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2nd
Unit of Study 1: Place Value Concepts
Projected Time Allotment: 9 days
Global Concept Guides: Odd and Even Numbers, Place Value Concepts, Thinking Flexibly About Numbers
Prior Learning: MACC.K.NBT.1, MACC.1.NBT.2
Progressions Document Link
Sample Show What You Know Task: Use the Go Math Ch. 1 Show What You Know or the Diagnostic Interview
Task TE p. 10
Common Core State Standards for Mathematical Content :
Comments:
Work with equal groups of objects to gain foundations for
multiplication.
Strikethroughs indicate that only
MAFS.2.OA.3.3 Determine whether a group of objects (up to 20) has an two-digit numbers will be the focus
odd or even number of members, e.g., by pairing objects or counting
of this unit and will be building
them by 2’s; write an equation to express an even number as a sum of
blocks for three-digit numbers in
two equal addends.
future units.
Understand place value.
MAFS.2.NBT.1.1 Understand that the three (two) digits of a three
(two)-digit number represent amounts of hundreds, tens, and ones;
e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the
Notes on Assessment:
following as special cases:
a. 100 can be thought of as a bundle of ten tens –called a “hundred.”
Assessment: Unit 1
b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to
one, two, three, four, five, six, seven, eight, or nine hundreds (and 0
See common performance task link
tens and 0 ones).
MAFS.2.NBT.1.3 Read and write numbers to 1000 (100) using base-ten below. Please administer AFTER the
second GCG.
numerals, number names, and expanded form.
Unpacking the Standards for this Unit:
“Understanding the value of the digits is more than telling the number of tens and hundreds. Second grade
students who truly understand the position and place value of the digits are also able to confidently model the
number with some type of visual representation. Others who seem like they know, because they can state
which number is in the tens place, may not truly know what each digit represents.” Click here for more
information. Second graders apply their understanding of place value concepts from first grade to help them
represent numbers flexibly with base ten blocks. Having a deep understanding of this concept will help lay the
groundwork for using operations with numbers.
Common Performance Task with Rubric for this Unit:
Students will represent the number 63 four different ways by drawing quick pictures of base ten blocks.
Students will determine if a number is even or odd and explain their reasoning.
Click here for the performance task and rubric.
Future learning:
In future units, students will work with multi-digit numbers to represent them flexibly, identify and extend
number patterns, and compare three-digit numbers. Students will apply place value concepts when adding
and subtracting multi-digit numbers and understand that it is necessary to compose and decompose numbers
when regrouping.
“Research has shown that it is difficult to develop procedural fluency with multi-digit arithmetic without
understanding of the base ten system. If such understanding is missing, students make many different errors
in multi-digit computations.” (National Research Council, 2001, p. 199)
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2nd
Global Concept 1 of 3 for this Unit of Study: Odd and Even Numbers
Projected Time
Allotment: 2 days
Sample Essential Questions:
Day 1: How can you prove that a number is even or odd?
Day 2: Is the sum of two equal groups always an even number? Explain.
Related Unit 2 Assessment: Go Math Ch. 1 # 1, 2, 19, 20, 21
Instructional Resources
Manipulatives:
 10 frames and counters to model numbers, make pairs to determine odd or even. (Go Math Lesson 1.1). Click
here to see a model of how to use ten frames to teach concept of odd and even.
 Snap cubes to model numbers and make pairs to determine odd or even. (Go Math 1.2). Snap cubes model 2
equal addends.
Lesson Ideas:
 Go Math Lesson 1.1 Essentials: #11-16 p. 15 -to practice modeling odd and even numbers with ten frames. Use
#17-20 p. 15-16 to problem solve and communicate thinking in words about odd and even numbers. Click here
to learn more about how teach odd and even numbers conceptually.
 Go Math Lesson 1.2 Essentials: #9-12 p. 19 to illustrate odd numbers are 2 equal groups (doubles) plus 1 more
(left over). Click here to learn more about working with equal addends.
 Go Math Lesson 1.2 #13-15 p. 20 to practice problem solving even and odd.
 Go Math Center: Grab and Go – “Doubles Fun on the Farm” (doubles facts)
 Odd and Even Dodgeball Activity – activity to explain even and odd numbers
 Odd and Even Practice - odd and even practice
 Blackline master practice page with 10 frames - 10 frames to represent odd and even numbers
Interactive Online Resources:
 www.doorwayonline.org.UK/oddandeven.html - interactive games for practice with identifying odd and even
numbers
For more information about integrating the content within this GCG click here for the PowerPoint.
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1,3)



What does it mean for a number to be odd? Even?
Why are doubles important when thinking about odd and even?
There are an even number of boys in Gina’s class and an odd number of girls. Gina counted 18 students in her
class. Do you think Gina miscounted? Explain your thinking.
 Franco and Natalie picked up some shells on the beach. They each picked up an even amount. How many shells
could they have found? Justify your answer.
 When would you use odd and even numbers in real life? (fair shares, pairs, etc.)
 Will the sum of an odd and even number always be odd? Explain.
Our students are better able to…
Because as teachers we…
 Monitor students’ strategies used to justify
 Investigate if a number is odd or even by
whether a number is odd or even (SMP 3)
determining if the number of objects can be

Provide opportunities for students to utilize
divided into equal sets, arranged into pairs, or
manipulatives to model numbers and make pairs to
counted by twos (SMP 1, 5)
demonstrate even or odd (SMP 1, 5)
 Write equations representing even numbers as
 Emphasize precise use of vocabulary: odd, even,
the sum of two equal addends e.g. 7 + 7 = 14
doubles, fair share, pairs, addends, sum, doubles
plus one, equal (SMP 6)
(SMP 7, 8)
For more info on SMP’s click here.
