Numbers and Operations (2) – Fractions/Decimals/Percents/Ratios from Elevated Math

Twenty-five lessons provide initial instruction or intervention to help students with concepts involving fractions, decimals, exponents and powers, and percents.

Five of these lessons develop and deepen an understanding of mathematical concepts and relationships. Lessons include diagrams and illustrations of fraction strips, hundredths squares, number lines, grids, Venn diagrams, factor trees, symbols, drawings, and blocks. Problem solving is an integral part of each lesson.
M4.1 Concepts of Fractions, Ratios and Percents
M4.2 Concepts of Decimal Place Value and Fraction and Percent Equivalents
M4.3 Factors and Prime Factorization
M4.4 Prime Factorization, GCF, and LCM
M4.5 Simplifying and Converting Fractions

The next seven lessons present instruction in decimal operations, exponents and powers. When working with decimal numbers, student success depends on an understanding of whole numbers and place value. Students are hindered if a solid conceptual foundation is not built. In lessons 5.1 and 5.2 students use number lines to establish an understanding of relative location while converting, comparing, and ordering fractions and decimals. Lessons 5.3, 5.4, and 5.5 apply the four basic operations of adding, subtracting, multiplying and dividing. These lessons utilize models, illustrations, and/or diagrams to reinforce conceptual understanding of the content and development of algorithms. Lessons 5.6 and 5.7 help students develop a solid understanding of these unique numbers in contexts encountered outside the classroom in everyday life or in other subject areas. Estimation strategies and “reasonableness of answer” thinking are stressed throughout these lessons to develop the student’s number sense and flexibility of thought.
M5.1 Rounding and Comparing Decimals
M5.2 Converting, Comparing, and Ordering
M5.3 Adding and Subtracting Decimals
M5.4 Multiplying Decimals
M5.5 Dividing Decimals
M5.6 Exponents and Powers
M5.7 Scientific Notation

The next six lessons integrate diagrams, models, and illustrations of egg cartons, fraction strips, and fraction circles to help students develop conceptual understanding of what takes places when fractions are added, subtracted, multiplied and divided. Estimation strategies and “reasonableness of answer” thinking are stressed.
M6.1 Adding and Subtracting Fractions with Like Denominators
M6.2 Adding Fractions with Unlike Denominators
M6.3 Subtracting Fractions with Unlike Denominators
M6.4 Adding and Subtracting Mixed Numbers
M6.5 Multiplying Fractions
M6.6 Dividing Fractions

The last seven lessons focus on ratio, proportion, percent, and problem solving with percents. Models are used to differentiate between perfect squares up to 100 and other numbers, students recognize and identify perfect squares and their square roots, and students solve problem situations involving square roots and perfect squares in lesson 7.1. The lessons include:
M7.1 Square Roots
M7.2 Finding Percents
M7.3 Decimal and Percent Equivalents
M7.4 Ratios, Rates, and Proportional Reasoning
M7.5 Percent Proportions
M7.6 Using Percent Equations
M7.7 Problem Solving with Percents

Student print materials and Teachers notes are available for download at www.elevatedmath.com.

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