Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Official wording from the Common Core State Standards for Mathematics (Β© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Two fractions are equivalent when they are the same size or sit at the same point on a number line. Third graders find simple examples with models: folding a strip in half and then in half again shows 1/2 = 2/4, and lining up strips for thirds and sixths shows 2/3 = 4/6. They also recognize whole numbers in fraction form, such as 3 = 3/1 and 4/4 = 1, which helps explain why fractions and whole numbers share the same number line.
The second part is comparison by reasoning, not by rule. When two fractions have the same denominator, like 3/8 and 5/8, the pieces are the same size, so the one with more pieces is greater. When they share a numerator, like 2/3 and 2/6, there are the same number of pieces, but thirds are bigger than sixths, so 2/3 is greater. Students record results with >, = or < and justify them with a picture. The comparison only makes sense when both fractions refer to the same whole: half of a large pizza is more than half of a small one.
Students may say 1/6 > 1/3 because 6 > 3. Use strips to show that sixths are smaller pieces than thirds.
A child may claim 1/2 of a small cake equals 1/2 of a large cake. Comparisons are only valid when the wholes are the same size.
Some students think 1/2 = 2/3 because both numbers went up by 1. Line up the models to see the shaded amounts differ.
Students may not accept that 8/8 equals 1. Show 8 eighths filling the whole strip and landing on 1 on the number line.
Compare 2/3 and 2/6 using >, = or <, and justify your answer.
Answer: 2/3 > 2/6
Fraction walls or strip charts let students see equivalences line up and compare pieces at a glance. Ask students to explain comparisons in words, such as "same size pieces, so more pieces is more" or "same number of pieces, so bigger pieces is more", before writing the symbol.
Expect items that ask students to pick an equivalent fraction from a model, place equivalent fractions at the same point on a number line, or compare fractions and select the correct symbol. Grade 4 extends this to any denominators with 4.NF.A.1 and 4.NF.A.2.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: B) 3/6
3/6 is 3 of 6 equal parts, which covers half the whole, so 3/6 = 1/2.
Answer: C) <
Same denominator means same-size pieces. 3 eighths is less than 5 eighths, so 3/8 < 5/8.
Answer: A) >
Same numerator: one piece each. Thirds are bigger than sixths, so 1/3 > 1/6.
Answer: 4/1
4 wholes, each counted as 1/1, is 4/1.
Answer: 4
Each third splits into 2 sixths, so 2 thirds is 4 sixths: 2/3 = 4/6.
Answer: C) 6/6
6/6 is all six sixths of the whole, so it equals 1.
A full lesson with slides, activities and an exit ticket on equivalent fractions and comparing fractions, pitched to grade 3 and editable in PowerPoint or Google Slides.
Make a lesson βA printable, differentiated worksheet on 3.NF.A.3 with an answer key, ready in about a minute.
Make a worksheet βTurn equivalent fractions and comparing fractions into a quiz students answer online that marks itself, with a class summary for you.
Build a test β(a) equivalent fractions are the same size or point; (b) recognize and generate simple equivalent fractions; (c) write whole numbers as fractions; (d) compare fractions with the same numerator or denominator.
No. That comes in 4.NF.A.2. In grade 3, comparisons use the same numerator or the same denominator.