3rd Grade Unit 1
September 9th – October 25th
3rd Grade: Unit 1
Curriculum Map: September 9th – October 25th
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September 9th – October 25th
3rd Grade Unit 1
Common Core Standards
REVIEW OF GRADE 2 FLUENCIES
2.OA.2
2.NBT.5
Fluently add and subtract within 20 using mental strategies.2 By end of
Grade 2, know from memory all sums of two one-digit numbers.
Fluently add and subtract within 100 using strategies based on place value, properties
of operations, and/or the relationship between addition and subtraction.
EXPECTED GRADE 3 FLUENCIES
3.OA.7
3.NBT.2
Fluently multiply and divide within 100, using strategies such as the relationship between
multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of
operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
Fluently add and subtract within 1000 using strategies and algorithms based on place value,
properties of operations, and/or the relationship between addition and subtraction.
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3rd Grade Unit 1
September 9th – October 25th
GRADE 3 MEASUREMENT AND DATA
3.MD.1
Tell and write time to the nearest minute and measure time intervals in minutes. Solve word
problems involving addition and subtraction of time intervals in minutes, e.g., by representing the
problem on a number line diagram.
Students in second grade learned to tell time to the nearest five minutes. In third grade, they extend telling time
and measure elapsed time both in and out of context using clocks and number lines. Students may use an
interactive whiteboard to demonstrate understanding and justify their thinking.
3.MD.3
Draw a scaled picture graph and a scaled bar graph to represent a data set with several
categories. Solve one- and two-step “how many more” and “how many less” problems using
information presented in scaled bar graphs. For example, draw a bar graph in which each
square in the bar graph might represent 5 pets.
Students should have opportunities reading and solving problems using scaled graphs before being asked to
draw one. The following graphs all use five as the scale interval, but students should experience different intervals
to further develop their understanding of scale graphs and number facts.
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Pictographs: Scaled pictographs include symbols that represent multiple units. Below is an example of a
pictograph with symbols that represent multiple units. Graphs should include a title, categories, category
label, key, and data.
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Single Bar Graphs: Students use both horizontal and vertical bar graphs. Bar graphs include a title, scale,
scale label, categories, category label, and data.
GRADE 3 NUMBERS AND OPERATIONS IN BASE TEN
3.NBT.1
Use place value understanding to round whole numbers to the nearest
10 or 100.
Students learn when and why to round numbers. They identify possible answers and halfway points. Then they
narrow where the given number falls between the possible answers and halfway points. They also understand
that by convention if a number is exactly at the halfway point of the two possible answers, the number is rounded
up.
3.NBT.2
Fluently add and subtract within 1000 using strategies and algorithms based on place value,
properties of operations, and/or the relationship between addition and subtraction.
Problems should include both vertical and horizontal forms, including opportunities for students to apply the
commutative and associative properties. Adding and subtracting fluently refers to knowledge of procedures,
knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and
efficiently. Students explain their thinking and show their work by using strategies and algorithms, and verify that
their answer is reasonable. An interactive whiteboard or document camera may be used to show and share
student thinking.
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3rd Grade Unit 1
September 9th – October 25th
GRADE 3 OPERATIONS AND ALGEBRAIC THINKING
3.OA.8
Solve two-step word problems using the four operations. Represent these problems using
equations with a letter standing for the unknown quantity. Assess the reasonableness of
answers using mental computation and estimation strategies including rounding. 3
Students should be exposed to multiple problem-solving strategies (using any combination of words, numbers,
diagrams, physical objects or symbols) and be able to choose which ones to use. When students solve word
problems, they use various estimation skills which include identifying when estimation is appropriate, determining
the level of accuracy needed, selecting the appropriate method of estimation, and verifying solutions or
determining the reasonableness of solutions.
Estimation strategies include, but are not limited to:
• using benchmark numbers that are easy to compute
• front-end estimation with adjusting (using the highest place value and estimating from the
front end making adjustments to the estimate by taking into account the remaining amounts)
• rounding and adjusting (students round down or round up and then adjust their estimate depending on how
much the rounding changed the original values)
3.OA.9
Identify arithmetic patterns (including patterns in the addition table or multiplication table), and
explain them using properties of operations. For example, observe that 4 times a number is
always even, and explain why 4 times a number can be decomposed into two equal addends.
Students need ample opportunities to observe and identify important numerical patterns related to operations.
They should build on their previous experiences with properties related to addition and subtraction. Students
investigate addition and multiplication tables in search of patterns and explain why these patterns make sense
mathematically.
For example:
• Any sum of two even numbers is even.
• Any sum of two odd numbers is even.
• Any sum of an even number and an odd number is odd.
