Overview

At the heart of the Numeracy Ninjas programme is the Ninja Skill Check. This is a 30 question quiz that takes approximately 5 minutes during a lesson. Each Ninja Skill Check includes a selection of 72 individual numeracy skills (Ninja Skills) that learners need to gain fluency with to succeed in 11-16 mathematics study. The Ninja Skill Check is scheduled routinely during mathematics lessons. Learners complete the quiz against the clock and then mark their answers to obtain their Ninja Score which relates to a particular colour Ninja Belt achieved. Through regular completion of Ninja Skill Checks and regular feedback from their teacher, over time learners aim to achieve the coveted Ninja Score of 30/30, Black Belt showing mastery of their numeracy skills.

  • WHITE
  • YELLOW
  • ORANGE
  • GREEN
  • BLUE
  • PURPLE
  • RED
  • BROWN
  • BLACK

When you purchase a Numeracy Ninjas subscription you receive access to the Ninja Skill Book pdfs. Over a single week the topics in a Ninja Skill Check remain the same and so you choose whether you want to run 1, 2, 3, 4 or 5 sessions per week with your class. You then download the relevant Ninja Skill Books and print them for each learner.

Each of the 72 individual Ninja Skills is based around 3 categories:

Mental Strategies

Questions developing the basics of mental calculation skills. 30 topics including number bonds, addition and subtraction strategies, time and more.

Times Tables

The most important pre-requisite skill for success in 11-16 mathematics. Learners need high levels of fluency with the times tables to thrive in class.

Key Skills

30 fundamental numeracy skills which are the foundation for 11-16 mathematics success. Four operations, negative numbers etc.

Each Ninja Skill Check contains 10 questions from each category, giving 30 questions overall. Learners are encouraged to answer Mental Strategies and Times Tables questions in their head, and they can use written calculation methods to answer Key Skills questions on the workings pages in the Ninja Skill Books. Ninja Skills Checks work best if completed in a low-stakes way and regularly during lessons.

To stretch and challenge learners who master Ninja Skill Checks and to enrich the learning of all learners who enjoy mathematics, there is a weekly Extension Problem in all Ninja Skill Books which are designed to develop students’ reasoning and problem-solving skills.

Ninja Skill Book Answers

Once your learners have completed a Ninja Skill Check they mark their answers by you projecting the Ninja Skill Book Answers pdf. Students then calculate their Ninja Score (out of 30) and then look at the Ninja Belt slide showing which colour belt they have achieved in that session.

Empowered By Cognitive Science

Decades of research within a branch of Cognitive Science called the Science of Learning has shown a number of phenomena which improve human learning, specifically retention and transferability. Three of these phenomena are the Retrieval, Spacing and Interleaving Effects. The team behind Numeracy Ninjas are experts in the Science of Learning, including published authors, and have worked closely with world experts in human memory and cognition. Numeracy Ninjas resources have been designed at their core to utilise the considerable benefits of the Retrieval, Spacing and Interleaving Effects.

Click the titles below to learn more about how each effect is incorporated into Ninja Skill Checks:

Cognitive Scientists have shown that retrieving information from memory is a more effective learning strategy that rereading information if the aim is to build long-term retention of knowledge. Numeracy Ninjas focuses on retrieval-type activities, such as the 30 question Ninja Skill Checks in order build learners’ retention of the 72 Ninja Skills.

Another essential component in building long-term retention of knowledge is to utilise the Spacing Effect. The Spacing Effect is the idea that learning and retention are improved when studying is spread out over time, rather than being concentrated in a single session. It allows for better consolidation of information in long-term memory, and stronger connections between new information and existing knowledge.

Ninja Skill Checks utilise the Spacing Effect by revisiting each of the 72 Ninja Skills regularly with spacing gaps in between. For example, during the first 12 weeks of the programme, each of the Mental Strategies and Key Skills Ninja Skills appear in the Ninja Skill Check quizzes for a full week, every 3 weeks. Over the course of the academic year each Ninja Skill is revisited over 10 times with a spacing gap in between.

By completing a Ninja Skill Check with your learners multiple times each week and doing so routinely over the whole academic year you will be fully exploiting the benefits of the Spacing Effect to support their learning.

The Interleaving Effect is a learning technique where different topics or skills are mixed together during practice sessions. It is has been shown to improve long-term retention and transfer of learning to new situations by challenging the brain to constantly switch between different types of problems.

