Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations.

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.

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Integer Arithmetic http://enlvm.usu.edu/ma/nav/toc.jsp?sid=__shared&cid=emready@integers&cf=activity

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. (From eNLVM : Interactive online math lessons — MSP full record)

eNLVM : Interactive online math lessons http://enlvm.usu.edu/ma/nav/index.jsp

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. MSP full record

Late delivery http://www.bbc.co.uk/education/mathsfile/shockwave/games/postie.html

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. MSP full record

Number Line Bounce (grades 6-8) http://nlvm.usu.edu/en/nav/frames_asid_107_g_3_t_1.html

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 http://mathforum.org/alejandre/algfac.html

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. MSP full record

Building Bridges http://illuminations.nctm.org/LessonDetail.aspx?id=L247

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. (From Illuminations, National Council of Teachers of Mathematics Vision for School Mathematics — MSP full record)

Rectangle Pattern Challenges http://math.rice.edu/~lanius/Lessons/Patterns/rect.html

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. (From Mathematics Lessons that are Fun! Fun! Fun! — MSP full record)

Function machine (grades 6-8) http://nlvm.usu.edu/en/nav/frames_asid_191_g_3_t_1.html

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. MSP full record

Hop to It! http://www.pbs.org/teachersource/mathline/lessonplans/atmp/hoptoit/hoptoit_procedure.shtm

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. (From Ohio resource center for mathematics, science, and reading — MSP full record)

Algebra balance scales : negatives (grades 6-8) http://nlvm.usu.edu/en/nav/frames_asid_324_g_3_t_2.html

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. MSP full record

Equation Match http://www.bbc.co.uk/education/mathsfile/shockwave/games/equationmatch.html

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. (From The Maths File Game Show — MSP full record)

NCTM. (2006). Curriculum Focal Points for Kindergarten Through Grade 8 Mathematics: A Quest for Coherence. Reston, VA: Author

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Copyright May 2008 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0424671. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons License.