Mathematics 2016-2017—Grade 2
Weeks 22-24—February/March
enVisionmath2.0—Topic 9
Standards for Mathematical Practice
Critical Area: Extending understanding of base-ten notation
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
FOCUS for Grade 2
Supporting Work
20% of Time
2.OA.C.3-4
2.MD.C.7-8
2.MD.D.9-10
Major Work
Additional Work
70% of time
10% of Time
2.OA.A.1
2.G.A.1-2-3
2.OA.B.2
2.NBT.A.1-2-3-4
2.NBT.B.5-6-7-8-9
2.MD.A.1-2-3-4
2.MD.B.5-6
Required fluency: 2.OA.B.2 and 2.NBT.B.5
Standards in bold are specifically targeted within instructional materials.
Domains:
Number and Operations in Base Ten
Clusters:
Clusters outlined in bold should drive the learning for this period of instruction.
2.NBT.B Use place value understanding and properties of operations to add
and subtract.
Standards:
2.NBT.A Understand place value.
2.NBT.A.1 Understand that the three digits of a three-digit number represent
amounts of hundreds, tens and ones; e.g., 706 equals 7 hundreds, 0 tens, and
6 ones. Understand the following as special cases:
a. 100 can be thought of as a bundle of ten tens- call a “hundred.”
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 tens
and 0 ones.)
2.NBT.A.2 Count within 1000; skip-count by 5s, 10s, and 100s.
2.NBT.A.3 Read and write numbers to 1000 using base-ten numerals,
number names, and expanded form.
2.NBT.A.4 Compare two three-digit numbers based on meanings of the
hundreds, tens, and ones, digits, using >, =, < symbols to record the results of
comparisons.
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2.NBT.B.8 Mentally add 10 or 100 to a given number 100-900, and mentally
subtract 10 or 100 from a given number 100-900.
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Mathematics 2016-2017—Grade 2
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enVisionmath2.0—Topic 9
Foundational Learning
1.NBT.B.2-3
Future Learning
2.NBT.B.7
3.NBT.A.1-2
Key Student Understandings
 Students understand that the base-ten number system is a structure based on groups of ten; the value of a
digit is determined by its place in the number.
 Students understand that numbers can be decomposed and named in equivalent ways using place value
(e.g., 2 hundreds 4 tens is equivalent to 24 tens.)
 Students understand that tens and hundreds can be perceived as a single quantity or as a set of quantities
when interpreting numbers using place value (e.g., 1 hundred is one quantity; it can also be decomposed
as 10 tens or as 100 ones).
 Students extend their understanding of the base-10 system by writing multi-digit numbers up to 1,000 in
standard form, word form, and expanded form, recognizing that the digits in each place represent
amounts of hundreds, tens, or ones.
 Students understand that the structure of place value is used to compare numbers.
Assessments

Formative Assessment Strategies

Evidence for Standards-Based Grading
Common Misconceptions/Challenges
2.NBT.A Understand place value.
 Students struggle to count forward and backward in units of ten from any given digit. Use a 100s chart to make the base-ten structure of our number
system explicit. Students can use mini-ten frames to make a number and find out what is 10 more and 10 less of that number.
 Some students may not move beyond thinking of the number 358 as 300 ones plus 50 ones plus 8 ones to the concept of 8 ones, 5 bundles of 10 ones or
5 tens, and 3 bundles of 10 tens or 3 hundreds. Use base-ten blocks to model the collecting of 10 ones (units) to make a ten (a rod/stick) or 10 tens to
make a hundred (a flat). It is important that students connect a group of 10 ones with the word ten and a group of 10 tens with the word hundred.
 Students see the numbers as individual digits instead of a quantity, i.e., 4 in 46 represents 4, not 4 tens or 40.
 Students may develop a rigid understanding of place value based on given digits and their places: they see 436 = 400 + 30 + 6, but fail to understand that
there are more ways to show the value: 436 = 300 + 130 + 6; 436 = 4 hundreds + 2 tens + 16 ones; 436 = 300 + 120 + 16; 436 = 4 hundreds + 36 ones.
2.NBT.B Use place value understanding and properties of operations to add and subtract.
 Students think that the 4 in 46 represents 4, not 40. Students need many experiences representing two-and three-digit numbers with manipulatives that
group (base ten blocks) and those that do NOT group, such as counters, etc.
 Students who are forced to rely on algorithms and procedural understanding of mathematics struggle with the ability to fluently add and subtract 10
and/or 100 to numbers. These students often try to rewrite the problem in an algorithmic fashion because they believe that is what they have to do to
“do math”. Ask students to use the hundreds chart to add or subtract 10. Ensure that they understand that moving down a row means you are adding 10
and moving up a row means you are subtracting 10. If they have to count by ones to add the 10 they do not see this relationship.
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Mathematics 2016-2017—Grade 2
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enVisionmath2.0—Topic 9
Instructional Practices
Domain: 2.NBT
Cluster: 2.NBT.A Understand place value.
2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens and ones; e.g., 706 equals 7 hundreds, 0 tens,
and 6 ones. Understand the following as special cases:
 100 can be thought of as a bundle of ten tens- call a “hundred.”
 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 tens and 0 ones.)

