Introducing the 9 quantities
Every word problem on every page of every textbook, grades K - 8, and most of the problems in 9 - 12, begin with a sentence about an object or activity that has been counted or measured—length and other linear distances, area including surface area, volume, time, weight, money, number, temperature, and occasionally angles!
Counting & Measuring K - 2
In K - 2, we focus on number, counting the number of sets of objects, such as animals, books, colored objects, food stuffs, or office supplies and sometimes activities such as jumping jacks or finger snapping. But they can also count inches you can line up along the side of a box (linear), tablespoons it takes to fill a cup (volume), ounces it takes to be as heavy as a can of beans (weight) or coins (money).
CounTING & MeasurING Grades 3 - 5
ALL nine quantities can be measured in grades 3 to 5. You can measure the length of a shoe in centimeters or the distance between two wall of a classroom in feet, weight of a back pack in pounds or a pencil in grams, value of a cup of coins or all the money in a Monopoly game or the Game of Life, area of a table or countertop in square inches or feet, volume of vases of different sizes and shapes in ounces or cups and volume of boxes in cubic centimeters, time to write the alphabet forwards in seconds or backwards in minutes, temperature of a bottle of water in the refrigerator in ºF, angle you can jump or need to turn to face the door, and finally the number of students in a class, grade, school, district.
RELATIONSHIPS BETWEEN COUNTS & MEASURES Grades 6 - 8
Relationships can be made between ALL of the nine quantities. You can find a relationship between the weight of bulk peanuts and the cost of them, the area of a lawn and the time it takes to cut it, volume of fruit juice and the number of calories, the angle the revolving door turns and the time it takes to turn, the length of the lumber or lace and the cost of it, the time the ice is out of the freezer and its temperature.