September 9, 2009

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This resource guide provides links to exemplary resources and insight on how to teach mathematics and science concepts at the middle school level. Concepts supported by this particular guide include decimals, fractions, division of whole numbers, and geometry. The guides provide information on the needed content knowledge, science and mathematical pedagogical knowledge, exemplary lessons and activities, career information, and correlations to national mathematics and science standards.

- Mathematics > General

- Grade 6
- Grade 7
- Grade 8

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This resource was reviewed using the Curriki Review rubric and received an overall Curriki Review System rating of 3, as of -0001-11-30.

Curriki Review System

September 17, 2009

This resource received a 3* rating because it is part of the larger resource, Math Focal Points: Grade 7, which received a rating of 3-Exemplary in the Curriki Review System. You can learn more about this larger resource by reading its review and comments.

Table of Contents

- Math Focal Points - Grade 7: Introduction
- Math Focal Points - Grade 7: Background Information for Teachers
- Math Focal Points - Grade 7: Ration and Proportion
- Math Focal Points - Grade 7: Surface Area and Volume
- Math Focal Points - Grade 7: Integers and Algebra
- NCTM Standards & Author and Copyright Information

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With the intention of streamlining the preK-8 mathematics curriculum, the National Council of Teachers of Mathematics (NCTM) has developed Curriculum Focal Points for Prekindergarten Through Grade 8 Mathematics. NCTM emphasizes that a curriculum focal point is a “cluster of related knowledge, skills, and concepts,” rather than a discrete topic to be checked off a list. The focal points, three at each grade level, specify “the mathematical content that a student needs to understand deeply and thoroughly for future mathematics learning.”

In this publication, Math Focal Points: Grade 7, the third in our Middle School Portal series, we offer resources that support the teaching of the three areas of emphasis highlighted for seventh-grade learners. The three focal points and the related sections of resources are:

NCTM recommends that students at this level should develop an understanding of and apply proportionality, including scale factor, percentage, and unit rate problems. Resources in the section titled ratio and proportion deal with real-world situations, such as finding percentages and building scale models, as well as online scenarios that help students visualize the mathematical concepts involved.

In grade 7, students should develop an understanding of and use formulas for surface area and volume of three-dimensional shapes, and apply them in problems involving prisms and cylinders. In this publication, we offer measurement resources that will engage students in work with not only surface area and volume but also circumference and areas of circles, topics that also figure in this area of emphasis.

Students in grade 7 should develop as well an understanding of operations on all rational numbers and solutions of linear equations. In the integers and algebraic expressions section, the activities range from operations on the concepts to building mathematical models in algebraic language to solving equations. You will find a variety of formats as well: tutorials, well-constructed lesson plans, interactive problem solving, even games!

In Background Information for Teachers, you will find professional learning resources. Finally, we discuss the focal points as they are related to the NCTM Principles and Standards for School Mathematics.

The first publications in our Middle School Portal series featured teaching of the Math Focal Points: Grade 5 and Math Focal Points for Grade 6.

NCTM Curriculum Focal Points for Grade 7

Number and Operations and Algebra and Geometry: Developing an understanding of and applying proportionality, including similarity. Students extend their work with ratios to develop an understanding of proportionality that they apply to solve single and multistep problems in numerous contexts. They use ratio and proportionality to solve a wide variety of percent problems, including problems involving discounts, interest, taxes, tips, and percent increase or decrease. They also solve problems about similar objects (including figures) by using scale factors that relate corresponding lengths of the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and identify the unit rate as the slope of the related line. They distinguish proportional relationships (y/x = k, or y = kx) from other relationships, including inverse proportionality (xy = k, or y = k/x).

Measurement and Geometry and Algebra: Developing an understanding of and using formulas to determine surface areas and volumes of three-dimensional shapes. By decomposing two- and three-dimensional shapes into smaller, component shapes, students find surface areas and develop and justify formulas for the surface areas and volumes of prisms and cylinders. As students decompose prisms and cylinders by slicing them, they develop and understand formulas for their volumes (Volume = Area of base × Height). They apply these formulas in problem solving to determine volumes of prisms and cylinders. Students see that the formula for the area of a circle is plausible by decomposing a circle into a number of wedges and rearranging them into a shape that approximates a parallelogram. They select appropriate two- and three dimensional shapes to model real-world situations and solve a variety of problems (including multistep problems) involving surface areas, areas and circumferences of circles, and volumes of prisms and cylinders.

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations. Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.

Reprinted with permission from Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence, copyright 2006 by the National Council of Teachers of Mathematics. All rights reserved.

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