text: # Search by Topic
  
  #### Resources tagged with Visualising similar to Sending a Parcel:
  
  Filter by: Content type:
  Stage:
  Challenge level:
  
  ### Cuboid Challenge
  
  ##### Stage: 3 Challenge Level:
  
  What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
  
  ### Marbles in a Box
  
  ##### Stage: 3 Challenge Level:
  
  How many winning lines can you make in a three-dimensional version of noughts and crosses?
  
  ### Frogs
  
  ##### Stage: 3 Challenge Level:
  
  How many moves does it take to swap over some red and blue frogs? Do you have a method?
  
  ### Picturing Square Numbers
  
  ##### Stage: 3 Challenge Level:
  
  Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
  
  ### On the Edge
  
  ##### Stage: 3 Challenge Level:
  
  If you move the tiles around, can you make squares with different coloured edges?
  
  ### Painted Cube
  
  ##### Stage: 3 Challenge Level:
  
  Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
  
  ### Cuboids
  
  ##### Stage: 3 Challenge Level:
  
  Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
  
  ### Route to Infinity
  
  ##### Stage: 3 Challenge Level:
  
  Can you describe this route to infinity? Where will the arrows take you next?
  
  ### Partly Painted Cube
  
  ##### Stage: 4 Challenge Level:
  
  Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
  
  ### Christmas Chocolates
  
  ##### Stage: 3 Challenge Level:
  
  How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
  
  ### Squares in Rectangles
  
  ##### Stage: 3 Challenge Level:
  
  A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
  
  ##### Stage: 3 Challenge Level:
  
  How many different symmetrical shapes can you make by shading triangles or squares?
  
  ### Threesomes
  
  ##### Stage: 3 Challenge Level:
  
  Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
  
  ### Seven Squares - Group-worthy Task
  
  ##### Stage: 3 Challenge Level:
  
  Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
  
  ### Squares, Squares and More Squares
  
  ##### Stage: 3 Challenge Level:
  
  Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?
  
  ### Concrete Wheel
  
  ##### Stage: 3 Challenge Level:
  
  A huge wheel is rolling past your window. What do you see?
  
  ### Semi-regular Tessellations
  
  ##### Stage: 3 Challenge Level:
  
  Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
  
  ### Fence It
  
  ##### Stage: 3 Challenge Level:
  
  If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
  
  ### The Spider and the Fly
  
  ##### Stage: 4 Challenge Level:
  
  A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
  
  ### Tourism
  
  ##### Stage: 3 Challenge Level:
  
  If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
  
  ### An Unusual Shape
  
  ##### Stage: 3 Challenge Level:
  
  Can you maximise the area available to a grazing goat?
  
  ### Is There a Theorem?
  
  ##### Stage: 3 Challenge Level:
  
  Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
  
  ### Picturing Triangular Numbers
  
  ##### Stage: 3 Challenge Level:
  
  Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
  
  ### Konigsberg Plus
  
  ##### Stage: 3 Challenge Level:
  
  Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
  
  ### Triangles to Tetrahedra
  
  ##### Stage: 3 Challenge Level:
  
  Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
  
  ### Cubes Within Cubes Revisited
  
  ##### Stage: 3 Challenge Level:
  
  Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
  
  ### Square Coordinates
  
  ##### Stage: 3 Challenge Level:
  
  A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
  
  ### Tic Tac Toe
  
  ##### Stage: 3 Challenge Level:
  
  In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?
  
  ### Intersecting Circles
  
  ##### Stage: 3 Challenge Level:
  
  Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?
  
  ##### Stage: 3 Challenge Level:
  
  Can you mark 4 points on a flat surface so that there are only two different distances between them?
  
  ### Eight Hidden Squares
  
  ##### Stage: 2 and 3 Challenge Level:
  
  On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
  
  ### Seven Squares
  
  ##### Stage: 3 Challenge Level:
  
  Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
  
  ### Drilling Many Cubes
  
  ##### Stage: 3 Challenge Level:
  
  A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet.
  
  ### Chess
  
  ##### Stage: 3 Challenge Level:
  
  What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?
  
