Scientific Notation, Exponents and Square Roots:

A conceptual approach

• Exponents, Square Root and Scientific Notation:  This lesson develops the concept behind the power of a number. It starts by presenting the square and cube geometric meanings and their roots. Students learn to figure out in between what whole numbers is a given root. The activity is extended to learn about powers of 10, and finalizes with scientific notation.

FRACTIONS: A conceptual approach

• Adding and Subtracting: In this lesson students learn to add and subtract fractions with fraction bars. They learn the concept of equivalent fraction and how to go from lowest terms to highest terms.

• Multiplying: This lesson presents how to get the fractional part of a number, and the concept of multiplying a given number by a fraction. Fraction bars are used and it is illustrated this in terms of the area of a rectangle.

• Fractional Part of a Number and Improper Fractions to Mixed numbers: In these exercises students are presented with the different formats that getting a part of a number may have. It extends the lesson before covered. It finalizes presenting the conceptual meaning of an improper fraction and how to changed to mixed number and vice versa.

• Multiplying Mixed Numbers: Students learn how to multiply a mixed number by a fraction, by a whole number and by another mixed number. They start with an interesting problem that involves mixed numbers.

• Dividing Fractions: In this activity students learn how many parts a number or a fraction fits into another whole number or fraction. This is done using fraction bars.

DECIMALS: A conceptual approach

• Adding: In this lesson students learn with the help of manipulative (place value mat) the concept of a tenth, hundredth, thousandth and how to apply it to addition problems that involve decimals.

• Subtracting:  The lesson of adding decimals is extended in this one to subtraction using the place value mat and the manipulative. Students learn how to compare decimals by going from the factional representation to the decimal one.

• Multiply by a decimal: Students 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. Students solve several word problems.

• Divide by a decimal: This lesson uses the place value mat and the manipulative to teach the conceptual meaning of a division, and it is extended to division by a decimal number.

• Fractions to Decimals to Percent: 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.

PERCENTS: A conceptual approach

• Percent of a Number: This lesson presents the procedure to get the percent of a number using a grid of 10x10 and linking it to the fractional and decimal representations for the area that is shaded and this is extended to get the percent of a  number.

• Comparing Numbers as a Percent: In this lesson students are able to go from comparing two numbers to getting the percent of a given number of objects in a set.

• Calculate the Percent of Increase or Decrease of a Quantity: This lesson shows students how to understand a percent of increase and decrease as a change in area, from one initial one to final one. This is extended to word problems that involve this same concept.

• Finding the Amount of a Discount or a Commission: In this lesson students apply everything they learnt about fractions, decimals and percents to figure out discounts and commissions in sale prices.

• Calculating Simple Interest: This lesson presents three word problems that involve getting the simple interest of one amount.