A three-section survey of the whole 3rd grade fraction standard set, from naming shaded parts to defending a comparison. Students read a strip with 3 of 4 rectangles shaded, place and label points on number lines cut into fourths and sixths, pair the 1/2 and 2/4 bar models, and take on Leo's claim that 1/4 beats 1/2 because 4 beats 2. Answer explanations accompany every question, including the reasoning behind each comparison symbol.
3.NF.1
“Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.”
All of Section 1, from the 3/4 strip to Maya giving away 1 of 4 ribbon pieces.
3.NF.2.a
“Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at O locates the number 1/b on the number line.”
Section 2, question 3, where students describe splitting the 0-to-1 interval into 3 equal parts to place 1/3.
3.NF.2.b
“Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from O. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.”
Locating point A at 3/4 and filling the missing sixths labels in Section 2.
3.NF.3.a
“Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.”
The paired bar models in Section 3 showing 1/2 and 2/4 covering the same amount of the same whole.
3.NF.3.b
“Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.”
The completion statement "1/2 is equal to ______" under the two bar models.
3.NF.3.c
“Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3=3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.”
The third comparison in Section 3, where 4/4 is set against the whole number 1.
3.NF.3.d
“Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.”
The three symbol comparisons and Leo's 1/4-versus-1/2 argument, which must be answered in writing.
Students count parts and shaded parts on a 4-part strip, then name the fractions in a circle (1 of 6 slices), an eight-square rectangle (5 shaded), and a triangle in thirds, before answering Maya's ribbon question.
Point A sits at 3/4 on a line cut into fourths. A second line in sixths has two blank labels to fill (3/6 and 5/6), and question 3 asks students to explain in words how to locate 1/3.
Matching bars show 1/2 and 2/4 over the same whole. Students then write <, >, or = for 2/4 vs 3/4, 1/3 vs 1/6, and 4/4 vs 1, and finish by explaining why Leo is wrong that 1/4 is bigger than 1/2.
Unit checkpoint
Give the full sheet at the end of the fraction unit. The sheet samples all seven 3.NF substandards, so the gradebook column means something.
Reteach sort
Score each section separately. A student who aces Section 1 but misplaces point A needs number-line work, not more pie pictures.
Writing in math
Use Leo's claim as a silent written argument first, then debate it. The key's answer about fourths being smaller than halves gives you the landing point.
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