Maryland Math 5.NOS.D.16

5.NOS.D.16 is a cluster heading. These are the individual standards under it.

• 5.NOS.D.16.a

  Apply estimation strategies to estimate quotients and assess reasonableness of answers.

• 5.NOS.D.16.b

  Use visual fraction models and equations to interpret division of a unit fraction by a non-zero whole number and compute quotients.

• 5.NOS.D.16.c

  Use visual fraction models and equations to interpret division of a whole number by a unit fraction and compute quotients.

• 5.NOS.D.16.d

  Represent and explain the computation by connecting visual fraction models and/or equations to the meaning of division with unit fractions.

01

What Students Need to Do

Students split a unit fraction into equal shares or count how many unit fractions fit in whole numbers. They draw fraction bars, write division equations, and estimate to check their answers.

02

What Mastery Looks Like

A student shows 1/2 ÷ 3 = 1/6 by splitting half a bar into three equal parts. They show 3 ÷ 1/2 = 6 by counting the half-bars in three whole bars. They explain why the first answer is smaller than 1/2 and the second is larger than 3.

03

Common Misconceptions

Students may swap the order of the numbers in a division problem. Some think division always makes a number smaller, so they reject 3 ÷ 1/2 = 6. Others multiply 3 by 1/2 instead of counting how many halves fit in 3.

04

How to Assess It

Exit ticket: Draw bars and write equations for half a pizza shared equally by three people and for three pizzas served in half-pizza portions. Before solving, estimate whether each answer is larger or smaller than the amount you started with.

1. 01

   Fold a paper strip into thirds, then split one third into two equal pieces; label a piece and write 1/3 ÷ 2 = 1/6.

2. 02

   Ask, 'Why does 3 ÷ 1/4 give more than 3?' Have partners draw bars and explain their answers.

3. 03

   Match cards showing bar models, equations, and quotients for 1/2 ÷ 4 and 2 ÷ 1/4; explain each match.

4. 04

   Use a recipe needing 1/4 cup of oats per batch; draw cups to find how many batches 2 cups make.

• 5.NOS.B.7

  Apply and extend previous understanding of multiplication and division of whole numbers to multiply and divide decimals to hundredths in context.

• 5.NOS.D.13

  Apply and extend previous understandings of multiplication to multiply a fraction by a fraction, with one or both factors greater than 1.

• 5.NOS.D.12

  Apply and extend previous understandings of multiplication to multiply a fraction by a fraction.

• 4.NOS.E.12

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