In order to track our progress each year, I try to quantify the harvest as best I can. I keep a written journal of most of the important activities and progress in the garden, and the journal includes a penciled-in log of any harvests that happen during each week of the season. When I have the chance, I copy that handwritten data into a little spreadsheet I made which handles some of the calculations I’m interested in and updates the totals automatically for me. This spreadsheet is designed specifically for small gardens, not farms, and possibly not even for very large gardens. It’s targeted for situations where you harvest small amounts and can keep track of harvested items as single units (for most things) or small bunches (for herbs), rather than as large bulk amounts such as bushels.
The concept behind this spreadsheet is that once you add in some typical values at the start of the season for the weight of a given variety when harvested (like the average weight of one cherry tomato), the spreadsheet does all the rest of the calculations as you add to your counts each week. It does its math based on counts, so that you don’t have to keep weighing each time you harvest, just tally how many single items you harvested that week.
Here is a PDF version of our 2015 harvest spreadsheet:
Harvest Spreadsheet PDF
I’ll post a link to a working .xlsx spreadsheet at the end of this post, which is free for you to use and tweak as you see fit.
Here’s how it works:
Column A: (Name and Variety)
B (Ounces per Unit): A unit might be a Single (for things like tomatoes or cucumbers), or a Bunch (for things like greens or herbs), or I could call one a Dozen, which would work for some varieties.
C (Unit Name): Name of the Unit referred to in B.
D (Singles per Unit): How many single items are there in a Unit? This is arbitrary and up to you. For example, 20 in a Bunch or 12 in a dozen. I have 10 leaves of Kale equals one Bunch, for example. This is only for determining the average weight of a single leaf, bean, etc so that further math can be done later.
E (Calculated ounces per single): This assists in the next calculation. This is the weight of one tomato, or pepper, or eggplant, or bunch of basil or kale, etc. I can just weigh a total harvest of say 20 beans, and let the spreadsheet calculate the very small weight of one bean—probably too small for my scale to measure accurately. Then when I harvest, I can count the singles, for example 127 beans in a given week, and the spreadsheet does the rest of the multiplication.
F: Lbs (pounds) total. This is the calculated sum of all of the harvested single items in the row (F), times the calculated ounces per single (E), divided by 16 (ounces per pound) to convert to pounds from ounces. So the value is the total pounds of harvest for this variety all season. At the bottom of Column F is the grand total weight of the season’s harvest across the board.
G (Count Total): Here, the total count of singles for the season for that variety is calculated. For example, total number of tomatoes picked all season, or total number of leaves of kale picked.
I’ve added some additional columns as well.
H (Market Price per lb): This is the price I see at the local farmer’s market for a similar item, so it is what I would have paid per pound if we had purchased it rather than grown it ourselves.
I (Harvest Value): This is the calculated value of the equivalent amount of produce if our own season’s harvest was purchased at the market. For example, Our twenty Brandywines added up to 11.56 lbs, so at the local price of $4/lb we grew the equivalent of $46.25 worth of them.
J (Designated Space): This is a rough idea of how much total space this variety took up in the garden. For example, we had two Fox Cherry plants which each took up about two square feet of soil, so I have them taking up a total of eight square feet. The bottom of this column should add up to the total amount of soil I have available to plant, in our case roughly 220 sq ft.
K (Productivity): This is a calculation of the Harvest Value (I) dividied by the Designated Space (J), and shows the relative value of using garden space for growing one crop versus another, in pure dollar terms. So I can see that using a square foot of soil to grow Brandywines ($7.71 per sq ft) is more than twice as valuable than using the same square foot to grow Pickling Cucumbers
($3.09 per sq ft). I can also see that herbs are the most productive crop in dollar per square foot terms. This makes sense, as shoppers pay a proportionally large amount for the tiny bunches of herbs that they need for cooking. A bunch of kale might weigh half a pound and cost $3, but a home cook would never buy a pound of sage; they might pay $3 for half an ounce. This is why most of the herbs show very high equivalent market prices per pound.
Further over to the right, we see the actual harvest data, divided up by week. These are always singles, as in three individual tomatoes or 73 individual beans or 12 individual leaves of collards. Each date marks the last day of that week, so the value in the Aug 21 entry would be the total of that variety harvested from the week ending on the 21st. This means that the last ‘week’ of each month might be ten or eleven days—each month has three 7-day weeks followed by one long week in order to bring us to the end of the month without extra days.
So in summary, to use the spreadsheet:
- Enter the names of your varieties in Column A.
- Determine the average weight per unit using a scale. For example, weigh 5 cucumbers together and divide the total weight by 5. Or weigh 10 leaves of kale, call that a Bunch, enter 10 in column D, and the spreadsheet will figure out the single leaf weight. At this point you really won’t need your scale again.
- Optionally enter your own figures for H, I and J if these calculations are of interest to you regarding dollar values and productivity.
- At the end of each week of the season, enter your total counts. Again, it’s a single count for a tomato, or a single count for a leaf of greens. If I picked 25 leaves of kale on a single day and no more kale for the week, I put ’25’ as the value for that week. Two tomatoes on the first day of the week and two more on the last day of the week? The value for that week would be ‘4’.
- Let the spreadsheet calculate the rest!
Using this method, after the initial setup of the first few columns, I simply tally up my counts for the week and enter them. The rest is done for me.
The spreadsheet tells me, for example:
— We harvested about 87.44 lbs of produce this year—similar to last year.
— We harvested the equivalent of about $458.23 worth of produce.
— The award for the longest growing season goes to… Chives! April – December.
— Chives also brought in the best value per square foot, at $43.75/sq ft.
This is due to their high equivalent market price, multiplied by their long season.
— Our average value of harvested produce per sq ft of soil is $2.06.
— 1333 hops cones, totaling 1.88 pounds… all given to local homebrewers.
— Each square foot of soil used for Cherry tomatoes proves to be slightly more productive in dollar terms ($8.13) than if it were used for Brandywines ($7.71).
Here is a link to the same spreadsheet, ready for you to customize. I hope you find it useful.


The Maxwell-Boltzmann Distribution
The Maxwell-Boltzmann statistic describes the velocity distribution of the particles that compose a gas at a certain temperature in the thermodynamic equilibrium. The Maxwell-Boltzmann distribution is represented by Figure 2.
The y-axis represents the number of molecules per unit of speed. So if the graph is higher in a certain region it means that there are more molecules moving at that speed.
The study of Maxwell-Boltzmann distribution began in the 1857 paper “On the Nature of the Motion which we Call Heat” by German physicist Rudolf Clausius, in which the speeds of atoms were calculated.
James Maxwell, In 1860, published “On the Dynamical Theory of Gases”, demonstrated using kinetic theory how to obtain physical properties of gases from the distribution of velocities, taking into account not simply the average speed of the atoms, but their distribution of speeds greater or smaller than the average. Ludwig Boltzmann, In 1868, published a more convincing physical explanation for the Maxwell formula had derived, showing that Maxwell's formula correctly predicted how the number of atoms or molecules with a particular energy would change.
To obtain the velocity distribution of Maxwell-Boltzmann it is possible to use the formalism of the grand canonical ensemble.
The Maxwell-Boltzmann Distribution In The Grand Canonical Ensemble
The grand canonical ensemble It is a way of modeling a thermodynamic system with fixed temperature and fixed chemical potential. For this is used the grand canonical partition function, given by:
β =1/Kb T, T is the temperature and Kb is the Boltzmann´s constant;
ϵj is the energy of the j-th state;
μ is the chemical potential.
The thermodynamic number of particles is:
And the average value of particles in the j-th state is
As in the grand canonical ensemble the chemical potential is fixed, we define the fugacity of the system as
and equation 1 becomes:so,
and equation 2 becomes:
which is the discrete form of the classical Maxwell-Boltzmann distribution.
In the thermodynamic limit (N → ∞, V → ∞, N / V = constant), the summation becomes an integral. Knowing that the transformation of a sum into an integral is given by:
And for free particles, in the absence of spin terms in the Hamiltonian operator, the continuous energy spectrum is given by:
and equation 8 becomes:
Using Gaussian integral, that is:
And in 3 dimensions:Then
Due to the isotropy of the space of the molecular speeds, that is, to the fact that all the properties of the space are the same in all the directions, we can write in spherical coordinates:so,
It is the probability density of the molecular speed modules.
Speed values can be extracted from the Maxwell-Boltzmann speed distribution function.
The most probable velocity (vmp): corresponds to the maximization of p0 (v).
The average speed <v> is defined as
using the result
The mean square velocity is defined as:
using the result
and the root mean square (vrms) is
The energy of an ideal gas
The average energy of a molecule of an ideal gas is:
Since there are N molecules, the ideal gas energy is:
From the graph of the distribution of Maxwell-Boltzmann can extract other information as:
The total area under the entire curve is equal to the total number of molecules in the gas (Figure 4).
The higher the peak height in the Maxwell-Boltzmann distribution graph the lower the average temperature of the molecules that compose the gas. In addition, the higher the gas temperature shifted to the right of the x-axis the graph will be (Figure 5). this happens so that the area under the curve (total number of molecules) remains constant.
SALINAS S. R. A. Introduction to Statistical Physics, 2a Ed., Edusp, São Paulo (2013)
 TEIXEIRA, Alessandra de Souza et al. Estudo dos Gases. Available in: <http://processostermodina.wixsite.com/termodinamica/estudo-dos-gases>. Accessed in: 01/14/2019.
 KHAN ACADEMY. What is the Maxwell-Boltzmann distribution?. Available in: <https://www.khanacademy.org/science/physics/thermodynamics/temp-kinetic-theory-ideal-gas-law/a/what-is-the-maxwell-boltzmann-distribution>. Accessed in: 01/14/2019.Nature motion we call heat - Clausius (1857)


