3rd Grade Math Instructional Focus Units 2015/2016
Revised 5/6/2015
Instructional Focus Units
Estimated Time
Focus 1
Introduction to Multiplication and Division
5 Weeks
Focus 2
4 Weeks
Focus 3
Applying Place Value, Properties and Operations to Add/Sub Multi- Digit
Numbers
Develop Understanding of Fractions as Numbers
Focus 4
Develop Understanding of Multiplication and Division
5 Weeks
Focus 5
Demonstrating Computational Fluency in Problem Solving
2 Weeks
Focus 6
4 Weeks
Focus 7
Extending Understanding of Multiplication & Division/Attributes of
Geometric Figures
Connecting Data to the Four Operations and Fractions
Focus 8
Extending Understanding of Fractions as Numbers
3 Weeks
Focus 9
Understanding measures of Liquid Volume, Weight and Mass.
3 Weeks
1
Standards in BOLD and UNDERLINED are found under major clusters.
5 Weeks
4 Weeks
3rd Grade Math Instructional Focus Units 2015/2016
Revised 5/6/2015
***Based on the standards, not all lessons within the resource may be needed to meet the
needs of your students.
2
Standards in BOLD and UNDERLINED are found under major clusters.
3rd Grade Math Instructional Focus Units 2015/2016
Revised 5/6/2015
Focus 1: Introduction to Multiplication and Division
Students begin developing these concepts by working with numbers with which they are more familiar, such
as 2s, 5s, and 10s, in addition to numbers that are easily skip counted such as 3s and 4s. Since multiplication
is a critical area for grade 3, students will build on these concepts throughout the year, working towards
fluency by the end of the year.
Standards Estimated
Principal Resource
Additional Resource
3.OA.A.1
Time
-Fosnot Grocery Stamps
3.OA.A.2
5 weeks
and Measuring Strips
3.OA.A.3
3.OA.A.4
AND
Routines3.OA.B.5
-Use mini-lesson in Grocery Stamps &
3.OA.B.6
-IDS Unit 5, including
Measuring Strips
3.OA.C.7
Common Core Resource
-Routines in addition to Ten-Minute math:
3.OA.D.8
3.1A, 3.5A, 3.5B, 3.7A
word problems -equal groups unknown product,
3.OA.D.9
-Fosnot mini-lessons Early Mult/Div. A1 – A10
3.MD.C.7
Notes
**Because there are two principal resources listed in this focus unit, teachers need to determine the best
sequencing for their population’s needs. Please note: not all lessons in every resource unit may be needed
for every group of students. Please use your professional judgement when planning your instruction.
End of the year 3rd grade fluency expectations –
3.OA.C.7 Multiply/Divide within 100 Fluently –Rote memorization of basic facts is not fluency. Fluency with
multiplication facts includes deeper understanding of concepts and flexible thinking.
3.NBT.A.2 Add/Subtract within 1000
3
Standards in BOLD and UNDERLINED are found under major clusters.
3rd Grade Math Instructional Focus Units 2015/2016
Revised 5/6/2015
Focus 2: Applying Place Value, Properties and Operations to Add/Sub Multi- Digit Numbers
In this focus students increase the sophistication of computation strategies that include place value
understanding for addition and subtraction within 1,000. The concept of rounding is introduced to offer the
students another strategy to judge the reasonableness (MP.3) of their answers in addition and subtraction
situations.
Standards Estimated Principal Resource
Additional Resource
3.OA.D.8
Time
IDS Unit 3 - Include
-3.NBT.A.1 – Engage NY – Module 2, Topic C, lesson
3.OA.D.9
4 weeks
Common Core IDS Book,
14
3.NBT.A.1
sessions 1.7A and
3.NBT.A.2
EXCLUDE session 3.1
Routines
In addition to Ten-Minute math -Fosnot Mini-lessons
Principal resource for
in Extending add. & sub. B1-B15
3.MD.A.1
3.MD.A.1 Engage NY –
-Number Talks pg. 186-196
Module 2, Topic A,
-Problem solving: Add To (Join, Result Unknown) Take
lessons 1-5
from (Separate, Result Unknown), Put Together/Take
Apart (Part-Part-Whole) and Compare problems.
Refer to Table 1, p. 21 (in 2nd grade CCSS). Problems
into the 1,000’s for add. & sub. Include multi-step
word problems.
Notes
**Because there are two principal resources listed in this focus unit, teachers need to determine the best
sequencing for their population’s needs. Please note: not all lessons in every resource unit may be needed
for every group of students. Please use your professional judgement when planning your instruction.
