**Decimals, Percentages, and Ratios**

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**Decimals: **

-Decimal place value is an extension of whole number place value.

-The base 10 numeration system extends infinitely to very large and very small numbers (millions and millionths)

**Percentages**

-Percentages are simply hundredths and as such are a way of writing both fractions and decimals

**Ratios**

-Ratios are multiplicative comparisons of quantities; there are different types of comparisons that can be represented as ratios.

-Ratios give the relative sizes of the quantities being compared, not necessarily the actual sizes.

-Equal ratios result from multiplication or division, not from addition or subtraction.

(Bahr, de Garcia. 2009)

**Decimal Instruction**

-Why do we use decimals? (When we need to express numbers with more precision than whole numbers can provide)

-Just like with whole numbers, a digit in a decimal number has a value that depends on where that decimals is located

-This list shows the value of each place:

1.234567 ones

1.234567 tenths

1.234567 hundredths

1.234567 thousandths

1.234567 ten thousandths

1.234567 hundred thousandths

1.234567 millionths

-Remember that adding zeros to the end of a decimal number does not change the value of the number

-An expanded decimal is a decimal written as a sum of its whole numbers and decimal components by place value, ex:

1 + 0.2 + 0.03 + 0.004 + 0.0005 + 0.00006 + 0.000007 = 1.234567

**Percent Instruction**

-If we break down percent to per-cent, we can see where this word comes from, and what it really means “for every hundred”

-A percent is a ratio that compares a part to a whole using 100 as the whole

-Percents transfer to decimals very easily because decimals work in powers of 10 and 100 which is used in percents is a power of 10.

-Students should be given the chance to find their way to convert back and forth between decimals and percentages

-Percentage forms of numbers help us compare numbers in an easier manner

**Ratio Instruction**

-Start by reviewing the reducing of fractions

-Ratios help us compare two numbers, and help us understand how they are related to each other

-There are two ways ratios can be written:

3/5 and 3:5

-Here is a sentence that can be used to work with ratios:

For every ____ there are ____

**Useful Websites to Enhance Decimals, Percentages, and Ratios Instruction: **

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http://www.shodor.org/interactivate/activities/SierpinskiTriangle/

Manipulate the triangle lengths by pushing the next button and watching the lengths of the sides divide in half shown as decimal lengths.

http://www.mathgoodies.com/lessons/vol4/meaning_percent.html

This is a great resource where the student uses grids to find the fractions and ratios of the shaded regions in the grid.

http://nlvm.usu.edu/en/nav/frames_asid_160_g_3_t_1.html?open=activities&from=category_g_3_t_1.html

With this virtual manipulative you may specify any two of the three quantities, “Part,” “Whole,” or “Percent.” When you click the Compute button, the computer will calculate the remaining quantity. The percentage relationship is displayed visually in the vertical column of the Percent Gauge and in a pie chart. An equation shows how to compute the unknown quantity, and the result is stated verbally.

http://www.bbc.co.uk/skillswise/numbers/fractiondecimalpercentage/comparing/comparingall3/game.shtml

The students will match the equivalent fraction, decimal, or percentage pairs in this interactive game. You can choose how many matches you want to work with and whether the connection is between which combination of decimals, percentages, and fractions, or you have an option to use all three within the numbers that will come up for you to match. This is an especially fun game to play as a review with the whole class on a Smart Board where the children can actually manipulate the game from the board.

http://www.funbrain.com/penguin/index.html

This website provides realistic application with decimals and percentages. Figure out how much are we going to tip the waiter? A problem will be presented and you have to type in the answer. If you get it correct then the waiter penguin approves and you get a point.

http://www.imathlearning.com/worksheets/3fraction/fraction73.html

This website provides a whole worksheet of twenty-one grids that have various amounts of shading on them. The students are required to write the fractions next to each grid. The teacher has the option to change the worksheet to equal any new varieties of fractions depicted on the grids.

Works Cited:

Bahr, D., de Garcia, L. 2009. Elementary mathematics is anything but elementary-Content and methods from a developmental perspective. Wadsworth Cengage Learning. pg. 353)