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Math Simple Addition Coloring Worksheets For Kindergarten
Help them gain confidence and have fun with math.
Math simple addition coloring worksheets for kindergarten. This is one of our favorite kindergarten math worksheets because of the way it presents the. With colorful designs and tons of neat themes kids will equate practice time with fun time as they add things like soccer balls fish fruit veggies and dinosaurs. We hope that these addition math. Children who have an ipad or other tablet device can actually draw on the worksheets with their fingers.
Print all of our worksheets. Top 10 addition and subtraction coloring pages. Aug 17 2019 for practicing some math skills like simple addition there is just nothing more efficient than a pencil and paper. Learn simple math concepts practice addition and subtraction match numbers and pictures and more.
Coloring pages that facilitate mathematical calculations are pretty popular with teachers as well as parents. You can now print this beautiful addition kindergarten math worksheet coloring page or color online for free. We also have more kindergarten worksheets including phonics and. Once kindergartners nail down their numbers they get to graduate to basic addition which also means they get to graduate to our kindergarten addition worksheets.
After solving the math kids can color the caterpillar in any shade they like. We even have practice test kindergarten addition worksheets so. These addition worksheets for the addition math worksheets start with simple addition. They love solving and working on these math worksheets for kindergarten addition with so many colours and pictures and things to do.
Worksheetschool math worksheets for kindergarten addition are created in a way so as to make learning the first step of addition fun for these tiny tots. Math may not be the easiest subject for some kids but the more the practice the quicker it clicks. Addition practice for kindergarten students. Printable addition kindergarten math worksheet coloring page.
You will get the rewards in the form of less nagging and more smiles. You can help your kid by introducing simple addition and subtraction coloring worksheets. Math worksheets for kindergarten addition. These are free coloring pages with addition and subtraction exercises to.
Here s a simple addition kindergarten math worksheet where you need to instruct your child to add the numbers written on the caterpillars bodies. When creating these free kindergarten worksheets we tried to make the learning material both fun and educational. Math addition addition and subtraction simple addition math worksheets math resources math activities go math kindergarten fun preschool. Even teachers love these worksheets.
Kindergartners teachers and parents who homeschool their kids can print download or use the free kindergarten math worksheets online. Free printable kindergarten worksheets shapes addition picture addition dice subtraction picture most popular preschool and kindergarten worksheets dice worksheets number counting dice phonics pattern shape patterns numbers missin.
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The key person will join our Flight Dynamics team supporting on a daily basis our customer ESA/ESOC. The ESOC Flight Dynamics division provides mission analysis and flight dynamics operations support to ESA and third party missions during all mission phases. Flight Dynamics cooperates with different elements of the ground segment, such as the flight control teams, ground operations teams, science teams, the projects teams and the spacecraft manufacturers.
More specifically, the selected key person will primarily support the Flight Dynamics operations for the Sentinel missions of the EU Copernicus programme.
How to apply: firstname.lastname@example.org
Tasks & Responsibilities
The key person will join a team responsible of the following tasks (not limited to):
- Orbit determination and manoeuvre optimization
- Attitude determination and on-board systems monitoring and verification
- AOCS command generation
- AOCS and optical sensors calibration
- Test & Validation for the above
- Performing studies and technical analyses to support the above
- Routine mission operations
- Pre-launch activities, like software development and testing, procedure writing, technical analyses, support to test and simulation campaigns
- Support during critical mission phases (e.g. launch and commissioning, end of mission activities)
- Support of collision avoidance manoeuvres (with space debris) including on-call service
- Maintenance and evolution of the flight dynamics system.
- University degree in a relevant engineering field, astronomy, mathematics or physics
- Very good skills in linear algebra, in particular for problem solving related to geometry in the Euclidean 3–dimensional space.
- Being familiar with different representations of rotation in 3D, thus including the representation of S/C attitude (cosine direction matrix, Euler symmetric parameters/ quaternions, Euler-angles …) is an asset.
- Very good skills in calculus in one or several variables.
- Skills in numerical methods for:
- equations solving,
- integration of differential equations,
- function approximation and interpolation,
- linear algebra problems.
- Very good skills in classical mechanics, including:
- kinematics and dynamics of point masses,
- dynamics of rigid bodies,
- dynamics expressed in non-inertial reference frames, e.g. including dynamics in rotating frames, rotation dynamics expressed in body fixed frame,
- conservation laws in mechanics,
- gravitational forces and field,
- orbit dynamics, Keplerian orbits and Kepler laws.
- Ability to solve mechanics problems via analytical mechanics methods (e.g. Lagrangian formulation) is a valuable asset.
- Skills to apply their knowledge to develop solutions to technical (mathematical and dynamical) problems in cooperation with customers and other experts
- Ability to define, implement, validate and operate software which applies the above solutions (using e.g. Unix and/or Linux scripting languages, Fortran 77 and/or 95, Python, C++)
- Will to take operational responsibility in multi-discipline teams
- Fluency in English, both in speech and writing
- Coordinate and interact with other service providers in operations and other fields.
- Ability to work independently
- The ability to multi-task efficiently; working on multiple activities, multiple subsystems and multiple missions simultaneously.
Additional skills (which will be considered as an advantage):
- Familiarity with the ESOC environment
- Familiarity/experience with Flight Dynamics operations engineering tasks
- Experience dealing with external interfaces


Everything you need to know before joining
Name: Vidhi Bubna
Hometown: Mumbai, India
Hi! I am Vidhi and I am currently pursuing the IBDP. I love to explore different cities. I love to explore wildlife and nature. I am interested in learning about different cultures and lifestyles. I play the guitar and I am also passionate for writing. My favorite subjects are Math and Economics. I like to solve problems and I associate that with my risk taking abilities. I like to play chess, football, table tennis and I like to solve the Rubik’s cube. I also love partying. I am super excited to know my new classmates. I hope that our years together will be all set and amazing. I am keen to explore new things and learn more.