End of the year 3rd grade fluency expectations –
3.OA.C.7 Multiply/Divide within 100 fluently - Rote memorization of basic facts is not fluency. Fluency with
multiplication facts includes deeper understanding of concepts and flexible thinking.
3.NBT.A.2 Add/Subtract within 1000
4
Standards in BOLD and UNDERLINED are found under major clusters.
3rd Grade Math Instructional Focus Units 2015/2016
Revised 5/6/2015
Focus 3: Develop Understanding of Fractions as Numbers
Students have had experience partitioning shapes into fair shares (1.G.3 and 2.G.3) using words to describe
the quantity. In this focus students extend this understanding to partition shapes and number lines
representing these fair shares using fraction notation. Students learn to view unit fractions as building
blocks-understating that every fraction is an iteration of unit fractions. (2/3 = 2 pieces of size one-third)
Standards Estimated
Principal Resource
Additional Resource
3.NF.A.1
Time
Engage NY Module 5 Topic http://www.k-5mathteachingresources.com/
3.NF.A.2
5 weeks
A, B, & C
http://www.illustrativemathematics.org/illustra
3.NF.A.3
tions
3.G.A.2
AND
RoutinesIDS Unit 7 Investigations 2 -In addition to Ten-Minute math: Problem
&3
solving with strong emphasis on fractions in real
world context
-Number Talks pgs. 197-216.
Notes
Students develop an understanding of fractions, beginning with unit fractions. Students view fractions in
general as being built out of unit fractions, and they use fractions along with visual fraction models to
represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the
whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger
bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3
equal parts, the parts are longer than when the ribbon is divided into 5 equal parts.
**Because there are two principal resources listed in this focus unit, teachers need to determine the best
sequencing for their population’s needs. Please note: not all lessons in every resource unit may be needed
for every group of students. Please use your professional judgement when planning your instruction.
End of the year 3rd grade fluency expectations –
3.OA.C.7 Multiply/Divide within 100 fluently - Rote memorization of basic facts is not fluency. Fluency with
multiplication facts includes deeper understanding of concepts and flexible thinking.
3.NBT.A.2 Add/Subtract within 1000
5
Standards in BOLD and UNDERLINED are found under major clusters.
3rd Grade Math Instructional Focus Units 2015/2016
Revised 5/6/2015
Focus 4: Develop Understanding of Multiplication and Division
This focus provides students a solid foundation in solving problems with equal groups and arrays. This is
necessary to support future success with measurement problems. It includes multiple experiences to
explore the connections between distributive property and multiplying the side lengths to determine area.
Students recognize that multiplication strategies can be used to make sense of and solve division problems.
Standards Estimated
Principal Resource
Additional Resource3.OA.A.3
Time
Fosnot Muffles and
www.k-5mathteachingresources.com/3rd3.OA.A.4
5 weeks
Truffles
grade-number-activities.html
3.OA.B.5
http://www.illustrativemathematics.org/illustra
3.OA.C.7
AND
tions
3.OA.D.8
http://www.insidemathematics.org/index.php/
3.OA.D.9
Engage NY Module 3, Topic 3rd-grade
3.MD.C.7
A, B, C, D, E, & F
3.NBT.A.3
Routines-Fosnot mini-lessons from Muffles and Truffles
-Problem solving refer to CCSS pg. 29
Arrays/area- (unknown product- group size
unknown- number of groups unknown).
Notes
During Muffles Truffles make sure to use the term AREA where applicable. Make the connection of
multiplication and area.
**Because there are two principal resources listed in this focus unit, teachers need to determine the best
sequencing for their population’s needs. Please note: not all lessons in every resource unit may be needed
for every group of students. Please use your professional judgement when planning your instruction.
End of the year 3rd grade fluency expectations –
3.OA.C.7 Multiply/Divide within 100 fluently – Rote memorization of basic facts is not fluency. Fluency with
multiplication facts includes deeper understanding of concepts and flexible thinking.
3.NBT.A.2 Add/Subtract within 1000
6
Standards in BOLD and UNDERLINED are found under major clusters.
3rd Grade Math Instructional Focus Units 2015/2016
Revised 5/6/2015
Focus 5: Demonstrating Computational Fluency in Problem Solving
Students will focus on problems solving in order to demonstrate fluency with addition and subtraction to
1,000. Include two-step word problems.
