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Fractions, Decimals, & Percents Geometry Measurement

Fractions, Decimals, & Percents Geometry Measurement. EDU 592 Class 3. Developing Fraction Concepts.

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Fractions, Decimals, & Percents Geometry Measurement

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  1. Fractions, Decimals, & PercentsGeometryMeasurement EDU 592 Class 3

  2. Developing Fraction Concepts • Fractional parts are equal shares or equal sized portions of a whole or a unit. A unit can be an object or a collection of objects. More abstractly, the unit is counted as 1. On the number line, the distance from 0 to 1 is the unit. • Fractional parts have special names that tell how many parts of that size are needed to make the whole. For example, thirds require three parts to make a whole.

  3. Developing Fraction Concepts • The more fractional parts used to make the whole, the smaller the parts. For example, eighths are smaller than fifths. • The denominator of a fraction indicates by what number the whole has been divided in order to produce the type of part under consideration. The denominator is a divisor. It names the kind of fractional part under consideration.

  4. What fraction of the large square is shaded…

  5. Developing Fraction Concepts • The numerator tell how many of these fractional parts are under consideration. It is a multiplier - it indicates a multiple of the given fractional part. • Two equivalent fractions are two ways of describing the same amount by using different-sized fractional parts.

  6. Decimal and Percent Concepts • Decimal numbers are simply another way of writing fractions. Both notations have value, and students need to understand how the two symbol systems are related. • Our base-ten place-value system extends infinitely in both directions. Between any two place values, the 10:1 ratio remains the same.

  7. Match the Decimal Number with the closest fraction expression: 1 .41 7 5 8 .804 .6271 .211 1 3 5 8

  8. Decimal and Percent Concepts • The decimal point is simply a convention that has been developed to indicate the units position. • Percents are hundredths. They are another way of writing fractions and decimals. • Addition and subtraction with decimals are based on the fundamental concept of adding and subtracting numbers in like position values.

  9. Decimal and Percent Concepts • Multiplication and division of two numbers will produce the same digits, regardless of the positions of the decimal point. Computations should be performed as whole numbers with the decimal point placed using estimation. .6 x 2.5 = Think: 6 x 25 = 150 What would be reasonable?

  10. Geometric Thinking • Many different geometric properties influence what makes shapes alike and different. For example, shapes have sides that are parallel, perpendicular, or neither; they have a line of symmetry, rotational symmetry or neither; they are similar, congruent, or neither. • Shapes can be moved in a plane or in space (translations, rotations, reflections).

  11. Geometric Thinking • Shapes can be described in terms of their location in a plane or in space- coordinate systems can be used to describe these locations precisely. • Shapes can be seen from different perspectives, which helps us understand relationships between 2 and 3-dimensional figures.

  12. Name the Property Have it: Don’t have it:

  13. Name the Property Which of these has it?

  14. Developing Measurement Concepts • Measurement involves a comparison of an attribute with a unit that has the same attribute (length to length, time to time, etc.). • Meaningful measurement and estimation of measurements depend on a personal familiarity with the unit of measure being used.

  15. Developing Measurement Concepts • Estimation of measures and the development of personal benchmarks for frequently used units of measure help students increase their familiarity with units and help to prevent errors. • Measurement tools replace the need for actual measurement units. We need to understand how they are used to accurately and meaningfully use them.

  16. Developing Measurement Concepts • Area and volume formulas provide a method of measuring these attributes by using only measures of length. • Area, perimeter, and volume are related to each other, although not precisely or by formula.

  17. Developing Measurement Concepts How many different rectangles can you make with an area of 36 square units? • For each rectangle, record the perimeter. • Make a conjecture about the relationship you see.

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