We incorporate the Interleaving Effect into the Ninja Skill Book resources by:

  • Weeks 1-12: listing 10 different Ninja Skills in each of the mental strategies, timestables and key skills sections
  • Weeks 13-19: varying the order in which the interleaved skills appear in each of the mental strategies, timestables and key skills sections
  • Weeks 20-40: removing the topic tables of mental strategies, timestables and key skills and instead choosing 10 skills from each, but arranging them in a set of 30 questions in a randomised order

The degree of interleaving in the sequencing of the questions in the Ninja Skill Books is phased in across the weeks which increases the level of challenge for students steadily over time.

Furthermore, each of the 72 individual Ninja Skills has multiple variations in which the question could be phrased. For example, if the question engine decided to ask the ‘number bonds to 5’ question 2 + ☐ = 5, it could choose from that variation or others such as ☐ + 2 = 5 or 2 + 3 = ☐. By contextually-varying the number of ways in which each individual Ninja Skill could be asked we further increased the degree of interleaving within the Numeracy Ninjas resources.

By incorporating both spacing and interleaving in the question scheduling for our resources, and basing the question topics on a prior-learning dependency analysis, Numeracy Ninjas is at the forefront of using cognitive science findings in educational resources to accelerate learning.

Boosting Motivation Through Gamification and Behavioural Science

Gamification strategies are central to the design of Ninja Skill Checks whereby students compete against their own previous performance to improve their score. Furthermore, we incorporated into our design the latest Behavioural Science research findings about the factors which most influence human motivation and did so in a way that was visually appealing to the target audience. These principles include: social normalisation, instant rewards and progress monitoring.

Click the headings below to learn more about how behaviour science principles were integrated into the design of Ninja Skill Checks:

Social normalisation is the process by which behaviors or beliefs become accepted and considered as “normal” within a particular social group, such as your class. This can occur through various means, such as repeated exposure to high expectations, social reinforcement from peers or teachers, and a desire to conform to group norms.

Ninja Skills Checks are designed to be run in a low-stakes-but-high-participation way to enable you to create an ‘everyone is having a go, so I should do too’ culture in your classroom. By including Ninja Skills across a broad range of levels of challenge, the majority of learners will find the Ninja Skills Checks accessible, but still require effort over time to master.

It has been shown that by giving rewards as soon as possible after the achievement, motivation to continue is enhanced. The Ninja Skill Checks are supported by the Ninja Belt structure whereby learners graduate through the coloured belts as their Ninja Score improves. Furthermore, we taking out a subscription to Numeracy Ninjas, each of your learners receives a Ninja Achievement Certificate and Ninja Belt Stickers which provides you with a way to instantly reward your learners for progress in their learning.

Learners are more motivated to improve if they are provided with regular ways to monitor their progress. By incorporating the Ninja Score concept into Ninja Skill Checks, supported by a ladder-style Ninja Belt structure, learners receive feedback after every session on their progress.

In additon, the Ninja Score Record Spreadsheet is included as part of Numeracy Ninjas subscription which allows you to track the progress of your learners over time so you can celebrate progress and quickly support learners whose Ninja Scores begin to plateau before their motivation to improve falls.

Ninja Skills- The Gatekeepers to Progress in Mathematics

The 72 individual Ninja Skills are based on 3 categories: Mental Strategies, Times Tables and Key Skills. The 30 Mental Strategies Ninja Skills were identified by consulting best-practice literature on essential skills for numeracy development. The Times Tables and Key Skills Ninja Skills were identified through a novel Prior-Learning Dependency Analysis.

Prior-Learning Dependency Analysis

The network diagram shows a Prior-Learning Dependency Analysis of the UK GCSE Mathematics curriculum circa 2015. Each node represents a particular content skill from the curriculum, for example, rounding numbers to a given number of decimal places.

Nodes are linked by lines if one skill is a prior-learning dependency of another. For example, in order to be able to simplify fractions you need first to be able to find the factors of a number. Thus the simplifying fractions and finding factors nodes would be linked.

The nodes are then scaled proportionally to the number of outgoing links they have. I.e. the largest nodes are the skills which are the prior-learning dependencies for the most number of topics.

The largest nodes in the network are the times tables. This is undoubtedly not a surprise to mathematics teachers who know through experience how a lack of fluency with timestables multiplication (and related divisions) can be to students making progress in 11-16 maths study. For this reason, timestables multiplication and division get one third of all the question allocation in Ninja Skill Checks.

The next 30 largest nodes form the Key Skills section within the Numeracy Ninjas programme. If learners can master these individual skills to high levels of mastery, they form an excellent foundation of secure prior-learning dependencies to lay the path for success at 11-16 maths study.

By focussing your learners’ numeracy development on the 72 Ninja Skills you are ensuring they are building the right foundations for future success in mathematics.

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