Transcript chapter 11. fraction and decimals: meanings and operations

Expectations from the Number
and Operations Standard
Principles and Standards for School
Mathematics
National Council of Teachers of
Mathematics
2000
Understand numbers, ways of representing
numbers, relationships among numbers, and
number systems.
Grades Pre-K-2
• Understand and represent commonly used
fractions, such as 1/4, 1/3, and 1/2.
Understand numbers, ways of representing
numbers, relationships among numbers, and
number systems.
Grades 3-5
Develop understanding of fractions as parts of unit
wholes, as parts of a collection, as locations on
number lines, and as divisions of whole numbers.
Use models, benchmarks, and equivalent forms to
judge the size of fractions.
Recognize and generate equivalent forms of
commonly used fractions, decimals, and percents.
Explore numbers less than 0 by extending the
number line and through familiar applications.
Understand numbers, ways of representing
numbers, relationships among numbers, and
number systems.
Grades 6-8
Work flexibly with fractions, decimals, and
percents to solve problems.
Compare and order fractions, decimals, and
percents efficiently and find their
approximate locations on a number line.
Understand meanings of operations and how
they relate to one another.
Grades 6-8
Understand the meaning and effects of arithmetic
operations with fractions, decimals, and integers.
Use the associative and commutative properties of
addition and multiplication and the distributive
property of multiplication over addition to
simplify computations with integers, fractions,
and decimals.
Compute fluently and make reasonable
estimates.
Grades 3-5
Develop and use strategies to estimate
computations involving fractions and
decimals in situations relevant to students’
experience.
Use visual models, benchmarks, and
equivalent forms to add and subtract
commonly used fractions and decimals.
Compute fluently and make reasonable
estimates.
Grades 6-8
• Select appropriate methods and tools for computing
with fractions and decimals from among mental
computation, estimation, calculators or computers, and
paper and pencil, depending on the situation, and apply the
selected methods.
Develop and analyze algorithms for computing with
fractions, decimals, and integers and develop fluency in
their use.
Develop and use strategies to estimate the results of
rational-number computations and judge the
reasonableness of the results.
Fraction Connections
Model:
Symbol: 1/2
Word: one-half
Decimal Connections
Model:
Symbol:
.1 or 1/10
Word:
one-tenth
Fraction Letters
Use one of each of the rods. Make an H
with the same number of rods in each
vertical part and the cross bar being onefifth as long as the vertical parts.
One possible solution =>
Interviewer, "Which fraction is more, 1/3 or 1/4?
2/5 or 2/7?“
Charles: Fifth Month of Fourth Grade
Interviewer, "Add
these fractions. 3/8 +
2/8, 2/3 + 1/4.“
Amanda: Fifth
Month of Fourth
Grade
Interviewer, "Add these fractions. 3/8 + 2/8, 2/3 +
1/4.“ Amy: Fifth Month of Fourth Grade