Standards Estimated
Principal Resource
Additional Resource
3.OA.A.3
Time
IDS Unit 8
http://www.insidemathematics.org/index.php/
3.OA.C.7
2 weeks
3rd-grade
3.OA.D.8
Teacher links two-step
http://www.illustrativemathematics.org/illustra
3.OA.D.9
word problems
tions
3.NBT.A.2
Routines
-In addition to Ten-Minute mathProblem solving refer to CCSS 2nd grade pg. 22
compare - difference unknown. Problem
solving refer to CCSS 3rd grade pG.A.29
compare unknown product, group size
unknown, and number of groups unknown. **2
step word problems must be incorporated**
Notes
**Because there are two principal resources listed in this focus unit, teachers need to determine the best
sequencing for their population’s needs. Please note: not all lessons in every resource unit may be needed
for every group of students. Please use your professional judgement when planning your instruction.
End of the year 3rd grade fluency expectations –
3.OA.C.7 Multiply/Divide within 100 fluently - Rote memorization of basic facts is not fluency. Fluency with
multiplication facts includes deeper understanding of concepts and flexible thinking.
3.NBT.A.2 Add/Subtract within 1000
7
Standards in BOLD and UNDERLINED are found under major clusters.
3rd Grade Math Instructional Focus Units 2015/2016
Revised 5/6/2015
Focus 6: Extending Understanding of Multiplication & Division/Attributes of Geometric Figures
Students will focus on reasoning with shapes and their attributes, including area and perimeter. The
standards in this focus strongly support one another because perimeter, like area, is an attribute of shape.
The focus extends student’s understanding of multiplication and division.
Standards
Estimated
Principal Resource
Additional Resource
3.MD.C.5
Time
IDS unit 4
3.MD.C.6
4 weeks
EXCLUDE investigation 2
3.MD.C.7
Routines
3.MD.D.8
In addition to Ten-Minute math3.G.A.1
Engage NY Module 4,
Fosnot Mini-lessons Extending Add & Sub. C7Topics A, B, C & D
C12
-Continue problem solving for add/sub. within
1000's or mult/div within 100 **2 step word
problems must be incorporated**
-Number Talks pg. 278-285.
Notes
Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by
finding the total number of same-size units of area required to cover the shape without gaps or overlaps, a
square with sides of unit length being the standard unit for measuring area. Students understand that
rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing
rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using
multiplication to determine the area of a rectangle.
**Because there are two principal resources listed in this focus unit, teachers need to determine the best
sequencing for their population’s needs. Please note: not all lessons in every resource unit may be needed
for every group of students. Please use your professional judgement when planning your instruction.
End of the year 3rd grade fluency expectations –
3.OA.C.7 Multiply/Divide within 100 fluently - Rote memorization of basic facts is not fluency. Fluency with
multiplication facts includes deeper understanding of concepts and flexible thinking.
3.NBT.A.2 Add/Subtract within 1000
8
Standards in BOLD and UNDERLINED are found under major clusters.
3rd Grade Math Instructional Focus Units 2015/2016
Revised 5/6/2015
Focus 7: Connecting Data to the Four Operations and Fractions
In this focus students will represent and interpret data in various formats (line plot, tables and bar graphs,
etc…) that includes measurement of lengths with whole numbers and fractions. Students will solve one and
two step “how many more” and “how many less” problems using the date presented in these graphs.
Standards
Estimated Principal Resource
Additional Resource
3.MD.B.3
Time
-IDS Unit 2 Include Common
http://illuminations.nctm.org/LessonDetail.aspx
3.MD.B.4
4 weeks
Core Book, session 2.3A and
?id=U149
3.OA.A.3
exclude sessions 2.3 - 2.7
3.OA.C.7
Routines
3.OA.D.8
4.MD.B.4 - Engage NY Module In addition to Ten-Minute math3.OA.D.9
6, Topic B
Fosnot mini-lessons extended Add and Sub.
3.NBT.A.2
C24-C32
-Problem solving into the 1,000’s for add. & sub.
**2 step word problems must be
incorporated** refer to Table 1, pg. 21 (in 2nd
grade CCSS) problem solving using
multiplication and division refer to pg. 29 in 3rd
grade CCSS.
Notes
**Because there are two principal resources listed in this focus unit, teachers need to determine the best
sequencing for their population’s needs. Please note: not all lessons in every resource unit may be needed
for every group of students. Please use your professional judgement when planning your instruction.
End of the year 3rd grade fluency expectations –
3.OA.C.7 Multiply/Divide within 100 fluently - Rote memorization of basic facts is not fluency. Fluency with
multiplication facts includes deeper understanding of concepts and flexible thinking.
3.NBT.A.2 Add/Subtract within 1000
9
Standards in BOLD and UNDERLINED are found under major clusters.
