UNIT III
DECIMALS: A conceptual approach

 Adding: Many of us learned to read a problem with a sentence like this: "0.001 of the water volume was spilled of the cup." {which we read: zero point zero zero one of the water...} (not all of us, but some of us) Now the question is what is the real meaning of 0.001? In this lesson students learn with the help of manipulatives
(place value mat) the concept of a tenth, hundredth, thousandth and
how to apply it to addition problems that involve decimals. The reading above might more properly be done: " A thousand of the water volume ..." Would you be able to answer how many mililiters were spilled if the volume was 77 millimeters?

 Subtracting: All these lessons are part of the number sense. In a car shop you have millimetric tools that have measurements referred in millimetric units. others have units in the English system and use fractions where the millimetric tools use decimals. Sometimes you have the equivalent from one to the other, but not always. So if you dad tells you while fixing the car in the garage: "Could you pass me the three fourths wrench?" and you realize is missing... Would you be able to get the closest matching one of the millimetric set without looking at the size but just at the engraved numbers? The
lesson of adding decimals is extended in this one to subtraction
using the place value mat and the manipulatives. Students learn how
to compare decimals by going from the factional representation to
the decimal one.

 Multiply
by a decimal: You learned in the section for fractions the effect of multiplying fractions and whether the answer is a smaller or larger number that each one of the factors in the product. Now, you will do the same but with decimals. By covering the lesson you will
learn in this lesson how to get the fractional part of a number and
then its meaning as decimal part of that same number. They extend
this understanding to multiplication of any number by a decimal. Once, you mastered the concept then the opportunity is given to
solve several word problems.

 Divide by a decimal: In previous lessons you practice fractions adding, subtracting, multiplying or dividing them. You learned that when you divide three fourths by a fourth you don't get a fraction, you get three. Because a fourth fits three times in three fourths. Now this is done with decimals. In this
lesson you will use the place value mat and the manipulatives to master the
conceptual meaning of a division, and it is extended to division by
a decimal number.

 Fractions to Decimals to Percent: You read in the news that only 5% of the starts in a constellation of 7000 trillion of starts are Nova starts. Is that an insignificant amount of stars? Then you hear somebody saying that he marked in the forest 500 trees. The forest has millions of them. Did he marked a large portion of them?
In this lesson students learn how to extend the concept of a
fraction represented as decimal and how it relates to the percentage
representation. Students go from a geometric representation in a
10x10 grid to the formal notation. This lesson is the introduction
for the unit dedicated to percents.
