By Suzanne H. Chapin
Read Online or Download Math Matters: Understanding the Math You Teach Grades K-8, 2nd Edition PDF
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Extra resources for Math Matters: Understanding the Math You Teach Grades K-8, 2nd Edition
Even though subtraction is not commutative, there are interesting relationships in the differences of numbers when their order is reversed for subtraction. , Ϫ4). This can be represented formally as: a Ϫ b ϭ c and b Ϫ a ϭ Ϫc if a b 0. , ϩ4 ϩ Ϫ4 ϭ 0)? The number 0 is the identity element for addition. You can add 0 to any other number and the sum will be the original number. Why does this pattern of opposites occur when we change the order of the numbers in a subtraction problem? The difference between two numbers can be represented on a number line as an interval—the distance between two points.
Qxd 2/8/06 1:30 PM Page 26 one hundred thousand, 5 groups of ten thousand, and 6 groups of one thousand (which is equivalent to 456 groups of one thousand); plus 7 hundreds, 8 tens, and 9 ones. While we say the quantity in each period as if we are only focusing on face value (“four hundred fifty-six thousand”), students must be able to interpret the place value meaning of each digit within the periods (which involves more than simply identifying the place value of each digit). Helping Students Understand Our Place Value System How can we help students understand our place value system?
In addition to using counting to make sense of quantities, children also use imagery. In general, children are interested in developing more efficient ways to count, and over time they learn to “see” small numbers without counting. They instantly recognize ◆◆◆ as three. The identification of small quantities without counting is known as subitizing and appears to develop after children have had repeated practice in counting such sets. Sometimes students recognize only particular arrangements of objects such as the dots on a die.