Transcript Module 3 Lesson 17 - Peoria Public Schools

Math Module 3
Multi-Digit Multiplication and Division
Topic E: Division of Tens and Ones with Successive Remainders
Lesson 17: Represent and solve division problems requiring decomposing a remainder in the tens
4.OA.3 4.NBT.6
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Lesson 17
Target
You will represent and
solve division problems
requiring decomposing a
remainder in the tens
Count forward and backward by twos to 20.
Fluency
Group Count
Lesson 17
8
10 12
14
6
16
4
18
2
20
Count forward and backward by threes to 30.
Fluency
Group Count
Lesson 17
12
15 18
21
9
24
6
27
3
30
Count forward and backward by fours to 40.
Fluency
Group Count
Lesson 17
16
20 24
28
12
32
8
36
4
40
Count forward and backward by fives to 50.
Fluency
Group Count
Lesson 17
20
25 30
35
15
40
10
45
5
50
Fluency
4 tens 8 ones
divided by 2
equals 2 tens
4 ones.
40 ÷ 2
• Say the completed division
equation in unit form.
• 4 tens divided by 2 equals 2 tens.
Lesson 17
Divide Mentally
48 ÷ 2
48 divided by
2 equals 24.
8÷2
Say the
completed
division
equation
ininregular
unit
form.
• Say the completed division
equation in unit form.
• 8 ones divided by 2 equals 4 ones.
Fluency
9 tens 3 ones
divided by 3
equals 3 tens
1 one.
90 ÷ 3
• Say the completed division
equation in unit form.
• 9 tens divided by 3 equals 3 tens.
Lesson 17
Divide Mentally
93 ÷ 3
93 divided by
3 equals 31.
3÷3
Say the
completed
division
equation
unit
ininregular
form.
• Say the completed division
equation in unit form.
• 3 ones divided by 3 equals 1 one.
Fluency
8 tens 8 ones
divided by 4
equals 2 tens
2 ones.
80 ÷ 4
• Say the completed division
equation in unit form.
• 8 tens divided by 4 equals 2 tens.
Lesson 17
Divide Mentally
88 ÷ 4
88 divided by
4 equals 22.
8÷4
Say the
completed
division
equation
unit
ininregular
form.
• Say the completed division
equation in unit form.
• 8 ones divided by 4 equals 2 ones.
Fluency
Lesson 17
Divide Using the Standard Algorithm
On your boards, solve the division problem using the vertical method.
24÷2
36÷3
24
3 36
2
57÷5
5 57
88÷4
4 88
37÷3
3 37
87÷4
4 87
55÷5
5 55
96÷3
3 96
95÷3
3 95
Application Problem
5 Minutes
Audrey and her sister found 9 dimes and 8
pennies. If they share the money equally, how
much money will each sister get?
Lesson 17
Concept Development
Lesson 17
Problem 1: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
3÷2
• Model this problem on your place
value chart.
• 3 ones divided by 2 is?
• One with a remainder of 1.
• Record 3 ÷ 2 as long division.
Tens
Ones
//
===
=
=
1 one
Concept Development
Lesson 17
Problem 1: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
30 ÷ 2
Tens
• Can we rename the left
over ten?
• Yes! Change 1 ten for 10
ones.
• Let’s rename 1 ten.
Ones
//
===
=
=
=====
=====
=====
=====
Concept Development
Lesson 17
Problem 1: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
30 ÷ 2
• Now rename and distribute the 10
ones with your partner.
• Our answer is 1 ten 5 ones, or 15.
• Why didn’t we stop when we had a
remainder of 1 ten?
• Because 1 ten is just 10 ones, and you
can keep dividing.
• So why did we stop when we got a
remainder of 1 one?
• The ones are the smallest unit on our
place value chart, so we stopped there
and made a remainder.
Tens
Ones
//
===
=
=
=====
=====
=====
=====
1 ten
5 ones
Concept Development
Lesson 17
Problem 1: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
30 ÷ 2
•
•
•
•
•
Let’s solve 30 ÷ 2 using long division.
3 tens divided by 2?
2u
1 ten.
You recorded 1 ten, twice.
Say a multiplication equation that
tells that.
