# Cracked Clock

A clock broke into two pieces.
The numbers on each of the pieces add up to the same total.

Draw a diagram to show how the clock cracked.

## A Mathematics Lesson Starter Of The Day

Topics: Starter | Arithmetic | Problem Solving

• Ruth Seward, Hagley Park Sports College
•
• Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work
• Y8 set 1 Rawthorpe High School, The Cushtie Krew
•
• We think that this was very good. We liked the clock, in fact we thought it was a cracking starter!
Maths rules, Cushtie!
• Sue, St Albans
•
• The question can be extended to 'the clock is broken into three pieces with equal sum of 26 -- piece one contains numbers 11, 12, 1, and 2; piece two contains 3, 4, 9, & 10; the rest is piece three'.
Equally, it can be broken into 6 pieces with an equal sum of 13 -- piece one has 12 and 1; piece two has 2 and 11; piece three 3 and 10.
• Russ Skinner, Winnipeg, MB
•
• This problem also works by breaking the clock into 3 pieces and 6 pieces. The sum of all the numbers around the clock (1 + 2 + 3...10 + 11 + 12) equals 78. 78 is divisible by 3 and 6.
• The Best Class Ever (8cd/m2), King Alfred's College OXON
•
• We decided that this starter was not explained enough to work it out, so we tried both ways we could thing of and then realised that they were both the same answer.Tash, Ryan and Liam worked this out straight away with others not far behind them.
• Kieran, Weston
•
• I found this easy to understand, and once I found pairs of 13 it was easy.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

Excellent, I would like to see more like this
Good, achieved the results I required
Satisfactory
Didn't really capture the interest of the students
Not for me! I wouldn't use this type of activity.

This starter has scored a mean of 3.4 out of 5 based on 145 votes.

Previous Day | This starter is for 24 May | Next Day

Christmas Present Ideas

It is often very difficult choosing Christmas presents for family and friends but so here are some seasonal, mathematics-related gifts chosen and recommended by Transum Mathematics.

## Equate board game

Here's a great board game that will give any family with school-aged kids hours of worthwhile fun. Christmas is a time for board games but this one will still be useful at any time of year. Games can be adapted to suit many levels of Mathematical ability.

For Maths tutors working with just one or small groups of pupils this game has proved to be an excellent activity for a tutorial. Deciding on the best moves can spark pertinent discussions about mathematical concepts.

Equate looks a bit like Scrabble--for aspiring mathematicians, that is. Designed by a real mathematician, it works like this: You put down tiles on a board and make points by correctly completing simple equations. Your nine tiles include both numbers and mathematical symbols; you can add on to previous plays both vertically and horizontally. more...

## How Not To Be Wrong

The maths we learn in school can seem like an abstract set of rules, laid down by the ancients and not to be questioned. In fact, Jordan Ellenberg shows us, maths touches on everything we do, and a little mathematical knowledge reveals the hidden structures that lie beneath the world's messy and chaotic surface. In How Not to be Wrong, Ellenberg explores the mathematician's method of analyzing life, from the everyday to the cosmic, showing us which numbers to defend, which ones to ignore, and when to change the equation entirely. Along the way, he explains calculus in a single page, describes Gödel's theorem using only one-syllable words, and reveals how early you actually need to get to the airport.

What more could the inquisitive adult want for Christmas? This book makes a cosy, interesting read in front of the fire on those cold winter evenings. more...

## Graphic Display Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life it is a great investment. Bought as a Christmas present but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent Christmas gift for anyone.

You have to hold iPad Air to believe it. It’s just 7.5 millimeters thin and weighs just one pound. The stunning Retina display sits inside thinner bezels, so all you see is your content. And an incredible amount of power lies inside the sleek enclosure. So you can do so much more. With so much less. more...

## Aristotle's Number Puzzle

It’s a bit of a tradition to give puzzles as Christmas Gifts to nieces and nephews. This puzzle is ideal for the keen puzzle solver who would like a challenge that will continue over the festive period (at least!).