‘Mathematics is, in its way, the poetry of logical ideas.’ Albert Einstein
Children’s chances of success are maximised if they develop deep and lasting understanding of mathematical procedures and concepts.
At Barrow Hill Primary Academy, our aim is to raise levels of achievement in maths, and increasing appreciation of the power and wonder of maths. Mastering maths means children acquiring a deep, long-term, secure and adaptable understanding of the subject. The phrase ‘teaching for mastery’ describes the elements of classroom practice and school organisation that combine to give pupils the best chances of mastering maths. Achieving mastery means acquiring a solid enough understanding of the maths that’s been taught to enable children to move on to more advanced material.
Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy. Crucially, a sound knowledge of mathematics is vital for young people seeking employment, and securing a qualification in mathematics is a fundamental requirement for the majority of employers.
A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.
In line with the National Curriculum Objectives for Mathematics, our intent is that all children:
- become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately
- reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
- can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions
Mathematics is an interconnected subject in which children need to be able to move fluently between representations of mathematical ideas. The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects.
Central to our approach are the 5 Big Ideas which underpin mastery in mathematics.
In line with our whole school focus on oracy and vocabulary, we expect and encourage children to use mathematical language to describe, discuss, examine, explain, justify and analyse.
The essence of Maths Teaching for Mastery is that it rejects the idea that a large proportion of children ‘just can’t do maths’. At Barrow Hill Primary Academy, we have created a whole school approach that is underpinned by the belief that by working hard all children can succeed.
Children are taught in mixed ability year groups for mathematics. In each class, the teacher is responsible for the planning, teaching and assessment of all children. Highly skilled teaching assistants take responsibility for the delivery of the maths lesson for a year group of children in each class. This enables our groups to remain under 15 children and allows for mixed ability teaching whilst focusing on the conceptual journey for each year group.
Each year group has a long-term plan for the sequence of learning. This plan maps out the conceptual journey to ensure there is complete national curriculum coverage by the end of each key stage. The long term plan has evolved significantly due to gaps in learning as a result of the Covid-19 pandemic, and continually updated, high quality resources created by the NCETM. Small steps of learning are planned using Inspire Maths and the NCETM Curriculum Prioritsation document. The Professional Development Spines support teachers with their mathematical understanding and planning small steps. White Rose Maths and other sources are used to create well sequenced lessons. This has been adapted to suit the needs of our children and can be found in appendices 7.
For each conceptual journey the class teachers, alongside their supporting maths teaching assistant, produce an S plan. This method addresses a theme and aims to strip it down into smaller steps by which teachers can reflect on the strategies to move learners along the "learning journey". Once the steps have been identified teachers can focus on how best learners can master the conceptual & procedural skills and knowledge of each one in turn. Where possible links are made to previous learning. Many of these steps are planned for using the Inspire Maths Teacher Guide and NCETM prioritisation documents but knowing the journey in advance and planning for further opportunities ensures that the needs of all children are planned for and nothing is left to chance.
This planning is visible in the classroom and is a working document shared with the children.
Class teachers intervene when a child/children are having difficulty keeping up. This may be within a lesson or during timetabled ‘Keep up time’. There may also be occasions when children are pre-taught a concept prior to whole class teaching. Where appropriate ‘Keep Up’ time may also be used to pre read content to a child/ group of children. Where appropriate, Ready to Progress exemplification is used to support struggling learners. If there are children who do not require specific keep up then the time should be used to practice mental skills e.g. time tables, finish off earlier work, attempt additional challenges or explain their learning. Rapid graspers are challenged by having opportunities to deepen their learning through carefully chosen challenges/ problem solving activities.
The first few years of a child’s life are especially important for mathematics development. Research shows that early mathematical knowledge predicts later reading ability and general education and social progress(ii). Conversely, children who start behind in mathematics tend to stay behind throughout their whole educational journey(iii). The objective for those working in Early Years, then, is to ensure that all children develop firm mathematical foundations in a way that is engaging, and appropriate for their age. The materials in this section (https://www.ncetm.org.uk/resources/51439 of the website) are primarily designed to support Reception teachers (those working with 4-5 year olds), and are based on international research. The materials are organised into key concepts (not individual objectives), which underpin many early mathematics curricula. The typical progression highlights the range of experiences (some of which may be appropriate for younger children) but the activities and opportunities could be developed across the Reception provision.
There are six key areas of early mathematics learning, which collectively provide a platform for everything children will encounter as they progress through their maths learning at primary school, and beyond:
- Cardinality and Counting
- Shape and Space
You can explore these areas in further detail in a special Early Years episode of our podcast with Dr Sue Gifford and Viv Lloyd.
These areas form the fundamental mathematical basis of a CBeebies series of five-minute animated programmes called Numberblocks. The NCETM has provided support materials linked to the Numberblocks programmes. These are designed to help Early Years practitioners draw out and build on the maths embedded in the stories contained in each episode.
At Barrow Hill, the Foundation stage use the principles of mastery to ensure the children are building firm, mathematical foundations. The learning environment enables the children to see and experience maths through play and interaction with adults and other children. Early use of concrete resources such as tens frames, Numicon, counters, objects etc support children with their understanding of maths. The environment in Early Years is language rich and children are encouraged to use the environment to support their learning. In addition to the continuous play and adult led activities there is also a daily 20 minute discrete lesson for all reception children. The NCETM, White Rose Maths Hub and Inspire Maths are used to plan and prepare these lessons. This ensures the five elements of mastery are promoted in Early Years.
In 2021-2022, we have been part of the DfE Mastering Number programme organised and led by NCETM. The project aims to secure firm foundations in the development of good number sense for all children from Reception through to Year 1 and Year 2. The aim over time is that children will leave KS1 with fluency in calculation and a confidence and flexibility with number. Attention will be given to key knowledge and understanding needed in Reception classes, and progression through KS1 to support success in the future. Staff participants in the workgroup will:
- develop skills in working in a professional learning community, reflecting with other colleagues on their own practice, and refining skills through support and challenge within a community
- develop a secure understanding of how to build firm mathematical foundations with a stronger subject and pedagogical understanding for EYFS and KS1
- work to develop intentional teaching strategies focused on developing fluency in calculation and number sense for ALL children
- develop understanding and their use of appropriate manipulatives to support their teaching of mathematical structures.
Children spend 15 minutes every day following the Mastering Number programme. In EYFS, this is enhanced through the continuous provision, learning environment and interactions with children throughout the day. In Y1/2, Mastering Number is taught in addition to the daily 45 minutes mastery lesson.
From year 3 onwards, children practice their times tables every day to build fluency, accuracy and automaticity. The booklets used in school have been carefully created by the NCETM to reduce cognitive load, build on from known facts and learn times tables systematically. Each child completes a 2-minute times table challenge, ideally twice per day. The challenges are times but children may go over the time if needed; they just record their time using the class timer. This is a low threat, high challenge quiz where children aim to beat their own times and own scores. The booklets are worked through in the following order, to match the order suggested in the National Curriculum Guidance (July 2020)
Booklet A: 10 times table
Booklet B: 5 times table
Booklet C: 2 times table
Booklet D: 4 times table
Booklet E: 8 times table
Booklet F: 3 times table
Booklet G: 6 times table
Booklet H: 9 times table
Booklet I: 7 times table
Booklet J: 11 times table
Booklet K: 12 times table
Within each booklet there are 22 tests, ordered as follows:
- Tests 1 – 4: First half of the new times table
- Tests 5 – 8: Second half of the new times table
- Tests 9 – 12: All the new times table
- Tests 13 – 22: The new times table combined with previously learnt times tables.
There are two exceptions to this, the 10 times and 11 times table booklets. As these are quicker for children to learn, all the facts are introduced at once rather than split into ‘first half’ and ‘second half’ of the times table.
- Children must work through the booklets in the order provided in the table above, otherwise they will meet facts in tests 13 – 22 that they have not yet learnt.
- The NC Guidance explains that the facts it is essential to master in Year 4 to be ready to progress to Year 5 are the facts up to 9 x 9, as these facts are the ones that occur as within column calculations in formal written methods. Therefore, Booklets B – I include facts with multipliers of 2 – 9 only.
- Times tables facts with a factor of 11 and 12 are only introduced in the final 2 booklets, so that most of the time can be spent learning the most essential facts. However, all booklets should be complete so that children are secure in all times tables facts prior to the Year 4 check.
- Facts with a multiplier of 0 and 1 are not included, as these do not need to be learnt in the same was as other facts.
- The 10 times table is of course also essential for progression, and this is learnt in booklet A, and then included in tests 13 – 22 in each of the subsequent booklets.
- About 20% of the facts are expressed as division facts, to give children practice deriving division facts from learnt multiplication facts.
In addition to the Times Table Booklets, children have access to Times Table Rockstars. Practicing on the app encourages the children to respond with speed and accuracy. Children play the app both at home and school. This prepares the children well for the statutory multiplication check in Y4 and for automaticity in upper key stage two reducing cognitive load during more challenging mathematical concepts.
The impact of our mathematics curriculum is that children are fluent in the fundamentals of mathematics. They are able to solve problems by applying their mathematics to a variety of questions and have resilience when faced with more challenging and complex problems. Through pupil voice and pupil interviews, we will ensure that children are enjoying mathematics and feel they are received appropriate support and challenge. Where there are gaps in knowledge, children are given additional support to keep up with their peers.
At the end of reception, we report to parents the age related expectation levels. Children in foundation stage are assessed within the Foundation Stage Framework and their progress is tracked termly using EAZMags. At the end of Key Stage 1, children are assesses using the national SATs tests. It is reported to parents whether child has reached the expected levels of attainment.
In year 4, the national Multiplication Check is administered to determine whether children can recall their time tables fluently, which is essential for future success in mathematics and to identify children who have not yet mastered their times tables so that additional support can be provided.
Progress and attainment are monitored daily though assessment for learning strategies. Children in Key Stage 2 are assessed termly using NFER tests. At the end of Key Stage 2, national SATs tests assess if the children are meeting the national expected standard, are working towards or are working at greater depth. This information is reported to parents.
Children will develop a lifelong enjoyment of mathematics and will understand how the concepts they have been learning relate to real life.
The Maths lead will monitor for appropriate pitch and progression, monitoring will take the form of:
- Lesson observations and feedback;
- Learning walks and pupil voice conversations;
- Planning scrutiny followed by support where necessary;
- Book/work/digital media scrutiny
- Monitoring of book band progression and 1:1 reading via GoRead
- Quality of learning environments including reading areas across school
- Purchasing and organizing resources
- Keeping up to date with research and best practice
The Maths Lead conducts staff audits and along with SLT, designs appropriate Professional Development for staff in school. The Maths Leader models excellent practice leading by example and supporting colleagues in school to develop their knowledge and skills of the subject.
The Maths Lead ensures that school engages with workgroups led by the East Midlands West Maths Hub. As an NCETM Primary Mastery Specialist, the Maths Lead receives high quality PD training which is disseminated to staff and improves practice in school.


