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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.
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.
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.
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.
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.
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: Subtraction of Fractions
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Crossnumber Puzzle: Subtraction of Fractions

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Students have to complete a cross-number puzzle whose clues are all the subtraction 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.
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 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.
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: Quadratic Equations 1
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Crossnumber Puzzle: Quadratic Equations 1

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This activity consists of a Crossnumber Puzzle which is completed by solving 22 quadratic equations. Instructions are given regarding the method for entering solutions onto the grid. All the quadratic equations have 1 as the coefficient of the x-squared term. The answer to the puzzle is provided in the Teacher's Guide along with a few relevant notes.
Number of Letters of Numbers
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Number of Letters of Numbers

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A fun activity involving a self-referential property of number names as written in English. A structured diagram has to be completed correctly with the names of the numbers from 1 to 20. This is not a straightforward task and lends itself to plenty of discussion. The Teacher's Guide gives "the rule" along with the completed diagram. There is also advice given on approaches to using the resource along with many suggestions for further investigational activities.
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.
Cycling with the Primes
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Cycling with the Primes

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This resource consists of 5 worksheets and a 6 page Teacher's Guide. These worksheets explore the amazing symmetries occurring in the decimal expansions of prime reciprocals. Students investigate the cycles of digits in these expansions and complete beautiful cyclic diagrams, templates of which are supplied in these worksheets. The primes 3, 7, 13, 17, 19, 23, 29, 31 and 37 are explored. Hidden patterns are revealed and a connection between the number of cycles and the length of the cycles is discovered. The completed diagrams are given in the Teacher's Guide which also contains the outline of an investigative approach to the topic. Details are given of the various stages of the investigation and how the worksheets may be incorporated. Various extensions are suggested including the use of a spreadsheet. This is a fascinating topic which will provide rich and rewarding mathematical experiences for the students.
Crossnumber Puzzle: Multiplication of Fractions
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Crossnumber Puzzle: Multiplication of Fractions

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Students have to complete a cross-number puzzle whose clues are all the multiplication 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.
Famous Mathematicians Word Search
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Famous Mathematicians Word Search

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This word search grid contains the names of 50 famous mathematicians. Students are asked to give the direction, coordinates and name. Geographical directions of the compass are used for how you read the name and coordinates of the position of the starting letter are asked for. Templates for filling in this information are given below the grid. The three page Teacher's Guide contains the full solutions, guidance on possible approaches and uses for the word search and also a page of crib sheets whose use is also explained in the notes.