# 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!

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#### 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.

#### 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.

#### 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.

#### 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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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.

#### 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.

#### 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.

#### Pentominoes: Symmetry

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Students explore the symmetry properties of the pentominoes then create symmetric shapes using pairs of pentominoes. A cut-out sheet is provided for making the set of pentominoes. There are then 4 worksheets which include finding axes and centres of symmetry, completion of a pentomino summary sheet, discussion of bilateral and rotational symmetry and order of symmetry. There are 3 pages of a Teacher's Guide which give full answers to all the activities. Possible approaches to lessons are given and useful extension activities are outlined.

#### 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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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.

#### 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.

#### 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.

#### 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.

#### 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.

#### 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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Number bases, decimal system, place value, number puzzle, reflection, addition &amp; 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 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.