Fascinated by both art and science, especially astronomy and astrophysics, Dorothea Rockburne believes that art and science originate from a single source and are informed by the same reality. In her paintings, many which look like swirling astrological subjects, she expresses her sense of harmony, correspondences and patterns that she regards as ultimate beauty with metaphysical significance. Some of her work is also described as minimalist and geometric because she has folded canvas into parallelograms and triangles with variations of surface texture.
In the 1970s and 1980s, Rockburne relied upon the Fibonacci series, a set theory of mathematics of chance as taught by the French mathematician Henri Poincare. She was also inspired by the early Italian painters Giotto and Ambrogio Lorenzetti.
A Canadian, she attended the Ecole des Beaux Arts in Montreal throughout her childhood and early teenage years and in the 1950s studied at the Black Mountain School in North Carolina.


brand identity, naming, copywriting, packaging
individual project @ The Shillington School in 2021
"Therefore, the stereotype of the mathematician does not correspond to reality and the characteristics of his/her profession are in some respects very similar to those in other scientific fields. But there is a unique characteristic among them. This feature has been highlighted in one of the most famous and cited descriptions of the mathematicians’ activity, written by the mathematician Godfrey Harold Hardy in his book ‘A mathematician's apology’: "A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas." Hence, doing mathematics is not just creating and demonstrating theorems. Doing mathematics is a form of art and every true mathematician is an artist. As painters create their works with brushes and colors, mathematicians create their works of art, namely theorems and their proofs, with ideas and their imagination is free to go in search of beauty. Although defining the concept of beauty in mathematics is certainly difficult, it is nevertheless intimately associated with elegance and simplicity and every mathematician develops his/her own aesthetic sense."
The Myth of Being a Mathematician by Renato Pelessoni
Hypatia (360-415 AD) was one of the first female mathematicians and one of the last great thinkers of ancient Alexandria. She believed that mathematics have a spiritual aspect and that numbers are the sacred language of the universe, teaching others of an ultimate reality beyond the reach of human thought and understanding. Hypatia was murdered for these strong beliefs, and much of her life has remained a mystery as no written records of her work survived.


This week we’re petrified.. petrified wood that is. Learn what it is and how it’s made – then we tie it all up with a fun paper about mathematical ways to tie neckties.
Fun Paper Friday
- How many ways are there to tie a necktie? Find out in this week’s fun paper!
- Fink, Thomas M., and Yong Mao. “Designing tie knots by random walks.” Nature 398.6722 (1999): 31.


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Leonhard euler was a swiss mathematician counted among the greatest mathematicians of all times this biography of leonhard euler provides detailed information about his childhood, life, achievements, works & timeline. Grade 12 definition essay timeline for geometry comments (-1) science biology comments (-1) chemistry comments (-1) earth science. What is geometry, geometry is perhaps the most elementary of the sciences that enable man, by purely intellectual processes, to make predictions (based on observation) about physical world. The history of geometry geometry's origins go back to approximately 3,000 bc in ancient egypt ancient egyptians used an early stage of geometry in several ways, including the surveying of land, construction of pyramids, and astronomy.
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Book of ezra timeline book of nonrenewable energy answer key holt geometry 10 3 answers houghton mifflin geometry chapter14 answer key help answering essay. Robert hooke's theories and discoveries formed the basis for some of the robert hooke timeline timeline hooke had become the gresham professor of geometry. Read and learn for free about the following article: introduction to greek architecture.
History of mathematics: arithmetic, intuition and logic, philosophy of geometry add keywords: timeline, bibliography. The pythagorean theorem is one of the earliest theorems this famous theorem is named after the greek mathematician and philosopher, pythagoras. History of regents examinations: plane geometry plane although most of the examinations still retain questions of the free answer or essay type. Major figures of the scientific revolution dr robert a hatch the conclusions of mathematics, especially those of geometry, are demonstrable. This dynamically illustrated edition of euclid's elements includes 13 books on plane geometry, geometric and abstract algebra, number theory, incommensurables, and solid geometry.
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Civil rights timeline worksheet answers 2015 2015 waec answer on literature bth essay and objective 2015 geometry regents answer key 2015 preap energy 1 answer. The story of mathematics historically, it was regarded as the science of quantity, whether of magnitudes (as in geometry) or of numbers (as in arithmetic).
Xem video study effectively for the gre this gre test prep course prepares students for the analytical writing, verbal reasoning, and quantitative reasoning sections of the exam, and includes gre practice questions, sample essay. A time-line for the history of mathematics a course in the history of mathematics cannot overlook monumental work in geometry 1640 ce pascal's essay pour. Euclid enters history as one of the greatest of all mathematicians and he is often referred to as the father of geometry. The latest tweets from geometry (@geoliterary) twitter will use this to make your timeline better identity and home in her personal essay 'from here.


The fun, unique, and educational game Smart Darts 4 Kids is now available to buy from our online shop.
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3D, Art, C++, Data Visualization, Design, Electronics, GLSL, GLUT, Inspiration, Java, Jitter, MAT, Math Art, Maxmsp, Maya, MEL, OpenFrameWorks, OpenGL, Particles, Physical Computing, Processing.org, Reza, Scripting, Special Effects, Technology, UCSB, Visualization, Visuals, VJ
November 5, 2010
This is a post about a presentation I gave at LAVA: Los Angeles Visual Artists, a group of people dedicated to exploring new ways of creating and mixing visuals, VJs/DJs/Artists/Designers.
April 17, 2010
3D Field Flow is an exploration of invisible space, fluid flow, thermodynamics and dynamical systems. Empty space surrounds us, however is this space really empty? The space around us is governed by the rules of thermodynamics and physics and shows some interesting behavior when simulated and visualized in 3D.
April 3, 2010
LORMALIZED = Lorenz + nOrmalization + Real-tiMe + interActive + visuaLize + partIcles + reZa + procEssing.org + 4D
February 6, 2010
January 31, 2010
Recently, I have been exploring SuperShapes, which are organic shapes that are rendered by evaluating the superformula with different parameters. This formula creates some beautiful and very organic shapes that can be used in other graphics to make a dynamic graphic composition (either interactive or static). Doing this in Matlab or Mathematica is interesting, but I wanted to make something a little more interactive, minimal and fun to play with so I designed a application that can be used to create these shapes and render an image of them at a super high resolution.
November 23, 2009
This is an audio-reactive algorithmic visual art piece that uses the concept of charged particles and flocking to simulate a organism that is alive and composed of micro-organisms. The movement is rather pleasing thus I decided to exhibit the algorithm in a rather catchy video art fashion. Enjoy.
© 2014 Reza Ali


Vedic Mathematics Introduction
The subject of Vedic Mathematics has become a household name in recent years. In fact the subject of Vedic Maths is very ancient and is known in India for several thousands of years.The term Vedic mathematics indicates that mathematics which is related to the Vedas.Then, what is Veda? Veda means knowledge, which includes both the spiritual knowledge and worldly knowledge.
The Vedas are treated with highest reverence by all the followers of Sanatana Dharma. The traditionalists believe that the Vedas are eternal, that is, the Vedas exist for ever. The Vedas are also known as Sabda Brahma, as they are considered as the sound form of the Supreme God, Paramatma.
In addition to the intellectual debates of highest level on various aspects of spiritual knowledge, the Vedas extensively deal with the rituals also, that is Yajnas or, sacrifices, of several kinds, for the upliftment of the humanity. These rituals involve several topics which are directly related to mathematics. Hence a thorough knowledge of mathematics is essential for proper performance of the rituals.
Books of Vedas & Vedangas
The Vedas have several books under the headings of Rigveda, Yajurveda, Samaveda and Atharvaveda. To understand these Vedas, there is a need to study some more books, called Vedangas. The Vedangas are declared as six in number, and include Siksha, Vyakarana, Chandas, Niruktam, Jyotisha and Kalpa. Among them, the Kalpa, Jyotisha and Chandas involve mathematics extensively. In particular, The Kalpa, dealing with the preparation of altars, or yajnavedikas, utilizes several Geometrical principles, which are called as Sulba sutras. Presently few of them traced are in the names of Boudhayana, Apastamba, Katyayana and others.
The Jyotisha is made of three parts, siddhanta, jataka and samhita. Among them, the siddhanta bhaga involves intensive mathematical calculations related to the relative positions of the planets and other celestial bodies. For this they utilize spherical geometry, and Trikonamiti, or alternatively called as Trigonometry.
Because of the vast coverage of mathematics and its significance, the Jyotisha is adored from times immemorial. Lagadha, the great mathematician of India of about 1500b.c., states in his book of Vedanga Jyotisha that
Yathaa sikhaa mayuraanaam naagaanaam manayo yathaa
Tadvadvedaanga saastraanaam ganitam (/jyotisham) muurdhani sthitam
“Like the crest of a peacock, and like the gems on the hoods of serpants, the mathematics (Jyotisha) lies at the top of all Vedanga Sastras.”
Similarly the Chandas has lot of knowledge related to the mathematics like permutations and combinations.
Thus lot of mathematical principles were discovered by our sages, who include Surya, Pitamaha, Vasishtha, Medhatithi, Garga, Lomasa and several others.
Other Major Contributors in India
In addition to the sages, we have a long list of astronomer-cum- mathematicians like Varahamihira, Aryabhatta, Bhaskaracharya I, Bhaskaracharya 2, Brahmagupta, Mahaviracharya, Kalakacharya, Prithuyasas , Pavuluri Mallanna and a host of others. They developed the subject of mathematics beyond our imagination.
Because of the contributions of these stalwarts, India is known as the land of mathematics for several millennia. Its contributions include the digits, decimal system, Pi, zero, infinity and so on.
Spread of Vedic Mathematics to Other Countries
In course of time, the literature related to mathematics was taken from India to foreign countries. In fact a mathematician by name Kanka of Ujjain was taken to Arab countries and was requested to translate the books of mathematics from Sanskrit to Arabic language.It is said that Alzafer, under whose name the subject of Algebra is popular, adopted the Sanskrit numerals for the digits in his works.
Subsequently the subject of Indian mathematics spread to Spain, Germany, France, England and other countries.
Names of Indian Mathematicians Suppressed
During the alien rule, the same mathematics was introduced through English language,in the curriculum in India, but with the names of original Indian contributors suppressed.
For illustration, the Boudhayana siddhanta, related to the areas of the sides of a right angled triangle, is now known in the name of Pythogorus of about 500 b.c., who was born about three centuries after Boudhayana.
The theorem of interpolation, introduced by Govinda Swami of 300 b.c., is now known in the names of Newton and Gauss, born after a gap of about 1800 years.
The theory of earth revolving around the sun was recorded by Aryabhatta in 5th century a.d. However, it is known in the name of Copernicus who was born 1000 years after Aryabhatta. There are several examples of this kind.
Vedic Mathematics of Swami Bharati Krishna Tirtha Maharaj
It is not that only sages of ancient times developed Vedic mathematics. In 1960s, Swami Bharati Krishna Tirtha of Govardhan peeth of Puri Jagannath, authored a book and titled it as “VEDIC MATHEMATICS”. This book mainly contains description of 16 mathematical formulae, or sutras. Most of them are useful to handle the arithmatic at a very high speed.
The present series of lessons prepared under the banner of SVB, include most of the mathematical principles identified by Swami Bharati Krishna Tirtha Maharaj. In addition, the techniques given in Lilavati Ganitam and other related books are also covered.


