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Gifted and Exceptional Students and Math Problem Solving

written by: Barbara • edited by: SForsyth • updated: 7/12/2012

Gifted students may be the best problem-solvers in your math classroom or the ones who will assert that they are just not into math. Either way, teachers can take a simple math lesson on ratios and create both a challenging opportunity and a teaching moment for gifted students in math classes.

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    Learning Experience with Ratios

    Whether gifted students are exemplary in math skills or struggling to find a niche in a math class, teachers can create powerful learning opportunities for all gifted students at any given level in the classroom. Using strategies that define, describe and demonstrate real life applications of the math concept, teachers can use instruction to reach all math learners in elementary to high school classrooms. In creating a lesson on ratios, teachers can provide visual, auditory and kinesthetic learning opportunities that invite students with differentiated learning styles to construct ways to process and solve problems in a way that makes sense to them.

    Teaching Strategies - Problem-solving Ratios

    • When you introduce a new math term into your learning objectives make sure you provide definitions and examples for your student's math journals. Definition: Ratios compare two quantities by showing how one quantity relates to the other mathematically. For example, if you place a dime and ten pennies on a table, you can show students that the ratio of 1 dime to 10 pennies is 1:10, 1 to 10 or 1/10 which means that there are 10 pennies in 1 dime and 1 dime contains 10 pennies, not 9, 8, or 7 pennies, but 10 pennies.
    • Solve the following ratio problems using the example given above to express your answers. You can also provide students with manipulatives to create a visual of the problems.
    1. 1. 5 Lego cubes to 10 paper clips

    Answer: 5/10, 5:10, 5 to 10

    2. 6 pencils to 2 pennies

    Answer: 6/2, 6:2, 6 to 2

    • Introducing another level of ratio problem-solving can create a new challenge of learning for gifted students. Teachers can have students problem solve independently in their math journals, on the board, in collaborative groups or have them generate their own problems using the concepts learned from comparing ratios of learning aids provided. Now let's take it further by solving the next set of problems by writing each into at least three equivalent ratios:

    3. 8/16

    Answer: 1/2, 16/32, or 24/48 (see a pattern yet?)

    4. 1 to 4

    Answer: 2/8, 4/16 or 12/48

    The pattern for #3 of 8/16 is 1/2, so every ratio equivalent (16/32 and 24/48), equals a half. If you divide the top number into itself and into the bottom number, you will always get 1/2, so any of those ratios equals half of the given number.

    By taking a simple math concept and creating academic success and access for gifted students in math classrooms, teachers can create learning opportunities that challenge and motivate learners in understanding that ratios are a part of their daily life and are simple comparisons of two quantities that could be red and green marbles or math level 1 books to math level 2 books or any number of comparisons in real life.

    Source: author experience