Session 4: Final Algorithms in A Story of Units
Sequence of Sessions
Overarching Objectives of this July 2013 Network Team Institute
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Implementation: Participants will be able to articulate and model the instructional approaches to teaching the content of the lessons of
the first module.
Standards alignment and focus: Participants will be able to articulate how the topics and lessons promote mastery of the focus standards
and how the module addresses the major work of the grade.
Coherence: Participants will be able to articulate connections from the content of previous grade levels to the content of this module.
Participants will be able to articulate critical aspects of instruction that prepare students to express reasoning and/or conduct modeling
required on the mid-module assessment and end of module assessment.
G6-7: Participants build the foundation to develop tape diagram skills for themselves and for students and fellow teachers.
G8&10: Participants experience content from Grade 8 geometry and relate those experiences to the content of Grade 10 geometry,
building instructional capacity to bridge gaps for incoming 10th graders.
G9: Participants can articulate the coherence across the grade 9 curriculum, describing the focus of each module and relating the modules
to each other.
High-Level Purpose of this Session
 To examine and practice the algorithms employed in A Story of Units.
 Understand the coherence within and across grades in order to promote conceptual understanding.
Related Learning Experiences
● In Session 1, a curriculum overview, participants will gain an understanding of how each module contributes to the overall
progression of concepts throughout the grade-level.
● Session 3, Exploration of Models, will prepare participants to utilize models appropriately in promoting conceptual
understanding throughout A Story of Units.
● Session 4, Algorithms, will prepare participants to utilize algorithms appropriately in promoting conceptual understanding
throughout
A Story of Units.
● Session 6, Leadership to Support A Story of Units, will help participants articulate examples of how to support implementation
of the curriculum and draw connections to the Evidence Guide for Planning and Practice in a Single Lesson.
Key Points



All algorithms involve the manipulation of units.
Each algorithm builds towards the next, culminating in the long division algorithm.
The long division algorithm is foundational to an understanding of the real number system and advanced mathematics.
Session Outcomes
What do we want participants to be able to do as a result of this
session?


Examine and practice the algorithms employed in A Story of
Units.
Understand the coherence within and across grades in order
to promote conceptual understanding.
How will we know that they are able to do this?

Participants will be able to successfully work the sample
algorithms and explain how the algorithms build to long
division
Session Overview 9-10:30
Section
Time
Introduction to the
Algorithms
23 min
Addition and
Multiplication
Overview
Explanation of algorithms


PowerPoint
Facilitator’s Guide

Review PowerPoint and
Session Notes

Demonstration of use of
algorithms and the
development of the
Numbers base Ten
Progression
Practice using the
algorithms


PowerPoint
Facilitator’s Guide

Review PowerPoint and
Session Notes
Demonstration of use of
algorithms and the
development of the
Numbers base Ten
Progression


PowerPoint
Facilitator’s Guide

Review PowerPoint and
Session Notes
33 min

31 min
Facilitator Preparation


Subtraction and
Division
Prepared Resources

Practice using the
algorithms
Session Roadmap
Section: Introduction to the Algorithms
Time: 23 min 9:00- 9:23
[minutes] In this section, you will
 Examine the use of algorithms in preparation for using this
information to teach students and colleagues
Materials used include:

