North Adams Public Schools
2015-2016
Grade 2 Math Unit 1:
Addition and Subtraction within 20 (29 days)
In this unit and throughout the year, students learn to recognize various problem structures including Add To/Take From, Put
Together/Take Apart, and Compare. In first grade, students worked with all these problem types. To extend this learning, in second
grade, they learn to identify the problem type before solving. Compare and contrast activities help develop this skill. Students also
begin the year-long work of developing fluency with addition and subtraction within 20. Math Mountain diagrams help students use
the relationship between part and whole. Students learn strategies such as Counting On/Counting Back, Make a Ten, and Doubles to
build a critical foundation for computational skills. Even and odd numbers are first introduced in second grade. Equations are shown
in many forms so that students understand that the equals sign means “has the same value as.” Math practice standards are
incorporated into every lesson. Teachers create a “community of learners” through Math Talk and student leaders with daily
number activities.
The following standard is a Massachusetts-only standard and is not included in Math Expressions. Reinforce time relationships
throughout the year with calendar and center activities.
2.MD.MA.7.a. Know the relationships of time, including seconds in a minute, minutes in an hour, hours in a day, days in a
week, a month, and a year; and weeks in a month and a year.
Note: This unit is allotted twenty-nine days and contains twenty-one lessons (#19 may be omitted). Eight additional days are set
aside for catching up, challenging concepts, Path to Fluency activities, and vocabulary/language development.
Key Math Vocabulary
Addend
Equation
Odd
Teen
Apart
Even
Pairs
Together
Day
Horizontal
Pattern
Unknown Addend
Diagram
Hour
Penny
Vertical
Dime
Minute
Second
Week
Double
Month
Sum
Year
Equals =
Not Equal ≠
North Adams Public Schools
2015-2016
Grade 2 Math Unit 1:
Addition and Subtraction within 20 (29 days)
Big Idea 1: Strategies for Addition and Subtraction
2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking
from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem.1
2.OA 2 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. MA.2.a. By the end of grade 2, know from memory related subtraction facts of sums of two one-digit numbers.
2.OA.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting
them by 2s; write an equation to express an even number as a sum of two equal addends.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship
between addition and subtraction.
2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations.3
Day
Lesson
Student Learning Objective(s)
Notes
Tue.
Lesson 1
Introduce Daily Routines and Quick Practice
 Relate addition and subtraction to word
activities.
9/8/15 Represent
problems using Math Mountains.
Addition and
Subtraction
Formative Assessment
Math Talk routines are established on Day 1. See TE
MX pp. 1-10
p. 8 Check for Understanding. Ask students to
p. 7 for how to use Solve and Discuss every day to
draw a Math Mountain and explain it with
promote mathematical discourse.
addition and subtraction.
1
See Glossary, Table 1.
See standard 1.OA.6 for a list of mental strategies.
3 Explanations may be supported by drawings or objects.
2
North Adams Public Schools
2015-2016
Thu.
Lesson 3
9/10/15 Make-a-Ten
Strategy
MX pp. 17-22
Grade 2 Math Unit 1:
Addition and Subtraction within 20 (29 days)
 Relate addition and subtraction to twenty to PREP: Secret Code Cards
word problems using Math Mountains.
Turn and Talk: What happens when a single digit
 Solve problems with both addends
number is added to 10?
unknown.
Formative Assessment
p. 14 Check for Understanding. Students make a Ask for the rule. Record it on chart paper with an
example for student reference.
Math Mountain and write 1 addition equation
and 2 subtraction equations for it.
Use penny strips to illustrate the Make-a-Ten
 Use the Make-a-Ten strategy to add two
strategy. This is a critical concept for developing
numbers to make a teen total.
computational fluency. Students need lots of
 Tell your partner about the strategy using
practice and talk to truly understand the idea.
word sum in your discussion.
Fri.
Lesson 4
9/11/15 Relate Unknown
Addends and
Subtraction
MX pp. 23-30
Formative Assessment
p. 20 Check for Understanding. Describe the
Make-a-Ten strategy with 7 + 5.
 Solve unknown addend and subtraction
problems using the Make-a-Ten strategy.
 Compare the advantages and disadvantages
of different methods for addition and
subtraction.
Wed.
9/9/15
Lesson 2
Relate Addition
and Subtraction
MX pp. 11-16
Formative Assessment
p. 28 Check for Understanding. Explain how to
use the Make-a-Ten strategy to find the
unknown addend in the equation 8 + ? = 13.
