# Mathematics

5th Grade

*Houghton Mifflin Harcourt’s Into Math National - Grade 5 *focuses on three critical areas: developing fluency with addition and subtraction of fractions while gaining an understanding of multiplication and division of fractions in limited cases, extending division to 2-digit divisors with the integration of decimal fractions into the place value system through operations with decimals and fluency with whole numbers, and finally, developing an understanding of volume. It constructs this focus by engaging students to be fearless problem solvers, fostering their growth mindset and introduces an interactive online component to guide learning in the 21st century. To adhere to the four critical areas, the text is broken down into eight units: (1) Whole Numbers, Expressions, and Volume, (2) Add and Subtract Fractions and Mixed Numbers, (3) Multiply Fractions and Mixed Numbers, (4) Divide Fractions and Convert Customary Units, (5) Add and Subtract Decimals, (6) Multiply Decimals, (7) Divide Decimals and Convert Metric Units, and (8) Graphs, Patterns, and Geometry. Into Math: Grade 5 is aligned to the Common Core Standards along with the Pennsylvania Academic Content Standards by allowing for extended time and practice on the heavily used standards on the PSSAs: Numbers and Operations - Fractions (A-F), Algebraic Thinking (B-O), and Geometry (C-G) while guiding students through the Mathematical Practice standards of Common Core.

6th Grade

*Houghton Mifflin Harcourt’s Into Math National - Grade 6* focuses on four critical areas: connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems, completing understanding of division of fractions and extending the notion of number to the system of rational numbers, writing, interpreting, and using expressions and equations and finally, developing understanding of statistical thinking. It constructs this focus by engaging students to be fearless problem solvers, fostering their growth mindset and introduces an interactive online component to guide learning in the 21st century. To adhere to the four critical areas, the text is broken down into five units: (1)Number Systems and Operations, (2)Ratio and Rate Reasoning, (3)Expressions, Equations, and Inequalities, (4)Geometry, (5)Data Collection and Analysis. Into Math: Grade 6 is aligned to the Common Core Standards along with the Pennsylvania Academic Content Standards by allowing for extended time and practice on the heavily used standards on the PSSAs: Ratios and Proportional Relationships (A-R), The Number System (A-N), and Expressions and Equations (B-E) while guiding students through the Mathematical Practice standards of Common Core.

7th Grade

*Houghton Mifflin Harcourt’s Into Math National *-* Grade 7 *focuses on four critical areas: developing understanding of and applying proportional relationships, developing understanding of operations with rational numbers and working with expressions and equations, solving problems using scale drawings and geometric shapes in both 2-dimensions and 3-dimensions to solve area, surface area and volume problems, and finally, drawing conclusions about populations based on samples. It constructs this focus by engaging students to be fearless problem solvers, fostering their growth mindset and introducing an interactive online component to guide learning in the 21st century. To adhere to the four critical areas, the text is broken down into six units: (1)Proportional Relationships, (2)Rational Number Operations, (3)Model with Expressions, Equations and Inequalities, (4)Geometry, (5)Statistics and (6)Probability. Into Math: Grade 7 is aligned to the Common Core Standards along with the Pennsylvania Academic Content Standards by allowing for extended time and practice on the heavily used standards on the PSSAs: Ratios and Proportional Relationships (A-R) and Expressions and Equations (B-E) while guiding students through the Mathematical Practice standards of Common Core.

8th Grade

*Houghton Mifflin Harcourt: Into Math National-Grade 8* focuses on three critical areas: formulating and reasoning about expressions and equations (including bivariate data, linear equations and systems of linear equations), grasping the concept of a function and using them to describe relationships, and analyzing two- and three-dimensional space and figures using distance, angles, similarity, congruence and the Pythagorean Theorem. It constructs this focus by engaging students to be fearless problem solvers, fostering their growth mindset and introducing an interactive online component to guide learning in the 21st century. To adhere to the three critical areas, the text is broken down into six units: (1)Transformational Geometry, (2)Linear Equations and Applications, (3)Relationships and Functions, (4)Statistics and Probability, (5)Real Numbers and the Pythagorean Theorem and (6)Exponents, Scientific Notation, and Volume. Into Math: Grade 8 is aligned to the Common Core Standards along with the Pennsylvania Academic Content Standards by allowing for extended time and practice on the heavily used standards on the PSSAs: Geometry (C-G) and Expressions and Equations (B-E) while guiding students through the Mathematical Practice standards of Common Core.