Here are a few simple mathematics games that can be played at home or in class to improve students’ mathematical thinking and reasoning strategies.

These two games come from a website called NRICH.

NRICH believe that successful mathematicians understand curriculum concepts and are fluent in mathematical skills and procedures.  They also believe that they can solve problems, explain and justify their thinking, and have a positive attitude towards mathematics and to themselves as learners of mathematics.

With this in mind, NRICH mathematical activities aim to nurture curious, resourceful and confident learners of mathematics.

Game 1: You will need seven counters.

Nim-7

1. Place seven counters in a line and decide who will go first. (In the next game, the other player will have the first turn.)
2. Each player takes it in turns to take away either one counter or two counters.
3. The player who takes the last counter (or counters) wins.
4. Play several times so that you get a good ‘feel’ for the game.

Are there any points in the game, before the end, when you know who the winner is going to be? How do you know?

Can you find a way to play so that you are sure you will win right from the start?

Does it matter who has the first turn? Why or why not?

Once you are an expert at this game, you may like to try playing Daisy, which is another Nim-like game.

Game 2:

Got-it

Got It is an adding game for two players. You can play against the computer or with a friend. It is a version of a well-known game called Nim.

Start with the Got It target 23.

1. The first player chooses a whole number from 1 to 4.
2. Players take turns to add a whole number from 1 to 4 to the running total.
3. The player who hits the target of 23 wins the game.
   
   Play the game several times.
   Can you find a winning strategy?
   Can you always win?
   
   Does your strategy depend on whether or not you go first?

This can also be played on-line.

https://nrich.maths.org/1272

To change the game, choose a new Got It target or a new range of numbers to add on.

Test out the strategy you found earlier. Does it need adapting?

Can you work out a winning strategy for any target?
Can you work out a winning strategy for any range of numbers?

Is it best to start the game? Always?

Away from the computer, challenge your friends:
One of you names the target and range and lets the other player start.

Extensions:
Can you play without writing anything down?

Consider playing the game where a player CANNOT add the same number as that used previously by the opponent.

Mrs Bennett
Mathematics Department 

Analysis of proficient mathematicians’ problem-solving shows that their thinking is highly organised. It draws on a well-connected knowledge base of facts, methods and strategies that have been used to solve problems with a similar deep structure before. Successful problem-solving is therefore not just an activity but an outcome of successful learning of the facts and methods and their useful combinations as strategies. Conversely, if a problem-solver does not have conditional knowledge, they are more likely to be distracted by the surface features of problems. This has implications for how problem-solving as an activity is implemented in classrooms where teachers expect students to learn how to problem-solve by problem-solving.

 Teachers could use a curricular approach that better engineers success in problem-solving by teaching:

• the useful combinations of facts and methods
• how to recognise the problem types
• the deep structures that these strategies pair to

Students need to be fluent with the relevant facts and methods before being expected to learn how to apply them to problem-solving conditions.

Teaching for Mastery has been at the heart of our lessons and in the forefront of our mind when teaching mathematics and planning our five-year curriculum for coherence. We have worked hard as a department, ensuring that key facts are mastered and effective representations expose the structure of the mathematics to enable conceptual understanding. We ensure fluency by carefully planning a wide range of questions and tasks in our lessons where students need to draw on prior knowledge. Our next target is to improve conditional knowledge by embedding variation tasks into our lessons to enable pupils to make connections and improve their reasoning skills. We are also embedding mathematical thinking strategies to enable pupils to improve their problem-solving skills.

Mrs Bennett

Mathematics Department

Lancaster University School of Mathematics (LUSOM) Online and on Campus Revision Sessions

As part of our continuing links with LUSoM, there are a number of taster sessions and lectures, both online and on the campus that are available for pupils in KS3 and KS4.

 LUSoM Revise

This is a 13-week revision programme designed for Year 11 pupils aiming for grades 7 – 9 at GCSE. Starting in September, and meeting each week online, these sessions will go through various key topics to secure a top grade at GCSE and support the transition to A-level Mathematics.

These sessions received fantastic feedback last year with 96% of pupils agreeing they found the lectures very useful and 86% confirming they sessions were at the correct difficulty level.

Each session will cover a different topic, and hence students should aim to attend all 10 sessions.

To register for this, please visit https://go.cardinalnewman.ac.uk/form/reviselectures23?event_id=123

LUSoM Extend

This programme is designed for high-ability KS3/KS4 students who have a passion and interest for mathematics and want to go beyond their normal lessons. The sessions will cover material which is not on the GCSE syllabus and will show students some of the incredible uses that mathematics can have once it’s taken at a higher level.

Meeting once every half term on campus for 1.5 hours, students will tackle mathematics in completely new contexts to develop their problem-solving techniques and their breadth of mathematical knowledge.

Last year, 100% of students agreed that these sessions helped in developing mathematical thinking, increased the depth of understanding and improved presentation skills.

To register for this, please visit https://go.cardinalnewman.ac.uk/form/lusomextend2023?event_id=124

Miss Hasan

The Mathematics Department

At the start of a new academic year, I would like to take the opportunity to remind all Year 10 and 11 students of the importance that Method Maths can have in revision and the practice of mathematics.

Method Maths is a website that the school subscribes to and it has played an effective role in assisting pupils to prepare for their examinations and practice mathematical skills throughout the two years of the GCSE maths course.

Method Maths provides access to past GCSE papers of both the Foundation and Higher tiers and provides guided support when needed to assist students to understand and complete past exam questions. The website also marks your answers as you go so that you can check your progress. It also indicates what grade of work that you are currently achieving, as well as showing what needs to be done to improve your grade.

The Method Maths website is also used in school as part of our intervention strategies and has been shown to make a positive impact on results.

All students have been allocated a Method Maths account and their classroom teacher has or will provide these details. Room 11 is available after school on Wednesdays for Method Maths practice supported by members of the mathematics department.

Mr S Cheal

The Mathematics Department

This year in the Mathematics department, we are continuing to use Sparx Maths which provides personalised homework for each student. It creates a weekly set of questions tailored to the level of understanding and learning pace of each student. The questions are designed to be achievable, whilst offering the stretch that learners need to make progress. Questions from previous topics will also be included in the homework so that students can keep practising the skills they have learned.

We appreciate that you will of course want to support your child with their home learning but please try not to help them with a question until they’ve had a go first. It is really important that students complete their homework independently, and that questions are marked as correct. In the Maths department, we provide a lot of support in school to enable every student the opportunity to achieve 100% on their homework. There are drop-in sessions most lunch times, including a Sparx Maths club on a Monday in room 11. This way, Sparx can make sure you child continues to set homework that is at the correct level for them.  

Updates

Over the summer, Sparx Maths has had some up-dates. There is a new look when you login, which is better on the eyes when it comes to reading and answering the questions. There has also been an up-date when it comes to the bookwork checks. This previously picked random codes but they have now adopted the use of 1A, 1B, 1C etc going onto 2A, 2B etc. This allows the student to easily find the code for the requested bookwork check rather than sifting through all their work.

Achievements

The top 3 pupils with the highest XP currently for each year group are:

After our first year of using Sparx Maths,  there has been some tremendous achievements across school. We have answered over 2.1 million questions correctly in 26,626 hours across 800 students. The impact of changing to Sparx Maths has been that engagement has improved threefold!

Currently the top 3 Maths classes are:

The top 3 students in each year are:

Well done to the above students in their continued pursuit for excellence in Mathematics.

Mr Cafferkey

Maths Department