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Fun resources for the mathematics classroom featuring puzzles, investigations and other challenging activities. Many of these activities open up opportunities for further investigation . Listen for that unexpected question from your student and be prepared to follow it especially if you, as a teacher, don't know the answer or where it will lead!

Fun resources for the mathematics classroom featuring puzzles, investigations and other challenging activities. Many of these activities open up opportunities for further investigation . Listen for that unexpected question from your student and be prepared to follow it especially if you, as a teacher, don't know the answer or where it will lead!
Factor Trees No2
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Factor Trees No2

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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.
Roman Numerals I & II (Cross-number Puzzles)
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Roman Numerals I & II (Cross-number Puzzles)

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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.
Factor Trees  No3
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Factor Trees No3

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In the first activity students complete the given factor trees. Further activities involve students creating similarly structured factor trees for further numbers then differently structured trees for all the previous numbers. Suggestions are made to link the activities to the prime factorisation of numbers. The Teacher's Guide supplies answers to all the activities with a few additional notes.
Factor Trees No1
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Factor Trees No1

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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.
Chinese Numbers No1 (Cross-number Puzzles)
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Chinese Numbers No1 (Cross-number Puzzles)

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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.
Hailstone Numbers
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Hailstone Numbers

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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!
Substitution No1 (Crossnumber Puzzles)
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Substitution No1 (Crossnumber Puzzles)

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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.
Hexagonal Numbers (Cross-number Puzzle)
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Hexagonal Numbers (Cross-number Puzzle)

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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.
Cross-Number Puzzles: Triangular Numbers No1
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Cross-Number Puzzles: Triangular Numbers No1

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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.
Crossnumber Puzzle: Addition of Fractions
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Crossnumber Puzzle: Addition of Fractions

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Students have to complete a cross-number puzzle whose clues are all the addition of two fractions. Instructions are given on the worksheet as to how to enter a fractional answer in the grid. The answers are given in the Teacher's Guide along with a few relevant notes regarding the puzzle.
Crossnumber Puzzle: Quadratic Equation 2
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Crossnumber Puzzle: Quadratic Equation 2

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This activity consists of a Crossnumber Puzzle which is completed by solving 18 quadratic equations. Instructions are given regarding the method for entering solutions onto the grid. All the quadratic equations have an x-squared coefficient that is not 1. The answer to the puzzle is provided in the Teacher's Guide along with a few relevant notes.
Pattern No1
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Pattern No1

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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.
Crossnumber Puzzle: Fibonacci and Lucas Numbers
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Crossnumber Puzzle: Fibonacci and Lucas Numbers

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Sequences, sequence notation, recurrence relations, number calculations. Students completing this cross-number puzzle are eventually required to calculate just over the first thirty Fibonacci and Lucas numbers. 'nth term' notation is used and recurrence relations are given. The calculations involved are addition, subtraction and a few basic multiplications. The Teacher's Guide gives the answers to the puzzle. Also outlined are some further investigative activities exploring the many relationships between the two sequences of numbers.
Substitution No 2 (Cross-Number Puzzle)
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Substitution No 2 (Cross-Number Puzzle)

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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.
Chinese Numbers No2 (Cross-number Puzzles)
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Chinese Numbers No2 (Cross-number Puzzles)

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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 Square No1 (Cut-out Sheet)
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Magic Square No1 (Cut-out Sheet)

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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.
Digimirror Maths
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Digimirror Maths

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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!
Digimirror Numbers (Cross-Number Puzzles)
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Digimirror Numbers (Cross-Number Puzzles)

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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.
Equations No1 (Crossword Puzzles)
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Equations No1 (Crossword Puzzles)

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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.
Equations No2 (Crossword Puzzles)
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Equations No2 (Crossword Puzzles)

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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.