Mathematics 2016-2017—Grade 2
Weeks 20-21—January/February
enVisionmath2.0—Topic 8
Standards for Mathematical Practice
Critical Area: Building Fluency with Addition and Subtraction
Beyond the Critical Areas: Using data representations
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:
Measurement and Data
Numbers and Operations in Base Ten
Clusters:
Clusters outlined in bold should drive the learning for this period of instruction.
2.MD.C Work with time and money.
2.NBT.A Understand place value.
Standards:
2.MD.C.7 Tell and write time from analog and digital clocks to the nearest
five minutes using a.m. and p.m.
2.NBT.A.2 Count within 1,000; skip-count by 5’s, 10’s, and 100’s.
2.MD.C.8 Solve word problems involving dollar bills, quarters, dimes, nickels
and pennies, using $ and ¢ symbols appropriately. Example: If you have 2
dimes and 3 pennies, how many cents do you have?
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enVisionmath2.0—Topic 8
Foundational Learning
Future Learning
1.MD.B.3
2.MD.A
2.OA.C.4
3.MD.A.1
Key Student Understandings
Assessments
 Students understand that some attributes of objects are measurable and can be quantified using unit
amounts.
 Students learn that coins and bills have varying values, and that money amounts can be counted in
 Formative Assessment Strategies
different ways; students understand that the value of a coin is not related to its size.
 Students develop an understanding of a.m. and p.m. by making connections to events in their day.
 Evidence for Standards-Based Grading
 Students learn that time can be measured and expressed in hours and minutes; students learn to express
time in 5-minute intervals, and understand the difference between p.m. and a.m.
Common Misconceptions/Challenges
2.MD.C Work with time and money.
 Students confuse the hour and minute hands. For the time of 3:45, they say the time is 9:15.
 Students name the numeral closest to the hands. For instance, for the time of 3:45 they say the time is 3:09 or 9:03. Assess students’ understanding of
the roles of the minute and hour hands and the relationship between them. Have them focus on the movement and features of the hands on real or
geared manipulative clocks.
 Students might overgeneralize the value of coins when they count them. They might count coins as individual objects, rather than attending to the
relative value of individual coins.
 Students may think that the value of a coin is directly related to its size, so the bigger the coin, the more it is worth. Place pictures of a nickel on the top
of five-frames that are filled with five pennies; attach pictures of dimes and pennies to ten-frames and pictures of quarters to 5 x 5 grids filled with
pennies. Have students use these materials to determine the value of a set of coins in cents.
 Students sometimes fail to make the transition from counting dimes to counting nickels. To help students understand 5, 10, and 25, tape a penny onto a
connecting cube, a nickel onto 5 connected cubes, a dime onto 2 lengths of 5 connected cubes placed side by side, and a quarter onto 5 lengths of 5
connected cubes placed side by side. This technique will help students make sense of the values of coins and how to use these values to count and
compare sets of coin.
 Sometimes students will record dollar amounts incorrectly, i.e., 29$; remind them that the dollar sign goes in front. The cent sign goes after the number
and there is no decimal point used with the cent sign.
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.
 Students are unable to unitize to 10 (see 10 ones as 1 ten), i.e., 358 is 300 ones plus 50 ones plus 8 ones, rather than 3 hundreds, 5 tens, and 8 ones.


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.
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Instructional Practices
Domain: 2.MD
Cluster: 2.MD.C Work with time and money.
2.MD.C.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

Grade 2 students extend their work with telling time to the hour and half-hour from Grade 1 in order to tell (orally and in writing) the time indicated on
both analog and digital clocks to the nearest five minutes. Help students make connections between skip-counting by 5s (2.NBT.2) and telling time to the
nearest five minutes on an analog clock. Students also indicate if the time is in the morning (a.m.) or in the afternoon/evening (p.m.) as they record the
time.

Learning to tell time is challenging for children. In order to read an analog clock, they must be able to read a dial-type instrument. They must realize that
the hour hand indicates broad, approximate time while the minute hand indicates the minutes in between each hour. As students experience clocks with
only hour hands, they begin to realize that when the time is two o’clock, two-fifteen, or two forty-five, the hour hand looks different—but is still
considered “two”. Discussing time as “about 2 o’clock”, “a little past 2 o’clock”, and “almost 3 o’clock” helps build vocabulary to use when introducing
time to the nearest 5 minutes.
All of these clocks indicate the hour of “two”, although they look slightly different.
This is an important idea for students as they learn to tell time.

It is important that students communicate their understanding of time using both numbers and language. Common time phrases include: quarter till/to
___, quarter after ___, ten till/to ___, ten after ___, and half past ___.

Students should understand that there are 2 cycles of 12 hours in a day - a.m. and p.m. Recording their daily actions in a journal would be helpful for
making real-world connections and understanding the difference between these two cycles.
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2.MD.C.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2
dimes and 3 pennies, how many cents do you have?

In Grade 2, students solve word problems involving either dollars or cents. Since students have not been introduced to decimals, problems should focus
on whole dollar amounts or cents.

