Algebra In Action

Instructions Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help. When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

	You are learning this because future ideas are built on previous ideas and the more ideas you learn the more power you have to learn anything, ever! The world's best football player engages in rigorous training, practicing skills repeatedly to prepare for the big game. While the specific actions rehearsed during these exercises are rarely needed in the match, the very process of performing these drills enhances their overall prowess as a top player. more...	More Activities: Maths Map Go Maths Games Puzzles Times Tables TablesMaster iPad Maths Investigations Exam Questions
Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician? Comment recorded on the 24 May 'Starter of the Day' page by 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" Comment recorded on the 19 November 'Starter of the Day' page by Lesley Sewell, Ysgol Aberconwy, Wales: "A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being able to access Starters for the whole month so I can use favourites with classes I see at different times of the week. Thanks."		Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month. The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing. Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.
Featured Activity Numskull Interactive, randomly-generated, number-based logic puzzle based on the Latin square designed to develop numeracy skills. These puzzles are drag and drop and can earn you a Transum Trophy.	Answers There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer. A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves. Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members. If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now: Subscribe
Go Maths Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school. Maths Map Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.
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If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:	Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.	It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org. When planning to use technology in your lesson always have a plan B!
Transum, Sunday, January 26, 2014 "These questions have been adapted from 'A First Book in Algebra' by Wallace Boyden. They all are designed to encourage an algebraic solution by setting up an equation (or alternatively simultaneous equations) and solving it. Some of the questions could be classified under the topic of ratio. In his introduction Wallace Boyden states 'Algebra is so much like arithmetic that all that you know about addition, subtraction, multiplication, and division, the signs that you have been using and the ways of working out problems, will be very useful to you in this study. There are two things the introduction of which really makes all the difference between arithmetic and algebra. One of these is the use of letters to represent numbers, and you will see in the following exercises that this change makes the solution of problems much easier.'." I'm Not A Humanist But..., Planet Earth Saturday, May 24, 2014 "On level 4 of the 'algebra in action' section, question 11 says: "Divide the number 137 into three parts, such that the second is 3 more than the first, and the third five times the second. What is the third part?" The answer is 100, but it was marked as being wrong, so I tried again, but with 20 (the second number) and 17 (the first number) and it marked 17 as being correct. Just thought you should know about this mistake so that you can correct it. [Transum: Thank you so much for taking the time to highlight this error. You were indeed right and the error has now been corrected. Thank you so much.]" Nick Staples, Waipahu Intermediate Wednesday, August 18, 2021 "Is there a way these algebra in action activities can be made into printable worksheets please. [Transum: Thanks for your feedback Nick. Most of the Transum online exercises can be printed directly from your browser. The input boxes transform into dotted lines for pupils to write their answers on and if the page is being printed by a Transum subscriber, the answers appear at the bottom of the worksheet.]"

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Back in 1895 Mr Boyden wrote 'Algebra is so much like arithmetic that all that you know about addition, subtraction, multiplication, and division, the signs that you have been using and the ways of working out problems, will be very useful to you in this study. There are two things the introduction of which really makes all the difference between arithmetic and algebra. One of these is the use of letters to represent numbers, and you will see in the following exercises that this change makes the solution of problems much easier'.

Example for level 4

The sum of two numbers is 25, and the larger is 3 less than three times the smaller. What are the numbers?

Let $x$ be the smaller number,
then $3x - 3$ represents the larger number.
$$x + 3x - 3 = 25 \\ 4x - 3 = 25 \\ 4x = 28 \\ x = 7 \\ 3x - 3 = 18$$
The numbers are 7 and 18.

Second Example. Mr Y gave $6 to his three boys. To the second he gave 25 cents more than to the third, and to the first three times as much as to the second. How much did each receive?

Let $x$ be the number of cents the third boy received,
then $x + 25$ is the number of cents the second boy received,
and $3x + 75$ is the number of cents the first boy received.
$$x + x + 25 + 3x + 75 = 600 \\ 5x + 100 = 600 \\ 5x = 500 \\ x = 100 \\ x + 25 = 125 \\ 3x + 75 = 375$$
1st boy received $3.75, 2nd boy received $1.25 and the 3rd boy received $1.00.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

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1. Charles and Henry together have 49 marbles, and Charles has twice as many as Henry and 4 more. How many marbles has Henry?	Working:
2. In an orchard containing 33 trees the number of pear trees is 5 more than three times the number of apple trees. How many pear trees are there?	Working:
3. John and Mary gathered 23kg of nuts. John gathered 2kg more than twice as many as Mary. How many kilograms did Mary gather?	Working: kg
4. To the double of a number I add 17 and obtain as a result 147. What is the number?	Working:
5. To four times a number I add 23 and obtain 95. What is the number?	Working:
6. From three times a number I take 25 and obtain 47. What is the number?	Working:
7. Find a number which being multiplied by 5 and having 14 added to the product will equal 69.	Working:
8. I bought some tea and coffee for £10.39. If I paid for the tea 61 pence more than five times as much as for the coffee, how much did I pay for the coffee?	Working: £
9. Two houses together contain 48 rooms. If the second house has 3 more than twice as many rooms as the first, how many rooms has the larger house?	Working:
10. Divide the number 23 into three parts, such that the second is 1 more than the first, and the third is twice the second. What is the first part?	Working:
11. Divide the number 137 into three parts, such that the second is 3 more than the first, and the third five times the second. What is the third part?	Working:
12. Three sisters have 574 CDs between them. Jess has 15 less than Helen, and Tasha has 4 more than Jess. How many does Tasha have?	Working: CDs

Real life problems adapted from an old Mathematics textbook (A First Book in Algebra, by Wallace C. Boyden 1895) which can be solved using algebra and common sense!

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Numskull

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Example for level 4