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Resources tagged with: Mass and weight

There are 20 NRICH Mathematical resources connected to Mass and weight , you may find related items under Measuring and calculating with units .

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Order, Order!

Can you place these quantities in order from smallest to largest?

All in a Jumble

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

Being Resilient - Primary Measures

Measure problems at primary level that may require resilience.

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Measure problems at primary level that require careful consideration.

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Watermelons

These watermelons have been entered into a competition. Use the information to work out the number of points each one was awarded.

2010: A Year of Investigations

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Weighing Fruit

Can you use this information to estimate how much the different fruit selections weigh in kilos and pounds?

Working with Dinosaurs

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Measure for Measure

This article, written for students, looks at how some measuring units and devices were developed.

Weigh to Go

This article for teachers recounts the history of measurement, encouraging it to be used as a spring board for cross-curricular activity.

Money Measure

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

Do You Measure Up?

A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.

Oranges and Lemons

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

What's My Weight?

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

Measuring mass: problem solving

Work out the weights of items on a set of scales.

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Differentiated Weight Word Problems

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

18 May 2019

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Our grade 2 math worksheets are free and printable in PDF format. Based on the Singaporean math curriculum for second graders, these math worksheets are made for students in grade level 2. However, also students in other grade levels can benefit from doing these math worksheets. Feel free to print them. Our math worksheets cover important math topics such as: whole numbers, spelling, place value, skip counting, addition and subtraction, multiplication tables, basic division facts, fractions, mixed operations, geometry, graphing, picture graphs, measurement of time, mass, length and volume.

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Welcome to Math Salamanders Year 2 Maths Worksheets hub page.

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Year 2 Maths Learning

Here are some of the key learning objectives for the end of Year 2:

• know and use Place value up to 100
• Compare and order numbers up to 100
• Counting on and back in 1s and 10s
• count in 2s, 5s and 10s
• Position numbers on a number line up to 1000
• use addition and subtraction facts to 20
• use related facts for addition and subtraction
• add or subtract 1 or 10 from a 2-digit number
• add and subtract 2-digit numbers
• number bonds to 100 using tens only
• add three single-digit numbers
• recognise and make equal groups
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• know multiplication facts for the 2, 5 and 10 times table
• recognise and find a half, a quarter and a third
• understand and use fraction notation
• understand the equivalence of a half and two-quarters
• count on in halves, thirds and quarters up to 10
• count in pence: 1p, 2p ,5p, 10p and 20p
• count in pounds: £1, £2, £5, £10 and £20
• find a simple total or difference between two money amounts
• find the change from simple amounts
• tell the time: o'clock, half-past, quarter-past and to
• understand and compare durations of time
• compare and measure length, mass, volume, capacity and temperature
• read a variety of scales going up in 1s, 2s, 5s and 10s
• recognise 2D and 3D shapes
• count sides and vertices on 2D shapes
• count faces, edges and vertices on 3D shapes
• sort and make patterns with 2D and 3D shapes
• describe movement and turns
• make tally charts
• draw and interpret pictograms
• understand and use block diagrams

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• Place Value to 20 Worksheets
• Math Place Value Worksheets Tens and Ones
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Solving the cost minimization problem of optimal reactive power dispatch in a renewable energy integrated distribution system using rock hyraxes swarm optimization

• Original Paper
• Published: 27 June 2024

Cite this article

• Tanmay Das 1 ,
• Ranjit Roy 2 &
• Kamal Krishna Mandal 1  

The optimal reactive power dispatch problem optimizes the shunt capacitor bank installation in distribution systems, reducing power loss and also reducing the financial loss for the electricity market associated with power loss. Moreover, the sharing of both active and reactive power from different renewable energy sources like PV and wind in the form of distributed generation also contributes toward reducing power loss and improving the voltage profile of the system. But the installation and maintenance costs associated with these additional set-ups are rarely taken into consideration any optimization problem. This paper aims to reduce the power loss and improve the voltage profile of a radial distribution network with the integration of capacitor banks, PV, and wind energy sources, while taking into account the overall associated cost of each parameter during optimization. The problem is formulated as a novel cost minimization problem aiming to achieve the optimal settings for a life-long capacitor bank-PV-wind integrated distribution network with the least possible installation, operational, and maintenance costs while reducing its power loss significantly for a span of 20 years. The uncertain nature of PV and wind power output has been modeled using the beta probability distribution function and the Weibull probability distribution function, respectively. This unique proposed problem statement of the capacitor bank-PV-wind power integrated distribution network has been tested on the IEEE 33 and IEEE 141 bus systems and solved using the rock hyraxes swarm optimization (RHSO) algorithm. The results were compared with those from other nine well-established techniques, from which it was concluded that the RHSO algorithm has obtained optimal conditions for both systems to operate efficiently. The problem has also been tested on a practical 13-bus 33 kV distribution network in Maharashtra, India, to validate its performance on a practical system. The RHSO has successfully reduced the power loss to almost 17.48% w.r.t. the base case for the practical network while maintaining a minimum overall cost of $51,073,687.7582 for an entire life-span of 20 years.

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Department of Power Engineering, Jadavpur University, Salt Lake Campus, Kolkata, India

Tanmay Das & Kamal Krishna Mandal

Department of Electrical and Electronics Engineering, SRM University, Sonipat, Haryana, India

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Mr. Tanmay Das carried out basic design and simulation work and prepared a draft paper. Dr. Ranjit Roy and Dr. Kamal Krishna Mandal participated in checking simulation work, results and discussions, and sequence of writing and helped to organize the manuscript. All authors read and approved the final manuscript.

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Correspondence to Ranjit Roy .

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Das, T., Roy, R. & Mandal, K.K. Solving the cost minimization problem of optimal reactive power dispatch in a renewable energy integrated distribution system using rock hyraxes swarm optimization. Electr Eng (2024). https://doi.org/10.1007/s00202-024-02548-9

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Received : 09 February 2024

Accepted : 13 June 2024

Published : 27 June 2024

DOI : https://doi.org/10.1007/s00202-024-02548-9

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