2 
 determine, through investigation using concrete materials, the relationship between the number of fractional parts of a whole and the size of the fractional parts (e.g., a paper plate divided into fourths has larger parts than a
paper plate divided into eighths) (Sample problem: Use paper squares to show which is bigger, one half of a square or one fourth of a square.)

2 
 compare fractions using concrete materials, without using standard fractional notation (e.g., use fraction pieces to show that three fourths are bigger than one half, but smaller than one whole).

4 
 compare and order fractions (i.e., halves, thirds, fourths, fifths, tenths) by considering the size and the number of fractional parts (e.g., ^{4}⁄_{5}
is greater than ^{3}⁄_{5} because there are more parts in ^{4}⁄_{5};
^{1}⁄_{4} is greater than ^{1}⁄_{5}
because the size of the part is larger in ^{1}⁄_{4});

4 
 compare fractions to the benchmarks of 0, ^{1}⁄_{2} and 1 ( e.g., ^{1}⁄_{8}
is closer to 0 than ^{1}⁄_{2}; ^{3}⁄_{5}
is more than ^{1}⁄_{2});

5 
 represent, compare, and order fractional amounts with like denominators, including proper and improper fractions and mixed numbers, using a variety of tools (e.g., fraction circles, Cuisenaire rods, number lines) and using
standard fractional notation;

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

8 
 represent, compare, and order rational numbers;

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

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;

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

9D 
 identify, through investigation, properties of the slopes of lines and line segments (e.g., direction, positive or negative rate of change, steepness, parallelism, perpendicularity), using graphing technology to facilitate
investigations, where appropriate