BIG IDEA: Reasoning and Proportions
The work you see below builds on the work students did to interpret Animal Jump Graphs in a visualizing activity in math. Students thought about animal jump graphs they studied previously as a jumping-off point for this activity. In this activity students were asked to think creatively about data sets, proportions and then display that data. They needed to make decisions about how to display data creatively while showing clarity and precision.
Students used mathematical concepts such as measurement, intervals, area, data, proportions, ratios and ratio equivalents, factors and multiples.
Students then participated in a Gallery Walk whereupon they provided feedback including:
Name something you observed (without judgement)
Name something you noticed that the mathematician did to make the graph easy to understand
Give the mathematician constructive feedback.
You can ask your child more about the math we are doing in 6A and use the photographs of their work below as a reference point.


Half-life calculation by non-linear least squares curvefitting
In order to improve the statistical rigor and accuracy of the half-life calculation, the data for each RNA was fitted to an exponential function (of the form A = A0ekt) using a non-linear least squares algorithm implented in MATLAB (function nlinfit in the statistics toolbox which uses the Gauss-Newton method). The function nlparci was then used to estimate 95% confidence intervals for the two parameters (A0,low, klow, A0,hi, and khi) which were then used to calculate upper and lower bounds of the half lives. Half-lives were calculated for 2,679 RNAs for which A0,low was positive (95% confidence of detection) and khi was negative (95% confidence of decrease). Half-lives are reported in minutes. 907 half-lives calculated by both methods are plotted in figure 1.
Transcripts which fall along the line fit an exponential degradation pattern, whereas those that fall off the line do not. Those above the line degrade more slowly at the beginning of the timecourse (over their first 2-fold change) and more quickly later on. Those below the line have the opposite pattern.


For example, there is data like the picture below, how much is the price of an Apple iPhone XS?
What is the formula to find the price, there are two criteria, manufacture=”Apple” and Model=”iPhone XS”. Is it possible to use the VLOOKUP function or is there another solution?
If the lookup result is a number then forget the VLOOKUP function, you can use mathematical functions and produce a simpler formula, one of them is the SUMIFS function.
The result is $1,340
Another mathematical function that you can use to look up a number with multiple criteria is the SUMPRODUCT function.
The last solution is to use the SUM function, not the usual SUM function but the SUM function that processes an array formula.
Because it is an array formula, you can’t end the writing of the formula by pressing the ENTER button but by pressing the CTRL+SHIFT+ENTER button simultaneously.
For example, there is data like the picture below, where does Evelyn Thao live?
The limitation of the VLOOKUP function is only lookup for one condition, that is lookup_value. If there are two or more criteria the easiest way is to concatenate all the criteria in the lookup_value.
The next step is to create the helper column that contains a merge of two columns in table_array. The helper column will be the first column of table_array, where the VLOOKUP function will look for lookup_value that has been merged from two criteria.
The Formula for Helper Column
The Formula to Lookup the State
The solution #B uses the helper column too. The difference is solution #A using a worksheet for the helper column location while solution #B using a formula for the helper column location.
The CHOOSE function will occupy the table_array argument of the VLOOKUP function; the role is to create a virtual helper column in the formula. The virtual helper column consists of two columns. The first column contains a combination of first name and last name. The second column contains the name of the state.
Because it is an array formula, end the formula writing by pressing the CTRL+SHIFT+ENTER button simultaneously.
No helper column in the worksheet but the VLOOKUP function can do vlookup with two criteria.
The solution #C is similar to solution #B, creating a virtual helper column in the formula. If the solution #B uses the CHOOSE function to form a virtual helper column. Solution #C uses the INDEX and MATCH functions where the MATCH function is assigned to create a virtual helper column.
End the formula writing by pressing CTRL+SHIFT+ENTER simultaneously, because the formula above is an array formula
For Numeric Result
The SUMIFS function is the best solution, simple and answers the questions. If the SUMIFS function is not available in your excel (seriously? you should upgrade your excel version 😊), then you can use the SUMPRODUCT function, or you can use SUMIF with multiple criteria.
For Non-Numeric Result
The easiest solution is to use the VLOOKUP function and the helper column. If you want no helper column in the worksheet, then you can use the virtual helper column in the formula.
There are two options, The VLOOKUP and CHOOSE function or INDEX and MATCH function, both is an array formula. Choose the most comfortable formula for you.


Welcome to Second Grade!
“We may all be different,
but in this class we swim together!”
For the detailed Peek at the Week go to the Documents page!
Reading: This Monday, we began our new Reading unit on Ancient Greek Myths. Students are taking the information they learned about Ancient Greece and applying it to reading all different Greek Myths. At the end of the unit, each student will write their own Myth!
Math: We also started our third unit in Math, Place Value. So far this year the students have learned about addition and subtraction and measurement. This unit on Place Value is one of the most important units all year. This is where students build their foundational understanding of Place Value that will be built on every year.
- Book Fair ends this Friday 11/18!
- Aldrich Art Museum Field Trip Monday 11/21!
- No school Wednesday November 23!
(203) 857- 0306, ext. 119


Continuous Compounding of interest
If an annual interest rate compounds semi-annual, then it should be compounded twice a year. If an annual interest rate compounds quarterly, then it should be compounded 4 times per year. If an annual interest rate compounds monthly, then it should be compounded 12 times per year. If an annual interest rate compounds daily, then it should be compounded 365 times per year. And if the compounding period becomes smaller, then the number of compoundings per year, m, becomes larger. In the limit as m goes to infinity, period interest, i, approaches zero. This case is called Continues Compounding of Interest. Using differential calculus, Continues Interest Single Discrete Payment Compound-Amount Factor (F/Pr,letter) can be calculated as:
r are affordable interest rate compounded constantly n is actually quantity of distinct valuation attacks age is feet regarding pure log (ln) = 2.7183
P = dos , one hundred thousand * ( P / F 12 % , step one ) + dos , 100 * ( P / F 12 % , dos ) + 2 , one hundred thousand * ( P / F twelve % , 3 ) = 2000 [ step one / elizabeth 0.several * 1 ] + 2000 [ 1 / e 0.twelve * dos ] + 2000 [ step one / e 0.twelve * step 3 ] = $ 4 , F = 2 , 000 * ( F / P twelve % , 2 ) + 2 , 100000 * ( F / P a dozen % , step one ) + dos , 000 = 2000 * age 0.12 * dos + 2000 * e 0.twelve * 1 + 2000 = $ six ,
Note: Another website links explains the way you use the newest excel function (EXP) so you’re able to calculate e raised with the energy out-of number:
In this video, I’m going to identify persisted compounding appeal, and i also will show you how exactly to estimate the future and expose really worth in the eventuality of continuous compounding.
When we have more and compounding period a-year, then compounding several months will get shorter and you will faster. Up coming number of compounding several months a-year, meters, will get huge and you will huge. So in this situation, future worth can be computed while the present time, proliferate 1 in addition to i stamina n multiply m. M ‘s the number of compounding period a year. I is the months interest, which translates to roentgen divided of the meters, and you can r is the affordable interest, which is m proliferate we.
In the limitation since meters goes toward infinity, several months interest i, that’s r split up from the meters, methods to 0. In this instance, it is called continuing compounding of interest.
Now, let us calculate material-number grounds, F over P, or coming really worth grounds to own proceeded interest. Which means this grounds equals 1 in addition to i electricity n multiply yards, and we normally write i given that roentgen over m.
Today, we have to assess the fresh maximum as meters visits infinity. In such a case, so it term remedies for 0, and this title solutions to infinity. Therefore we can be extract an elizabeth title right here, therefore determine brand new restriction because elizabeth electricity rn.
So substance-count foundation, or coming value basis, for persisted attention could well be elizabeth electricity registered nurse, or coming value will likely be computed as the P proliferate by e power rn. F is the coming worthy of to own persisted compounding attention. Roentgen is the moderate rate of interest compounded continuously, n, quantity of distinct valuation attacks, and is 12 months, two year, three years, and so on. And you may age is the legs out of natural diary.
Furthermore, we could determine the present worth in case there is continuing Little People dating compounding appeal. The present really worth basis translates to the inverse out-of coming worthy of basis. Therefore expose worth might be computed once the P means F split up by the elizabeth energy roentgen,n. P is the establish well worth to possess proceeded compounding appeal.


