NUMBER - RATIONAL NUMBERS
Creating Integers
Find a positive integer so that when you multiply 0.20 by that integer, the
product is an
integer. What is the smallest positive integer that will "work"? What are the
smallest
positive integers that will work for other decimals such as 0.05, 1.25, 0.375,
0.444..., ,
0.142857?
Compare your answers with the fraction equivalents of 0.20, 0.05, 1.25, 0.375,
0.444....
and, 0.142857? Describe how a fraction equivalent can be determined from a
decimal
number.
Extensions
Will this method work for all decimal numbers?
| GPS |
As seen in Problem Exploration |
M6N1. Students will understand the
meaning of the four arithmetic operations
as related to positive rational numbers and
percents using these concepts to solve
problems.
a. Use factors and multiples.
e. Use fractions, decimals, and percents
interchangeably.
f. Solve problems involving fractions,
decimals, and percents and justify the
process. |
a. The student can look at multiples of the
decimals to find the first integer value easily
especially if a spreadsheet is used.
e. The student is converting decimals to fractions
(therefore, “interchanging” them).
f. In order to solve the problem, the student uses
fractions and decimals. |
M7N1. Students will understand the
meaning of positive and negative numbers
including rational numbers and will
compute with them.
b.! Compare and order rational numbers
including repeating decimals.
d.! Solve problems using rational numbers. |
b. If using a spreadsheet program, the student
can put the numbers in ascending or descending
order, which allows the student to compare the
rational numbers.
d. This investigation involves solving a problem
that uses rational numbers. |
The Salesman and the Eggs
An egg salesman was asked how many eggs he had sold that day. He replied, "My
first
customer said, 'I'll buy half your eggs and half an egg more.' My second and
third
customers said the same thing. When I had filled all three orders I was sold out
and I did
not have to break a single egg all day." How many eggs had he sold in all?
Extensions
What if the customers bought one-third of the eggs and one-third an egg more?
How many
eggs would be sold in all?
| GPS |
As seen in Problem Exploration |
M6N1. Students will understand the
meaning of the four arithmetic operations
as related to positive rational numbers and
percents using these concepts to solve
problems.
d. Multiply and divide fractions and mixed
numbers.
e. Use fractions, decimals, and percents
interchangeably,
f. Solve problems involving fractions,
decimals, and percents and justify the
process. |
d. You are taking half the eggs, so you can
multiply the number of eggs you think he started
with by 1/2.
e. Some students may find it helpful to work this
problem using decimals and in order to do so,
must first convert the fraction to a decimal.
f. In solving this investigation, the student uses
fractions and decimals. |
M7N1. Students will understand the
meaning of positive and negative numbers
including rational numbers and will
compute with them.
c.! Add, subtract, multiply and divide
positive and negative rational
numbers.
d.! Solve problems using rational numbers. |
c. Students may find themselves adding fractions
of eggs.! A discussion should ensue as to why
they really should not be adding fractions of
eggs.
d. In solving this investigation, the student uses
rational numbers. |
|