• The multiples of 4, 6, 8, and 10 are all even because they can all be decomposed into two equal groups.
• The doubles (2 addends the same) in an addition table fall on a diagonal while the doubles (multiples of 2) in a
multiplication table fall on horizontal and vertical lines.
• The multiples of any number fall on a horizontal and a vertical line due to the commutative property.
• All the multiples of 5 end in a 0 or 5 while all the multiples of 10 end with 0. Every other multiple of 5 is a multiple
of 10.
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3rd Grade Unit 1
September 9th – October 25th
Model Curriculum Student Learning Objectives
SLO
Description
CCSS
1
Tell and write time to the nearest minute to solve word problems with
addition and subtraction involving time intervals in minutes.
3.MD.1
2
Create and interpret scaled picture (or bar) graph to represent data in
1- and 2-step word problems.
3.MD.3
3
Round whole numbers to the nearest 10 or 100.
3.NBT.1
4
Fluently add and subtract (with regrouping) two 2-digit whole numbers
within 100.
3.NBT.2
5
Find the value of an unknown (expressed as a letter) in an equation
that is a representation of a two-step word problem (with any four
operations) and assess the reasonableness of the value.
3.OA.8
6
Recognize arithmetic patterns in addition or multiplication tables and
explain the pattern using the properties of operations.
3.OA.9
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September 9th – October 25th
3rd Grade Unit 1
Vocabulary
Term
Definition
Addition/Add
the process of finding the sum or total value
Analog
Measuring by values along a continuous scale. ex. An old-fashioned clock is analog, not
digital
Bar Graph
chart using parallel rectangles as values
Base Ten
The base 10 system is a number system based on 10. It is also known as the Decimal System
Data
collection of facts or figures
Digital
readable by computer, electronic
Dividend
a number compared to another to get a quotient
Division/Divide
the opposite of multiplication in math
Divisor
number by which a dividend is divided
Equation
a math statement using symbols and numbers
Graph
a visual representation of information
Minute
a unit of time measuring sixty seconds
Multiply/Multiplication
find the product of
Operation
mathematic process such as addition or subtraction
Pattern
a set of repeating features
Picture Graph
a visual representation of data using symbols
Product
an answer found through multiplication
Quotient
the result obtained by dividing two numbers
Subtraction/Subtract
the process of reducing a number by another number
Table
a set of columns or rows to organize data
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3rd Grade Unit 1
September 9th – October 25th
Potential Student Misconceptions
Operations and Algebraic Thinking
Students don’t understand story problems.
Maintain student focus on the meaning of the actions and number relationships, and encourage them to model
the problem or draw as needed. Students often depend on key words, a strategy that often is not effective. For
example, they might assume that the word left always means that subtraction must be used. Providing problems
in which key words are used to represent different operations is essential. For example, the use of the word left in
this problem does not indicate subtraction: Suzy took the 28 stickers she no longer wanted and gave them to
Anna. Now Suzy has 50 stickers left. How many stickers did Suzy have to begin with? Students need to analyze
word problems and avoid using key words to solve them.
Students don’t interpret multiplication by considering one factor as the number of groups and the other
factor as the number in each group.
Have students model multiplication situations with manipulatives or pictorially. Have students write multiplication
and division word problems.
Students solve multiplication word problems by adding or division problems by subtracting.
Students need to consider whether a word problem involves taking apart or putting together equal groups. Have
students model word problems and focus on the equal groups that they see.
Students believe that you can use the commutative property for division.
For example, students think that 3÷15 =5 is the same as 15÷3=5. Have students represent the problem using
models to see the difference between these two equations. Have them investigate division word problems and
understand that division problems give the whole and an unknown, either the number of groups or the number in
each group.
Students don’t understand the relationship between addition/multiplication and subtraction/division.
Multiplication can be understood as repeated addition of equal groups; division is repeated subtraction of equal
groups. Provide students with word problems and invite students to solve them. When students solve
multiplication problems with addition, note the relationship between the operations of addition and multiplication
and the efficiency that multiplication offers. Do the same with division problems and subtraction. .
Students don’t understand the two types of division problems.
Division problems are of two different types--finding the number of groups (“measurement”) and finding the
number in each group (“sharing”). Make sure that students solve word problems of these two different types.
Have them create illustrations or diagrams of each type, and discuss how they are the same and different.
Connect the diagrams to the equations.
Students use the addition, subtraction, multiplication or division algorithms incorrectly.
Remember that the traditional algorithms are only one strategy. Partial sums, partial products and partial
quotients are examples of alternative strategies that highlight place value and properties of operations. Have
students solve problems using multiple models, including numbers, pictures, and words.
