Houghton Mifflin Mathematics: Structure and Method Course 1, Teacher's Edition ... Some of the ways I had been taught as a student were made simpler (ways to find the least common multiple and greatest common factor for example). ... My son started using this book during 6th grade. We wanted him to keep up on his math concepts over the summer ...
structure introduced in the K–8 grade levels of the Califor-nia Common Core State Standards for Mathematics (CA CCSSM); they present mathematics as a coherent subject and blend standards from different conceptual categories. The standards in the integrated Mathematics I course come from the following conceptual categories: Modeling, Func-
In Grade 1, instructional time should focus on four critical areas: (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating …
The curriculum covers five content areas at the primary level: Number; Shape and Space; Measurement; Data Handling; and Algebra. 20 Algebra is introduced in Grade 5 (Primary 5). Exhibit 1 presents the mathematics topics taught in each content area at the primary level.
The Standards for Mathematical Practice (MP) apply throughout each course and, together with the Standards for Mathematical Content , prescribe that students experience mathematics as a coherent , relevant, and meaningful subject. The Standards for Mathematical Practice represent a picture of what it looks like for students to do mathematics and, to the extent possible, content instruction should include attention to appropriate practice standards.
The Mathematics I course is organized by conceptual category, domains, clusters, and then standards. The overall purpose and progression of the standards included in Mathematics I are described below, according to each conceptual category. Standards that are considered new for secondary-grades teach-ers are discussed more thoroughly than other standards.
In the Algebra conceptual category, students extend the work with expressions that they started in grades six through eight. They create and solve equations in context, utilizing the power of variable expressions to model real-world problems and solve them with attention to units and the meaning of the answers they obtain. They continue to graph equations, understanding the resulting picture as a representation of the points satisfying the equation. This conceptual category accounts for a large portion of the Mathematics I course and, along with the Functions category, represents the main body of content.
The standards for grades seven and eight introduced students to seeing two-dimensional shapes as part of a generic plane (the Euclidean plane) and exploring transformations of this plane as a way to deter-mine whether two shapes are congruent or similar. These notions are formalized In Mathematics I, and students use transformations to prove geometric theorems about triangles. Students then apply these triangle congruence theorems to prove other geometric results, engaging throughout in standard M P. 3.
In Mathematics I, students build on their understanding of key ideas for describing distributions—shape, center, and spread—presented in the standards for grades six through eight. This enhanced understanding allows students to give more precise answers to deeper questions, often involving comparisons of data sets.
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpretunits consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
This sequence of equations is shorthand for a line of reasoning: “If twice a number minus 5 equals 16 minus that number, then three of that number minus 5 must be 16, by the properties of equality. But that means three times that number is 21, so the number is 7.”
The mission of the University of Massachusetts Lowell is to promote and sustain regional economic development. The Graduate School of Education (GSE) contributes to this mission by developing professionals who help transform the region through leadership roles in education. The GSE’s commitment to “Education for Transformation” produces graduates who:
The purpose of this course is to help pre-service teachers discover how elementary children think about and learn mathematics. The overall objective of teaching mathematics should be to help each child to understand mathematical concepts, enabling them to become mathematically literate.