Time Slide Slide #/ Pic of Slide
#
X
1
Script/ Activity directions
NOTE THAT THIS SESSION IS DESIGNED TO BE 90 MINUTES IN
LENGTH.
This session is the beginning of Day 2 of the NTI. Day 1 provided an
overview of the curriculum, grade-level Module Focus sessions, and
demonstrations of instructional models that support implementation of A
Story of Units. Additional grade-level Module Focus sessions will follow
this session on algorithms and the final session will address the role of
principals and other school leaders.
GROUP
5 min
2
Put these problems up as participants come into the session.
Get started with mental math.
Take 3 minutes to work a few different mental math strategies to solve
the problems on the board. We’ll only check the ones in black. If you
finish early tell your neighbor how you solved.
Highlight that each solution employs the associative property as a
compensation strategy.
Addition
Associative Property 298 + 357 = 298 + 2 + 355 (A compensation
strategy)
Associative Property 4527 + 3219 = (45 hundreds + 32 hundreds) +
(27 ones + 19 ones) (place value strategy)
Subtraction
Compensation 658- 298 = 658 – 300
Count up from $3.68 to $4 to $10 (Cashiers’ method)
Multiplication
Associative property. 5 x 248 = 5 x 2 x 124 (Compensation for
multiplication)
Distributive property 25 x 34 = (32 x 25) + (2 x 25) = 8 x (4 x 25) + (2 x
25) = 850
Associative property 6 x 24 = 12 x 12 (Compensation for
multiplication)
Division
1240 ÷ 5 = 2 x (1240 ÷ 10) = 248 (Compensation)
850 ÷ 25 = (800 ÷ 25) + (50 ÷ 25)
4281 ÷ 3 = 42 hundreds ÷ 3 + 81 ones ÷ 3 = 14 hundreds + 27 ones =
1427
10
3
seconds
Our objectives for this session are to:
• Examine and practice the algorithms employed in A Story of
Units.
• Understand the coherence within and across grades in order
to promote conceptual understanding.
10
4
seconds
We will start with a rationale for the session.
1 min
Looking out over the room I see a lot of laptops, tablets, and smartphones.
So I feel confident in saying that we all use algorithms every day. For
example, simplistic spell checking algorithm might read in one word at a
time from a document, check it against a database of “correctly spelled”
words, and if it finds it, great! If not, it’s marked as a potentially misspelled
word. But such an algorithm, put simply is just a step by step procedure
for solving a class of problems, whether we’re talking about math or not.
You feed in the data, execute the steps and out pops a result (hopefully). It
could be a spell-checker, a computer game, or a guidance system on a
cruise missile, there’s an algorithm guiding the process. So we don’t want
to give students the idea that “use the algorithm” just means “record b.”
Instead, “algorithm” is more about the process, even if we do adopt a
particular way of recording it.
5
2 min
6
In elementary school we have what we call the “standard algorithms.” The
term even appears in the CCLS. These are cyclic procedures for solving any
arithmetic problem. The things is, we have all sorts of algorithms to
choose from. For example one could say that counting up, one at a time, is
an algorithm for addition. You can certainly solve any whole number
addition problem that way (and even decimal addition with some
tweaking). But while this works fine for some cases: 5 + 2 (fiiiiive, 6, 7), in
other cases, it’s not so great: try counting up for 437 + 875. But there are
numerous, efficient algorithms. On top of that students learn all sorts of
mental math strategies, so why target a specific one as “standard?”
Having a standard algorithm provides a fall-back position. When they don’t
see a quick mental math option, they know they can use the algorithm
(they don’t have to choose from a menu at that point). This frees them up,
when reading a word problem for example, to recognize an embedded
arithmetic problem for what it is, know that they have a way to solve it
when the time comes to do so, and focus on the higher level relationships
within the problem. In that way, the algorithm serves as a support for
their ability to contextualize and decontextualize, which is the content of
MP.2—they read the word problem, analyze the contextual relationships,
and then strip away the context, and solve abstractly. They then
reinterpret the result based on the context of the problem.
1 min
7
For examples, students might say, “The answer is 5 kilograms 790 grams!”
They have decontextualized the arithmetic effectively but have not
contextualized it back into the story.
The teacher asks them to make a statement answering the question.
“The potatoes and the onions weigh 5 kilograms 790 grams together.”
Now they have contextualized the problem again.
10 min 8
Importance of the System of Algorithms
There are really strong relationships between the operations.
Addition and subtraction are two sides of the same coin. Multiplication
and division are similarly related. Multiplication can be solved by addition,
