```Mathematics Alignment Lesson
Grade 5 Quarter 1 Day 7
Common Core State Standard(s)
5.NBT.6 Find whole number quotients of
whole numbers with up to four-digit
dividends and two-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.
Standards for Mathematical Practice
Standard 3- Construct viable arguments and
critique reasoning of others
Standard 7- Look for and make use of
structure
Standard 8- Look for and express regularity
in repeated reasoning


Materials Needed:
Transparencies/Blackline Masters“Airplane”, “Paper Chains”,
Blackline Master - “Division
Strategy Practice” “Division
Strategies Journal Prompt”
Assessment
Informal:
 Division Strategies Journal Prompt –
Homework
 Assess students’ work on “Division
Strategy Practice”
Homework
“Division Strategy Practice”
“Division Strategies Journal Prompt”
Alignment Lesson
Explore Division Strategies
Note: No formal algorithm for division is required.
1. Display Transparency/Blackline Master “Airplane” and
ask students to solve the word problem using any
method they can. Strategically select several students
to show various strategies on the board. Give students
time to discuss their strategies.
2. Use the “Area Model Notes Page 1” and “Area Model
Notes Page 2” to demonstrate how to use this strategy
for solving the “Airplane” problem.
3. As time permits, share strategies from “Additional
Strategies” that meet the needs of your students.
4. Have students practice using the area model strategy to
solve 1,284 ÷ 6. They can record their work on
MathBoards or in their journals. Circulate to check
students’ work.
5. Display Transparency/Blackline Master “Paper
Chains” and allow students to use any strategy to solve.
Again, strategically select several students to show their
work on the board.
6. Once you’ve discussed the solution to “Paper Chains”,
ask student groups to discuss the following question:
Could there be a remainder of 9 for the problem? Why
or why not? (No, the remainder cannot be larger
than the divisor because a new group of the divisor
would be formed if it was. The largest the
remainder would be for this problem is 7.)
7. Students can begin to work on Blackline Master
“Division Strategy Practice” independently in class and
finish for homework. Student will also complete
“Division Strategies Journal Prompt” for homework.
Note: You may want to provide students with copies of the “Area
Model Notes Pages 1” and “Area Model Notes Pages 2”
for their reference after you’ve modeled or have them copy
this (or a subsequent example) in their notebooks.
Source: Teacher Created; Math Expressions U7, L12
Vocabulary
Divisor – the number that divides the dividend
Dividend – then number to be divided
Quotient – the number, not including the remainder, which results from dividing
Remainder – the amount left over when a number cannot be divided equally
Wake County Public School System, 2012
Transparency/Blackline Master
Day 7
Standards(s) 5. NBT.6
Airplane
An airplane travels the same distance every day. It travels 3,822
miles in a week. How far does the airplane travel each day?
Wake County Public School System, 2012
Day 7
Standards(s) 5. NBT.6
Area Model Notes Page 1
Background: This method (referred to as Rectangle Sections in Math Expressions) is very concrete and
shows that your goal is to find the unknown factor when we divide. With this method, you know the area
of the rectangle and the length of one side, but we do not know the other side length. (from Math
Expressions Teacher Guide p. 721)
Step 1 – Create a rectangle (can either be longer horizontally or vertically) and label the known
information.
7
3,822
Step 2 – Ask yourself “7 x what number is close to 3,822?” Think aloud that using numbers with zeros
will make it easy to multiply. (500) Write 500 above this first section of the rectangle. Then,
multiply 7 x 500 and subtract 3,500 from 3,822.
500
7
3,822
3,500
322
Step 3 – Build a new section of rectangle and write the remaining area (322) in the section.
500
7
3,822
3,500
322
Wake County Public School System, 2012
322
Day 7
Standards(s) 5. NBT.6
Area Model Notes Page 2
Step 4 – Ask yourself “7 x what number is close to 322?” Think aloud again that using numbers with
zeros will make it easy to multiply. (40) Write 40 above this new section of the rectangle. Then,
multiply 7 x 40 and subtract 280 from 322.
7
500
40
3,822
3,500
322
322
280
42
Step 5 – Build a new section of the rectangle and write the remaining area (42) in this section.
7
500
40
3,822
3,500
322
322
280
42
42
Step 6 – Ask yourself “7 x what number is close to or equal to 42?” (6) Write 6 above this new section
of the rectangle. Then, multiply 7 x 6 and subtract 42 from 42.
7
500
40
6
3,822
3,500
322
322
280
42
42
42
0
Step 7 – Add the three new factors together (500 + 40 + 6 = 546). Since there was no remainder, 546 is
the quotient. This gives you the length of the unknown side in the area model, which is the
quotient.
Wake County Public School System, 2012
Day 7
Standards(s) 5. NBT.6
Student A –
3,822 ÷ 7 =
I know I want to get to 3,822.
