Content Area: Math

 

Index: 4.3C Grade 7 CPI 2

 

Standard: 4.3 - Patterns and Algebra

 

Strand: C - Modeling

 

Cumulative Progress Indicator: 2 -  The student will use patterns, relations, symbolic algebra, and linear functions to model situations

·        Using manipulatives, tables, graphs, verbal rules, algebraic expressions/equations/inequalities

·        Growth situations, such as population growth and compound interest, using recursive (e.g., NOW-NEXT) formulas (cf. science standard 5.5 and social studies standard 6.6)

 

Grade: 7

 

Sample Activities:

 

·        Students analyze a given series of terms and fill in the missing terms. Patterns include various arithmetic (repeating patterns) and geometric (growing patterns) sequences and other number and picture patterns. Students develop an awareness of the assumptions they are making. For example, given the sequence 0, 10, 20, 30, 40, 50, one might expect 60 to be next; but not on a football field, where the numbers now decrease!

 

·        Students compare different pay scales, deciding which is a better deal. For example, is it better to be paid a salary of $250 per week or to be paid $6 per hour? They create a table comparing the pay for different numbers of hours worked and decide at what point the hourly rate becomes a better deal.

 

·        Students supply missing fractions between any two given numbers on a number line. They might label each of eight intervals between 1 and 2, or they might label the next 16 intervals from 23 1/2 to 24. They extend this to decimals, labeling each missing number in increments of .1 or .01. For example, students might label each of five intervals between 59.34 and 59.35.

 

·        Students decide how many different double-dip ice cream cones can be made from two flavors, three flavors, and so on up to Baskin and Robbins' 31 flavors. They arrange the information in a table. They discuss whether one flavor on top and another on the bottom is a different arrangement from the other way around, and how that would change their results. They also discuss a similar problem: How many different types of pizzas can be made using different toppings?

 

·        Students predict how many times they will be able to fold a piece of paper in half. Then they fold a paper in half repeatedly, recording the number of sections formed each time in a table. They find that the number of folds physically possible is surprisingly small (about 7). The students try different kinds of paper: tissue paper, foil, etc. They describe in writing any patterns they discover and generate a rule for finding the number of sections after 10, 20, or n folds. They also graph the data on a rectangular coordinate plane using integral values. They extend this problem to a new situation by finding the number of ancestors each person had ten generations ago and also to the problem of telling a secret to two people who each tell two people, etc.

 

Vignettes (PDF Format):

 

·        Pizza Possibilities