Module+4

Module 4 – Rational Expressions **The Beginning** Throughout the introduction to fractions, students will begin with visual introductions and then progress to abstract manipulation.

**Visualizing Fractions** The unit begins with a visual introduction to fractions. Fractions will be represented as parts of a pie, rectangular arrays, and distance on a number line. Students will translate from picture to fraction and from fraction to picture. Mixed numbers will also be introduced at this point.

**Comparing Fractions** Students begin using pictures to compare fractions and then develop the ability to compare fractions without pictures. Students begin comparing fractions with the same denominator, then fractions with the same numerator. This leads to the concept of comparing any two fractions and common denominators. Included in this section is being able to recognize and write equivalent fractions.

**Mixed Numbers** Starting with pictures and progressing to fraction notation, students will convert fractions to mixed numbers and mixed numbers to improper fractions.

**Operations** Throughout this section, students will begin with a review of operations using integers. Then, students will begin operations with fractions through visual introductions and then progress to abstract manipulation.

**Addition and Subtraction** Students will learn how to add and subtract fractions with common denominators. When presented with fractions with different denominators, students will be prompted to refer back to the idea of comparing fractions and finding a common denominator. By the end of the unit, students will have the knowledge to add or subtract any given fractions.

**Multiplication**

**Exponents**

**Division**

<span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 14pt; font-style: normal; text-decoration: none; vertical-align: baseline;">**Mixed Practice**

<span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16pt; font-style: normal; text-decoration: none; vertical-align: baseline;">**Tie-In to Algebra** <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 14pt; font-style: normal; text-decoration: none; vertical-align: baseline;">**Expressions** <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Students will combine their previous knowledge of simplifying and evaluating expressions with their ability to work with fractions. Students will evaluate expressions when variables represent fractions and integers. Students will use the distributive property and combine like terms with expressions that have fractional and integer coefficients.

<span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 14pt; font-style: normal; text-decoration: none; vertical-align: baseline;">**Solve linear equations of 1 variable with fractional coefficients** <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Students will combine their previous knowledge of solving equations with their ability to work with fractions. Students will practice solving equations by performing the operations with fractions. Students will then use the multiplication property of equality to clear the equation of fractions.

<span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16pt; font-style: normal; text-decoration: none; vertical-align: baseline;">**Decimals** <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 14pt; font-style: normal; text-decoration: none; vertical-align: baseline;">**Decimals** <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">The unit will begin with a review of place value and introduce the places after the decimal point. Students will begin by converting decimals to fractions. Students will then learn to convert fractions to decimals, starting with denominators that are factors of a power of 10 and building on the idea of equivalent fractions. Then students will generalize the procedure to write any fraction as a decimal. Students will compare and graph decimals and fractions on a number line.

<span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 14pt; font-style: normal; text-decoration: none; vertical-align: baseline;">**Operations** <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Students will continue building on the idea of adding like items to add and subtract decimals. Students will also learn how to multiply decimals. What about dividing??

<span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 14pt; font-style: normal; text-decoration: none; vertical-align: baseline;">**Algebraic Manipulation** <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Students will evaluate expressions when variables represent decimals and integers. Students will use the distributive property and combine like terms with expressions that have decimal and integer coefficients. Equations with decimal coefficients will also be studied. Students will practice solving equations by performing the operations with decimals. Students will then use the multiplication property of equality to clear the equation of decimals.

<span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 14pt; font-style: normal; text-decoration: none; vertical-align: baseline;">**Applications** <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Converting metric measures <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Metric to English gas prices <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Money problems

<span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16pt; font-style: normal; text-decoration: none; vertical-align: baseline;">**Percents, Ratio, Rates, and Proportions** <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 14pt; font-style: normal; text-decoration: none; vertical-align: baseline;">**Proportion** <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">includes dividing decimals by writing as equivalent fractions with integer denominator

<span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 14pt; font-style: normal; text-decoration: none; vertical-align: baseline;">**Percents** <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">The concept of percent will be developed using equivalent fractions and proportions. Students will begin writing fractions with denominators that are a factor of 100 as percents. Students will then move to writing decimals as percents. Finally, students will learn to write any fraction as a percent.

<span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 14pt; font-style: normal; text-decoration: none; vertical-align: baseline;">**Circle Graphs** <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">time <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">creating <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">reading

<span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 14pt; font-style: normal; text-decoration: none; vertical-align: baseline;">**Applications with Percents** <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Sales tax and tip problems <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Percent increase and percent decrease problems <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Credit cards <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Pay check (taxes)

<span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 16pt; font-style: normal; text-decoration: none; vertical-align: baseline;">**Extended Investigation** <span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Choose a topic that can be related to social justice such as unemployment, poverty rates, or educational attainment and download data tables from the census website.

Involves
 * <span style="background-color: transparent; color: #000000; display: block; font-family: Courier New; font-size: 10pt; font-style: normal; font-weight: normal; list-style-type: circle; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">student empowerment – selecting particular focus
 * <span style="background-color: transparent; color: #000000; display: block; font-family: Courier New; font-size: 10pt; font-style: normal; font-weight: normal; list-style-type: circle; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">understanding real world data and reading tables
 * <span style="background-color: transparent; color: #000000; display: block; font-family: Courier New; font-size: 10pt; font-style: normal; font-weight: normal; list-style-type: circle; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">translating from words to fractions to percents
 * <span style="background-color: transparent; color: #000000; display: block; font-family: Courier New; font-size: 10pt; font-style: normal; font-weight: normal; list-style-type: circle; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">creating circle graphs
 * <span style="background-color: transparent; color: #000000; display: block; font-family: Courier New; font-size: 10pt; font-style: normal; font-weight: normal; list-style-type: circle; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">knowing when to use a circle graph versus a bar graph
 * <span style="background-color: transparent; color: #000000; display: block; font-family: Courier New; font-size: 10pt; font-style: normal; font-weight: normal; list-style-type: circle; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">using critical thinking skills to compare information across years or groups
 * <span style="background-color: transparent; color: #000000; display: block; font-family: Courier New; font-size: 10pt; font-style: normal; font-weight: normal; list-style-type: circle; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">misleading graphs

<span style="background-color: transparent; color: #000000; display: block; font-family: Times New Roman; font-size: 12pt; font-style: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"> Reading credit card statements, pay statements