Number and Operations

• develop number sense for pi as one example
of an irrational number.

• understand and use ratios and proportions to
represent quantitative relationships.

• develop an understanding of large numbers
(billions) & recognize and appropriately use
exponential , scientific, and calculator
notation.

• compute percentages of numbers and
compare, order, estimate, and determine
equivalent relationships among fractions,
decimals, and percentages.

• extend understanding of operations (=, -, +, x,
÷) to include percents and integers.

• explain and apply properties such as 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 .

• understand the meaning and effects of whole
number exponents (squaring) to simplify
computations and solve problems.

• develop understanding of the meaning and
effects of operations with decimals, integers,
fractions, and percents (including percents
greater than 100% and less than 1%.)

• add, subtract, multiply and divide rational
numbers (fractions, decimals, percents,
integers) both concretely and symbolically
(mental, paper and pencil, calculators) to
solve problems.

• develop proportional thinking and explain
methods such as rates, scaling, and similarity
to solve problems involving proportion.

• compare and order rational and irrational
numbers and find their approximate location
on a number line.

• represent numbers and operations in a variety
of equivalent forms using models, diagrams,
and symbols (number lines, 10 by 10 grids,
rectangular arrays, number sentences.)

• understand and apply how whole numbers,
natural numbers, integers, fractions, decimals,
percents, and irrational numbers ( square roots
and pi) relate to each other (e.g. convert
between forms of rational numbers, compare,
order.)

• develop an understanding of estimation of the
size of rational numbers.

• determine the inverse relationship between
addition and subtraction , multiplication and
division, and squaring and taking the square
root of a number .

• work flexibly with decimals, integers,
fractions, and percents (including percents
greater than 100% and less than 1%) to solve
problems.

• use the associative and commutative
properties of addition and multiplication
and the distributive property of
multiplication over addition to show
relationships and justify steps in problem
solving.

• use percentages and proportions in consumer
applications (e.g., simple interest, percentages
of increase or decrease, discounts, unit
pricing, and sale pricing.)

• develop and use strategies to estimate the
results of rational-number computations and
judge the reasonableness of the results.

• develop and analyze algorithms for computing
with fractions , decimals, and integers and
develop fluency in their use.