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A team of students from University School in Milwaukee took first place in Milwaukee School of Engineering’s annual “OP”portunity Math Conference. The team was coached by Michael Bartl. The OP Conference gives high school students the opportunity to demonstrate excellence in academic pursuits. The competitions challenge the skills and abilities of students at all levels. For the OP Math competition, students worked to solve problems in a number of categories including: algebra, geometry, advanced math and problem solving. There also was a team competition, in which 24 teams participated. The team from University School completed the most problems correctly to win first place. Whitefish Bay (Wis.) High School took second place and Homestead High School (Mequon, Wis.) took third place in the competition.
MSOE is an independent university with 2,600 students. MSOE offers 18 bachelor’s degrees and 10 master’s degrees in the engineering, engineering technology, architectural engineering and building construction, computer, business, nursing and health-related fields. The university has a national academic reputation; longstanding ties to business and industry; dedicated professors with real-world experience; and extremely high placement rates and starting salaries. MSOE graduates are well-rounded, technologically experienced and highly productive professionals and leaders.
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Math solver calculator
In this blog post, we will show you how to work with math solver calculator. Math can be a difficult subject for many students, but there are ways to make it more manageable.
The Best Math solver calculator
In the algebra stage, I think the most important thing is to develop your mathematical modeling ability. Solving algebraic equations is just a step-by-step and practice makes perfect operation. However, how to transform practical problems into algebraic solvable abstract problems is a more challenging and practical task. Mathematical modeling is not necessarily very important to the exam (because most of the math exam focuses on solving), but in real life, especially in scientific research of science and engineering, mathematical modeling ability is a hard core ability. If a simpler and more accurate mathematical model can be established, it will almost be the final victory, and the rest of the solution will be left to the computer. The mathematics part is divided into two parts: usable calculators and unusable calculators. It mainly examines algebra, problem solving and data analysis, introduction to higher mathematics, geometry, trigonometry and other related contents. Wherein: IB math exam has strict requirements on the setting of calculators. If the invigilator clears the setting of calculators during the exam, you need to be able to quickly change it to the original mode. Therefore, it is also necessary to spend some time doing calculator exercises. If you can't, you can ask pineapple's online teacher to demonstrate it to you. This is due to another great creation in the history of Mathematics: analytic geometry. Since the advent of analytic geometry, geometric problems with strong skills can be solved by algebraic methods and programmed and step-by-step methods. It was the invention of analytic geometry that communicated the two mathematical fields of geometry and algebra. Since then, the two fields can learn from each other's advantages and gradually integrate. Therefore, analytic geometry is a great tool, and its invention is a leap in the history of mathematical development. In ancient Greece, geometry was the whole content of mathematics. In addition to the appearance of geometry, algebra often relied on geometric methods to solve and demonstrate. Euclid, a mathematician, wrote one of the most important mathematical works in human history, called the original geometry. Therefore, classical geometry is also called Euclidean geometry. In European geometry, people can solve and prove almost all problems in plane geometry through several axioms [Note 3] and ruler and gauge drawing. Geometry is also a highly skilled field, and many problems need to be solved by skillfully adding auxiliary lines or using highly skilled methods. However, this is not too troublesome. With the gradual deepening of your mathematics learning, you will find an interesting phenomenon: in junior high school, mathematics will be divided into two branches: algebra and geometry. After high school, the two branches were merged again. Even in all the courses of higher mathematics, we can hardly touch the geometry course of drawing with ruler and gauge any more. You can't even see a compass on a mathematician's desk. For example, in high school mathematics, the sum of the general terms of the number series is a relatively difficult problem, and the solving skills are varied. The number series is often regarded as the final item in college entrance examination mathematics. For example, the following question: As with equations, analytic geometry is not the sooner the better. Compared with the Euclidean geometry, it not only makes solving problems become programmed, but also greatly weakens mathematical thinking ability. Therefore, it is only suitable to use analytic geometry to solve problems after fully training the thinking of planar geometry and mastering the physical concepts such as coordinate transformation. Otherwise, if we encourage the sprouts, copy mechanically, and turn the solution of geometric problems into a set of formulas, we will have no way to start when facing complex problems, which is harmful to mathematical learning. This is what Dad wants to explain to you. People usually think that quick oral arithmetic and familiar formulas is a standard of strong mathematical ability. In fact, it is only the ability to solve problems (computational ability) in mathematical ability, and it can not be directly equivalent to mathematical ability itself. We should know that the Olympiad is solved in the known field and the fields award is solved in the unknown field. There is a difference between the two. We cultivate students' problem-solving ability, ignoring innovation, so we can only produce mathematical engineers, and it is difficult to produce mathematicians. Therefore, it is more important to cultivate students' innovative ideas. I sincerely wish the God and man who really love mathematics to achieve results. The 2022 new college entrance examination volume I thoroughly implemented the general plan for deepening the reform of education evaluation in the new era proposed by the CPC Central Committee and the State Council, steadily promoted the reform of the college entrance examination, built an examination content system that guides students to develop in an all-round way in morality, intelligence, physique, art and labor, changed the relatively fixed form of examination questions, increased the innovation of open questions, used open questions to test the core qualities and key abilities of mathematics, and reduced the phenomenon of rote memorization and mechanically brushing questions. The college entrance examination of mathematics actively implemented the requirements of the overall plan, gave full play to the selection function of the college entrance examination of mathematics, and comprehensively examined logical thinking, operation solving, spatial imagination, mathematical modeling and innovation ability, especially the ability of logical thinking and operation solving, throughout the examination paper. The background materials of the test questions are closely related to the social and economic development, production and life reality of the country. For example, question 4 takes the south to North Water Diversion project, a major construction achievement in China, as the material, and integrates the examinee's spatial imagination, mathematical reading and understanding, and computing and solving abilities. It also puts forward corresponding requirements for mathematical core qualities such as mathematical abstraction and mathematical modeling, so as to guide the examinee to pay attention to the great achievements of socialist construction and increase their sense of social responsibility. It mainly consists of parts that can't use calculators and parts that can use calculators. It mainly examines problem solving and data analysis, core algebra, and basic knowledge of higher mathematics. You can't use the math part of the calculator for 20 questions in total; There are 38 questions in the math part of the calculator, mainly multiple-choice questions, and some questions are short answer questions. After a certain amount of analysis, reasoning and mathematical ability, the known conditions of the problem are skillfully combined with the knowledge we have learned, and the problem is solved. It is extremely happy to analyze and solve such mathematical problems, which is the charm of mathematics. It is also a good way to teach and learn mathematics. Learning to solve in this way can exercise one's mathematical ability and is also a good way to solve some difficult problems. This also means that God does not know whether the answers to many mathematical problems exist. Because the problem of solving indefinite equations is only a small part of mathematical problems, there are far more problems that can not be judged whether there are solutions in reality than those with answers. It is impossible to solve problems that can not even be judged whether the answer exists or not by calculation. This may be the boundary of mathematics. Therefore, artificial intelligence is not omnipotent, it only accelerates the process of solving problems with mathematics. We can't expect artificial intelligence to predict the stock market, and we don't need to worry that robots will rule mankind. Because mathematical ability has boundaries. What engineers need to do is to approach this boundary step by step.
We will support you with math difficulties
This app is so easy to use and I love how it has a solving step this app is really helpful when I got a hard time understanding math!! Great explanations and amazing fast speed of calculations and no words for accuracy it is brilliant, improved then a previous
It's a great app for students when they have problems solving equations. It guides you through the steps you have to make in order to solve the equation. You can even get further info if you didn't understand one of the steps. I think it's amazing, but don't use it to do your entire homework


The main attraction of pair-matching on strongly predictive baseline risk factors is the potential increase it brings in statistical efficiency and trial power. Dealing first with the case of a quantitative outcome measure, let denote the difference in means for the jth pair of clusters, j =1,2,...k. Then the variance of dj is given by 2σ2(1- ρM), where v denotes the variance of the outcome measure and the “matching correlation” ρM denotes the Pearson product-moment correlation between and . This simple result shows that the matched-pair design will always be more powerful than a completely randomized design provided ρM is positive. However this result ignores the difference in degrees of freedom used to test the effect of intervention in the two designs. Thus in the completely randomized design the analysis would typically take the form of a two-sample t-test with 2(k-1) degrees of freedom, while for a pair-matched design, it would typically take the form of a paired t-test with only k-1 degrees of freedom.
This discrepancy will have little impact on power in trials enrolling, say, 30 or more matched pairs. However logistical and cost considerations dictate that many CRTs, particularly those designed to evaluate community-based interventions, are forced to enroll far fewer pairs. The question then arises as to what point the gain in efficiency due to pair-matching on important baseline risk factors outweighs the loss in efficiency resulting from halving the available degrees of freedom. This question was addressed by Martin et al., 1993, who used numerical evaluation to conclude that if the number of pairs k is 10 or less, the pair-matched design should only be used if the investigators are confident that the value of ρM is at least 0.20. More generally they stated "It is unlikely that effective matching would be possible for small studies. Matching may be overused as a design tool." This point was also made by LaPrelle et al., 1992, who stated that matching on variables poorly related to outcome will "do little but reduce power by shifting the unit of analysis from the individual community to the pair of communities."


