4.NBT.6
2011
Domain: Number and Operations in Base Ten
Cluster: Use place value understanding and properties of operations to perform multi-digit arithmetic
Standards: Find whole number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies
based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain
the calculation by using equations, rectangular arrays, and/or area models.
Essential Questions
-Why do you have a
remainder in division?
-Why can’t the remainder
be equal to or greater than
the divisor?
-What are two ways to
interpret a remainder?
-How can you show
different models for
division?
Content Statements
- Students will use basic
facts and patterns of zeros
to solve division problems
with 3-digit dividends and
1-digit divisors.
- Students will use
compatible numbers and
rounding to estimate
quotients.
- Students will estimate
quotients of multi –digit
division problems using
multiplication facts and
Enduring Understandings
- Basic Facts and place value
patterns can be used to divide
multiples of 10 and 100 by 1digit numbers.
- There is more than one way to
estimate a quotient. Substituting
compatible numbers is an
efficient technique for estimating
quotients.
- Mentally multiplying by
different powers of ten will help
you arrive at an estimate for the
quotient of a multi-digit division
problem.
- The remainder when dividing
must be less than the divisor.
The nature of the question asked
determines how to interpret and
use the remainder.
- Some real world problems
involving joining equal groups,
separating equal groups, or
comparison can be solved using
multiplication; others can be
solved using division.
Activities, Investigation, and Student Experiences
Use base ten blocks or money to create equal groups to illustrate
the division process and understand the concept of left over
items.
Small leveled group work.
4.NBT.6
place-value concepts.
- Students will divide
whole numbers by 1-digit
divisors resulting in
quotients with remainders.
- Students use words and
models to represent
multiplication and division
problems accurately.
- Students will draw
pictures and write related
number sentences to solve
problems.
- Students will use repeated
subtraction to model
division
- Students will record
division as repeated
subtraction
-Students will use place
value to understand the
algorithm of long division
- Students will use the
standard algorithm to
divide a two-digit number
by a one-digit number
- Students will use the
standard algorithm to
divide 3-digit numbers by
1-digit numbers.
- Students will use the
standard algorithm to
divide 3 – digit numbers by
- Information in a problem can
often be shown with a picture or
diagram and used to understand
and solve the problem. Some
problems can be solved by
writing and completing a
number sentence or equation
- Repeated subtraction situations
can be modeled and solved using
division
- Repeated subtractions situations
can be solved using a division
algorithm different from the
standard algorithm
- The sharing interpretation of
division can be used to model the
standard division algorithm
- The standard division algorithm
breaks the calculation into simpler
calculations using basic facts,
place-value, the relationship
between multiplication and
division and estimation.
- The standard division algorithm
breaks the calculation into simpler
calculations using basic facts,
place-value, the relationship
between multiplication and
division, and estimation.
- The relationship between
multiplication and division and
estimation can be used to
determine the place value of the
2011
4.NBT.6
1-digit numbers and
properly decide where to
begin dividing.
- Students will estimate and
find quotients for 4 – digit
dividends and 1-digit
divisors.
2011
largest digit in a quotient.
- The process for the standard
division algorithm with one-digit
divisors is the same when
extended from 2 – 3 digit
dividends to 4-digit dividends
Assessments
-Series Assessments
–Teacher Observation
-Teacher made Assessments
-Open-ended word problems
A 4th grade student bought 4 new pencil boxes. She has 2616
pencils. The student would like to put the same number of
pencils in each box. How many pencils are in each box?
Equipment Needed: Math manipulatives, available
technology, pencil, paper.
Teacher Resources:
Series Textbook
Supplemental Worksheets
http://aaaknow.com/div41_x3.htm step by step instructions
http://www.youtube.com/watch?v=ITloMQvj-lU you tube
video showing the traditional algorithm and the inverse
operation
4.NBT.6
2011
http://www.mathplayground.com/division02.html
interactive math game to practice long division
http://studyjams.scholastic.com/studyjams/jams/mat
h/index.htm Math Movies
http://www.k-5mathteachingresources.com/
illuminations.nctm.org - look for websites and lesson
plans
http://nlvm.usu.edu/en/nav/vlibrary.html
www.softschools.com
http://math.pppst.com/ - Many free Pre-made Power
Point Presentations for Math and across the
curriculum