This number puzzle involves nineteen numbers arranged into a hexagon. The goal of the puzzle is to rearrange the numbers so each of the fifteen rows add up to 38. It comes in a wooden style with an antique, aged look.

Keep the Maths in Christmaths with this reasonably priced stocking filler. more...

## The Story Of Maths [DVD]

The films in this ambitious series offer clear, accessible explanations of important mathematical ideas but are also packed with engaging anecdotes, fascinating biographical details, and pivotal episodes in the lives of the great mathematicians. Engaging, enlightening and entertaining, the series gives viewers new and often surprising insights into the central importance of mathematics, establishing this discipline to be one of humanity s greatest cultural achievements. This DVD contains all four programmes from the BBC series.

Marcus du Sautoy's wonderful programmes make a perfect Christmas gift more...

Click the images above to see all the details of these gift ideas and to buy them online.

 Teacher, do your students have access to computers?Do they have iPads or Laptops in Lessons? Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Transum.org/go/?Start=May24

Here is the URL which will take them to a related student activity.

Transum.org/go/?to=cracked

## Extension

Which clockface is the odd one out?

The answer can be found by looking closely at the roman numerals used.

The clock on the right uses IIII for the number 4 while the other two clocks use IV.

Investigate which system of numbers is most common on clocks in your school, home or place of work.

More questions:

• At exactly which times are the hands of the clock pointing in the same direction?
• At exactly which times are the hands of the clock pointing in opposite directions?
• At exactly which times are the hands of the clock perpendicular?

There are more questions like these on the interactive Clock page.

For Students:

For All:
The text passage describes a mathematical problem involving a clock that has broken into pieces, with the condition that the numbers on each piece add up to the same total. It also includes comments from various users discussing the problem and suggesting extensions.
single_question

the passage presents a single mathematical question about how a clock can break into pieces with equal sums of the numbers on each piece. however, it does not provide an answer to this question. instead, it offers additional comments and extensions to the problem.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Cracked Clock

A clock broke into two pieces.
The numbers on each of the pieces add up to the same total.

Draw a diagram to show how the clock cracked.

## A Mathematics Lesson Starter Of The Day

Topics: Starter | Arithmetic | Problem Solving

• Ruth Seward, Hagley Park Sports College
•
• Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work
• Y8 set 1 Rawthorpe High School, The Cushtie Krew
•
• We think that this was very good. We liked the clock, in fact we thought it was a cracking starter!
Maths rules, Cushtie!
• Sue, St Albans
•
• The question can be extended to 'the clock is broken into three pieces with equal sum of 26 -- piece one contains numbers 11, 12, 1, and 2; piece two contains 3, 4, 9, & 10; the rest is piece three'.
Equally, it can be broken into 6 pieces with an equal sum of 13 -- piece one has 12 and 1; piece two has 2 and 11; piece three 3 and 10.
• Russ Skinner, Winnipeg, MB
•
• This problem also works by breaking the clock into 3 pieces and 6 pieces. The sum of all the numbers around the clock (1 + 2 + 3...10 + 11 + 12) equals 78. 78 is divisible by 3 and 6.
• The Best Class Ever (8cd/m2), King Alfred's College OXON
•
• We decided that this starter was not explained enough to work it out, so we tried both ways we could thing of and then realised that they were both the same answer.Tash, Ryan and Liam worked this out straight away with others not far behind them.
• Kieran, Weston
•
• I found this easy to understand, and once I found pairs of 13 it was easy.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

Excellent, I would like to see more like this
Good, achieved the results I required
Satisfactory
Didn't really capture the interest of the students
Not for me! I wouldn't use this type of activity.

This starter has scored a mean of 3.4 out of 5 based on 145 votes.

Previous Day | This starter is for 24 May | Next Day

Christmas Present Ideas

It is often very difficult choosing Christmas presents for family and friends but so here are some seasonal, mathematics-related gifts chosen and recommended by Transum Mathematics.

