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How to Teach Problem Solving for Algebra Through Graphic Representations

You can explain math to students using manipulatives and analogies. A manipulative is a physical object that students can see and touch, and that is used to represent mathematical quantities. To teach basic algebra skills, you will need to buy some props that the students can use to solve problems. By using concrete objects to solve problems, students are given a more gradual introduction to abstract thinking.

Things You'll Need

  • 1 Pack Index Cards
  • 1 Box, approx. 4" x 4"
  • Bag of marbles
  • Permanent marker
  • Scotch tape
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Instructions

    • 1

      Use your permanent marker to write some operators on your index cards. Make sure to have at least one labeled with an equal sign (=), an addition sign (+) and a minus sign (-). Then label at least one index card with an X, representing a variable. Attach this index card to the top of the small box and place 3 marbles in that box.

    • 2

      Show your student the index card with the = sign, and place four marbles in a bunch on either side of it. Explain that the = sign means that there are the same number of marbles on either side. Remove three marbles from one side and demonstrate that, in order for the equality relation to hold, you must remove three marbles from the other side as well.

    • 3

      Remove the single marble on one side and replace it with the box: ask your student how many marbles are in X, assuming that the equality relation is correct. When the student answers, open the box and show him that there are three marbles inside.

    • 4

      Place two more marbles in the box without allowing the student to see what you're doing. Then, put the box back on one side of the = sign, and place two more marbles beside the box on the same side: put the index card marked "+" between them. Then, place seven marbles on the other side of the equal sign. By this time, the student should understand that if the box is by itself on one side of the = sign, then the number of marbles on the other side is the number of marbles in the box. Ask your student how many marbles he must remove from each side to find the number of marbles in the box.

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