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

Curriki Rating

On a scale of 0 to 3

3On a scale of 0 to 3

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.

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.

You will find that the first five activities require students to apply the properties of arithmetic to all rational numbers, including negative integers. Beginning with the activity titled “Building Bridges” below, the resources center on creating algebraic models of mathematical scenarios. These may appear as games or puzzles, but each moves from a concrete problem to an abstract representation. The last two activities deal directly with solving equations.

Integer Arithmetic These guided, interactive activities use number lines, color chips, and a variety of scenarios to help students understand what an integer is and how to do signed addition, subtraction, and multiplication.

eNLVM: Interactive online math lessons Check out this online tutorial offering a pre-test, practice exercises, and a post-test. It is especially handy as a quick review for students working independently.

Late delivery In this game, the student helps the mail carrier deliver five letters to houses with numbers such as 3(a + 2) and (2a + 5)/5. The value of ais held by the dog. This is a good exercise in substituting for variables. Three levels of difficulty are available; levels 2 and 3 are most appropriate for seventh-grade learners.

Number Line Bounce (grades 6-8) This number line game challenges the student to find a sequence of operations with four numbers that results in a given target number. The numbers are illustrated as bouncing balls on a number line. Each bounce can be in either a positive or negative direction. The student can use a guess-and-check approach to solving the problem or a more sophisticated strategy. In the final step, the student forms the number sentence that illustrates the sequence of operations used to arrive at the target number.

Algebraic Factoring An excellent set of lesson plans introduces factoring through finding areas of rectangles. Each step in the procedure is well explained and illustrated. Questions for the class are included. This unit is meant to be worked with algebra tiles, either the usual plastic ones or cut-out paper shapes.

Building Bridges Designed expressly for middle school classes, this lesson is built on the premise that "teachers need help in building a bridge between their current instructional goals and new goals that emphasize an earlier introduction to algebraic thinking." As students work through tasks, they organize values into tables and graphs as they move toward symbolic representations of the functions involved. The problem situations, carefully explained, employ linear, quadratic, and exponential models.

Rectangle Pattern Challenges Students analyze a colorful rectangular pattern, composed of red, green, and blue squares, and find the number of squares of each color as the rectangle grows. Again, the goal is to express the general patterns algebraically in terms of n.

Function machine (grades 6-8) Applying a machine metaphor for the critical concept of function, this virtual manipulative allows the learner to examine the relationship between input (domain) and output (range). The learner inputs numbers from 1 to 4 and the virtual machine generates output information in a table. At this point, the student must find the output for numbers 5 to 7; in other words, the function rule. Using a new function button, different types of functions are randomly offered for investigation.

Hop to It! This excellent lesson emphasizes establishing patterns and developing general rules. A pre-assessment problem asks: How many small triangles are contained in a sequence of increasingly large similar triangles? The core problem of the lesson asks: How can 10 frogs lined up on the left swap places with 10 frogs lined up on the right? For each problem, students work in small groups to devise a model and recording system, list their findings, and use the pattern they find to write a general rule that solves the problem. Well-illustrated handouts and solutions are included.

Algebra balance scales: negatives (grades 6-8) This online manipulative features a virtual balance scale. The activity offers students an experimental way to learn about solving linear equations involving negative numbers. The applet presents an equation for students to illustrate by balancing the scale, using blue blocks for positive units and variables and red balloons for negative units and variables. Students then work with the arithmetic operations to solve the equation. A record of the steps taken by the student is shown on the screen and on the scale. The applet reinforces the idea that what is done to one side of an equation must be done to the other side to maintain balance.

Equation Match Students must solve equations, from the most simple to the more complex, and in this way find pairs of equations that "match"; that is, both equations in the pair have the same value of x. When a match is found, part of a picture is revealed. Levels 2 and 3 require multistep solutions. At each return to the game, a new set of equations is given.

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