Roots of Reason
Roots of Reason
rootsofreason.org
same amount, new name
Anchor Chart · Grade 3 · 3.NF.A.3

Equivalent Fractions

12 = 24 = 36 the same amount of the same whole,
cut a different number of times.
1Same Point, Same Number
halves1/2fourths2/401
1/2 and 2/4 stop at the same point, so they are one number with two names.
2Cut Every Part Again
2/34/6cut each part in 2
Cutting each part in two doubles both numbers at once. The shaded edge does not move.
3Whole Numbers Are Fractions
0124/48/43 = 3/1 and 6/1 = 6a denominator of 1 counts whole pieces
One whole is 4/4, two wholes are 8/4. A denominator of 1 means the pieces are whole ones.
4Compare by Reasoning
same denominator3/85/83/8 < 5/8same numerator2/32/62/3 > 2/6
Same denominator, so count the pieces. Same numerator, so fewer cuts means bigger pieces.