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These could be five oranges, five grapes, five tennis balls, five bricks Line up all five objects and count them. Now remove one object from the lineup and place it to the side. This is the same as subtracting one from your original number, which was five. What is five minus one?

Count the remaining objects to find out: four. Return the object you removed to the lineup.

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You had four objects, now you have added one, and as you can see, there are now five objects again. So four plus one equals five -- the evidence is right in front of you. Reset your lineup of five objects, then repeat the exercise while removing two, three, four and, finally, all five of the objects. Once you've removed an object and calculated the result, add it back in and recalculate the result.

Basic addition

Expand your grasp of the subject, now that you understand the basic principle of it, by memorizing addition and subtraction tables. See the Resources section for links. Place one grape on the table in front of you. Now place another grape beside it. You've got one grape, twice -- in other words, one times two. If you count the grapes, you'll see that one times two is a total of two.

Eventually, students will be able to identify appropriate operations independently. Teach the concept of complements or partners for addition, subtraction, multiplication and division. For example, the number 5 is made up of 2 and 3, 1 and 4; 24 is made up of the factors 8 and 3, or 2 and 12, etc. This concept not only increases the student's ease with number facts; it also facilitates mental mathematics.

Mental Math Tricks - Addition, Subtraction, Multiplication & Division!

When teaching facts, focus on 2 or 3 related facts at a time. Emphasize accuracy first, then speed.

Addition and Subtraction

Maintain a chart of mastered facts to help the student recognize progress. Small flip charts can be provided at a student's desk, with cues for steps in particular types of problems as a reference or reminder. The number line APH can be used for working on operations, relationships, fractions, and decimals. Number lines are especially useful when they are stretched across the top of the student's desk, less helpful when confined to the dimensions of a braille page.

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  • The number line attached to the student's desk is particularly helpful when the student is using the braillewriter. Students can find the larger number, count forward for addition and count backward for subtraction. Students can use number lines for working on positive and negative numbers as well. Thermometers can also be useful in teaching positive and negative numbers. Flashcards can be used along with manipulatives for working on the basic operation facts and the Nemeth Code; later, students can braille out their own mathematical sentences.

    Students having difficulty learning addition, subtraction, multiplication or division facts can make cards of those facts with which they are having the most trouble. Write the problem on one side of the card and the answer on the reverse side. Teachers can use creativity and relevant examples, scratch and sniff stickers, etc. Many models of these types of aids can be found in teacher stores. To practice mathematics facts, students can roll dice, then add, subtract, multiply or divide the numbers thrown.

    A variety of rules can make this into a game. For example, the first student whose cumulative numbers add up to wins, or students start from and subtract numbers thrown and the first one reaching zero wins, or students multiply the two numbers thrown and then add these numbers cumulatively. Students could also rename fractions formed by combining the two numbers thrown. End There! The student then determines at least 3 ways to get from the first number to the second, brailling each series of computations below the number pair.

    He or she may use any combination of addition, subtraction, multiplication, and division. While the above tips relate to teaching any of the basic arithmetic facts, the following suggestions could be especially appropriate for working on addition and subtraction: For students who have great difficulty remembering number facts, an additive principle may be helpful.


    Magnets can be used on a small cookie sheet or magnet board to form groups for addition or subtraction problems. Unlike the manipulatives usually found in primary level classrooms, individual magnets can be moved easily without falling off the surface. At a more advanced level, a cookie sheet or magnet board could be used as a personal "chalkboard" where individual tiles labeled with Nemeth Code numbers and signs of operation and affixed to magnetic tape could be arranged to form a variety of problems.

    Wikki Stix could be used for separation lines. The student could work on a variety of problems at his or her desk while the teacher works the problems at the board. Classroom teachers would have to cooperate by verbalizing the problems clearly! The work tray from the American Printing House for the Blind can serve as a good organizer for making simple addition and subtraction statements.

    Example #1

    For example, a collection of small manipulatives can be placed in the larger section on the left of the tray. Four of these objects could be placed in the first of the three smaller sections and 2 more placed in the second section. The student could then take the objects from both sections and place them in the third section, counting them for the total of 6. The same procedure could be used for subtraction statements.

    Problems involving the addition or subtraction of zeros could also be worked out in a very concrete manner using this approach. To teach addition to young children, cubes that attach to each other e. The student can be given a specific number of cubes, and asked to count them; then the student can be given a second group of cubes which are counted and attached to the first group. The total number of cubes can then be counted. Beads on a string can also be used by giving the child a string with first 2 beads of one shape circles , then 3 beads of a different shape squares.

    When setting up spatial arrangements involving regrouping i.

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    As the student fills the frame with counters, he or she can see that if another place is needed for a sum larger than the 9 available, he or she must place it above the frame. A separated section above the frame could be added to hold the carryover number. Students can work on the concepts of "greater than" and "less than" while they work on addition and subtraction. For example, two numbers 8,13 could be given to the student in a particular sequence, and the student would have to state the relationship of the first number to the second 8 is less than