Use manipulative materials and pictorial representations to help make a connection between the written three-digit numbers and hundreds, tens and
ones. (Models can include: base ten blocks, number lines, bundles, place value mats, and other manipulatives that support students’ discovery of place
value patterns.

Grade 2 students extend their base-ten understanding to hundreds as they view 10 tens as a unit called a “hundred”. They use manipulative materials
and pictorial representations to help make a connection between the written three-digit numbers and hundreds, tens, and ones.

As in Grade 1, Grade 2 students’ understanding about hundreds also moves through several stages: Counting by Ones; Counting by Groups & Singles;
and Counting by Hundreds, Tens and Ones.
o Counting by Ones: At first, even though second graders will have grouped objects into hundreds, tens and ones, they rely on counting all of the
individual cubes by ones to determine the final amount. It is seen as the only way to determine how many.
o Counting by Groups and Singles: While students are able to group objects into collections of hundreds, tens, and ones and now tell how many
groups of hundreds, tens and ones there are, they still rely on counting by ones to determine the final amount. They are unable to use the
groups and units to determine how many.

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Example:
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Mathematics 2016-2017—Grade 2
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Teacher:
Student:
Teacher:
Student:
How many blocks do you have?
I have 3 hundreds, 4 tens, and 2 ones.
Does that help you know how many? How many do you have?
Let me see. 100, 200, 300… ten, twenty, thirty, forty. So that’s 340 so far. Then 2 more. 342.

Counting by Hundreds, Tens & Ones: Students are able to group objects into hundreds, tens and ones, tell how many groups and left-overs there are,
and now use that information to tell how many. Occasionally, as this stage becomes fully developed, second graders rely on counting to “really” know
the amount, even though they may have just counted the total by groups and left-overs.
o Example:
Teacher: How many blocks do you have?
Student: I have 3 hundreds, 4 tens and 2 ones.
Teacher: Does that help you know how many? How many do you have?
Student: Yes. That means that I have 342.
Teacher: Are you sure?
Student: Um. Let me count to make sure. 100, 200, 300,…340, 341, 342. Yes. I was right. There are 342 blocks.

Understanding the value of the digits is more than telling the number of tens or hundreds. Grade 2 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. Seek out activities and materials that develop place
value understanding, rather than simply location of digits.
2.NBT.A.2 Count within 1000; skip-count by 5s, 10s, and 100s.

Allow students opportunities to count, up to 1000, from different starting points. They should also have many experiences skip-counting by 5s, 10s, and
100s to develop the concept of place value.
o What are the next 3 numbers after 498? 499, 500, 501
o Count forward from 79 by 10s.
o When you count back from 201, what are the first 3 numbers that you say? 200, 199, 198

The use of a 100 chart, number line, and/or base-ten blocks may be helpful visual cues for students to identify counting patterns.

