Maryland Math 5.NOS.B.5

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

• 5.NOS.B.5.a

  Apply estimation strategies to estimate quotients.

• 5.NOS.B.5.b

  Use partial quotients efficiently to divide.

• 5.NOS.B.5.c

  Use properties of operations and/or the inverse relationship between multiplication and division to divide.

• 5.NOS.B.5.d

  Represent and explain the computation by connecting rectangular arrays, area models, and/or equations to the meaning of division.

01

What Students Need to Do

Students estimate the answer before dividing a number of up to four digits by a two-digit number. They subtract large multiples of the divisor and add the group counts. They show those groups in an area model and an equation.

02

What Mastery Looks Like

A student estimates that 1,248 ÷ 24 is near 50, then finds 52 by subtracting 1,200 and 48. They label both parts on a rectangle and check that 24 × 52 = 1,248.

03

Common Misconceptions

Students may calculate 24 × 50 as 120 instead of 1,200. They may forget to add all the partial quotients or stop when the remainder is still 24 or more.

04

How to Assess It

Exit ticket: Estimate 1,248 ÷ 24, then solve it using partial quotients. Label the parts of an area model and check your answer with multiplication.

1. 01

   Have pairs cut 24-by-50 and 24-by-2 rectangles from grid paper, then join them to model 1,248 ÷ 24.

2. 02

   Ask, “Why is 24 × 50 a useful first step for 1,248 ÷ 24, and what do you do with the remaining 48?”

3. 03

   Play quotient match with cards for 1,344 ÷ 24, an estimate of 60, partial quotients 50 + 6, and 24 × 56 = 1,344.

4. 04

   A club packs 1,375 pencils in boxes of 24; have students estimate, calculate the number of full boxes, and explain the leftovers.

• 6.NOS.B.3

  Fluently multiply and divide multi-digit decimals to the thousandths in context.

• 4.NOS.B.6

  Divide whole numbers with up to four-digit dividends and one-digit divisors with and without remainders.

• 4.NOS.B.5

  Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers.

• 6.NOS.B.2

  Fluently divide multi-digit numbers.