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Content Area: Math
Index: 4.3B Grade 6 CPI 1
Standard: 4.3 - Patterns and Algebra
Strand: B - Functions and Relationships
Cumulative Progress Indicator: 1 - The student will describe the general behavior of functions given by formulas or verbal rules (e.g., graph to determine whether increasing or decreasing, linear or not).
Grade: 6
Sample Activities:
· Students use a geoboard to model squares with sides of 1, 2, 3, and 4 units. They determine the area and discover the rule for the area, A = s2, given that s is the length of the side of a square.
· Students use multilink cubes or base ten blocks to build rectangular solids. They find the volume of the rectangular solids (either by counting the cubes or by developing their own shortcuts), and record the length, width, and height of each solid along with its volume in a table. They use this information to discover a rule or formula for finding the volume of a rectangular solid.
· Students find the number of primes between 1 and 100 using a hundreds chart and applying the process of the Sieve of Eratosthenes. That is, they first cross out all multiples of 2, then all multiples of 3, then all multiples of 5, and so on; the numbers which remain are the primes.
· Students play the secret number calculator game. One student enters a secret number into the calculator by dividing the number by itself (e.g., 17 ÷ 17). She then asks her opponent to guess the number. Each guess is entered into the calculator and then the equals sign is pressed; the calculator shows the result of dividing the guess by the secret number. For example, if 17 is the secret number and 34 is guessed, then the student enters 34 = and sees 2 on the calculator. Play continues until 1 is shown on the calculator, so that the opponent has guessed the secret number. (Some calculators will need to have different keys pressed for the same result, such as 17 ÷ ÷ 34 =.)
· Students look for the numbers which are palindromes (remain the same value when the digits are reversed) between any given pair of numbers. They decide which years in the 21st century will be the first 5 palindromes.
· Students determine how much money is earned hourly for a job mowing lawns or babysitting. They find the amount earned for working different numbers of hours. They organize the data in chart or table form. They look for a pattern and write simple equations; for example, the sentence For babysitting or mowing lawns, I get $5 per hour. translates into the equation E = 5 x h (Earnings equal five times the number of hours worked).
· Students use patterns to help them find the value of a point on a number line between two whole numbers when the number line is divided into fractional or decimal parts.
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