## Number & Operations in Base Ten – 4th Grade

#### Use place value understanding and properties of operations to perform multi-digit arithmetic.

CCSS.Math.Content.4.NBT.B.6
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.

Teacher Notes
Students understanding the concept of division is foremost because the algorithm just has steps to follow in division.  Developing mental strategies and using models to divide first is very important.   Only after establishing the conceptual understanding will the algorithm make sense.
The biggest stumbling block for students is the student not having multiplication and division facts memorized. Studies show if the student doesn't know the fact, the steps of long division are lost.  Letting a student use a multiplication is a must if your goal is for them to learn the algorithm.

Student Knowledge Goals

I know division can be creating groups with the same quantity in each group.
I know division can be putting objects or numbers into an unknown number of groups.
I know division can be derived through repeated subtraction.
I know multiplication and division have an inverse relationship.
I can use models, such as rectangular arrays and area models, to show division concepts and solve division operations.
I know multiplication and division algorithms.
I know what the remainder means in a division problem.
I know how to check if my answer is reasonable.
I can use the properties of operations to solve division problems.
I can illustrate and explain which strategy/or model was used to find the quotient.

Vocabulary

dividend
divisor
product
properties of operations
remainder
quotient

Lessons
Engage NY Module 3 E-14 – Solve division word problems with remainders.
Engage NY Module 3 E-15 – Understand and solve division problems with a remainder using the array and area models.
Engage NY Module 3 E-16 – Understand and solve two-digit dividend division problems with a remainder in the ones place by using number disks.
Engage NY Module 3 E-17 – Represent and solve division problems requiring decomposing a remainder in the tens.
Engage NY Module 3 E-18 – Find whole number quotients and remainders.
Engage NY Module 3 E-19 – Explain remainders by using place value understanding and models.
Engage NY Module 3 E-20 – Solve division problems without remainders using the area model.
Engage NY Module 3 E-21 – Solve division problems with remainders using the area model.

Student Video Lessons
Learn Zillion - Whole number quotients & remainders with up to four-digit dividends
Study Jams – Divisibility
Study Jams – Long Division
Virtual Nerd – 4.NBT.B.6 Division

Printables
Division – Single Digit
4.NBT.B.6 - 53 pages of PDF worksheets
Soft Schools - Long Division