Content Area: Math

 

Index: 4.3D Grade 4 CPI 1

 

Standard: 4.3 - Patterns and Algebra

 

Strand: D - Procedures

 

Cumulative Progress Indicator: 1 -  The student will understand, name, and apply the properties of operations and numbers

·        Commutative (e.g., 3 x 7 = 7 x 3)

·        Identity element for multiplication is 1 (e.g., 1 x 8 = 8)

·        Associative (e.g., 2 x 4 x 25 can be found by first multiplying either 2 x 4 or 4 x 25)

·        Division by zero is undefined 

·        Any number multiplied by zero is zero.

 

Grade: 4

 

Sample Activities:

 

·        When the students are introduced to two digit by two digit multiplication, they begin with a problem of finding the area of a rectangular field which is 37 feet by 44 feet. They know they need to multiply the numbers to find the area, but they don't know how to multiply without calculators. The teacher draws a rectangle and uses a line to divide the width into two regions which are 30 feet and 7 feet. She does the same with the length, cutting it into lengths 40 feet and 4 feet. This divides the rectangle into four smaller rectangles (30×40, 30×4, 7×40, 7×4) all of which are multiplications the students can do.

 

·        Lea and Suzanne discovered a method for multiplying even numbers by six easily. Their method, applied to the example 6×24, is:  Cut the other even number in half: 12  Add a zero 120:  Add the number 120+24=144  When they told their classmates their discovery, they were stumped when they were asked why it worked. The teacher, grasping the teachable moment, divided the class into groups and challenged them to do a few examples using the girls' method and try to figure out and explain why it worked.

 

·        Students and teacher together work through Robert Froman's book, The Greatest Guessing Game: A Book about Dividing to reinforce their notions of division.

 

·        Students explain that they solved a problem like 300 - 56 mentally by first subtracting 50 and then subtracting 6, since that is the same as subtracting 56. They also do 25×7×4 by first multiplying 25×4 and then multiplying by 7. Such simplifications will give a good foundation for later work in algebra.