Your class will find many opportunities to manipulate decimal numbers in the grocery store. By sixth grade, students should be able to use all four operations. To add and subtract, students choose a recipe, find the price of each ingredient in flyers, and take the total cost of their recipe from a set budget. To multiply, students choose an item and figure out how much it would cost to buy in bulk such as 56 packages of hotdogs for the school social. To divide, students choose packaged items and compare unit prices; for example, $3.19 for the bargain brand's four rolls of toilet paper works out to a unit price of $0.7975 per single roll. If possible, students could help find actual cost savings for their school.
Challenge students to find a real-life object that demonstrates the relationship between tenths, hundredths and thousandths. A common example uses a loaf of bread to represent one whole. A slice of bread equals one tenth; a breadstick -- a tenth of a slice -- represents one hundredth; and a crouton -- a tenth of a breadstick -- represents one thousandth. Students can bring in their object to demonstrate to the class. If this is not possible, students could bring photos of their object and describe how it would be partitioned.
Using place value patterns, students generally understand that decimal numbers are very small. However, they should be given opportunities to discover that decimal numbers can represent both significant and insignificant figures, depending on context. For example, 0.15 can be a small amount if it is the sales tax on a candy bar, or a large amount if it is the sales tax on a house. Each student can choose a different decimal number, and create a list, poster or slide show to demonstrate when their decimal is small and when it is large.
Our math language allows many different representations for the same amount. Two and a half, 2.5 or 2 1/2 are different ways to write the same number, and so are 13.8 million and 13,800,000. Students could scan websites, newspapers, magazines, cookbooks and advertisements to find out which types of numbers are used in different situations, and why.
Students in the sixth grade should become proficient at comparing decimal numbers. Students can research a sport or athlete of interest, and order race times or game statistics from best to worst. They could research gasoline or heating fuel prices over time or by location, ranking them in order of affordability. Some students may be interested in ordering luxury home prices, which would allow an opportunity for using multiple representations: some advertisements will round a home price to $2.5 million while others would state $2,495,500.