Content Area: Math

 

Index: 4.1B Grade 6 CPI 2

 

Standard: 4.1 - Number and Numerical Operations

 

Strand: B - Numerical Operations

 

Cumulative Progress Indicator: 2 - The student will construct, use, and explain procedures for performing calculations with fractions and decimals with:

·        Pencil-and-paper

·        Mental math

·        Calculator

 

Grade: 6

 

Sample Activities:

 

·        Students work in groups to explore fraction multiplication and division. They use fraction circles and fraction strips to solve problems like: How can you divide four cakes among five people evenly? They solve the problems and then write in their math journals about the methods they used and the reasons they believe their answers to be good ones.

 

·        Students complete their study of fraction addition and subtraction by reading about Egyptian fractions. The Egyptians wrote every fraction as a unit fraction or the sum of a series of unit fractions with different denominators, for example, 7/8 = 1/2 + 1/4 + 1/8. They try to find Egyptian fractions for 2/3 (1/2 + 1/6); 2/5 (1/3 + 1/15); and 4/5 (1/2 + 1/5 + 1/10).

 

·        Students demonstrate their understanding of division of fractions on a test by drawing a picture to show that "1 1/2 ÷ 1/2" means: How many halves are there in 1 1/2?

 

·        Students use two-color chips to explore addition of integers. They each take ten chips and toss them ten times. Each time, the students record the number of yellow chips as a positive number (points earned) and the number of red chips as a negative number (points lost). For each toss, the student writes a number sentence, such as 6 + -4 = 2 for 6 points earned and 4 lost. Students may also keep a running total of points overall.

 

·        Students read and discuss If You Made a Million by David Schwartz, relating money to decimals.

 

·        Students read and discuss "Beasts of Burden" in The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan. In this story, three brothers must divide their Father's 35 camels so that one gets 1/2 of the camels, another 1/3, and the last 1/9. The narrator and a wise mathematician help them solve the problem by adding their camel to the 35, making 36. One brother then gets 18, another 12, and the third receives 4 making a total of 34. The narrator and mathematician take back their camel as well as the one left over.

 

·        Students demonstrate their understanding of addition and subtraction of unlike fractions on a test by finding the errors made by a fictitious student and explaining to that student what he/she did wrong.

 

·        Students read Shel Silverstein's poem A Giraffe and a Half and make up stories about mixed fractions.

 

·        Students discuss whether 2/3 x 5/4 is more or less than 2/3. They explain their reasoning.

 

·        Students listen to John Ciardi's poem "Little Bits" and discuss the concept that a whole can be described by an infinite number of equivalent names, such as 1/2 + 1/4 + 1/8 + 1/8 or 3/3.

 

·        Students solve missing link problems, like the one below, in which they must find number(s) and/or symbols that will make a true sentence: ______ + 3.1 - ______ - 5.4 = 8.7