This activity worksheet involves patterns of regularly increasing arrangements of dots. Students are required to calculate the number of dots in a given arrangement further along the pattern. They are then asked to generalise to “Pattern n”. A detailed Teacher’s Guide outlines different ways this resource may be used. Students should be encouraged to be creative and find different calculations methods which will lead to different algebraic forms. This then naturally leads to the algebraic simplification of the resulting expressions.

Two cross-number puzzles are provided in this resource. The main aim is for students to learn to read and write numbers using the Roman numeral system. To complete these puzzles the student will need to translate numbers from the Roman numeral system to their familiar decimal system, perform some basic calculations and then translate their answer back into the Roman numeral system. The Teacher’s Guide provides the answers to both puzzles along with some explanations of how the Roman number system works. There are also suggestions for further investigative work and a web-link to more activities.

This resource consists of a cross-number puzzle whose solution involves the calculation of hexagonal numbers. Geometric diagrams are given for the first few hexagonal numbers. Students will then have to devise methods to calculate larger such numbers. The Teachers Guide outlines three possible investigative approaches to these calculations. One involves generalising using the given geometric patterns. The other two approaches involve investigating numerical patterns which then leads to the construction of a nth term formula. One is through patterns in a difference table and the other involves patterns in the numerical factors of the hexagonal numbers. The answers to the puzzle clues are also given in the Teachers Guide.

Completion of this cross-number puzzle involves evaluation of algebraic expressions involving squaring and the use of brackets. Most of the calculations can be performed without the use of a calculator. Students should be encouraged to only use a calculator as a final checking process. There is also a double-check built in due to the overlapping structure of the cross-number grid so students should be encouraged to calculate all the clues not just a minimal set. The answers and further suggestions are provided in the teacher's guide.

This is a cross-number puzzle that requires Web searches to find the necessary information. Much of it involves finding information about special numbers e.g. Armstrong Numbers, Golden Primes, Repfigits, Vampire numbers and their Fangs, Tribonacci Numbers, Beastly Numbers, Smith Numbers and the Smith Brothers. Primes, squares, cubes and perfect numbers also get a look in along with the idea of permutations. And who is Kaprekar and what is his routine? A demanding fun-packed puzzle that should keep able pupils busy for at least a period! The answer is also supplied.

Factors, factorisation, prime numbers, investigation. Diagrams of incomplete factor trees are given for the student to complete. There are then follow-on tasks exploring the fact that one number may produce differently structured trees. In the Teacher's guide an investigation is outlined based on the activities covered in the worksheet. All answers are given.

A diagram of incomplete factor trees is given. Students have to complete these. There is an extra puzzle task given in the Teacher's guide for those that complete this worksheet early. The answers are supplied.

Algebraic substitution, expressions, evaluation. Students have to evaluate a set of linear expressions given the values of the variables. A teacher's guide is supplied and the answers are given.

Linear equation solving, solutions. Students are required to solve linear equations then write the value of the solution in the crossword grid. All equations have variables on both sides. The nature of the task encourages students to check their solutions. The teacher's guide gives some advice concerning strategies. The answers are provided.

3x+1 conjecture, Collatz problem, Syracuse problem, Kakutani's problem, Hasse's algorithm, Ulam's problem. This worksheet investigates a simple number recurrence algorithm: if it's odd multiply by 3 then add 1 but if it's even then halve, repeat. Students use the algorithm to complete missing numbers on the sheet. Very detailed background is given in the guide along with answers. Great to give students an understandable but unsolved (as yet) problem!

Linear equation solving, solutions. Students are required to solve simple linear equations then write the value of the solution in the crossword grid. The nature of the task encourages students to check their solutions. The teacher's guide gives some advice concerning strategies. The answer is provided.

Number bases, decimal system, place value, number puzzle, reflection, addition & subtraction of integers. This Cross-Number puzzle involves the use of a novel 'reverse notation' or 'looking glass arithmetic'. Students should be encouraged to investigate and discover rules for adding and subtracting digimirror numbers. A detailed teacher's guide is included which suggests possible classroom approaches. Answers are provided. My resource 'Digimirror Maths' would be a natural introduction to this activity.

Number bases, decimal system, place value, number puzzle, reflection. This worksheet introduces a novel 'numeric language' using 'reverse notation'. The digits 6, 7, 8 and 9 are banned. The allowed digits may be written in reverse (mirror image). Students should be given time to explore the given examples to see if they can discover the method. Four graded tasks are given. There is a detailed teacher's guide along with the answers to the tasks. Students love this activity!

Chinese characters, Chinese number system, place value, cross-cultural, cross-number puzzle. To complete this cross-number puzzle students are required to translate familiar arabic numbers into Chinese character numbers and to write these characters in the grid. A teacher's guide gives the necessary background and possible approaches. The answer is provided. This activity would follow naturally from my resource: Chinese Numbers No1.

Magic squares, tetrominoes, pentominoes, dissection puzzle, magic number. These two puzzles involve the student cutting out a set of tetromino or pentomino shapes with numbers on them. The task is to reconstruct a magic square using the pieces. A teachers guide suggests various approaches to the puzzle, one of which involves an investigation of what the 'magic number' will be. Answers are provided.

Chinese characters, Chinese number system, place value, cross-cultural, cross-number puzzle. To complete this cross-number puzzle students will be required to learn to recognise traditional Chinese number characters and to understand the place value system (base 10) that the Chinese use. A teacher's guide gives the necessary background and possible approaches. The answer is provided.

This resource consists of two cross-number puzzles suitable for Year 6 upwards (P7 upwards in Scotland). Geometric diagrams are given illustrating the first few triangular numbers. To solve both puzzles the student will need to calculate particular triangular numbers, The largest required is the 41st. Clues use a basic algebra subscript notation for each triangular number. The Teachers Guide outlines three possible approaches to the completion of the worksheet ranging from "brute force" calculation to more investigative approaches involving the triangular number formula. The answers to the puzzles are also supplied in the Teacher's Guide.