and actually embeds addition within the standard algorithm. And as for
long division? Think for a moment about the different operations required
to carry it out. All of these conceptual and even procedural ties mean that
we don’t want to think of the algorithms in isolation. They are intimately
connected.
It’s really easy when you’re tasked with preparing something for a
particular grade to put on your blinders and focus only on that one thing.
The problem with that is that choices we make early on impact what
happens later. Something as simple as how we show regrouping can either
support your work in building from addition to multiplication, or…not.
What we’ve done is to think about the progression of the entire system of
algorithms, so that it is consistent within itself, and each algorithm builds
toward the next, culminating in long division.
Importance of Long Division
Let’s talk about long division. Long division is one of those topics that a lot
of teachers and students dread. Some have even gone so far as to say that
long division is outdated, and not really needed anymore. After all, if
students understand what division means and how to use it, then for the
division problems that are computationally very difficult, why not just use
a calculator? We all carry cell phones now, and can whip out a calculator
at the drop of a hat. The thing is, they have a point. In fact, you could
make that argument with all of the algorithms. If all you’re interested in is
the ability to get the answer and apply it, then there may be some truth to
that. So, I get the feeling that some think of mathematicians as being just
like grumpy cat here when we say it’s important to do it. But I don’t think
of myself as a grumpy mathematician. So, why do we say it’s important?
There are lots of reasons. For one, the algorithms present a rich
opportunity to make use of and teach the arithmetic properties. These are
the things that carry on to algebra, trig, calculus, and beyond. For long
division in particular there’s a really cool reason:
Once students move beyond whole number division, they use long division
to relate fractions to decimal numbers. Now, that might sound a little
boring at first, but what it does is open the door for fractions like 1/3 or
1/7 to be converted into a decimal number (happens by grade 7), not just
the “easy” ones like 1/10 = 0.1.
Actually, that might’ve sounded boring too. So let me explain. Woven
throughout the K-12 curriculum there’s a story unfolding, and the idea of
what constitutes a number continues to expand as they build out the real
line. They begin right away with counting (using whole numbers), they’re
introduced to 0, and place value units. All of these numbers being neatly
organized into a cute little number line that, incidentally, hints at
something more (after all, it’s continuous…). In grade 3 students come to
the realization that there are more numbers than they realized: there are
fractions, and they’re on the number line too, between the whole numbers
they know and love! But here’s the thing, any interval can be subdivided
as many times as you want, and it appears that fractions “fill up” the
number line. In a sense, they do. However, in another sense, they don’t
even come close.
You see, every fraction, every one of these numbers that seems, on the
surface, to fill up the number line can be converted into a decimal number.
Sometimes that decimal number contains an infinite number of digits, e.g.
1/3 = 0.33333….., 1/7 = 0.142857. But no matter what, if we start with a
fraction, and convert it to a decimal number, the decimal will either
terminate in a finite number of digits, e.g. ¼ = 0.25, or it will have a finite
period (7.NS.2d it repeats!). But what about a decimal number with an
infinite number of digits, and NO period? Can it be written as a fraction of
the form a/b? The answer is NO WAY! Now, to the ancient Pythagoreans,
the rational numbers were IT, and they were pretty passionate about that.
According to one legend, Hippasus was at sea with some fellow
Pythagoreans, when he discovered the existence of irrational numbers,
and when he informed his shipmates, they had him thrown overboard!
Growing up in Texas people had bumper stickers that said “Don’t mess
with Texas.” I like to think these guys had the same mentality, “Don’t mess
with rational numbers”—they weren’t about to accept that there was
anything else out there.
Thus students see that there are irrational numbers and this allows them
to finally fill in the entire number line for the first time in their lives, and
it’s division that opens that door. This is where numbers like Pi, e, and
most square roots live.
There are other reasons of course. Division represents the first time
students see a truly cyclic algorithm that may not always terminate (e.g. 1
divided by 3) and they have to come to grips with that. The same ideas
show up when students work with polynomials in algebra, and partial