This is the first time money is introduced formally as a standard. Therefore, students will need numerous experiences with coin recognition and values of
coins before using coins to solve problems. Once students are solid with coin recognition and values, they can then begin using the values to count sets of
coins, compare two sets of coins, make and recognize equivalent collections of coins (same amount but different arrangements), select coins for a given
amount, and make change.

Just as students learn that a number (38) can be represented different ways (3 tens and 8 ones; 2 tens and 18 ones) and still remain the same amount
(38), students can apply this understanding to money. For example, 25 cents can look like one quarter; two dimes and one nickel; 5 nickels; 25 pennies;
and still all represent 25 cents. This concept of “equivalent worth” takes time and requires numerous opportunities to create different sets of coins,
count sets of coins, and recognize the “purchase power” of coins (a nickel can buy the same thing as 5 pennies).
o Example: How many different ways can you make 37¢ using pennies, nickels, dimes, and quarters?
o Example: How many different ways can you make 12 dollars using $1, $5, and $10 bills?

As teachers provide students with sufficient opportunities to explore coin values (25 cents) and actual coins (2 dimes, 1 nickel), teachers help guide
students over time to learn how to mentally give each coin in a set a value, place the random set of coins in order, and use mental math by adding on to
find differences, and/or skip-counting to determine the final amount.

Help students learn money concepts and solidify their understanding of other topics by providing activities where students make connections between
them. For instance, link the value of a dollar bill as 100 cents to the concept of 100 (2.NBT.A.1) and counting within 1000 (2.NBT.A.2). Use play money—
nickels, dimes, and dollar bills to skip-count by 5s, 10s, and 100s. Reinforce place value concepts with the values of dollar bills, dimes, and pennies.

Students use the context of money to find sums and differences less than or equal to 100 using the numbers 0 to 100. They add and subtract to solve
one- and two-step word problems involving money situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in
all positions. Students use drawings and equations with a symbol for the unknown number to represent the problem. The dollar sign, $, is used for
labeling whole-dollar amounts without decimals, such as $29. Students need to learn the relationships between the values of a penny, nickel, dime,
quarter and dollar bill. Work with money should keep dollars and cents separate; students don’t work with addition and subtraction of decimals until
Grade 5.

Since money is not specifically addressed in Kindergarten, Grade 1, or Grade 3, students should have multiple opportunities to identify, count, recognize,
and use coins and bills in and out of context. They should also experience making equivalent amounts using both coins and bills. “Dollar bills” should
include denominations up to one hundred ($1.00, $5.00, $10.00, $20.00, $100.00).
Students should solve story problems connecting the different representations. These representations may include objects, pictures, charts, tables,
words, and/or numbers. Students should communicate their mathematical thinking and justify their answers.
o Example: Sandra went to the store and received 76¢ in change. What are three different sets of coins she could have received?

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
Solving problems with money can be a challenge for young children because this work builds on prerequisite number and place value skills and concepts.
Many times money is introduced before students have the necessary number sense to work with money successfully:
For these values to make sense, students must have an understanding of 5, 10, and 25. More than that, they need to be
able to think of these quantities without seeing countable objects… A child whose number concepts remain tied to
counts of objects [one object is one count] is not going to be able to understand the value of coins.
Van de Walle & Lovin, p. 150, 2006
Domain: 2.NBT
Cluster: 2.NBT.A Understand place value.
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

As teachers build on students’ work with skip-counting by 10s in Kindergarten, they explore and discuss with students the patterns of numbers when
they 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?

The use of a 100 chart may be helpful for students to identify counting patterns.

The use of money (nickels, dimes, dollars) or base-ten blocks may be helpful visual cues.

Make explicit connections to skip-counting when working with time and money.
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Mathematics 2016-2017—Grade 2
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enVisionmath2.0—Topic 8
Differentiation
2.MD.C Work with time and money.
 Progression of learning for differentiation:
Literacy Connections

