The Visual / Auditory / Symbolic / Kinesthetic Approach to Algebra

More, Less, The Sum, The Difference, Double, Triple

      A working knowledge of the words more, less, sum, product, double, triple, zero, and opposite is necessary for work on this and its related practice pages. For a review of zero and opposite see "The Opposite and "Zero" and "'Zero In' and 'Zero Out' to Simplify". For review of the other words see MATH SPOKEN HERE! - an arithmetic and algebra dictionary.

      It is the teacher's job to determine what work is to be done manipulatively, mentally, or with paper and pencil (either in a computational way or for record keeping and debriefing). Because Term Tiles may be used from early primary through remedial college or adult basic education, the examples are representative of many levels of sophistication and need. Some times slightly different versions of the same questions are presented as examples of different wordings or tasks.

      While writing this page, I, Agnes, began a discussion with myself on whether the answer key should contain all the answers or just some of the answers. The teacher in me won over the author in me -- all answers are included below. Additional comments are also included.

      The reader is reminded that mental computation should be encouraged. For the student who chooses to work mentally and gets the wrong answer, explain that Term Tiles are a way for an outsider /the teacher / you to view of what is going on in the student's head and that may be very desirable. For the student who chooses to work mentally and gets the right answer, permit her that freedom or use the higher order skill and ask that she justify her answer.

Exercises, Set A. CONSTANTS ONLY.

Ex. 1 - 6: Represent.
1.  three
2.  six
3.  negative three
4.  zero
5.  zero in another way
6.  three in a way not already used
Ex. 7 - 12: Represent and simplify.
7.    three more than two
8.    three less two
9.    three decreased by two
10.  triple the value of 3 decreased by 2
11.  double five
12.  double the sum of two and one
Ex. 13 - 16: Write an expression.
13.  for the figure below.
14.  different but equivalent from that of ex. 13.
15.  equivalent to ex. 13, but which includes the word "sum."
16.  for the figure below.
Ex. 17 - 18: Prepare to explain out loud
17.  how to simplify the given expression.
18.  a starting expression, what was done, the final expression for the work below.
19.  Show tile techniques to explain how to represent then simplify ex. 10.
20.  What is the most idea you learned today? Explain the idea.
Ex. 21 - 24: Evaluate.
21.  the sum of -3, -3, 5, 4, and -1
22.  double the sum of -2 and 5
23.  triple the sum of -2 and 5
24.  the figure below.
Links to Set A Answers

Ex. 1 - 15.     Ex. 16 - 18.     Ex. 19 - 20.     Ex. 21 - 24.

Exercises, Set B

1.  What idea is represented here. Use a name other than "x" or "eks."
Ex. 2 - 24. Represent with Term Tiles and simplify if possible then write in symbols and simplify if possible.
2.  a number
3.  three more than a number
4.  three less than a number
5.  three decreased by a number
6.  a number decreased by three
7.  four decreased by a number
8.  four increased by a number
9.  a number decreased by four
10.  double the sum of a number and three
11.  one less than double the sum of a number and three
12.  three less than one more than a number
13.  four more than double a number
14.  the sum of four and double a number
15.  four less than five
16.  five less than four
17.  four less than a number
18.  the opposite of a number
19.  triple a number
20.  triple the sum of a number and two
21.  four times the sum of a number and 3
22.  the result when a number is doubled, increased 2, then decreased 3
23.  four less than double a number
24.  five more than double the sum of a number and one
25.  Which is greater x + 3 or x + 4 or state "you can't tell." Explain your answer.
26.  Which is greater 3x or 4x or state "you can't tell." Explain your answer.

Links to Set B Answers

Ex. 1 - 6.     Ex. 7 - 10.     Ex. 11 - 14.     Ex. 15 - 20.
Ex. 21 - 22.     Ex. 23 - 25.     Ex. 26., Unit 7   © 2008, A. Azzolino