There are 500 7’s in 3,822.
3,822 – 3,500 = 322
I know there are 40 7’s in 322 (there are not 50 7’s in 322 because that would be 350)
322 – 280 = 42
I know that there are 6 7’s in 42
42 – 42 = 0
500 + 40 + 6 = 546 (I just added up the groups of 7’s that I found in 3,822)
Student B – Expanded Notation (using numbers with zero to make multiplying easier)
3,822 ÷ 7 = (3,000 + 800 + 20 + 2) ÷ 7
3,000 ÷ 7 – the closest I can get to 3,000 is 7 x 400 = 2,800
3,000 – 2,800 = 200
Add that 200 with the 800 from the expanded notation and I have 1,000
1,000 ÷ 7 – the closest I can get to 1,000 is 7 x 100 = 700
1,000 – 700 = 300
Add that 300 with the 20 from the expanded notation and I have 320
320 ÷ 7 – the closest I can get to 320 is 7 x 40 = 280
320 – 280 = 40
Add that 40 with the 2 from the expanded notation and I have 42
42 ÷ 7 – I know 42 divided by 7 is 6
Now, I add up the partial quotients 400 + 100 + 40 + 6 = 546
Student C
3,822 ÷ 7 =
3,822
3,500
500
322
280
42
42
40
+
0
6
546
Adapted from NC DPI Unpacking Document
Wake County Public School System, 2012
There are 500 7’s in 3,822.
I subtract 3,500 from 3,822 and have 322 left.
There are 40 groups of 7 in 322.
I subtract 280 from 322 and have 42 left.
There are 6 groups of 7 in 42 (that’s a basic
fact I know).
I subtract 42 from 42 and have no remainder.
To determine the quotient, I add up the partial
quotients I used along the way and have the
Transparency/Blackline Master
Day 7
Standards(s) 5. NBT.6
Paper Chains
The 1st grade teachers at Teal Ridge Elementary are creating paper chains to
countdown the days of school. One teacher volunteered to cut the paper
they’d need for the chains and cut 1,446 strips of paper. The paper will be
evenly divided between the 8 teachers on the 1st grade team. How many strips
of paper will each teacher receive?
Teacher Created
Wake County Public School System, 2012
Day 7
Standards(s) 5. NBT.6
The 1st grade teachers at Teal Ridge Elementary are creating paper chains to countdown
the days of school. One teacher volunteered to cut the paper they’d need for the chains
and cut 1,446 strips of paper. The paper will be evenly divided between the 8 teachers on
the 1st grade team. How many strips of paper will each teacher receive?
8
100
80
1,446
800
646
646
640
6
I began by creating a rectangle and labeling the information I knew (8 and
1,446). I then asked myself, “8 x what number is close to 1,446?” I know numbers with
zeros are easier to work with so I used 100. I then multiplied 8 x 100 and subtracted 800
from 1,446. I still had 646 to divide so I created a new section on the rectangle and
asked myself “8 x what number is close to 646?” I know numbers with zeros are easier
to work with so I used 80 since I know that 8 x 8 = 64 and 8 x 80 would be 640. I then
multiplied 8 x 80 and subtracted 640 from 646. I now have 6 left. I know that this is my
remainder since it is smaller than the divisor. This means that each 1st grade teacher
will get 180 strips of paper for their chains. (There will be 6 strips of paper leftover.)
Teacher Created
Wake County Public School System, 2012
Blackline Master
Day 7
Standard(s) 5. NBT.6
Division Strategy Practice
Use the area model to solve the following:
1.
2,106 ÷ 9
2.
5,380 ÷ 6
Use any strategy to solve the following:
3.
4,914 ÷ 5
4.
3,372 ÷ 4
5. Nicky has \$1,536 in his bank account and plans to spend the same amount each month
for the next 6 months. How much money will he spend each month?
Wake County Public School System, 2012
Day 7
Standards(s) 5. NBT.6
Division Strategy Practice – Answer Key
Use the area model to solve the following:
1.
2,106 ÷ 9
9
2.
5,380 ÷ 6
6
200
30
4
2,106
1,800
306
306
270
36
36
36
0
800
90
6
5,380
4,800
580
580
540
40
40
36
4
Use any strategy to solve the following:
3.
4,914 ÷ 5
Strategies will vary.
4.
3,372 ÷ 4
Strategies will vary.
5. Nicky has \$1,536 in his bank account and plans to spend the same amount each month for the next 6
months. How much money will he spend each month?
Strategies will vary.
Wake County Public School System, 2012
Blackline Master
Day 7
Standards(s) 5. NBT.6
Name: ________________________
Date: ________________________
Division Strategies Journal Prompt
Choose one of the problems from Division Strategy Practice and write a
letter to a friend to explain the method you used to solve it.
Wake County Public School System, 2012
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