My Maths Key Stage 3 Answers

[Kahlil Algya]

Forthe first three weeks, one question is released every Wednesday. From Monday 14 October a question will be released every Monday, Wednesday and Friday with the final question of Stage 1 posted on Wednesday 20 November.Every correct answer reveals a piece of information that helps solve the Final Task.

The prize for the winning team is usually a maths hamper, containing a mix of prizes for individual team members and their school. It includes a free year-long subscription to Integral and a trophy for the school or college of the winning team!

Teams are asked not to use AI in Ritangle. The winning team will be asked to submit all their working for each question and it should be clear from this along with the timestamps associated with the submission of answers that AI has not been used.

When we explore maths for ourselves these days, we may have a spreadsheet, a graphing program, a CAS program and a programming environment open simultaneously, and we want Ritangle to have that flavour. We think it is reasonable to expect students to be able to use a graphing program and a spreadsheet. Programming knowledge will not, however, be required for the final question.

On the other hand, we accept that when working against the clock (such as while working on the final task) methods using technology may have outpaced more traditional methods. We bear this in mind when constructing tasks.

We have considered dropping the race-to-the-line element of the final task, and having a more qualitative task for those scoring fully on the final question. We have decided to shelve this alternative for now.

The winning team will receive a maths hamper, containing a mix of prizes for individual team members and their school. It includes a free year-long subscription to Integral, and a trophy for the school or college of the winning team. We reserve the right to substitute a prize of equivalent value but of less weight/bulk should the winning team be based abroad.

Scenario 1

The team scoring most highly on the final question will be declared the winner, subject to their working satisfying the judges.

Scenario 2

If there is more than one team with the highest score on the final question, the winner will be chosen, from such teams, as the team that submitted those answers first, subject to their working satisfying the judges.

Scenario 3

In the event that the above does not determine a winner, the winning team will be chosen at the discretion of the judges based on the answers submitted.

If there is a possibility a team has won, the judges will contact the Nominating Teacher to verify details of the team and their participation. If the answer is satisfactory to the judges then that team will be the winner. The decision of the judges is final. No discussion will be entered into regarding the decision over who is the winner. The winning team and the answers will be announced on this webpage and on the MEI Twitter feed.

Discover why quizzes are an easy way to learn and revise the KS1 subjects taught at primary school. Ideal preparation for the Mathematics SATS test papers taken at the end of Year 2 by children who are 6 and 7 years old.

The 99 quizzes in this section have clickable links below. Each quiz contains 10 questions, answers and helpful hints for Key Stage 1 Maths. Quizzes have titles that describe the subject and each one aligns with the KS1 National Curriculum for children aged 5 to 7 in Years 1 and 2.

Mathematics might be one of the trickier subjects for some students (or easier, for those who love numbers) but either way, our quizzes are fun and engaging. We take all the National Curriculum material and pop it into easy-to-digest quizzes that are enjoyable enough to keep students focussed but also challenge them. Hooray for non-complicated revision!

And you already know maths is important. Not only is it likely there will be class tests but students in Primary schools will also have to sit SATS tests with a maths paper. But don't worry, there's plenty of time to prepare! We've got revision covered. The Maths SATS consist of two separate papers: 'Arithmetic' and 'Problem Solving and Reasoning'. The good news? We tackle both areas in the quizzes, meaning revision doesn't have to be dull and tiresome! Phew.

It's not just about school and tests either. Basic maths is important for everyday life! People use maths a lot, even if they don't work as a mathematician or a maths teacher. Simple things like adding up the cost of shopping, or maybe working out how much money to tip the waitress, all involve maths. It might even mean working out how many week's pocket money it'll take to buy that new game...

A great set of maths puzzles for upper primary children. All answers are given. Many teachers use these as a weekly challenge. They are ideal for printing out in colour and laminating, making a long lasting resource.

In this article, members of the NRICH team explain the process they go through when they choose solutions to publish on the site. To have a go at the current live problems, visit the Primary or Secondary live problem pages, or to see the most recent solutions, visit the Primary or Secondary solutionpages.

Each time you visit the site you will see that there are some "live problems" which are open for solutions. This means we are inviting students to send in thoughts, ideas, workings out and solutions, and then we'll publish them after a suitable time so that our archives are complete with both problems and solutions. On average problems remain live for about six weeks. They have a "Submit asolution" link to the left of the Problem title.

As well as wanting to showcase the hard work and effort that has been put into solutions, we know that lots of students, teachers and parents find it useful to look at the solutions to the problems in our archive.

The first decision to make is whether a solver has sent us an "answer" or a "solution". An answer is brief and just contains answers to the questions we've posed. A solution may not be complete, but will include the solver's ideas, why they chose a certain method, and explanations of what they noticed. We want someone looking at the published solution to a problem to get some understandingabout the sort of thought processes that led to the answer, so they can learn from someone else's work and become a better problem-solver.

Secondly, we need to make sure that the solution is mathematically correct. If there are one or two minor errors, we will correct them and publish the solution, but if a solution showed a major misconception or the solver didn't really explain their method, we wouldn't publish their solution. Of course if a solution began very clearly but had lots of errors towards the end, we might publishjust the first part of that solver's work.

At Stages 1 and 2, to begin with we look out for solutions that perhaps tackle just the first part of the problem and we often publish these at the top of the page. We would then choose solutions that address the question more fully and we often order them to reflect increasingly sophisticated methods. We don't want to put anyone off having a go at the problem, which is whysolutions using higher-level mathematics come nearer the bottom of the page.

For example, in the published solutions to the Stage 1 task, The Add and Take-away Path, Jack and Ellie answer the first and second parts of the problem, giving us the scores for each grid. Then, the other solutions go on to explain why this always happens.

In a similar way, the solutions for the Stage 2 problem Three Dice begin with some observations and the suggestion of a "rule". Several learners then offer very clear explanations for why this always happens. Finally, we also include solutions which look at more than three dice and go on to generalise the problem.

For the Stage 3 and 4 solutions, we start by looking for solutions which make a good start on the problem but perhaps don't answer the whole question. For example, quite a few problems involve numerical relationships which can be analysed using algebra, so we regularly receive solutions from younger students who made lots of progress with the numerical part of the problem but don't alwaysproceed to the algebraic parts. We then pick out the solutions which develop the next part of the problem, and feature those next. If someone has used some particularly advanced mathematics (perhaps using ideas not normally met until Stage 5), we usually publish their solution nearer the bottom of the page. This means that anyone reading the solution can read as far as they understand and thentake a look at what might come next as they learn new mathematical techniques.

Take a look at the solutions to the March 2011 problem Multiplication Arithmagons. Lots of students came up with the method described by Alexander, so we chose to feature his very clear description and mention everyone else who had worked in the same way. Fionn's algebraic approach came next, and Francesco's solution added some extradetail (each solution could be multiplied by -1). At the bottom of the page, we provided links to those solutions we had received as uploaded attachments.

At stage 5 many of the problems are reasonably easy to start but somewhat more difficult to complete. We very often receive partial solutions to the problems and use these to piece together a full solution. We will correct minor mistakes and very often paraphrase solutions. As with other stages, we want to know what was going through your mind as you constructed your solution, as this isuseful to share with other solvers, as well as making the solutions more entertaining! One particular feature of many stage 5 problems is that they involve a great deal of mathematical symbolism. Taking care to format this appropriately will increase your chances of the solution appearing on the site. Sometimes, if a solution is good enough, we simply publish the entire contribution as anadditional download from the solutions page: see Escape from Planet Earth as an example of this.

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