Academic vocabulary terms

Vocabulary Strategies

Literacy Strategies
Support
 Students may have worked with meter strips, which are concrete number lines. A clock is a circular number line.
Visually demonstrate this for students by making the clock from a 24-inch ribbon marked off every 2 inches.
Consider measuring the intervals in advance, making the marks very lightly so that they are hard for others to see.
Then, begin the activity by making the marks dark enough for all to see as students count along by ones to notice
that there are 12 marks. https://www.engageny.org/resource/grade-2-mathematics-module-3
 Provide students working below grade level with extra practice using an online animated clock such as that found at
http://www.mathsisfun.com/time-clocks-analog-digital.html. English language learners would also benefit from
using such a clock that gives the digital time along with the analog clock, and writes the time out as well.
https://www.engageny.org/resource/grade-2-mathematics-module-8
 Count and Change Coins to 30 Cents https://www.engageny.org/resource/grade-2-mathematics-module-3
 Coin names are important and take time for English language learners to learn. It is wise to have a classroom
economy (search online under classroom economies for children) using coins so that they are used again and again.
Repetition is crucial for language acquisition. There are many suggestions online that meet the needs of diverse
classroom cultures. https://www.engageny.org/resource/grade-2-mathematics-module-3
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
Provide students working below grade level with the chance to continue using coin manipulatives and part–whole
templates for their personal white boards. This provides extra scaffolding to help them transition to drawing tape
diagrams. https://www.engageny.org/resource/grade-2-mathematics-module-7
Possible Enrichment Tasks
 Academically and/or Gifted Instructional Resources Project: The History of Telling Time
http://ncaigirp.ncdpi.wikispaces.net/Mathematics+K-2
 Academically and/or Gifted Instructional Resources Project: What time in the World?
http://ncaigirp.ncdpi.wikispaces.net/Mathematics+K-2
 Academically and/or Gifted Instructional Resources Project: Fun with Coins
http://ncaigirp.ncdpi.wikispaces.net/Mathematics+K-2
 Illustrative Mathematics:
o Ordering Time https://www.illustrativemathematics.org/content-standards/2/MD/C/7/tasks/1069
o Choices, Choices, Choices https://www.illustrativemathematics.org/contentstandards/2/MD/C/8/tasks/1073
o Pet Shop https://www.illustrativemathematics.org/content-standards/2/MD/C/8/tasks/1148
o Susan’s Choice https://www.illustrativemathematics.org/content-standards/2/MD/C/8/tasks/1285
o Visiting the Arcade https://www.illustrativemathematics.org/content-standards/2/MD/C/8/tasks/1296
o Alexander Who Used to Be Rich Last Sunday https://www.illustrativemathematics.org/contentstandards/2/MD/C/8/tasks/1314
 Discussion or Journal Prompts (https://hcpss.instructure.com/courses/106/pages/2-dot-md-dot-c-7-about-themath-learning-targets-and-increasing-rigor):
o If a cell phone alarm beeps every 5 minutes, how many times will it beep in 1 hour? In 30 minutes? In 2
hours?
o You eat dinner between 5:00 p.m. and 7:00 p.m. What are some possible times you can eat? (teacher can
ask to the hour/half hour, quarter hour, 5 minutes)
o What difference do you notice between the hour hands for 6:25 and 6:55? Why does it change?
o To make 4:45, how can you use your knowledge of equal parts to figure out where to draw the minute
hand?
o What is the difference between 12 a.m. and 12 p.m.? (not just morning and night) What might you be doing
at these times?
o When you are sleeping, are you sleeping in the a.m., p.m.? Explain your thinking.
 Discussion or Journal Prompts (https://hcpss.instructure.com/courses/106/pages/2-dot-md-dot-c-8-about-themath-learning-targets-and-increasing-rigor):
o A pencil costs 75¢, an eraser costs 45¢, and a piece of paper costs 59¢. Which one of these items can you
purchase with exactly 6 coins?
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o
o
o
o
o
o
Carla’s brother says he’ll trade her 2 quarters, 4 dimes, and 2 nickels for a one dollar bill. Is this a fair trade?
How do you know?
Donald has 12 quarters and 60 nickels. He has $3.00 more than Tanya. How much money does Tanya have?
Sam gets 92¢ change back from the cashier. What combination of coins might he have received? Is there
another possibility?
Sean buys a baseball card. He gives the cashier $1.00. He received 2 dimes, 1 quarter, and 1 penny as
change. How much did Sean’s baseball card cost?
Sally gets a job digging weeds. She gets paid 5¢ for each weed she digs up. At the end of the day she gets
paid 85¢. How many weeds did she dig up? (not division, skip counting) How many nickels will she get paid?
How many dimes could she receive if she trades in her nickels?
Denise has three dollars and seven dimes. Dave has three dollars and eight dimes. A smoothie costs $3.74.
Can either Denise or Dave buy a smoothie? How do you know?
2.NBT.A Understand place value.
 Progression of learning for differentiation:
Support
 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-2mathematics-module-3
 Skip-Count by Twos Beginning at 394 https://www.engageny.org/resource/grade-2-mathematics-module-3 lesson 9
Possible Enrichment Tasks
 Illustrative Mathematics: Saving Money 2 https://www.illustrativemathematics.org/contentstandards/2/NBT/A/2/tasks/1309
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
Discussion or Journal Prompts (https://hcpss.instructure.com/courses/106/pages/2-dot-nbt-dot-a-2-about-themath-learning-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
answer.
o If you start at 17 and count by 10s, will you land on 100? Why or why not?
o What patterns do you see in the ones, tens, and hundreds place when skip counting by 5s? 10s? 100s?
o Summer started on 205. She counted by 100s. Is 808 in her pattern? Explain how you know.
o 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?
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.
Resources
enVisionmath2.0
Developing Fluency
Grade 2 Fact Fluency Plan
Addition Fact Thinking Strategies
Topic 8 Pacing Guide
Grade 2 Games to Build Fluency
Multi-Digit Addition & Subtraction Resources
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