Carefully read Activity 1 Teaching Note on TE p. 24
for information on using unknown addends with
the Make-a-Ten strategy to solve subtraction
problems.
Begin a chart for strategies and add to it as new
strategies are learned. Start with the Make-a-Ten
strategy for addition and subtraction.
North Adams Public Schools
Mon.
Lesson 5
9/14/15 More Practice
with Unknown
Addends and
Teen Totals
MX pp. 31-36
Tue.
Lesson 6
9/15/15 Odd and Even
Numbers
MX pp. 37-46
Wed.
9/9/15
Lesson 7
Strategies Using
Doubles
MX pp. 47-54
2015-2016
Grade 2 Math Unit 1:
Addition and Subtraction within 20 (29 days)
Have students practice reading Math Mountain
 Solve unknown and subtraction problems.
cards to a partner in various formats. Provide
 Compare and contrast solution strategies.
sentence frames to structure the conversations.
Formative Assessment
p. 34 Check for Understanding. Explain how
unknown addend problems and subtraction
problems are the same. Give an example.
Odd and even are new to grade 2. Vocabulary and
 Count by 2s.
 Make pairs to determine if sets of cubes are concepts should be practiced throughout this unit.
odd or even.
MobyMax: Assign lessons in all four topic for odd
 Tech K-2: 3.2 Review teacher-selected
internet resources and explain why each and even numbers for center work. Check in with
students each day to see what was understood,
resource is or is not useful.
what needs further explanation. Tell students you
 Tech K-2 1.7 Explain that computers can
store and organize information so that it can see their work and which answers they chose
on MobyMax every day to see what they learned
can be searched.
and what they still need to learn. Show students
 Tech K-2 3.4 Use a variety of agethe Vibes icon and explain that you can send them
appropriate technologies to
Good Vibes or Bad Vibes for their work and effort.
communicate and exchange ideas.
Formative Assessment
p. 44 Check for Understanding. Describe two
ways to decide if a number is even or odd.
Add to the strategy chart with examples of Doubles
 Find totals using the Doubles Plus/Minus 1
Plus/Minus 1 or Doubles Plus/Minus 2.
or Doubles Plus/Minus 2 strategies.
 Discuss strategies and explain your thinking.
Formative Assessment
p. 52 Check for Understanding. Describe two
ways of using doubles to solve 6 + 8.
North Adams Public Schools
Thu.
Lesson 8
9/10/15 Equations,
Equation Chains,
and Teen Totals
MX pp. 55-62
Fri.
Lesson 9
9/11/15 Add Three or
Four Addends
MX pp. 83-88
2015-2016
Grade 2 Math Unit 1:
Addition and Subtraction within 20 (29 days)
SAB p. 23 This Puzzled Penguin activity is very
 Define equation.
valuable. Practice this with students over the year.
 Investigate the meaning of the not equals
It reinforces the meaning of the equals sign and
sign.
gives students a better understanding of equality.
Formative Assessment
p. 60 Check for Understanding. Write 7 + 5 = ? in
vertical form and solve.
Continue to reinforce the equals sign as meaning “is
 Develop strategies to add three or four
equal to.”
addends.
Students do not need to know the name of the
Associative Property; they need to know only that
Quick Quiz 1
with addition, order does not matter. Emphasize
Formative Assessment for Unit 1 Objectives:
1A Fluently add and subtract within 20 (2.OA.2) addition, but don’t get bogged down in a discussion
1B Determine whether a group of objects has an about why it doesn’t work with subtraction at this
point.
even or odd amount. Write an equation to
The example on TE p. 65 should be on a small chart
express an even number as the sum of two
for students to reference until it is no longer
equal addends. (2.OA.3)
1C Add 3 or 4 1-digit addends (2.OA.2, 2.NBT.6) needed.
North Adams Public Schools
2015-2016
Grade 2 Math Unit 1:
Addition and Subtraction within 20 (29 days)
Big Idea 2: Addition and Subtraction Situations
2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking
from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem.4
2.OA 2 Fluently add and subtract within 20 using mental strategies.5 By end of grade 2, know from memory all sums of two one-digit
numbers. MA.2.a. By the end of grade 2, know from memory related subtraction facts of sums of two one-digit numbers.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship
between addition and subtraction.
2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.
Day
Lesson
Student Learning Objective(s)
Notes
Mon.