fractions in calculus, and without them, high school and college level
mathematics can’t be fully realized. The concepts are not limited to just
doing division. They continue to show up in mathematics, computer
science, and science in general.
3 min
9
Last NTI we talked about the wall between elementary school and the
middle/high schools. Getting them started in the world of real numbers is
what we are doing in kindergarten through fifth grade. Without long
division, the complete number system stays closed.
Section: Addition and Multiplication
Time: 33 min 9:23-9:56
[minutes] In this section, you will
 Practice using the addition and multiplication algorithms in
preparation for redelivering this matetrial
Materials used include:
 Review PowerPoint and
 Session Notes
Time Slide Slide #/ Pic of Slide
#
Script/ Activity directions
GROUP
1 min
10
•
•
2 min
11
We are starting with addition and multiplication in which parts join
to make a whole. Smaller units are composed into larger units.
We follow with subtraction and division in which the whole is
separated into parts. Larger units are decomposed.
8 and 4. The most basic algorithm is to count fingers. (Demonstrate) There
are 12 in all.
As math advances, students find short cuts and are also taught valuable
short cuts such as this process, begun in first grade, of completing a unit.
Students have a process, a strategy, an algorithm. Decompose one addend
to complete a unit of ten.
Two components, one a thought process and the other a way of recording.
Counting to ten and then counting four more on the fingers is the process
and recording system for the demonstrated “counting all.”
The completion of the unit is the thought process and the two equations
are the recording system for the “make ten” strategy.
“Make ten’ is an algorithm in Grade 1 just as ‘counting all while tracking on
fingers ‘is an algorithm, though highly inefficient, in kindergarten.
This G1 algorithm sets the foundation for the addition algorithm by making
10 and adding on the remainder.
2 min 12
The addition algorithm from Grade 1 moves forward into the standard
algorithm for addition in Grade 2. Each addend is broken down,
decomposed by place value just as the 4 was decomposed in Grade 1.
Just as we saw the ‘4’ decomposed in 8 + 4, we now see the addends
decomposed so that we add like units.
Cycle 1:
Add the ones.
Change 10 ones for 1 ten.
Cycle 2:
Add the tens.
Standard algorithm, a place value strategy, is taught in grade 2, though we
don’t have to call it the standard algorithm. We started the presentation
with mental math because we want anyone doing mathematics to carefully
choose their strategies. Mental math is one, the algorithm is another when
no obvious mental strategy is evident.
Model on the place value chart how you add 24 + 58.
We’re going to add like units.
Make a 10 strategy on place value chart, then record it on the expression.
Explain that new units are recorded below because within the system of
algorithms, for multi digit multiplication, without this recording, new units
are put in the incorrect place as will be evidenced in slide 24.
2 min 13
Units change in Grades 4 and 5 as can be seen in the slide. We want to see
the relationship of the different units and the relevance of their earlier
work. 24 has mixed units (2 tens 4 ones) just as does 2 feet 4 inches or 3
boys and 2 girls.
Walk through the language of units with the tenths.
2.4 + 5.8
The presenter engages teachers in place value language while solving the
decimal addition problem.
Cycle 1
T: 4 tenths + 8 tenths is?
P: 12 tenths.
T: Can I make a larger unit?
P: Yes.
T: What unit?
T: A one
Cycle 2
T: 2 ones + 5 ones + 1 one is?
S: 8 ones.
T: The answer is?
S: 8 and 2tenths.
2 min
14
Give participants time to practice. Refer back to slide 12 to remind them
they have the language of units from the student’s earlier example and can
use it to support their words.
Remind to use the language of units when referring to the ones. This is the
most neglected place value.
2 min 15
The focus of G3 work with multiplication is developing the ability to treat
any number as a unit, and hence, counted.
Give each finger a value of 6 and count sixes on the fingers. 1 six, 2 sixes….
Early on we give them the count by process or repeated addition process
which at some point becomes the fact they don’t have to think about any
more.
Now we’re going to focus on multiplication.
Addition is the mother of all the operations.
Beginning in G3 we start with the distributive property, which really moves
the addition into the realm of multiplication.
2 sixes and 3 sixes is 5 sixes. That’s the distributive property.
2 min
16
By adding the units you can very clearly illustrate the distributive property.
Just as 2 apples + 3 apples is 5 apples, so too is 2 sixes + 3 sixes equal to 5
sixes.
We have 5 units of six that we decompose into 2 sixes and 3 sixes. We have
decomposed the number of groups.
We also on the right have 5 units of six but this time we have decomposed
