Content Area: Math

 

Index: 4.1A Grade 8 CPI 1

 

Standard: 4.1 - Number and Numerical Operations

 

Strand: C - Estimation

 

Cumulative Progress Indicator: 1 -  The student will extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 8 pertain to these sets of numbers as well):

·        Rational numbers

·        Percents

·        Exponents

·        Roots

·        Absolute values

·        Numbers represented in scientific notation

 

Grade: 8

 

Sample Activities:

 

·        Students develop a scientific notation Olympics by creating events like the 9.144 x 103 centimeter sprint (100 yard dash) or the 7.272 x 106 milligram hurl (shot put).

 

·        Students use a bookkeeping simulation to explore the effect of bills and credits coming into, or going out of, their business. These financial activities are recorded as various actions on positive and negative integers, all affecting the net worth of the business.

 

·        Students view the Powers of Ten video, developed to show how one's view of the world is affected by changes in the order of magnitude of one's position.

 

·        Students construct a hypothetical stock portfolio, using $10,000 to "buy" shares of stock, and track the performance of the portfolio and each individual stock day by day.

 

·        Students explore absolute values as the distance between two points on a number line and compare this to subtraction.

 

·        Students measure the circumference and diameter of 15 to 20 round objects, recording the results in a table. They make a scatterplot (with diameter on the horizontal axis) and use a piece of spaghetti to draw the line of best fit. They discuss why pi is represented in the drawing as the slope of the line.

 

·        Students construct line segments of varying irrational lengths on a geoboard or dot paper. For example, the diagonal of a unit square has length sqrt(2), the diagonal of a 1 x 2 rectangle has length sqrt(5), and the circumference of a circle with unit diameter has length pi. Through exploring these common irrational numbers that arise in problem situations, students learn that not all numbers can be represented as a ratio of two integers.

 

·        Students construct their own graph for the square roots of the numbers from 1 to 25, using trial-and-error to approximate each root to the nearest tenth. They plot the numbers on the horizontal scale, and their square roots on the vertical scale.

 

·        Students work on traditional "systems of equations" problems, involving two unknowns, by devising non-algebraic solution strategies for them. Some samples are: Two numbers have a sum of 32; they have a product of 240. What are the numbers? or Sally is 22 years younger than her Dad. In 3 years, her Dad will be 3 times as old as she. How old is Sally?