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High School — Mathematics
Number, Number Sense and Operations


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    Number, Number Sense and Operations


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      Strategies: Help with Fundamentals

      The following activities are suggestions for working with students who need help with fundamentals. We hope that the activities spark ideas and conversations among teachers about useful classroom strategies that can supplement existing curriculum.

      Difficulty 1

      Students have trouble converting between fractions, decimals and percentages and using each form to solve problems.

      • Broaden students' understanding of rational numbers by having students model fractions, decimals, and percentages on area models, such as fraction strips, number lines and 10 by 10 grids. Teach them to represent 0.5 as a fraction, decimal, percentage, and as a visual model. Have them repeat this with some of the other common numbers: 0.25, 0.33, 0.75, etc. When students are successful expressing rational numbers in various forms, move to a grade level activity that requires students to compare, order, and determine equivalent forms of real numbers. Allow students to represent the numbers with visual models as needed.

      Difficulty 2

      Students are often confused about which way to move the decimal point when converting numbers from scientific notation to expanded form.

      • Students often move the decimal point in the wrong direction because they don't understand the meaning of the powers of ten. First, find ways for students to model numbers such as , , , , , etc. Students should understand that a number such as is much larger than a number such as . Then display a list of numbers written in scientific notation. Have students determine which are large numbers and which are small numbers based on the powers of ten. Finally, have students use this information to convert the numbers expressed in scientific notation to expanded form.

      Difficulty 3

      Students have a difficult time remembering the exponent rules when simplifying expressions.

      • Many textbooks rely on a set of exponent rules that are meant to help students simplify expressions with exponents. For example, and . For some students, it can be difficult to memorize such rules and apply them. If the meaning of exponents is emphasized, then these students might not need the rules. For example, have students use linking cubes or other physical models to represent such problems as or . Students can then use the models to understand the meaning behind the exponent rules.

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