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Algebragons

Find the missing expressions in these partly completed algebraic arithmagon puzzles.

Menu Arithmagons Level 1 Level 2 Level 3 Level 4 Level 5 Help More Algebra

Complete the algebragons. The expressions in the rectangles are the sums of the linear expressions in the adjacent circles.

\(x\)

\(3x\)

\(2x\)

Correct Wrong

Correct Wrong

Correct Wrong

+

\(2x+1\)

\(5x-3\)

\(3x+2\)

Correct Wrong

Correct Wrong

Correct Wrong

+

\(2x\)

Correct Wrong

\(x-5\)

\(3x+4\)

Correct Wrong

Correct Wrong

+

\(9-3x\)

\(x+4\)

Correct Wrong

Correct Wrong

\(6x+4\)

Correct Wrong

+

\(1-x\)

Correct Wrong

Correct Wrong

\(x+6\)

Correct Wrong

\(6x+1\)

+

Correct Wrong

Correct Wrong

\(9-3x\)

\(10\)

\(16-2x\)

Correct Wrong

+

Check

This is Algebragons level 1. You can also try:
Level 2 Level 3 Level 4 Level 5

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.

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Description of Levels

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Arithmagons - The same sort of puzzle but with numbers not algebra.

Level 1 - The expressions in the rectangles are the sums of the linear expressions in the adjacent circles.

Level 2 - The expressions in the rectangles are the sums of the linear and quadratic expressions in the adjacent circles.

Level 3 - The expressions in the rectangles are the products of the monomial expressions in the adjacent circles.

Level 4 - The expressions in the rectangles are the products of the binomial expressions in the adjacent circles.

Level 5 - The expressions in the rectangles are the products of the mixed (including fractions) expressions in the adjacent circles.

Fractionagons - Different topic, same structure.

More Algebra including lesson Starters, visual aids, investigations and self-marking exercises.

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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Mathematical Notation

Use the ^ key to type in a power or index then the right arrow or tab key to end the power.

For example: Type 3x^2 to get 3x2.

Use the forward slash / to type a fraction then the right arrow or tab key to end the fraction.

For example: Type 1/2 to get ½.

Fractions should be given in their lowest terms.

Use brackets if the numerator has more than one term.

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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Here are some suggestions for how you may solve the puzzles in which only the three expressions in the rectangles are given (the last question in levels three and above):

For novice learners

  1. Guess an expression for the top circle
  2. From that calculate the values that would be in the bottom two circles
  3. Do these two values sum to the bottom rectangle? If so finish.
  4. If not is their sum too high or too low? Adjust the top circle value accordingly and go back to (2)

Replace 'sum' with 'product' if the operation is multiplication.

For advanced learners

  1. Let y stand for the top circle expression
  2. From that find expressions for the bottom two circles
  3. Make an equation from the bottom two circles and the bottom rectangle
  4. Make y the subject of that equation. Now you have the expression for the top circle.

A great 'trick'

This was found by Ann Roberts, a Transum subscriber, who wrote with this method of solving an arithmagon with 18, 15 and 11 in the rectangles. It also works for algebraic expressions.

  1. Add the numbers in the rectangles: 18 + 15 + 11 = 44. This is the same as adding the numbers in the blank circles twice.
  2. Divide this sum by two: 44 ÷ 2 = 22. This is now the same as adding the numbers in the blank circles once.
  3. Finally: 15 is the sum of the bottom white circles so 15 + top white circle = 22

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