Date registered: January 10, 2017
Send Jwolff3 a Private Message
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- A beechwood box with lid
- Beechwood skittles
- Plywood number tiles and counters
Like all Montessori mathematical experiences, the number tiles, counters and skittles are all colour coded where green = units and thousands, blue = tens and red = hundreds.
Tips & ideas
This experience supports children in learning the written symbol of numbers as they had previously been using the representation of numbers through the skittles and Golden Beads activities.
Here children are able to practice the arithmetic equations of addition, subtraction, multiplication and division. Children are also able to further investigate the decimal system as they explore large numbers.
Suitable for Age Group
- 2 - 3 years
- 3 - 4 years
- 4 years +


There are many worse ways to do research for a book. Simon Singh, a lifelong TV addict who “watches everything and anything on television, except for dramas”, would spend all day parked firmly on his couch binge-watching episodes of The Simpsons, freeze framing every time he saw a number appear on screen, hoping to catch some obscure mathematical joke made by the show’s writers, a disproportionate number of whom have university degrees in math or physics (all of this, much to the chagrin of his journalist wife Anita Anand, who would spend her days in the British Library, researching the life of Sophia Duleep Singh, the suffragette granddaughter of Maharaja Ranjit Singh she is writing a book about).
The result of all that effort is The Simpsons and Their Mathematical Secrets, a book that uses those mathematical references as starting points to tell stories about the maths involved. The math jokes are aplenty, both in the book (which has a series of exam-paper style set of jokes with the number of points you get if you either laugh or cringe at them) as well as the series. Some of them are highly obscure gags that require both a keen interest in mathematics as well as a keen eye for one to even notice, let alone understand. Others are lazy, often cringeworthy maths puns. In the episode ‘Simple Simpson’ (2004), for instance, Homer disguises himself as a superhero called Simple Simon, Your Friendly Neighbourhood Pie Man, punishing evildoers by flinging pies in their faces. At one point, a bystander remarks, “We all know ‘πr2’, but today ‘pie are justice’.” It’s a non sequitur, one that writer Al Jean, a Harvard math graduate who introduced the joke into the script, dismisses as an old chestnut probably created by someone from 1820s, but Singh uses it to talk about the meaning of π, of Archimedes’ and latter methods used to estimate its value, an anecdote about a US state legislature’s attempts to legislate the value of π. It’s classic learning by distraction, exploiting man’s love for the yellow denizens of Springfield to teach him some maths.
It is a skill Singh specialises in, making mathematics and science accessible for the lay reader. He has in the past written bestsellers about the Big Bang, cryptography and Fermat’s Last Theorem — rarely the stuff bestsellers are made of — breaking down complex scientific theory into digestible chunks and garnishing them with some of the many riveting stories in the history of science. “It’s really important to explain the math and science. My books have a lot of history in them, a lot of biography, many odd and weird things. But they must explain some science. The reason for writing books like this is that they reach three audiences. One is the core audience of people like me; I write books I want to read. So the geeks and nerds who are like me will read my books because they have that same interest that I do. That’s great, but then there are also two ends of the other spectrum. There are people who’re probably a bit older, who were scared of science, but also curious. It’s great when people say to me, ‘Oh, I always hated mathematics, but I read your book on Fermat’s Last Theorem and now I understand why it’s beautiful.’ Or, there are the younger people, who are thinking about what they’re going to do with their lives. Teachers have a lot of hard things they have to teach, like calculus or Newton’s Laws of Cooling. Some of it is not so interesting, and I have great admiration for teachers. But if my books can come in and say, ‘Once you do this calculus, there are these incredible things you can do later on,’ then that’s maybe the most important thing.”
Singh believes that both his background as a teacher (he has a PhD in particle physics) and as a television presenter (before writing Fermat’s Last Theorem in 1997, he worked in the BBC’s Science and Features Department) contributed in allowing him to understand “how other people struggle with ideas that you might not find so complicated, how to engage and interest them”. A transition from a PhD at Cambridge and CERN, Geneva, to a career in television isn’t the most obvious one. “In my final year,” he says, “I could see other people who were just sailing through their PhDs. If I was trying to understand something, they would understand it before me. If I was trying to find a solution to a problem, they would get there before me. So I thought, ‘Those are the people meant to be scientists’. I thought if I leave being a scientist, I should stay within science. And I thought that the best thing would be to become a science journalist.”
For many of the writers of The Simpsons, this transition from Ivy League math degrees to comedy writing wasn’t the result of a similar inferiority complex, but a decision to follow their dreams. At least four of them had worked for Harvard Lampoon while in college. Singh sees a connection between math and comedy. “Why a mathematician is funny…” he begins, before saying that most people think it impossible because “most people are outside that world”. “There’s no easy answer,” he says, “but I couldn’t ignore it. I let the writers put forward their own theories. David X Cohen emphasised the intuition side of it, that mathematicians have a very good intuition over whether a problem can be solved and what that solution is. Bad mathematicians pick impossible problems, and even if they pick soluble problems, they do not know how to solve them. It’s the same with comedy. If you’re a comedian, you’ve got to know whether this scenario is funny, and if it is, how do you find the joke? Other people said that it’s also the determination and the stamina, because again with a mathematical problem, you might have to work for hours, days, weeks banging your head against a wall trying to solve it. Similarly, if you’re doing a 20-minute The Simpsons episode, it’s a technically difficult story to tell and you need that stamina to really turn a story idea into a beautifully crafted episode. So people have lots of different ideas, but the one common theme that seemed to emerge was this idea of logic. Mathematicians love logic. They love playing with logic; they love bending logic; they love stretching it; sometimes, they even break it. When you break logic, you get the illogical. That’s where the humour is.”


Top honors is a free tutoring resource for middle school students looking for extra help in math. Tutoring sessions are held at every week in downtown Brooklyn locations, and the Upper West Side in Manhattan.
Saturdays, 10 a.m. - 12 p.m.
Saturdays, 1 p.m. to 3 p.m.
Wednesdays from 6:00 p.m. to 8:00 p.m. (begins in November, UWS only)
Top Honors is a not-for-profit, fundamentals-focused tutoring program that focuses on fifth, sixth, seventh, and eighth grade students who need help with basic math skills, are motivated to learn, and have strong adult support. They review student applications on a first-come, first-serve basis and admit students on a rolling basis throughout the academic year as space permits.


started 13th October 2016
I built a circuit which generates pulses at random times (see Phase Noise). To test how random they were I tried autocorrelation of the times between pulses and was surprised to find the lag 1 value was always -0.5. Eventually I read in  ("5.5.4. The Lag 1 Autocorrelation") that this value is expected. I could not see why and I could not find a derivation online. Hence this page.
The autocorrelation at lag k is defined as:
where ` z_t ` is the time series, μ is its mean value, ` σ_z^2 ` is its variance, and E denotes the expected value.
For a stationary process
for all `t`.
By the definition of `sigma` `rho_0` equals 1.
and ` E[(z_t-mu)]` is zero.
If ` z_t=r_t-r_(t-1)+mu ` with ` r_t ` a random variable with mean 0 then
Expanding the argument of E and removing the terms which are zero by the independence assumption
The best intuitive way of looking at this I can think of is to imagine three data values, the first and last will average out to their mean positions, the correlation between the difference between the middle point and the first and the difference between the middle point and last will always consist of a value less than the mean multiplied by a value greater than the mean.
Put it another way average values with a correlation of 1 with those with a correlation of 0 get a correlation of 0.5.
- NIST Special Publication 1065 Handbook of Frequency Stability Analysis - W.J. Riley
- Applied Time Series Analysis


I'm thinking for the balance of 2007 my lucky number is going to be 5. For the past few days the unlikely number 5 has been weaving it's way through my conscious and unconscious mind. Believe me I have better things to do than get distracted by a number, but I'm telling you as a number, 5 is persistant!
It's not easy changing your lucky number, is it bad luck to change your lucky number? Is your old lucky number still your real lucky number. Arghhhh, I didn't realize this would be so hard! But here goes... five good reasons for making 5 my lucky number.
1. My parent's celebrate their 55-year wedding anniversary today.
2. The number will be the only number in my birthday this year other than 0.
3. My in-laws will be celebrating their 50th wedding anniversary this year.
4. I met my husband on the 14th and 1 + 4 = 5.
5. My favorite car is a Porsche 911, in particular the 993. In case this one isn't obvious, 9 + 1 + 1 = 11, 9 + 9 + 3 = 21, 11 + 21 = 32, 3 + 2 = ... 5.


