Content Area: Math

 

Index: 4.1B Grade 7 CPI 1

 

Standard: 4.1 - Number and Numerical Operations

 

Strand: B - Numerical Operations

 

Cumulative Progress Indicator: 1 - The student will use and explain procedures for performing calculations with integers and all number types named above with:

·        Pencil-and-paper

·        Mental math

·        Calculator

 

Grade: 7

 

Sample Activities:

 

·        Students working in groups develop a method to estimate the products of two-digit whole numbers and decimals by using the kinds of base-ten block arrays described in Indicator 6 above. Usually just focusing on the "flats" results in a reasonable estimate.

 

·        Students follow up a good deal of experience with concrete models of fraction operations using materials such as fraction bars or fraction squares by developing and defending their own paper-and-pencil procedures for completing those operations.

 

·        Students develop rules for integer operations by using postman stories, as described in Robert Davis' Discovery in Mathematics. The teacher plays the role of a postman who delivers mail to the students. Sometimes the mail delivered contains money (positive integers) and sometimes bills (negative integers). Sometimes they are delivered to the students (addition) and sometimes picked up from them (subtraction).

 

·        Students model subtraction with two-color chips by adding pairs of red and yellow chips. (First, they must agree that an equal number of red and yellow chips has a value of 0.) For example, to show 4 - (-2), they lay out 4 red chips, add 2 pairs of red and yellow chips (whose value is 0), and then take away 2 yellow chips. They note that 4 - (-2) and 4 + 2 give the same answer and try to explain why this is so.