# Mistercorzi's Shop

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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!

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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!

#### Roblox: Factory Town Tycoon - Cross Number Puzzle No1

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A Cross-Number Puzzle based on Factory Town Tycoon (a Roblox game). The pupil’s Information Sheet provides: a list of Players and their current wealth; buying/selling prices for some goods; a simple production line example. Students are required to interpret the clues, extract relevant data from the Information Sheet and then to do the necessary calculations (manually or with calculator) Students who are not familiar with the game will not be at a disadvantage as the puzzle is self-contained. The Teacher’s Guide gives the answers by means of a completed grid. The actual calculations required to solve each clue are given. This allows the teacher to easily judge the difficulty level involved and whether calculators should be allowed. There are also descriptions and suggestions for use in the classroom and for further extension work.

#### 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!

#### 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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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.

#### Roblox: Booga Booga - Crossnumber Puzzle No1

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A Cross-Number Puzzle based on Booga Booga (a Roblox game). The Pupil Information Sheet provides: the effect of various tools (Axes, Rock etc) on health, facts about different Trees and Bushes, facts about a Campfire. Students are required to interpret the clues, extract relevant data from the Information Sheet and then to do the necessary calculations (manually or with calculator) Students who are not familiar with the game will not be at a disadvantage as the puzzle is self-contained. The Teacher Guide gives the answers by means of a completed grid. An indication of the difficulty level of the calculations required is given. This allows the teacher to easily judge whether or not calculators should be used.

#### 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.

#### 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.

#### 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.

#### 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 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.

#### 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.

#### Mixed Operations with Fractions (Cross-number Puzzle)

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There are three Cross-number Puzzles provided in this worksheet resource: Puzzle A, Puzzle B and Puzzle C. They are in increasing order of difficulty. All clues involve a mixture of addition, subtraction, multiplication and division of fractions. Puzzles A and B involve operations with two fractions or mixed fractions. It is possible to complete each of these two puzzles by ignoring the division clues. The clues in Puzzle C all involve operations with three fractions. Knowledge of the order of operations is essential to solve this third puzzle. There is an explanation given on each puzzle sheet of how fractions or mixed fractions are to be entered in the grid The full answers to the three puzzles are given in the Notes for Teachers along with a few relevant notes regarding the puzzles.

#### 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.

#### 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 &quot;the rule&quot; 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: 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.

#### 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: 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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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.

#### 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.

#### Pentominoes: Holey Rectangles

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Students use the cut-out sheet to make a set of 12 pentominoes. This puzzle pack has 20 shape templates. Each shape can be created using all 12 pentominoes. The shapes are themed as rectangles (including squares) with holes in them. The Teacher's Guide gives solutions for all puzzles and some advice for helping students who are stuck.