the groups of six into 5 fives and 1 five.
We can also think of the decompositions as that on the left being the
decomposition of the number of rows or the width; that on the right being
the decomposition of the number of columns or length.
3 min 17
How does this play out in G4?
Show the 6 units of twenty four on the place value chart.
Relate this to slide before with the arrays.
Here you see the unit of 24, but you see the units partitioned in Grade 4
(tens on one side, ones on the other.) We multiply the unit twenty four six
times. We compose 2 units. We can change 20 ones for 2 tens (does this
look familiar from the addition algorithm?)
Show this on the place value chart.
Relate the multiplication to repeated addition.
Students see that the composition is the same, and is recorded the same.
This is a cyclic algorithm.
Cycle 1
6 times 4 ones is 24 ones, 2 tens 4 ones.
Cycle 2
6 times 2 tens is 12 tens, 1 hundred 2 tens (or 12 tens since it is the final
place value.
Same with addition. Changing smaller units for larger units with addition.
Point out that the ‘2’ is the same regrouping that was done in addition.
Alternate way of saying:
This is six units of 24.
6 twenty fours.;
We use place value to break that down.
6 x 4 ones + 6 x 2 tens.
Developing the standard algorithm from the partial products.
1 min
18
2 min 19
Use this as an exemplar for the language of units.
Alternate algorithms (array model shown now as an area model). The array
transitions into the area model. Explain that the 24 has been partitioned,
and relates to the distributive property.
We want students to be able to manipulate numbers in unit from as well as
in number form. This flows right out of Grade 3 distributive property.
The partial products are listed from largest to smallest in the algorithm to
the left, assuming that is the way the person moved through the area
model, starting with the largest units and moving to the smallest.
The unit form is used on the right in the order of the standard algorithm,
starting by multiplying the ones and then multiplying the tens.
3 min 20
coupled
with
next
slide
30 units of 24.
Show the partitioned area model and explain how the model shows the
equation.
3 tens, or thirty, times 2 tens, or twenty equals 6 hundred.
10 x 10 is 100 (you get a new unit), if you do that 6 times you’ve got 600.
Translate into a much simpler model (next slide). We want ours students to
understand how the units are behaving. A length times a length gives a
square unit. 1 cm x 1 cm = 1 cm squared.
1 ten x 1 ten = 1 hundred square units.
We largely omit the language of square units until returning to word
problem situations involving actual measurements. Otherwise, the
language is too complex.
Notice, that in anticipation of the algorithm, just like on the place value
chart, we are starting with the ones and then multiplying the tens.
X
21
This is the simplified version of the prior slide.
Point out that when recording the “one” should not go in the tens place
but in the hundreds place (Relates to the recording of the standard
algorithm in slide 24.)
1 min
22
Use this slide to support practice with the language of units.
1 min 23
30 x 24 = 3 x (10 x 24)
Understand what’s going on the place value chart.
Explains the model slowly step by step.
Show the 24 shifting one place to the left when being multiplied by 10.
Once the unit has shifted over once more, it’s triple.
30 x 24 = 10 x (3 x 24)
We start by tripling the unit of twenty four.
The entire product then shifts one place value to the left as it is
multiplied by 10.
2 min
36 units of twenty-four.
Here the only difference is that instead of 30 twenty fours we have 36
twenty fours. We’re putting them together. There’s no new
mathematical complexity.
The two partial products have been modeled previously, 6 x 24 and 30
x 24.
Explain the connections between the model, the arithmetic, and the
distributive property as necessary. Point out that the regrouped unit,
the product of 3 tens and 2 tens is correctly recorded in the hundreds
place in super script above the second partial product. In the
“traditional” algorithm, this would have been incorrectly recorded
above the “2” of 24 in the tens place.
24
2 min
25
How many partial products now? 4.
Students see the product that matches each rectangle/part on the area
model.
Relate the partial products to the both algorithms. Return to slide 24 if
necessary to clarify the relationship of the standard algorithm to the
right, to the area model.
1 min
26
How does this relate to Grade 5 with decimals?
If students are multiplying 2.4 times 36, then don’t have to think of it as
2 and 4 tenths. They can think of it as 24 tenths, multiply the whole
numbers of tenth units and then reinterpret the answer in standard
form with decimal notation.
4 min
27
Section: Subtraction and Division
Time: 31 min 9:56-10:30
[minutes] In this section, you will ..
Materials used include:
 Session PowerPoint