## Equate board game

Here's a great board game that will give any family with school-aged kids hours of worthwhile fun. Christmas is a time for board games but this one will still be useful at any time of year. Games can be adapted to suit many levels of Mathematical ability.

For Maths tutors working with just one or small groups of pupils this game has proved to be an excellent activity for a tutorial. Deciding on the best moves can spark pertinent discussions about mathematical concepts.

Equate looks a bit like Scrabble--for aspiring mathematicians, that is. Designed by a real mathematician, it works like this: You put down tiles on a board and make points by correctly completing simple equations. Your nine tiles include both numbers and mathematical symbols; you can add on to previous plays both vertically and horizontally. more...

## How Not To Be Wrong

The maths we learn in school can seem like an abstract set of rules, laid down by the ancients and not to be questioned. In fact, Jordan Ellenberg shows us, maths touches on everything we do, and a little mathematical knowledge reveals the hidden structures that lie beneath the world's messy and chaotic surface. In How Not to be Wrong, Ellenberg explores the mathematician's method of analyzing life, from the everyday to the cosmic, showing us which numbers to defend, which ones to ignore, and when to change the equation entirely. Along the way, he explains calculus in a single page, describes Gödel's theorem using only one-syllable words, and reveals how early you actually need to get to the airport.

What more could the inquisitive adult want for Christmas? This book makes a cosy, interesting read in front of the fire on those cold winter evenings. more...

## Graphic Display Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life it is a great investment. Bought as a Christmas present but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent Christmas gift for anyone.

You have to hold iPad Air to believe it. It’s just 7.5 millimeters thin and weighs just one pound. The stunning Retina display sits inside thinner bezels, so all you see is your content. And an incredible amount of power lies inside the sleek enclosure. So you can do so much more. With so much less. more...

## Aristotle's Number Puzzle

It’s a bit of a tradition to give puzzles as Christmas Gifts to nieces and nephews. This puzzle is ideal for the keen puzzle solver who would like a challenge that will continue over the festive period (at least!).

This number puzzle involves nineteen numbers arranged into a hexagon. The goal of the puzzle is to rearrange the numbers so each of the fifteen rows add up to 38. It comes in a wooden style with an antique, aged look.

Keep the Maths in Christmaths with this reasonably priced stocking filler. more...

## The Story Of Maths [DVD]

The films in this ambitious series offer clear, accessible explanations of important mathematical ideas but are also packed with engaging anecdotes, fascinating biographical details, and pivotal episodes in the lives of the great mathematicians. Engaging, enlightening and entertaining, the series gives viewers new and often surprising insights into the central importance of mathematics, establishing this discipline to be one of humanity s greatest cultural achievements. This DVD contains all four programmes from the BBC series.

Marcus du Sautoy's wonderful programmes make a perfect Christmas gift more...

Click the images above to see all the details of these gift ideas and to buy them online.

 Teacher, do your students have access to computers?Do they have iPads or Laptops in Lessons? Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Transum.org/go/?Start=May24

Here is the URL which will take them to a related student activity.

Transum.org/go/?to=cracked

## Extension

Which clockface is the odd one out?

The answer can be found by looking closely at the roman numerals used.

The clock on the right uses IIII for the number 4 while the other two clocks use IV.

Investigate which system of numbers is most common on clocks in your school, home or place of work.

More questions:

• At exactly which times are the hands of the clock pointing in the same direction?
• At exactly which times are the hands of the clock pointing in opposite directions?
• At exactly which times are the hands of the clock perpendicular?

There are more questions like these on the interactive Clock page.

For Students:

For All:
user
The text passage describes a mathematical problem involving a clock that has broken into pieces, with the condition that the numbers on each piece add up to the same total. It also includes comments from various users discussing the problem and suggesting extensions.

TYPE: SINGLE_QUESTION

The passage presents a single mathematical question about how a clock can break into pieces with equal sums of the numbers on each piece. However, it does not provide an answer to this question. Instead, it offers additional comments and extensions to the problem.