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Trial And ImprovementLearn efficient ways of using trial and improvement to solve real-life and algebraic problems. |
Guess the answers, press the check buttons, improve your guesses and repeat until all of your answers are correct.
InstructionsTry 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. |
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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 17 November 'Starter of the Day' page by Amy Thay, Coventry: "Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils. Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales: "I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!" |
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Featured ActivityKey Stage 2 Tests There are some wonderful questions for Year 6 pupils in the Key Stage 2 Maths Tests (SATs) which normally take place at this time each year. Here are some links to Transum activities for the main Maths attainment statements. Click the image above to begin. |
AnswersThere 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 |
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Go MathsLearning 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 MapAre 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! |
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Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments. |
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❎Level 1 - Basic Guessing Exercise
Level 2 - Algebraic Questions
Level 3 - More Difficult Algebraic Questions
Consecutive
This activity explicitly mentions that "getting the correct answer first time can be done by trial and improvement." It encourages students to try different possibilities, adjusting their approach based on feedback until they find the solution.
Green Fingers
A very visual representation of the trial and improvement method. Choose the amount of liquid from each bottle needed to make the watermelon grow as big as possible.
Estimation Golf
Estimate the value of the unknown in the algebraic expression and see your accuracy in the form of a game of golf.
Consecy Brothers
Described as a "classic trial and improvement starter," this activity allows pupils to make guessed solutions and, if incorrect, try modified guesses. This iterative process is at the heart of the trial and improvement method.
THOAN (Think of a Number)
This problem involves students deducing a number based on a series of operations. While it can be solved algebraically, the activity notes that trial and improvement is a valid approach, especially for younger students or those not yet familiar with algebraic methods.
Less Than
This starter expects students to use a little 'trial and improvement,' especially if they are not yet comfortable with solving inequalities algebraically.
Rabbits and Chickens
A classic problem where students determine the number of rabbits and chickens given the total number of heads and feet. The activity suggests that "the most basic strategy could be one of trial and improvement," making it accessible to learners at different levels.
Four Problems
This set includes problems where "some allow for a trial-and-improvement method to arrive at the solution," giving students the opportunity to experiment with different approaches and refine their answers through iteration
Online Logo
Where estimating lengths and angles is required but trial and improvement will allow students to draw the polygons accurately.
Statistics Supplied
Find all of the sets of whole numbers matching the given statistical conditions. This is a more advanced application of the trial and improvement (or guess and test) strategy.
Iteration
Find approximate solutions to equations numerically using iteration.
More algebra including lesson Starters, visual aids, investigations and self-marking exercises.
This is an exercise where you use your brain and make clever guesses!
Each question will include a picture, like an old elephant, and ask you something like:
"How old is this elephant?"
Your job is to type in your best guess of the answer in the box. Then press the Check button.
If you’re right – well done! You’ll see a green tick.
If you’re not quite right, don’t worry. The page will tell you if your guess is:
Keep changing your guess and pressing Check until you get it just right!
You’ll do this for 10 different questions. If you get them all correct, you’ll earn a shiny virtual trophy!
Each student will get different answers, so it's all about your own thinking – no copying!
Take your time, use the clues, and enjoy the challenge. Good luck!
The video above is from the excellent Corbett Maths
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.
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
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