3rd Grade Math Instructional Focus Units 2015/2016
Revised 5/6/2015
Focus 8: Extending Understanding of Fractions as Numbers
Students will develop a conceptual understanding of equivalence. Multiple types of models and
representations should be used to help students develop this understanding. Students will apply their
understanding of equivalence to compare fractions. As a result students will develop conceptual
understanding of fraction comparisons and practice reasoning about size. Students defend their reasoning
and critique the reasoning of others using both visual models and their understanding of the structure of
fractions.
Standards Estimated
Principal Resource
Additional Resource
3.NF.A.2
Time
Engage NY Module 5 Topic Teaching Student Centered Mathematics 3-5
3.NF.A.3
3 weeks
D, E, & F
pgs. 131-152
3.G.A.2
http://www.insidemathematics.org/index.php/
3rd-grade
Routines
-Continue 2 step word problems. Integrate
fractions into word problems (use the book
Extending Children’s Mathematics Fractions and
Decimals for word problems examples)
Notes
Students are able to use fractions to represent numbers equal to, less than, and greater than one. They
solve problems that involve comparing fractions by using visual fraction models and strategies based on
noticing equal numerators or denominators.
**Because there are two principal resources listed in this focus unit, teachers need to determine the best
sequencing for their population’s needs. Please note: not all lessons in every resource unit may be needed
for every group of students. Please use your professional judgement when planning your instruction.
End of the year 3rd grade fluency expectations –
3.OA.C.7 Multiply/Divide within 100 fluently - Rote memorization of basic facts is not fluency. Fluency with
multiplication facts includes deeper understanding of concepts and flexible thinking.
3.NBT.A.2 Add/Subtract within 1000
10
Standards in BOLD and UNDERLINED are found under major clusters.
3rd Grade Math Instructional Focus Units 2015/2016
Revised 5/6/2015
Focus 9: Understanding measures of Liquid Volume, Weight and Mass.
In this focus students will solve problems involving measurement and estimation of liquid volumes and
masses of objects. Solve one-step word problems involving all four operations with grams, kilograms, liters,
and milliliters given in the same units.
Standards Estimated
Principal Resource
Additional Resource
3.MD.A.2 Time
IDS Unit 9 - ONLY Common http://www.illustrativemathematics.org/illustratio
3.NBT.A.1 3 weeks
Core IDS Book, sessions
ns
3.NBT.A.2
4A.1 - 4A.3
http://www.k-5mathteachingresources.com/3rdgrade-measurement-and-data.html
3.MD.2- Engage NY
Module 2, Topic B
Routines
In addition to Ten-Minute Math-Problem solving involving masses and volumes
that are given in the same units
Notes
**Because there are two principal resources listed in this focus unit, teachers need to determine the best
sequencing for their population’s needs. Please note: not all lessons in every resource unit may be needed
for every group of students. Please use your professional judgement when planning your instruction.
End of the year 3rd grade fluency expectations –
3.OA.C.7 Multiply/Divide within 100 fluently - Rote memorization of basic facts is not fluency. Fluency with
multiplication facts includes deeper understanding of concepts and flexible thinking.
3.NBT.A.2 Add/Subtract within 1000
11
Standards in BOLD and UNDERLINED are found under major clusters.
3rd Grade Math Instructional Focus Units 2015/2016
Revised 5/6/2015
Table 1: Common addition and subtraction
Result Unknown
Two bunnies sat on the grass.
Three more bunnies hopped there.
How many bunnies are on the grass
now?
2+3=?
Add to
Total Unknown
Three red apples and two green
apples are on the table. How many
apples are on the table?
3+2=?
Change Unknown
Two bunnies were sitting on the
grass. Some more bunnies hopped
there. Then there were five
bunnies. How
many bunnies hopped over to the
first two?
2+?=5
Five apples were on the table. I
ate some apples. Then there were
three apples. How many apples
did I eat?
5–?=3
Addend Unknown
Five apples are on the table. Three
are red and the rest are green.
How many apples are green?
3 + ? = 5, 5 – 3 = ?
Difference Unknown
(“How many more?” version):
Lucy has two apples. Julie has five
apples. How many more apples
does Julie have than Lucy?
Bigger Unknown
(Version with “more”):
Julie has three more apples than
Lucy. Lucy has two apples. How
many apples does Julie have?
Some apples were on the table. I
ate two apples. Then there were
three apples. How many apples
were on the table before?
?–2=3
Both Addends Unknown1
Grandma has five flowers. How
many can she put in her red vase
and how many in her blue vase?