  ### All in the Mind
  
  ##### Stage: 3 Challenge Level:
  
  Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .
  
  ### A Tilted Square
  
  ##### Stage: 4 Challenge Level:
  
  The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
  
  ### Clocked
  
  ##### Stage: 3 Challenge Level:
  
  Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
  
  ### Isosceles Triangles
  
  ##### Stage: 3 Challenge Level:
  
  Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
  
  ### Hidden Rectangles
  
  ##### Stage: 3 Challenge Level:
  
  Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
  
  ### Convex Polygons
  
  ##### Stage: 3 Challenge Level:
  
  Show that among the interior angles of a convex polygon there cannot be more than three acute angles.
  
  ### Tetra Square
  
  ##### Stage: 3 Challenge Level:
  
  ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
  
  ### Pattern Power
  
  ##### Stage: 1, 2 and 3
  
  Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.
  
  ### Coloured Edges
  
  ##### Stage: 3 Challenge Level:
  
  The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?
  
  ### Sea Defences
  
  ##### Stage: 2 and 3 Challenge Level:
  
  These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?
  
  ### Zooming in on the Squares
  
  ##### Stage: 2 and 3
  
  Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
  
  ### Königsberg
  
  ##### Stage: 3 Challenge Level:
  
  Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?
  
  ### Dice, Routes and Pathways
  
  ##### Stage: 1, 2 and 3
  
  This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .
  
  ### Troublesome Dice
  
  ##### Stage: 3 Challenge Level:
  
  When dice land edge-up, we usually roll again. But what if we didn't...?
  
  ### More Pebbles
  
  ##### Stage: 2 and 3 Challenge Level:
  
  Have a go at this 3D extension to the Pebbles problem.
  
  ### There and Back Again
  
  ##### Stage: 3 Challenge Level:
  
  Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?
explanation: The provided text is a collection of math problems and challenges, primarily focused on geometry and visualizing shapes and patterns. Each problem is tagged with a stage level indicating its difficulty. The text does not contain a single question and answer but rather multiple questions or problem statements.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Search by Topic
  
  #### Resources tagged with Visualising similar to Sending a Parcel:
  
  Filter by: Content type:
  Stage:
  Challenge level:
  
  ### Cuboid Challenge
  
  ##### Stage: 3 Challenge Level:
  
  What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
  
  ### Marbles in a Box
  
  ##### Stage: 3 Challenge Level:
  
  How many winning lines can you make in a three-dimensional version of noughts and crosses?
  
  ### Frogs
  
  ##### Stage: 3 Challenge Level:
  
  How many moves does it take to swap over some red and blue frogs? Do you have a method?
  
  ### Picturing Square Numbers
  
  ##### Stage: 3 Challenge Level:
  
  Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
  
  ### On the Edge
  
  ##### Stage: 3 Challenge Level:
  
  If you move the tiles around, can you make squares with different coloured edges?
  
  ### Painted Cube
  
  ##### Stage: 3 Challenge Level:
  
  Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
  
  ### Cuboids
  
  ##### Stage: 3 Challenge Level:
  
  Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
  
  ### Route to Infinity
  
  ##### Stage: 3 Challenge Level:
  
  Can you describe this route to infinity? Where will the arrows take you next?
  
  ### Partly Painted Cube
  
  ##### Stage: 4 Challenge Level:
  
  Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
  
  ### Christmas Chocolates
  
  ##### Stage: 3 Challenge Level:
  
  How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
  
  ### Squares in Rectangles
  
  ##### Stage: 3 Challenge Level:
  
  A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
  
  ##### Stage: 3 Challenge Level:
  
  How many different symmetrical shapes can you make by shading triangles or squares?
  
  ### Threesomes
  
  ##### Stage: 3 Challenge Level:
  
  Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
  
  ### Seven Squares - Group-worthy Task
  
  ##### Stage: 3 Challenge Level:
  
  Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
  
  ### Squares, Squares and More Squares
  
  ##### Stage: 3 Challenge Level:
  
  Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?
  