1 min
Practice using subtraction and division algorithms in
preparation for redelivery of this training

Session Notes
28
Now we’re going to move into algorithms that go from whole to
part, subtraction and division.
Decomposing, changing larger units into smaller units,
renaming, unbundling.
2 min 29
Walk the participants through the slide and how it relates to
what the students are thinking and recording.
We could use the really old fashioned way of counting down,
but we’re trying to teach more efficient processes for
subtraction.
Show how to decompose 12 to subtract 12 – 8.
Break 12 into 10 and 2. Can’t take 8 from 2 ones. Take it from
the ten. That leaves me 2 and 2 more.
This simple algorithm, strategy, process, pays off in Grade 2 as
Grade 1 students become accustomed to analyzing if there are
enough ones to subtract the ones or is it better to go to the tens.
2 min
Walk through the slide step by step.
Notice that we model only the whole amount, the total, on the
place value chart.
In grade 2 we again break the numbers apart by units on the
place value chart to subtract. We want to extract the 24 that’s
within 82 and find out what’s left. If I take the part, 24, out of
the whole, 82, we find the missing part.
Do I have enough ones or not? Take 1 ten and change it for 10
ones.
30
Why use the magnifying glass? Helps us avoid the
misconception of saying 4 – 2. Gets students to focus on the
whole number rather than inverting the ones.
A cyclic operation. Systematically say do I have enough ones to
subtract? Tens? Change all units until the entire total or whole,
is ready for subtraction. The magnifying glass is a mnemonic.
1 min
31
This is the language of units that we want to hear the students
speaking as they learn the algorithms. The ones are the most
neglected. Identify those ones!
3 min
32
Walk through the slide.
6 hundreds, no tens and ones. Go all the way to the hundreds
to get some units of one.
Two methods are shown:
Method 1
(Place value chart in the middle)
The place value chart models decomposing 1 hundred for 10
tens and then decomposing 1 ten for 10 ones.
Method 2
(Place value chart to the far right)
Models decomposing 1 hundred as 9 tens and 10 ones.
Much cleaner and avoids the mistakes that come in stacks of
regrouped numbers.
1 min
33
An exemplar of the language of units.
3 min
34
Circulate and support teachers in using their words.
1 min
35
The focus of G3 is the study of basic division facts as relates to
multiplication without remainders.
Long division. I have heard so many Grade 5 teachers saying
that long division is obsolete.
You might reiterate that long division matters.
When we’re looking at 6s one more time, we can count the
number of units of 6 in 24.
How many sixes in 24? 4.
That’s the measurement way of looking at division. We’re not
partitioning. We’re accustomed to thinking about sharing!
We can interpret the divisor to be telling us the size of the unit
rather than the number of units.
1 min
36
Analyze the number bonds relationship to the array.
This is not a situation we would readily use the distributive
property to subtract since most everyone knows that 30 ÷ 6 is
5.
However, 56 ÷ 8 might be since 56 decomposes nicely into 40
and 16, or 5 eights and 2 eights.
The point is that like with multiplication, where we find partial
products, we can find partial quotients and add them up.
3 min
37
Like subtraction, starting with the whole amount.
Unlike all the other standard algorithms, we are distributing
the largest units first, moving from left to right on the place
value chart..
Are students are going to distribute the largest bills first?
Cycle 1
4 tens distributed into 3 groups,
One ten in each group.
I made 3 groups of 1 ten.
One ten is remaining.
I can change 1 ten for 10 ones.
Ten ones + 2 ones is 12 ones.
Cycle 2
12 ones distributed into 3 groups,
Four ones in each group.
I made 3 groups of 4 ones.
No ones are remaining.
My quotient is 14.
Notice the notation that is analogous in the third place value
chart of the 3 tens distributed with the 12 ones to be
distributed.
2 min
38
What is the largest area I can make that is easy to divide by 3?
We make a rectangle with an area of 30 and a width of 3. The
side length is unknown.
Just like we had previously partial products, we now have a
partial quotient.
Show how to record that information on the algorithm.
I have an area of 12 remaining and I want to find its unknown
length. Show how this relates to the area model in
multiplication.
2 min
39
Give participants the opportunity to go through the thinking of
each of the children as they solve 420 divided by 30.
(The reason 42 is not subdivided in the place value chart is
because it was done on the prior pages.)
3 min
40
You can see immediately that this is related to 42 divided by 3.
Always round the divisor first therefore round 29 to 30.
Cycle 1
T: Estimate to find 42 hundreds divided by 30. (Show first
estimate.)
S: 1 hundred.
T: 1 hundred times 29?
S: 29 hundreds (Record and find the remainder in the hundreds
place, image #2)
T: How many hundreds remaining?
S: 13 hundreds.
T: Decompose those units into tens and add the tens from the
whole.
S: 138 tens.
Cycle 2.
T: Estimate to find 138 tens divided by 30. (Show second
estimate.)
S: 4 tens.
T: 4 tens times 29?
S: 116 tens (Record and find the remainder in the tens place,
image #3)
T: How many tens remaining?
S: 22 tens.
T: Decompose those units into ones and add the ones from the
whole.
S: 227 ones.
Cycle 3.
T: Estimate to find 227 ones divided by 30. (Show first
estimate.)
S: 7 ones.
T: 7 ones times 29?
S: 203 ones (Record and find the remainder in the ones place,
image #4)
T: How many ones remaining?
S: 24 ones.
T: Our remainder is 24 ones.
Note: In G5, we could certainly continue into the decimal place
values. Cycling through the process. We know from the
overview that because this is a rational number, the decimal
expansion will either terminate or result in a repeating decimal.
This one really shows how the operations and the algorithms
tie together.
5 min
41
2 min
42
Take 2 minutes to turn and talk with others at your table.
Share your observations and ask them to do the same.
1 min
43
Read the key points
Use the following icons in the script to indicate different learning modes.
Video
Reflect on a prompt
Turnkey Materials Provided
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Additional Suggested Resources
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Active learning
Turn and talk