Maryland Math 5.NOS.C.8

5.NOS.C.8 is a cluster heading. These are the individual standards under it.

• 5.NOS.C.8.a

  Estimate sums and differences by reasoning about benchmark numbers and assess reasonableness of answers (e.g., 2/3 + 3/4 will be more than 1 because both fracti...

• 5.NOS.C.8.b

  Apply and extend whole number addition and subtraction strategies (e.g. counting on, making a whole, partial sums, compensation, properties of operations, the i...

• 5.NOS.C.8.c

  Use equivalent fractions to produce an equivalent sum or difference of fractions with like denominators (e.g. 2/3 + 5/4 = 8/12 + 15/12 = 23/12. In general, a/b ...

01

What Students Need to Do

Students rename fractions with like denominators, then add or subtract the numerators. They estimate with 0, 1/2, and 1 to check their answers. They also try making a whole or counting on when it makes the work easier.

02

What Mastery Looks Like

A student predicts that 2/3 + 3/4 is greater than 1, then rewrites it as 8/12 + 9/12 and gets 17/12. For 5/6 minus 1/4, they get 7/12 and explain why that is close to 1/2.

03

Common Misconceptions

Students may add the denominators and write 2/3 + 3/4 as 5/7. Others change a denominator without changing the numerator, so the fraction no longer has the same value. Some accept a sum above 2 even though both starting fractions are less than 1.

04

How to Assess It

Exit ticket: Estimate 2/3 + 1/4 and 5/6 minus 1/3 using 0, 1/2, or 1. Then solve both by renaming fractions and check whether your answers fit your estimates.

1. 01

   Give pairs fraction strips for 2/3 and 3/4; have them build twelfths, add, and check whether the sum exceeds 1.

2. 02

   Ask, 'Is 5/6 minus 1/4 closer to 0, 1/2, or 1? How do you know before calculating?'

3. 03

   Play a card match game with 3/4 + 1/2, 3/4 + 2/4, and 1 1/4; students match the equal values.

4. 04

   A runner jogs 3/4 mile, then 2/3 mile; students estimate and calculate the total distance.

• 4.NOS.E.12.d

  Solve problems in context involving addition and subtraction of fractions using visual fraction models and equations to represent the problem.

• 5.NOS.C.9

  Solve problems in context involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators using visual fract...

• 4.NOS.E.12

  Apply and extend previous understanding of addition and subtraction of whole numbers to add and subtract fractions with like denominators.

• 7.NOS.A.1

  Add and subtract rational numbers using multiple strategies and representations.