Benchmarks
Below are the benchmarks and their respective levels that I expect Grade Nine students to have memorized:
Beginning
Integers, denominators of 2, 4 and 10 (halves, quarters, tenths and decimal equivalents)
Emerging
Integers, denominators of 2, 4 and 10 (halves, quarters, tenths and decimal equivalents)
AND denominators of 3 and 5 (thirds and fifths)
Progressing
Integers, denominators of 2, 4 and 10 (halves, quarters, tenths and decimal equivalents)
AND denominators of 3 and 5 (thirds and fifths)
AND denominators of 9 (ninths)
Advancing
Integers, denominators of 2, 4 and 10 (halves, quarters, tenths and decimal equivalents)
AND denominators of 3 and 5 (thirds and fifths)
AND denominators of 9 (ninths)
AND denominators of 6 (sixths)
Mastering
Integers, denominators of 2, 4 and 10 (halves, quarters, tenths and decimal equivalents)
AND denominators of 3 and 5 (thirds and fifths)
AND denominators of 9 (ninths)
AND denominators of 6 (sixths)
AND denominators of 7 (sevenths) along with equivalent fractions that can be reduced to any denominator