total Phenolic ◽  
French Fry ◽  
Russet Norkotah ◽  
Fry Color ◽  
Reduction Methods

The effect of three field heat reduction methods, including temperature lowering stepwise (TLS), temperature lowering gradually (TLG), and temperature lowering immediately (TLI), after harvesting on the quality of Russet Norkotah 3 and red skin numbered line CO 07102-1R potatoes were investigated. The tubers were analyzed at harvest (0 time), when they reached 3 °C, and after 6 months of storage at 3 °C for physiological weight loss, firmness, wound healing, total phenolics content, reducing sugars, and color of french fries. The results indicated that weight and firmness losses were lower under the TLS reduction method after 6 months of storage than TLG and TLI methods. The weight loss in TLS is 12%, TLG 14% and TLI 17% in CO 07102-1R whereas Russet Norkotah TLS is 4%, TLG 6%, and TLI 8% respectively. Wound healing was more effective using the TLS reduction method, especially in Russet Norkotah 3. French fry color was lighter at harvest (USDA grade 0), while there were no differences in the color of French fries prepared from tubers stored under the TLS and TLG methods (both had USDA grade 2). French fries were darker for tubers from the TLI method (USDA grade 4). The total phenolic content and reducing sugars were significantly increased in the TLI field heat reduction method. Keywords: Potato, Storage management, Wound healing, Weight loss, French fry

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