Both of these types of operations further expand the students' knowledge of the types of numbers that are used and the ways in which they are used. Estimation, mental math, and technology use begin to mature in seventh and eighth grades as students use these strategies in much the same way that they will as adults. The cumulative progress indicators for grade 8 appear below in boldface type. Each indicator is followed by activities which illustrate how it can be addressed in the classroom in grades 7 and 8. They might, for example, create a prototype on-line order blank for a school supply company that lists each of the ten items available, the individual price, a cell for each item in which to place the quantity ordered, the total computed price for each item, and the total price for the order.
Students regularly have human vs. calculator races .
They quickly come to realize that the human has the advantage in many situations. Extend their understanding and use of arithmetic operations to fractions, decimals, integers, and rational numbers. Given a decimal or a fractional value for a piece of a tangram puzzle, the students determine a value for each of the other pieces and a value for the whole puzzle. Students use fraction squares to show why the multiplication of two fractions less than one results in a product that is less than either. Extend their understanding of basic arithmetic operations on whole numbers to include powers and roots.