The English Meaning of Mathematical Symbols

At the top of the Gizmotm, you will see an algebraic equation. Underneath it is a scrambled set of word tiles. Your goal is to form an English sentence that matches the algebraic equation by selecting the correct tiles and arranging them in the proper order. To make a sentence, drag the word tiles one at a time from the middle bin to the bottom one.

  1. The first equation is x + 3 = 2. (If this is not the equation at the top of the Gizmo, you will need to restart the Gizmo.) This equation has a variable (x), two numbers (3 and 2), and two operators (+ and =).
    1. If numbers, variables, and operators are all considered to be objects, how many different objects are in this equation?
    2. Click on the HINT button to remove the word tiles that will not be used in this problem. How many tiles are left? How does this compare to the number of objects in the equation?
    3. An algebraic equation is read from left to right, just like an English sentence. The first part of the equation x + 3 = 2 is x. x is a variable. Variables are used to represent an unknown number. Which tile best stands for an unknown number? Drag that tile into the bottom bin.
    4. The second part of the equation is +. Drag the tile that you think corresponds to this operator into the bottom bin. Check your answer by seeing if the display at the bottom of the Gizmo shows x +.
    5. Drag the remaining tiles in the order that you would say them aloud. Your answer is correct if a check mark appears at the bottom of the screen. If not, look at the original equation and see if you can rearrange the tiles to obtain the correct solution. What English sentence did you make?
  2. Click on NEW to try another algebraic equation. If an English sentence appears at the top of the Gizmo instead of an algebraic equation, click on NEW again until you get an algebraic equation. This time, try to solve it without using the HINT button.
    1. What algebraic equation were you given?
    2. What English sentence did you make to match the equation?

Forming Algebraic Equations from Sentences

In the previous section, you translated algebraic equations into English sentences. Now, you will learn how to reverse the process and translate English sentences into algebraic equations.

  1. Click on NEW until an English sentence appears at the top of the Gizmo.
    1. What English sentence were you given?
    2. Identify each of the variables, numbers and operators within the sentence.
    3. Drag tiles one by one to the bottom bin to form an algebraic equation that matches the English sentence. If you find it difficult at first, click on the HINT button. What algebraic equation did you make?
  2. Try another example without using the HINT button.
    1. Write down the English sentence you were given.
    2. What algebraic equation did you form to model the sentence?

Equivalent Equations

Often, a mathematical relationship can be represented by more than one English sentence.

  1. Click NEW until an algebraic equation involving addition or multiplication is displayed at the top of the Gizmo.
    1. What algebraic equation were you given?
    2. Translate the equation into an English sentence using the Gizmo. What sentence did you make?
    3. There is more than one sentence that is equivalent to your equation. For example, the equation n + 5 = 6 is equivalent to all of these sentences:
      • a number plus five is equal to six
      • five plus a number is equal to six
      • six is equal to a number plus five
      • six is equal to five plus a number
      Even after you have made one correct English sentence, you can continue to move the tiles around. Try to make all four sentences that are equivalent to your equation in the Gizmo. What are the four sentences?
  2. Click NEW until you have an algebraic equation involving subtraction or division.
    1. What is your equation?
    2. Use the Gizmo to build as many English sentences that are equivalent to the given equation as you can. How many can you make? What are they?
  3. How many English sentences are equivalent to an algebraic equation involving addition or multiplication? How many English sentences are equivalent to an algebraic equation involving subtraction or division? Explain why these answers are different.