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Re: Waiter, there's a fly in my soup!
On Mon, 08 Dec 1997 20:27:33 -0400, geo wrote:
>Having replaced the timing belt on the 5kq I5 with the Paul Heneghan
>method of calibrating my wife, ie. placing my 110
>lb. green eyed beauty three feet out on the bar to get 330 lb/ft of
>torque on the damper bolt, I now have a new variable.
>>[ ... ]
>> Read your post re: 310 lbs of torque...
>> My recollection is this is not enough. The 310 lbs is the spec for when
>> using a torque multiplier.
>> You really want about twice that much. i.e. a 200 lb person on the end of
>> a three foot pipe.
>> Dave C.
>>[ ... ]
> It has been many years since I was in a physics class, but I'm assuming
>force = weight x radius with the axis being
>known. I really don't want to go at this sucker again, at least for another
>60k! Any help on this would be greatly appreciated.
Disclaimer: Fools go where angels fear to tread.
Apology: My belated apology to the list for being a smartass jerk the last
time this thread came around. Temperatures were running high then.
You are real close, Geo. The torque is the product of the force applied
(at a right angle to the radius of application) and the radius itself.
The trouble - and I do mean trouble - occurs when you add the
confusion of trying to measure torque directly with an instrument
calibrated for a different radius (moment arm) than the one you are
effectively using. If you can stay focused on your original
assumption, it will help you through the potential ensuing melee.
If a torque wrench - there, I've said it - is used in combination
with an extension to give greater leverage, a little math can
easily convert the torque readings to actual applied torque and
the other way round (provided the wrench and the extension are
kept in a nice straight line. Otherwise -gasp - it's trigonometry time).
This must appear in every shop math book in the world.
Let Lt be the effective length of the torque wrench, drive to handle mid-grip
" Lx be the effective length of the extension, drive center to drive center
" Tt be the torque reading from the wrench
" Tx be the torque generated at the business end of the extension
" F = the force applied (arbitrary amount for this problem) at mid-grip
Tx = F(Lt + Lx)
Tt = F(Lt)
The torque ratio is found by dividing one expression by the other.
Tx/Tt = (Lt + Lx)/Lt The force term cancels and does not appear
in the ratio.
The Audi documentation has generated some controversy in the
past because it gives a torque reading to be obtained using a special
extension tool (2079) without reference to the torque wrench
length. This seems to imply that the extension tool converts input
torque to output torque by simple arithmetic multiplication. Our
little torque ratio relationship above shows that this cannot be
since Tx/Tt is not a constant.
Fortunately, the raw torque at the bolt is also given as 450 Nm
(332 lb-ft) so you can always work out the correct wrench reading,
such as Tt = 332 Lt/(Lt + Lx) lb-ft. Phil has provided the appropriate
references from the RR engine manual. The torque readings with
and without the extension tool are 350 and 450 Nm. From this
torque ratio, 450/350 = 1.286, we can compute that the wrench
to extension length ratio is 3.5. Anybody got a 2079 lying about?
DeWitt Harrison email@example.com


Kevin, Alana and Uncle Norm..
Take one healthy measure of math, blend in two cousins and their wacky Uncle Norm. Next mix in some mayhem, music, a lot of laughs, and a big serving of learning. It’s a formula that amounts to plenty of mathe-magical fun with The Prime Radicals! This new live action series for kids aged 6-8 is compelling and entertaining – never didactic – and uses humourous, hands-on, real-world scenarios to make numbers cool for kids, based on the math curriculum for young learners. Stay tuned for The Prime Radicals season 2 in the fall of 2013!
More exciting episodes ...
The multi award-winning Canadian television series that has hooked children aall across Ontario is back for a second season. The Prime Radicals Season 2 officially launches on TVOKids on Thursday, September 5, 2013 at 6:30 p.m. in Ontario—and online across Canada at www.tvokids.com. Produced by Ottawa’s GAPC Entertainment, the series takes the mystery out of math and puts the fun back into learning for kids aged 6 to 8.
52 x 15 min.


A normal calculator, often referred to as a basic calculator or pocket calculator, is a simple device designed primarily for performing fundamental arithmetic operations. Here are the key characteristics of a normal calculator:
- Arithmetic Functions: A normal calculator can handle basic arithmetic functions, including addition, subtraction, multiplication, and division. It's ideal for everyday calculations like balancing your checkbook, calculating tips, or solving simple math problems.
- Limited Functions: Normal calculators typically have a limited set of functions and buttons. You'll find keys for numbers, basic operations (+, -, *, /), and possibly a percentage key.
- Compact and Portable: These calculators are compact, lightweight, and easy to carry around. They are battery-powered and fit easily in a pocket or purse.
- Affordable: Normal calculators are inexpensive and readily available. They are suitable for everyday use and are widely used in schools and offices.
A scientific calculator is a more advanced and versatile tool designed for complex mathematical and scientific calculations. Here's what sets it apart from a normal calculator:
- Advanced Functions: Scientific calculators are equipped with a wide range of functions beyond basic arithmetic. They can handle trigonometric functions (sin, cos, tan), logarithms, exponentiation, square roots, and more. These functions are essential for students and professionals in fields like mathematics, engineering, and science.
- Multi-line Display: Scientific calculators typically feature a multi-line display that allows users to see both the input and the result simultaneously. This is incredibly useful for tracking complex calculations.
- Constants and Variables: Scientific calculators often provide the ability to work with constants and variables, making them indispensable for solving algebraic equations and scientific problems.
- Programmable Features: Some high-end scientific calculators offer programmable functions, allowing users to create custom calculations and formulas. This is particularly useful in research and engineering.
- Notation Modes: Scientific calculators may support different notation modes, including degrees and radians, to accommodate various mathematical conventions.
When to Use Each Calculator:
Normal Calculator: Use a normal calculator for basic everyday math, such as addition, subtraction, multiplication, and division. It's perfect for quick calculations where advanced functions aren't necessary.
Scientific Calculator: Opt for a scientific calculator when you need to perform more complex mathematical or scientific calculations. These are invaluable tools for students, engineers, scientists, and professionals working with advanced mathematics.
In summary, normal calculators and scientific calculators serve different purposes, with the latter offering an array of advanced functions tailored to scientific and mathematical applications. Choosing the right calculator depends on your specific needs, so be sure to consider the complexity of your calculations before making your selection. Whether you need a basic calculator for simple math or a scientific calculator for advanced calculations, having the right tool on hand can make a world of difference in your work or studies.


[fee] = [PayIt2 fee] + [payment processor fee] f = $1.29 + (2.9%*[ticket price] + $0.30) f = $1.29 + 0.029t + $0.30
Profit, or the amount of money that finally gets to the organizer, is calculated based on:
[profit] = [ticket price] - [fee] p = t - (0.029t + $1.29 + $0.30) p = t - 0.029t - $1.59 p = 0.971t - $1.59
When the organizer opts to pays the fee, they're setting the ticket price and opting to get the profit left after the fee, which is simply found by the above equation. When the organizer opts to pass the fee to the buyer, they're setting the amount of money per item they want to receive. Therefore, to calculate the appropriate ticket price, we solve the above question for t:
p = 0.971t - $1.59 p + $1.59 = 0.971t (p + $1.59)/0.971 = t
Therefore, the above equation is used to set the ticket price the ultimately pays to cover the fees.


View This category in: USA > Arizona > Central Region > Maricopa County
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Teaching volume can be a daunting task. The materials I needed were not at my fingertips, so I needed to get creative. I knew I had one thing, and that was 3 tubs full of snap cubes. Why not have the students build the rectangular prisms, so they can break it apart and count how many it took to make it?
After I modeled and explained what volume is, I gave students the chance to build some rectangular prisms. On my Promethean Board I posted a shape where you can see the number cubes in each direction, and I asked the students to build a model of the picture on the board. Once they built it correctly, they had my permission to destroy it and count the number of cubes it took to build it, and they found the volume.
We practiced it a few more times and then I showed them the formula. The students would build the rectangular prism, destroy and count, then check with the formula!
Since I have taught volume this way, I will definitely continue this in the years to come. My students were able to conceptually see volume and how and why the formula works.
FREEBIE time! Below is a link for my Volume Anchor Chart Freebie!
Check out the other resources I have for teaching volume in my TPT store!
Until next time,