#### Fraction, Decimal, and Percent Concepts

Prior knowledge

Prior knowledge Whole numbers, place value of whole numbers, rational numbers (1/2, 1/3...), know the relationships of whole numbers and fractional numbers (> < =), order whole and fractional numbers, meaning of estimation, familiarity with percent.

Sample problems --->>> another sample problem

Connect fractions to decimals
Create a problem (subway sandwich) so that it can be represented in tenths. Students can solve with fractions and then transition to decimals
Represent whole, fractional, and decimal numbers in tenths, hundredths, thousandths and (><=)

Multiplication and division. Five and eight tenths meters of paper shared equally with five groups.

Fractions

• Fractions are part/whole relations
• Fraction is equal parts of a whole (one) or
• Fraction is equal parts of a set or group (of wholes or fractional parts) they are considered one whole.
• Human beings constructed fractions to deal with fair sharing situations.
• Fractional parts must be equivalent and they must be equivalent in relationship to the whole.
• The whole matters, fractions are relations.
• To compare fractions the whole must be the same
• Fractional parts don't need to be congruent to be equivalent.
• Can compensate: remove here, add there, as long as every loss has an equal gain.
• Fractions are division (three dollars shared with four people)
• Multiplication is connected to fractions (3/4 = 3 * 1/4)
• Multiplication and division or rational numbers are relations on relations
• If numerators are common only denominators matter when comparing
• If denominators are common only the numerators matter when comparing
• The bigger the denominator the smaller the piece
• Fractions represent division Fractions are equal parts of a whole, part, group, or set
• Equivalent fractions are equal representations of the same whole, part, group, or set
• Equivalent fractions represent different ways of describing the same amount using different sized fractional parts
• Fractions can represent parts and wholes
• Fractional names tell how many parts of equal size are needed at make a whole
• The more parts needed to make a whole, the smaller the parts
• The numerator tells the how many parts are represented and the denominator the kind or number of parts the numerator counts.
• Fractions can be added, subtracted, multiplied, and divided

Decimal

• Decimals represent fractions
• Decimals can represent percents
• Decimals can represent ratios
• Decimals represent division
• Decimals are based on place value
• Whenever a fraction has a denominator of ten the numerator represents tenths. 3/10 = .3, 53/10= 5.3…
• All 1/2 fractions are equal to .5
• Adding a zero to the divisor moves the decimal one place like it does when you divide or multiply whole numbers by 10 or 100…
• Adding decimals is like adding fractions with common denominators
• Dividing by 10, 100, 1000, gives an answer that has as many digits to the right of the decimal as zeros on the number you are dividing.
• It happens because you are dividing by ten…
• Base ten is infinite both for number values that increase and number values that decrease.
• The decimal point can reperesent "and" when reading decimal numbers.
• Decimal point locates the unit (ones) position.

Percent

• Percent represents hundredths.
• Fractions, decimals, and percents can be changed back and forth to make problems easier to solve. (1/2, .5, .50, 50%; 10%, .1, .10, 1/10; 1/4, .25, 25%;…)

Ratio and Proportion

• Ratios and proportions result in treating numbers in relation to each other to form new numbers.
• Ratios and proportions result in forming new ways to represent rational amounts and proving that many forms are equivalent even though they don't look alike.
• For equivalence the ratio must be kept constant

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Dr. Robert Sweetland's Notes ©