5 = 0 + 5, 5 = 5 + 0
5 = 1 + 4, 5 = 4 + 1
5 = 2 + 3, 5 = 3 + 2
Smaller Unknown
(Version with “more”):
Julie has three more apples than
Lucy. Julie has five apples. How
many apples does Lucy have?
(“How many fewer?” version):
Lucy has two apples. Julie has five
apples. How many fewer apples
does Lucy have than Julie?
2 + ? = 5, 5 – 2 = ?
(Version with “fewer”):
Lucy has 3 fewer apples than Julie.
Lucy has two apples. How many
apples does Julie have?
2 + 3 = ?, 3 + 2 = ?
(Version with “fewer”):
Lucy has 3 fewer apples than Julie.
Julie has five apples. How many
apples does Lucy have?
5 – 3 = ?, ? + 3 = 5
Five apples were on the table. I ate
two apples. How many apples are
on the table now?
5–2=?
Take from
Put Together /
Take Apart2
Compare3
situations.6
Start Unknown
Some bunnies were sitting on the
grass. Three more bunnies hopped
there. Then there were five
bunnies. How many bunnies were
on the grass before?
?+3=5
6
Adapted from Box 2-4 of Mathematics Learning in Early Childhood, National Research Council (2009, pp. 32, 33).
1These
take apart situations can be used to show all the decompositions of a given number. The associated equations, which have the total on the
left of the equal sign, help children understand that the = sign does not always mean makes or results in but always does mean is the same number
as.
2Either
addend can be unknown, so there are three variations of these problem situations. Both Addends Unknown is a productive extension of this basic situation,
especially for small numbers less than or equal to 10.
3For the Bigger Unknown or Smaller Unknown situations, one version directs the correct operation (the version using more for the bigger unknown and using less for
the smaller unknown). The other versions are more difficult.
12
Standards in BOLD and UNDERLINED are found under major clusters.
3rd Grade Math Instructional Focus Units 2015/2016
Revised 5/6/2015
Table 2: Common multiplication and division
situations.7
Unknown Product
Equal Groups
Arrays,4 Area5
Compare
General
Group Size Unknown
Number of Groups Unknown
(“How many in each group?”
Division)
(“How many groups?” Division)
3x6=?
3 x ? = 18, and 18 ÷ 3 = ?
? x 6 = 18, and 18 ÷ 6 = ?
There are 3 bags with 6 plums in
each bag. How many plums are
there in all?
If 18 plums are shared equally into
3 bags, then how many plums will
be in each bag?
If 18 plums are to be packed 6 to a
bag, then how many bags are
needed?
Measurement example.
Measurement example.
Measurement example.
You need 3 lengths of string, each
6 inches long. How much string
will you need altogether?
You have 18 inches of string,
which you will cut into 3 equal
pieces. How long will each piece of
string be?
You have 18 inches of string,
which you will cut into pieces that
are 6 inches long. How many
pieces of string will you have?
There are 3 rows of apples with 6
apples in each row. How many
apples are there?
If 18 apples are arranged into 3
equal rows, how many apples will
be in each row?
If 18 apples are arranged into
equal rows of 6 apples, how many
rows will there be?
Area example.
Area example.
What is the area of a 3 cm by 6 cm
rectangle?
A rectangle has area 18 square
centimeters. If one side is 3 cm
long, how long is a side next to it?
A blue hat costs $6. A red hat costs
3 times as much as the blue hat.
How much does the red hat cost?
A red hat costs $18 and that is 3
times as much as a blue hat costs.
How much does a blue hat cost?
Measurement example.
Measurement example.
A rubber band is 6 cm long. How
long will the rubber band be when
it is stretched to be 3 times as
long?
A rubber band is stretched to be
18 cm long and that is 3 times as
long as it was at first. How long
was the rubber band at first?
General a x b = ?
a x ? = p, and p ÷ a = ?
7The
Area example.
A rectangle has area 18 square
centimeters. If one side is 6 cm
long, how long is a side next to it?
A red hat costs $18 and a blue hat
costs $6. How many times as much
does the red hat cost as the blue
hat?
Measurement example.
A rubber band was 6 cm long at
first. Now it is stretched to be 18
cm long. How many times as long
is the rubber band now as it was at
first?
? x b = p, and p ÷ b = ?
first examples in each cell are examples of discrete things. These are easier for students and should be given before the measurement
examples.
4The language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in
the grocery window are in 3 rows and 6 columns. How many apples are in there? Both forms are valuable.
5Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially
important measurement situations.
13
Standards in BOLD and UNDERLINED are found under major clusters.