2 
 regroup fractional parts into wholes, using concrete materials (e.g., combine nine fourths to form two wholes and one fourth

4 
 represent fractions using concrete materials, words, and standard fractional notation, and explain the meaning of the denominator as the number of the fractional parts of a whole or a set, and the numerator as the number of
fractional parts being considered;

6 
 represent, compare, and order fractional amounts with unlike denominators, including propoer and improper fractions and mixed numbers, using a variety of tools and using standard fractional notation

6 
 determine and explain, through investigation using concrete materials, drawings, and calculators, the relationships among fractions, decimal numbers and percents.

7 
 divide whole numbers by simple fractions and by decimal numbers to hundredths, using concrete materials;

7 
 use a variety of mental strategies to solve problems involving the addition and subtraction of fractions and decimals;

7 
 add and subtract fractions with simple like and unlike denominators, using a variety of tools and algorithms;

7 
 demonstrate, using concrete materials, the relationship between the repeated addition of fractions and the multiplication of that fraction by a whole number;

7 
 determine, through investigation, the relationships among fractions, decimals, percents, and rations;

8 
 represent, compare, and order rational numbers;

8 
 translate between equivalent forms of a number;

8 
 use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to help judge the reasonableness of a solution;

8 
 represent the multiplication and division of fractions, using a variety of tools and strategies;

8 
 solve problems involving addition, subtraction, multiplication, and division with simple fractions;

9D 
 simplify numerical expressions involving integers and rational numbers, with and without the use of technology;

9D 
 solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion;

9P 
 solve problems requiring the expression of perecnts, fractions, and decimals in their equivalent forms