Number and Operations in Base Ten
Students misinterpret the value of digits in multi-digit numbers.
Students need to understand that when you have ten of one unit, you also have one unit of the next higher value.
Frequently refer to a place value chart and connect the digits to conceptual models, i.e., place value blocks and
pictorial representations. Have students create multiple ways to represent numbers, such as 132 can be made of
1 hundred, 3 tens and 2 ones, or 1 hundred, 1 ten and 22 ones, or 12 tens and 12 ones. When explaining
strategies used, students must identify the unit value; e.g., when adding 492 and 265, they state that they are
adding “two hundred” to “four hundred”, i.e., the 2 in 265 is named “two hundred”, rather than “two”.
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3rd Grade Unit 1
September 9th – October 25th
Students believe that subtraction is commutative.
After students have discovered and applied the commutative property for addition, ask them to investigate
whether this property works for subtraction. Have students share and discuss their reasoning and guide them to
conclude that the commutative property does not apply to subtraction.
Students misunderstand the meaning of the equal sign.
The equal sign means “is the same quantity as” but many primary students believe the equal sign tells you that
the “answer is coming up” to the right of the equal sign. Students need to see equations written multiple ways. It is
important to model equations in various ways 28 = 20 + 8, or 19 + 8 = 20 + 7.
Measurement and Data
Students confuse area and perimeter:
Introduce the ideas separately. Create real world connections for these ideas. For example the perimeter of a
white board is illustrated by the metal frame; the area of the floor is illustrated by the floor tiles. Use the
vocabulary of area and perimeter in the context of the school day. For example, have students sit on the
“perimeter” of the rug.
Students may have difficulty using known side lengths to determine unknown side lengths: Offer these
students identical problems on grid paper and without the gridlines. Have them compare the listed lengths to the
gridlines that the lines represent. Transition students to problems without gridlines, but have grid paper available
for students to use to confirm their answers.
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September 9th – October 25th
3rd Grade Unit 1
Pacing Guide
EDM Section
Common Core
Standards/SLO
1-1
SMP 6
1-2
SMP 7
1-3
SMP 6
1-4
3.MD.1
Estimated Time
Numbers and Number Sequences
Numbers Grids
Add enrichment activity
Introducing the Student Reference
Book
Tools for Mathematics
1-5
3.MD.3
1-6
3.MD.1
SMP 1
3.NBT.2
SMP 6
3.OA.9, 3.NBT.2
SMP 5
3.NBT.2, 3.MD.3
SMP 2
3.NBT.1, 3.NBT.2
SMP 6
Analyzing and Displaying Data
Equivalent Names
1-8
Finding Difference
1-9 Part 2 Only
Calculator Routines
1-10
Money
1-11
Solving Problems with Dollars and
Cent (Estimation)
1-12
SMP 7
Patterns
1-13
The Length of Day Project
1-14 Progress Check
2-1
Fact Families
2-2
Extension of Addition and
Subtract Facts
2-3
What’s my rule?
2-4
Parts-and-Total Number
Stories
2-5
Change Number Stories
2-6
Comparison Number Stories
2-7
The Partial-Sums Algorithm
3.MD.1
SMP 6
3.OA.9, 3.NBT.2
SMP 3
3.OA.9, 3.NBT.2
SMP 7
3.NBT.2
SMP 8
3.NBT.2
SMP 1
3.NBT.2
SMP 4
3.NBT.2
SMP 4
3.OA.8, 3.NBT.1, 3.NBT.2
SMP 1
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September 9th – October 25th
3rd Grade Unit 1
2-8
Subtraction Algorithms
2-9
Addition with Three or More
Addends
2-10
Progress Check 2
3.OA.8, 3.NBT.1, 3.NBT.2
SMP 4
3.OA.8, 3.NBT.2
SMP 1
3-1
A “Class Shoe” Unit of Length
3-2
Measuring with a Ruler
3-3
Standard Linear Measures
SMP 2 & 6
SMP 6
SMP 3 & 5
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3rd Grade Unit 1
September 9th – October 25th
Assessment Checks
3.MD.1
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3rd Grade Unit 1
September 9th – October 25th
3.MD.3
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3rd Grade Unit 1
September 9th – October 25th
3.NBT.1
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3rd Grade Unit 1
September 9th – October 25th
3.NBT.2
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3rd Grade Unit 1
September 9th – October 25th
3.OA.8
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3rd Grade Unit 1
September 9th – October 25th
3.OA.9
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3rd Grade Unit 1
September 9th – October 25th
Extensions
Online Resources
3.NBT.1
Rounding to 50 or 500
http://s3.amazonaws.com/illustrativemathematics/illustration_pdfs/000/000/745/original/illustrative_mathem
atics_745.pdf?1372632103
3.NBT.2