As teachers build on students’ work with skip-counting by 10s (Kindergarten), they explore and discuss with students the patterns of numbers when they
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Mathematics 2016-2017—Grade 2
Weeks 22-24—February/March
enVisionmath2.0—Topic 9
skip-count. For example, while using a 100 chart or number line, students learn that the ones digit alternates between 5 and 0 when skip counting by 5s
starting at 0. When students skip count by 100s, they learn that the hundreds digit is the only digit that changes and that it increases by one number.
o Count forward from 749 by 5s. What pattern do you notice?
2.NBT.A.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

Grade 2 students read, write, and represent a number of objects with a written numeral (number form or standard form). These representations can
include snap cubes, place value /base-10 blocks, pictorial representations, and other concrete materials. Be cognizant of the fact that when reading and
writing whole numbers, the word “and” should not be used (e.g., 235 is stated and written as “two hundred thirty-five”).

Expanded form (125 can be written as 100 + 20 + 5) is a valuable skill when students use place value strategies to add and subtract large numbers in
2.NBT.7. (http://maccss.ncdpi.wikispaces.net/2nd+Grade+Standards)

Students should explore reading and writing numerals in multiple ways.
o Examples:
 Base-ten numerals 637
(standard form)
 Number names
six hundred thirty seven (written form)
 Expanded form
600 + 30 + 7
(expanded notation)

Facilitate discussions highlighting concrete models, number lines, base-ten blocks, interactive whiteboards, written words, and/or spoken words that
represent two and three-digit numbers.
2.NBT.A.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones, digits, using >, =, < symbols to record the results of
comparisons.

Grade 2 students build on the work of 2.NBT.A.1 and 2.NBT.A.3 by examining the amount of hundreds, tens, and ones in each number. When comparing
numbers, students draw on the understanding that 1 hundred (the smallest three-digit number) is actually greater than any amount of tens and ones
represented by a two-digit number. When students truly understand this concept, it makes sense that one would compare three-digit numbers by
looking at the hundreds place first.

Comparative language includes but is not limited to: more than, less than, greater than, most, greatest, least, same as, equal to, and not equal to.
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
Students should have ample experiences communicating their comparisons in words before using symbols. Students were introduced to the symbols
greater than (>), less than (<) and equal to (=) in Grade 1 and continue to use them in Grade 2 with numbers within 1,000.
o Example: Compare these two numbers. 452 __ 455
Student A
Student B
Place Value
Counting
452 has 4 hundreds 5 tens and 2 ones. 455 has 4
hundreds 5 tens and 5 ones. They have the same
number of hundreds and the same number of tens,
but 455 has 5 ones and 452 only has 2 ones. 452 is
less than 455.
452 < 455
452 is less than 455. I know
this because when I count, I
say 452 before I say 455.
452 < 455
452 is less than 455.

Students may use models, number lines, base ten blocks, interactive whiteboards, written words, and/or spoken words that represent two three-digit
numbers. To compare, students apply their understanding of place value. They first attend to the numeral in the hundreds place, then the numeral in
tens place, then, if necessary, to the numeral in the ones place.

While students may have the skill to order more than 2 numbers, the focus of this Standard is on comparing two numbers and using reasoning about
place value to support the use of the various symbols.
Domain: 2.NBT
Cluster: 2.NBT.B Use place value understanding and properties of operations to add and subtract.
2.NBT.B.8 Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.

Grade 2 students mentally add or subtract either 10 or 100 to any number between 100 and 900. As teachers provide ample experiences for students to
work with pre-grouped objects and facilitate discussion, second graders realize that when one adds or subtracts 10 or 100 that only the digit in the tens
place or the digit in the hundreds place changes. As the teacher facilitates opportunities for patterns to emerge and be discussed, students notice the
patterns and connect the digit change with the amount changed.

Opportunities to solve problems in which students cross hundreds are also provided once students have become comfortable adding and subtracting
within the same hundred. Push students to share their thinking, to develop a shared understanding of a variety of strategies for all students.
o Example: Within the same hundred
What is 10 more than 218? When counting by tens, I know that 28 comes after 18; so I know that 10 more than 218 is 228.
What is 241 – 10? There are 4 tens in 241; if I take away a ten, that leaves 3 tens, so 241 – 10 = 231.
o
Example: Across hundreds
293 + 10 = ☐
Revised 2/2017
I added another ten to 9 tens makes 10 tens, which is another hundred; so 293 + 10 = 303)
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What is 10 less than 206? (requires flexible understanding of place value: There are no tens in the tens place, but I can think of 200 as 20 tens;
so if I take one ten away, that leaves 19 tens and 6 ones; so 10 less than 206 is 196.