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Global Concept 2 of 3 for this Unit of Study Place Value Concepts
2
nd
Projected Time
Allotment:
2 days
Sample Essential Questions:
Day 1: How can you determine the value of a digit depending on its place in a number?
Day 2: What are different ways to represent a 2-digit number?
Related Unit 2 Assessment: Go Math Ch. 1 # 5, 6, 7, 8, 9, 10, 22, 23, 24
Instructional Resources
Manipulatives:
 Base Ten Blocks (ten rods and unit cubes)- Students can use to flexibly represent numbers
 Tens frame cards/Secret Code Cards- Students can use to identify the value of a digit
 Objects that can be bundled in groupings of ten (Straws, sticks, coffee stirrers, snap cubes etc)- Students can use
to flexibly represent numbers
 Number Cubes- Students can use to create and build two digit numbers
 Hundreds Board- Students can use the hundreds boards to show groupings of tens and ones
 Dry erase boards/marker boards- Students can use to flexibly represent numbers
Lesson Ideas:
 Go Math Lesson 1.3 Essentials- Listen and Draw with Math Talk TE p. 21 – Use the scenario about Tyler’s
baseball cards to help students think flexibly about the value of the digits (25 or 52 cards). Pose similar
problems using some of the existing numbers in the Share and Show or On Your Own components. Use the
questions on the Problem Solving page SE p.24. See Math Talk in Action TE p. 23.
 Go Math Lesson 1.4 Essentials- Listen and Draw TE p. 25-Connect base ten manipulatives to quick pictures and
expanded form.
 Go Math Lesson 1.5 Essentials- Use 2-digit numbers to pose problem solving situations for students to
understand the size and meaning of numbers flexibly. Numbers used in problem solving contexts can be pulled
from components of lesson 1.5.
 Emily’s Problem- this is a task that can be used for students to model numbers in multiple ways.
Interactive Online Resources:
 Base Ten Virtual Manipulative – virtual manipulative
 iTools: Base Ten Blocks- virtual base ten blocks
 Place the Penguin - online game
For more information about integrating the content within this GCG click here for the PowerPoint.
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1 , 3)
 How would the value of the number change if you switched the digits? Explain.
 Maggie grabs some base ten blocks. She takes four ones and six tens. If she adds two more groups of ten, what
will the value be of her blocks?
 What are three different ways to represent the number ___?
 How can you prove that five tens and three ones is the equal to 50 + 3?
Our students are better able to…
Because as teachers we…
 Build and draw models to flexibly represent two Provide opportunities for students to utilize
digit numbers (SMP 2, 5).
manipulatives and quick pics to model numbers
(SMP 5).
 Discover the relationships between the different
representations of two-digit numbers (SMP 5).
 Facilitate rich conversations in connecting
manipulatives to pictorial representations (quick
 Engage in conversations to justify their
pictures) through use of the HOT questions
representation of a number and evaluate others’
referenced above (SMP 1, 3, 5).
reasoning (SMP 2, 3).
 Emphasize precise use of vocabulary: digit, value,
For more info on SMP’s click here.
tens, ones, represents, expanded form, word form,
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Global Concept 3 of 3 for this Unit of Study: Thinking Flexibly About Numbers
nd
2
Projected Time
Allotment:
4 days
Sample Essential Questions:
Day 1: How can you use base ten blocks and quick pictures to model the value of a number in different ways?
Day 2: How can you solve problems involving representing numbers flexibly?
Day 3: How can you organize and record your flexible representations of numbers?
Day 4: How does finding a pattern help you find all the ways to show a number?
Related Unit 2 Assessment: Go Math Ch. 1 # 13, 14, 15, 16, 17, 18
Instructional Resources
Manipulatives:
 Base Ten Blocks to model number representations.
 Place value chart with ten frames to help students represent numbers flexibly.
Lesson Ideas:
 Go Math Lesson 1.6 Essentials- Students should have multiple opportunities to explore representing numbers
flexibly prior to using the pictures in the lesson. SE p. 35-36, #’s 6, 8, 9, 10 & 11 would be a good focus.
 Go Math Lesson 1.7 Essentials- Students will need to use manipulatives to solve the problems throughout this
lesson. Lesson 1.7 word problems should be split up over day 3 and day 4.
 Word problems for representing numbers flexibly – sample word problems to help guide instruction
 “What Number Am I?” riddle cards – game to show numbers in multiple ways
For more information about integrating the content within this GCG click here for the PowerPoint .
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1 , 3)
 How can you prove the value of your number is the same as the number you started with?
 How do you know 0 tens and 26 ones is the same as 1 ten and 16 ones?
 What are all the ways to represent the number 74?
 How can you find a pattern to help you solve a problem?
 How does a chart help you look for patterns in flexible representations of numbers?
 How can you prove you have all the possible representations of the number ____?
Our students are better able to…
Because as teachers we…
 Use models and drawing pictures to represent
 Circulate and ask students to justify their models.
tens and ones. (SMP 5, 6)
(SMP 3)
 Solve real world problems to represent numbers
 Provide opportunities for students to use base ten
flexibly. (SMP 1, 6)
blocks every day to represent numbers flexibly.
(SMP 4)
 Organize representations into a chart to help look
for patterns. (SMP 5, 7)
 Facilitate rich discussion on how multiple
representations of numbers can have equal values.
 Find patterns in an organized list to prove all
(SMP 3)
representations of a number are created.
(SMP 7, 8)
 Emphasize precise use of vocabulary: compose,
decompose, pattern, table. (SMP 6)
For more info on SMP’s click here.
and standard form (SMP 6).