• 1 ten times 2 equals 2 tens.
1
2 30
2
//
1 ten
Twice
Concept Development
Lesson 17
Problem 1: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
30 ÷ 2
• We started with 3 tens, distributed 2
tens, and have 1 ten remaining. Tell
me a subtraction equation for that.
• 3 tens minus 2 tens equals 1 ten. 2 u
//
1
2 30
2
-2
1
Concept Development
Lesson 17
Problem 1: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
30 ÷ 2
• How many ones remain to
be divided?
• 10 ones.
• Yes. We changed 1 ten for
10 ones. Say a division
equation for how you
distributed 1 ten or 10
ones.
• 10 ones divided by 2 equals
5 ones.
2u
1
2 30
2
-2
1
Concept Development
Lesson 17
Problem 1: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
30 ÷ 2
• You recorded 5 ones, twice.
• Say a multiplication
equation that tells that.
• 5 ones times 2 equals 10
ones.
2u
115
2 30
2
-2
10
10
5 ones
Twice
Concept Development
Lesson 17
Problem 1: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
30 ÷ 2
• We renamed 10 ones, distributed 10 ones,
and have no ones remaining.2 Say
a
u
subtraction equation for that.
• 10 ones minus 10 ones equals 0 ones.
• Share with a partner how the model
matches the algorithm. Note that both
show equal groups and how both can be
used to check your work using
multiplication.
115
2 30
2
-2
10
-10
10
0
Concept Development
Lesson 17
Problem 2: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
4÷3
• Represent 4 ones on the place value chart.
With your partner, solve for 4 ÷ 3 using
2u
number disks and long division.
• The quotient is 1 and the remainder is 1.
Concept Development
Lesson 17
Problem 2: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
• Represent 4 tens 2 ones on
the place value chart and get
ready to solve using long
division.
• 4 tens divided by 3 is?
Distribute your disks and cross
off what is used. The answer
is?
• 1 ten with a remainder of 1
ten. Oh! I remember from last
time, we need to change 1 ten
for 10 ones.
42 ÷ 3
Tens
Ones
====
==
=====
=====
2u
=
=
=
Concept Development
Lesson 17
Problem 2: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
42 ÷ 3
•
•
•
•
How many ones remain?
12.
10 ones + 2 ones is 12 ones.
Show 12 ones divided by 3.
Complete the remaining
steps. What is the quotient?
• Our quotient is 1 ten 4 ones,
or 14.
Tens
Ones
====
==
=====
=====
====
====
====
2u
=
=
=
Concept Development
Lesson 17
Problem 3: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
84 ÷ 3
• Solve for 84 ÷ 3 by using
number disks and long
division.
• The quotient is 28.
• What was different about the
place value chart with this
problem?
• There were a lot more disks!
We had to decompose 2 tens
this time.
2u
Concept Development
Lesson 17
Problem 3: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
84 ÷ 3
• How many ones did you have
after decomposing your 2
tens?
• 24 ones.
• Show your partner where to
find 24 ones in the numerical
representation.
• Check your answer using
multiplication.
• 28 times 3 is 84. Our answer is
right!
2u
Problem Set
10 Minutes
Problem Set
10 Minutes
How did Problem 2
allow you to see
only the
remaining 1 ten in
the ones column?
Problem Set
10 Minutes
Explain why 1
ten remains in
Problem 4?
Problem Set
10 Minutes
Problem Set
10 Minutes
Debrief
Lesson Objective:
You will represent
and solve division
problems
requiring
decomposing a
remainder in the
tens
• How is the long division recording different in
today’s lesson compared to yesterday’s lesson?
• What different words are we using to describe
what we do when we have a remaining ten or
tens? (Break apart, unbundle, change, rename,
decompose, regroup.) Which of these words are
you most comfortable using yourself?
• What other operation involves changing 1 ten for
10 ones at times? What operations involve the
opposite, changing 10 ones for 1 ten at times?
• What would happen if we divided the ones before
the tens?
• What connection can you find between the
written division and the multiplication you used to
check your work?
• Why are we learning long division after addition,
subtraction, and multiplication?
• How did the Application Problem connect to
today’s lesson?
Exit Ticket
Lesson 1