This standard focuses only on adding and subtracting 10 or 100. Multiples of 10 or multiples of 100 can be explored; however, the focus of this standard
is to ensure that students are proficient with adding and subtracting 10 and 100 mentally. (Reference:
http://maccss.ncdpi.wikispaces.net/2nd+Grade+Standards)
Differentiation
2.NBT.A Understand place value.
 Progression of learning for differentiation:
Literacy Connections
Struggling/On-Level Learners
 Giving students opportunities to practice counting using ones and bundles of tens and hundreds while asking them to
identify benchmark numbers will cue them to the ease and efficiency of skip-counting. It will accustom them to look
for, and make use of, the structure provided by the base ten number system, not only to skip-count from multiples of
ten, but also multiples of 100, and later, larger units. https://www.engageny.org/resource/grade-2-mathematicsmodule-3
 Skip-Count by Twos Beginning at 394 https://www.engageny.org/resource/grade-2-mathematics-module-3 Lesson 9

Academic Vocabulary Terms

Vocabulary Strategies

Literacy Strategies
Possible Enrichment Tasks
 Illustrative Mathematics: Saving Money 2 https://www.illustrativemathematics.org/contentstandards/2/NBT/A/2/tasks/1309
 Discussion or Journal Prompts (https://hcpss.instructure.com/courses/106/pages/2-dot-nbt-dot-a-2-about-the-mathlearning-targets-and-increasing-rigor):
o If you count by 5’s, and start at 27, what other numbers will be in the pattern?
o If you start at 438 and count by 5s and then start at 438 and count by 10s, what are three numbers that will
come up in each pattern? (10s: 438, 448, 458, 468, 478) (5s: 438, 443, 448, 453, 458, 463, 468, 473, 478)
o Starting at 100, what are all the numbers you can skip count by to get to 150? Give examples to support your
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Mathematics 2016-2017—Grade 2
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o
o
o
o
answer.
If you start at 17 and count by 10s, will you land on 100? Why or why not?
What patterns do you see in the ones, tens, and hundreds place when skip counting by 5s? 10s? 100s?
Summer started on 205. She counted by 100s. Is 808 in her pattern? Explain how you know.
Mr. Sawyer is having a popcorn and movie party for his class. Each student will get a bag of popcorn to eat
during the movie. If each student gets 2 scoops of popcorn is his or her bag, how many scoops will it take to
fill bags for 5 students? How many scoops will it take to fill bags for 7 students?
2.NBT.B Use place value understanding and properties of operations to add and subtract.
 Progression of learning for differentiation:
Struggling/On-Level Learners
 Build numbers—Give students place value blocks (concrete, pictorial, or virtual) and practice building numbers up to
1,000 (varying magnitude of numbers to meet student needs).
 Use place value mats and place value blocks (or other manipulative) to demonstrate how small units can be
“regrouped” into a larger unit (10 ones = 1 ten; 10 tens= 1 hundred).
 Use a hundred or thousand chart to identify number patterns when counting by 5s, 10s, 100s.
 Skip-count backward; skip-count from numbers other than decade numbers/multiples of 10 (skip-count by 10 starting
at 43, 62, 78); skip-count by other numbers (2, 20, 50, 90).
 Practice mental math addition facts within 100 with the support of a hundreds chart so students can develop
confidence and fluency.
 Using cards with numbers represented by place value blocks, have students match standard, expanded and word
form.
The Common Core Approach to Differentiating Instruction (engageny How to Implement a Story of Units, p. 14-20)
Linked document includes scaffolds for English Language Learners, Students with Disabilities, Below Level Students, and
Above Level Students.
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Mathematics 2016-2017—Grade 2
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enVisionmath2.0—Topic 9
Resources
enVisionmath2.0
Developing Fluency
Grade 2 Fact Fluency Plan
Addition Fact Thinking Strategies
Topic 9 Pacing Guide
Grade 2 Games to Build Fluency
Multi-Digit Addition & Subtraction Resources
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