In sixth grade, students are at the beginning of middle-school mathematics, and facing new challenges. The mastery of the four operations (addition, subtraction, multiplication, and division) using fractions is a major component of the sixth-grade curriculum. Students learn various ways of finding the lowest common multiple of numbers (for
2,
3, and
4, it would be
12) as well as the greatest common factor of numbers (for
12,
18, and
24, it would be
6). In other areas, students construct and bisect angles; learn to write numbers using exponents (
22 = 4); place decimal numbers in their proper order; and use decimals to convert measurements to metric units. A new challenge for sixth-graders is converting percents to fractions and decimals. They also apply their growing knowledge of percentages to problem-solving situations, such as calculating a 20 percent tip for a restaurant bill, or finding the discounted price of goods on sale.
Does Singapore Have the Answers? In 2003, scores from the
Trends in International Mathematics and Science Study showed that Singapore students were at the top of the world rankings in fourth- and eighth-grade mathematics. Should U.S. schools adopt the Singapore method? Some already have, by purchasing textbooks based on Singapore's math curriculum, which relies primarily on traditional instructional methods. The Singapore approach makes frequent use of word problems, and the various strategies for solving them, and assumes that students are being drilled on basic math facts like multiplication tables elsewhere, an assumption that could leave some kids who don't get such practice at home falling behind. Another major criticism of the Singapore Method is that it does not include all the topics covered in most contemporary U.S. math programs, such as aspects of algebra and statistics at all grade levels.
• Trudi Hammel Garland's
Fascinating Fibonaccis (Dale Seymour, 1987) takes kids inside the unusual properties of "Fibonacci" numbers and their occurrence in the natural world. In the Fibonacci number sequence, each number is added to the number to its left to create the next number in the string (
0,
1,
1,
2,
3,
5,
8,
13,
21).
• Jean Lee Latham's
Carry On, Mr. Bowditch (Houghton Mifflin 2003) tells the fascinating story of "Nat," a nautical wonder and mathematical wizard in the early days of Salem, Mass.
• Explore a wide variety of brain puzzles and challenges, like the famous Tower of Hanoi puzzle, at
math.com.
• There's more to board games than rainy-day fun.
Monopoly, for example, builds calculating, estimating, and reasoning skills, and provides a terrific lesson in economics.
100 Up! Give your grandchildren four random digits. Challenge them to use those digits, in any order, and any of the four basic math operations (addition, subtraction, multiplication, or division), in any combination, so that the total is as close to 100 as possible, without going over (for example,
8 x 12 + 20 - 26 = 90).
Deck of Patterns. Using a standard deck of playing cards, lay out a line of cards that creates a pattern, and challenge your grandchildren to find a card that will continue the pattern. When they have found a card that continues the pattern, let them create a pattern to challenge you.
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