  ### Concrete Wheel
  
  ##### Stage: 3 Challenge Level:
  
  A huge wheel is rolling past your window. What do you see?
  
  ### Semi-regular Tessellations
  
  ##### Stage: 3 Challenge Level:
  
  Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
  
  ### Fence It
  
  ##### Stage: 3 Challenge Level:
  
  If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
  
  ### The Spider and the Fly
  
  ##### Stage: 4 Challenge Level:
  
  A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
  
  ### Tourism
  
  ##### Stage: 3 Challenge Level:
  
  If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
  
  ### An Unusual Shape
  
  ##### Stage: 3 Challenge Level:
  
  Can you maximise the area available to a grazing goat?
  
  ### Is There a Theorem?
  
  ##### Stage: 3 Challenge Level:
  
  Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
  
  ### Picturing Triangular Numbers
  
  ##### Stage: 3 Challenge Level:
  
  Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
  
  ### Konigsberg Plus
  
  ##### Stage: 3 Challenge Level:
  
  Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
  
  ### Triangles to Tetrahedra
  
  ##### Stage: 3 Challenge Level:
  
  Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
  
  ### Cubes Within Cubes Revisited
  
  ##### Stage: 3 Challenge Level:
  
  Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
  
  ### Square Coordinates
  
  ##### Stage: 3 Challenge Level:
  
  A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
  
  ### Tic Tac Toe
  
  ##### Stage: 3 Challenge Level:
  
  In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?
  
  ### Intersecting Circles
  
  ##### Stage: 3 Challenge Level:
  
  Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?
  
  ##### Stage: 3 Challenge Level:
  
  Can you mark 4 points on a flat surface so that there are only two different distances between them?
  
  ### Eight Hidden Squares
  
  ##### Stage: 2 and 3 Challenge Level:
  
  On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
  
  ### Seven Squares
  
  ##### Stage: 3 Challenge Level:
  
  Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
  
  ### Drilling Many Cubes
  
  ##### Stage: 3 Challenge Level:
  
  A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet.
  
  ### Chess
  
  ##### Stage: 3 Challenge Level:
  
  What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?
  
  ### All in the Mind
  
  ##### Stage: 3 Challenge Level:
  
  Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .
  
  ### A Tilted Square
  
  ##### Stage: 4 Challenge Level:
  
  The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
  
  ### Clocked
  
  ##### Stage: 3 Challenge Level:
  
  Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
  
  ### Isosceles Triangles
  
  ##### Stage: 3 Challenge Level:
  
  Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
  
  ### Hidden Rectangles
  
  ##### Stage: 3 Challenge Level:
  
  Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
  
  ### Convex Polygons
  
  ##### Stage: 3 Challenge Level:
  
  Show that among the interior angles of a convex polygon there cannot be more than three acute angles.
  
  ### Tetra Square
  
  ##### Stage: 3 Challenge Level:
  
  ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
  
  ### Pattern Power
  
  ##### Stage: 1, 2 and 3
  
  Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.
  
  ### Coloured Edges
  
  ##### Stage: 3 Challenge Level:
  
  The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?
  
  ### Sea Defences
  
  ##### Stage: 2 and 3 Challenge Level:
  
  These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?
  
  ### Zooming in on the Squares
  
  ##### Stage: 2 and 3
  
  Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
  
  ### Königsberg
  
  ##### Stage: 3 Challenge Level:
  
  Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?
  
  ### Dice, Routes and Pathways
  
  ##### Stage: 1, 2 and 3
  
  This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .
  
  ### Troublesome Dice
  
  ##### Stage: 3 Challenge Level:
  
  When dice land edge-up, we usually roll again. But what if we didn't...?
  
  ### More Pebbles
  
  ##### Stage: 2 and 3 Challenge Level:
  
  Have a go at this 3D extension to the Pebbles problem.
  
  ### There and Back Again
  
  ##### Stage: 3 Challenge Level:
  
  Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is a collection of math problems and challenges, primarily focused on geometry and visualizing shapes and patterns. Each problem is tagged with a stage level indicating its difficulty. The text does not contain a single question and answer but rather multiple questions or problem statements.
  
  Label: multiple-question