Classroom Supplies
http://s3.amazonaws.com/illustrativemathematics/illustration_pdfs/000/001/315/original/illustrative_mathem
atics_1315.pdf?1372632183
3.OA.8
The stamp collection
http://s3.amazonaws.com/illustrativemathematics/illustration_pdfs/000/000/013/original/illustrative_mathem
atics_13.pdf?1372632194
The class Trip
http://s3.amazonaws.com/illustrativemathematics/illustration_pdfs/000/001/301/original/illustrative_mathem
atics_1301.pdf?1372632193
3.OA.9
Addition Patterns
http://s3.amazonaws.com/illustrativemathematics/illustration_pdfs/000/000/953/original/illustrative_mathem
atics_953.pdf?1372632174
Patterns in a Multiplication Table
http://s3.amazonaws.com/illustrativemathematics/illustration_pdfs/000/000/956/original/illustrative_mathem
atics_956.pdf?1372632186
Symmetry of the Addition Table
http://s3.amazonaws.com/illustrativemathematics/illustration_pdfs/000/000/954/original/illustrative_mathem
atics_954.pdf?1372632191
Making a Ten
http://s3.amazonaws.com/illustrativemathematics/illustration_pdfs/000/000/955/original/illustrative_mathem
atics_955.pdf?1372632181
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September 9th – October 25th
3rd Grade Unit 1
Assessment Resources
3.MD.1
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Time:
Time:
Time:
Time:
Time:
Read clocks and write times (Third grade - O.1)
Elapsed time I (Third grade - O.2)
Elapsed time II (Third grade - O.3)
Time patterns (Third grade - O.6)
Time lines (Third grade - O.9)
3.MD.3
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Data
Data
Data
Data
and
and
and
and
graphs:
graphs:
graphs:
graphs:
Interpret bar graphs (Third grade - P.4)
Create bar graphs (Third grade - P.5)
Interpret pictographs (Third grade - P.8)
Create pictographs (Third grade - P.9)
3.NBT.1
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Estimation and rounding: Rounding (Third grade - L.1)
3.NBT.2
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Place values: Value of a digit (Third grade - B.3)
Place values: Identify the digit with a particular place value (Third grade - B.4)
Place values: Convert from expanded form (Third grade - B.7)
Addition: Add two numbers up to three digits (Third grade - C.1)
Addition: Add two numbers up to three digits - word problems (Third grade - C.3)
Addition: Complete the addition sentence - up to three digits (Third grade - C.4)
Addition: Balance addition equations - up to three digits (Third grade - C.5)
Addition: Addition patterns over increasing place values (Third grade - C.8)
Subtraction: Subtract numbers up to three digits (Third grade - D.1)
Subtraction: Subtract numbers up to three digits - word problems (Third grade - D.3)
Subtraction: Complete the subtraction sentence - up to three digits (Third grade - D.4)
Subtraction: Balance subtraction equations - up to three digits (Third grade - D.5)
Subtraction: Subtraction patterns over increasing place values (Third grade - D.6)
Properties: Properties of addition (Third grade - J.3)
Properties: Solve using properties of addition (Third grade - J.4)
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3rd Grade Unit 1
September 9th – October 25th
3.OA.8
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Mixed operations: Addition, subtraction, multiplication, and division facts (Third grade - I.1)
Mixed operations: Complete the addition, subtraction, multiplication, or division sentence (Third
grade - I.2)
Mixed operations: Add, subtract, multiply, and divide (Third grade - I.3)
Mixed operations: Addition, subtraction, multiplication, and division word problems (Third grade I.4)
Mixed operations: Multi-step word problems (Third grade - I.6)
Equations and variables: Solve for the variable - addition and subtraction only (Third grade - K.2)
Equations and variables: Solve for the variable - with multiplication and division (Third grade - K.3)
Equations and variables: Write variable equations to represent word problems (Third grade - K.4)
Estimation and rounding: Rounding (Third grade - L.1)
Estimation and rounding: Solve inequalities using estimation (Third grade - L.4)
Estimation and rounding: Estimate sums (Third grade - L.5)
Estimation and rounding: Estimate products (Third grade - L.6)
Estimation and rounding: Estimate quotients (Third grade - L.7)
3.OA.9
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Addition: Addition input/output tables - up to three digits (Third grade - C.2)
Subtraction: Subtraction input/output tables - up to three digits (Third grade - D.2)
Multiplication: Multiplication input/output tables (Third grade - E.14)
Division: Division input/output tables (Third grade - G.14)
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