Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
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
Real problems rarely arrive as a bare fraction sum. A recipe needs 3/4 cup of flour and 2/3 cup of sugar; a hiker walks 1 1/2 miles and then 7/8 of a mile. Students must decide that adding or subtracting is needed, check that both fractions refer to the same whole, and then use the equivalent fraction methods from 5.NF.A.1 to find the answer.
Equally important is judging whether an answer makes sense before and after calculating. Benchmark fractions such as 0, 1/2 and 1 give quick mental estimates: 3/4 and 2/3 are both more than 1/2, so their sum must be more than 1. The standard's own example is a student who claims 2/5 + 1/2 = 3/7; since 3/7 is less than 1/2, the sum cannot be correct, because adding a positive amount to 1/2 must give more than 1/2. Visual fraction models and equations both help students represent the situation clearly.
Half of one pizza and half of another are only comparable if the pizzas are the same size. Students should check that both fractions describe the same whole.
Students who calculate 2/5 + 1/2 as 3/7 and accept it have not compared it with 1/2. A five-second benchmark check reveals the error.
'Left' does not always mean subtract and 'total' does not always mean add. Students should picture the situation instead of hunting for key words.
An answer of 1 5/12 needs its unit: cups, miles or hours. Including the unit also checks that the question was answered.
Maya walks 1 1/2 miles before lunch and 7/8 of a mile after lunch. How far does she walk in total? Estimate first.
Answer: Maya walks 2 3/8 miles.
Ask students to sketch a bar or number line for each problem before writing an equation. Then insist on an estimate written beside the calculation, and a sentence that compares the final answer with the estimate.
Assessments include two-step fraction stories, problems asking how much more one amount is than another, and items asking which student's answer is unreasonable and why.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 1 5/12 (also accepted: 1 5/12 cups)
Use twelfths: 9/12 + 8/12 = 17/12 = 1 5/12 cups. Both amounts are more than 1/2, so a total above 1 makes sense.
Answer: D) Between 1 and 2
Both fractions are close to 1 but less than 1, so the sum is a little less than 2 and more than 1.
Answer: 1 7/12 (also accepted: 1 7/12 yards)
Use twelfths: 2 3/12 - 8/12. Regroup: 1 15/12 - 8/12 = 1 7/12 yards.
Answer: B) 3/7 is less than 1/2, but adding 2/5 to 1/2 must give more than 1/2
Adding a positive amount to 1/2 always gives more than 1/2. Since 3/7 is less than 1/2, it cannot be the sum.
Answer: 1/2 (also accepted: 3/6)
Use sixths: 5/6 - 2/6 = 3/6 = 1/2 of an hour.
A full lesson with slides, activities and an exit ticket on fraction word problems and estimation, pitched to grade 5 and editable in PowerPoint or Google Slides.
Make a lesson βA printable, differentiated worksheet on 5.NF.A.2 with an answer key, ready in about a minute.
Make a worksheet βTurn fraction word problems and estimation into a quiz students answer online that marks itself, with a class summary for you.
Build a test βFamiliar fractions such as 0, 1/4, 1/2, 3/4 and 1 that are easy to compare against. Rounding each fraction in a problem to a benchmark gives a quick mental estimate.
5.NF.A.1 is about the computation itself. 5.NF.A.2 applies that computation to word problems and adds estimation and reasonableness checks.