Lesson 10
 Represent and discuss solution methods for Throughout Math Expressions children are taught a
9/14/15 Add to and Take
consistent process for solving problems:
Add to and Take from word problems.
From Word
Problems
1. Interpret the problem.
Formative Assessment
MX pp. 71-76
2. Represent the situation.
p. 74 Check for Understanding. Choose a
3. Solve the problem.
problem from the SAB and explain how their
4. Check that the answer makes sense.
drawing matches the problem.
4
5
See Glossary, Table 1.
See standard 1.OA.6 for a list of mental strategies.
North Adams Public Schools
Tue.
Lesson 11
9/15/15 Add to and Take
From Problems
with Unknowns
in All Places
MX pp. 77-84
2015-2016
Grade 2 Math Unit 1:
Addition and Subtraction within 20 (29 days)
As the lesson progresses, create a poster using
 Write and represent Add to and Take from
examples on TE p. 78 and p. 79. Leave up as a
word problems.
student reference.
 Solve and discuss Add to and Take from
word problems.
Do not focus too much on the vocabulary situation
equation and solution equation. Students should
Formative Assessment
p. 82 Check for Understanding. Explain how you see that Math Mountains and equations can be
used to represent and solve problems.
represented the situation in #4 on SAB p. 34.
Focus on student understanding of situations. Avoid
discussing “key word” strategies. They are often
misleading. For more information on this, see the
article and video on this website:
http://edublog.scholastic.com/post/be-wary-usingkey-words-your-math-instruction
Wed.
Lesson 12
9/16/15 Put
Together/Take
Apart Problems
MX pp. 85-90


Discuss Put Together/Take Apart word
problems.
Use Math Mountains to solve Put
Together/Take Apart Word Problems.
Formative Assessment
p. 88 Check for Understanding. Draw Math
Mountains to represent #s 5 and 6 in SAB p. 36.
How are they alike? How are they different?
This type of problem involves sets.
iTools
North Adams Public Schools
Thu.
Lesson 13
9/17/15 Special Put
Together/Take
Apart Problems
MX pp. 91-98
Fri.
Lesson 14
9/18/15 Compare Word
Problems
MX pp. 99-104
Mon.
Lesson 15
9/21/15 More Compare
Problems
MX pp. 105-110
2015-2016
Grade 2 Math Unit 1:
Addition and Subtraction within 20 (29 days)
Classify similar objects with diagrams.
 Solve Put Together/Take Apart word
Both addend unknown problems are review from
problems.
grade 1.
Formative Assessment
p. 96 Check for Understanding. Make a drawing
of some grouped items from the classroom.
Name the group and the items in the group.
 Represent, solve, and discuss Compare word The language of comparisons is often confusing to
students. See Teaching Note on TE p. 100.
problems.
Comparison bars help children understand
comparison situations. Encourage students to find
Formative Assessment
out who has more and label drawings using this
p. 102 Check for Understanding. Choose a
information before trying to solve the problem.
problem from SAB p. 40 and use Comparison
Bars to represent the problem.
Teach children to state the comparison both ways,
 Paraphrase and solve Compare word
“Sally has 5 more than Joe.” And “Joe has 5 less
problems.
than Sally.”
 Create and solve Compare word problems.
Formative Assessment
p. 108 Check for Understanding. Choose a
problem from SAB p. 41 and tell how
comparison bars can be used to show
information in the problem.
North Adams Public Schools
Tue.
Lesson 16
9/22/15 Mixed Word
Problems
MX pp. 111-116
2015-2016
Grade 2 Math Unit 1:
Addition and Subtraction within 20 (29 days)
Have students work in partners to solve several of
 Represent and solve a variety of word
the problems. Ask partners to share their solutions.
problems.
Encourage use of charts to help students explain
 Practice making a ten to make a teen total.
their solution strategies.
Formative Assessment for Unit 1 Objectives
PREP: Make-a-Ten cards from SAB pp. 45-48
p. Quick Quiz 2
 1A: Fluently add and subtract within 20
Use the results of Quick Quiz 2 to make
(2.OA.2)
instructional groups during the daily RTI block.
 1D: Use addition and subtraction within
20 to solve one- and two-step word
problems (2.OA.1, 2.OA.2)
Big Idea 3: More Complex Situations
2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking
from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem.6
2.OA 2 Fluently add and subtract within 20 using mental strategies.7 By end of grade 2, know from memory all sums of two one-digit
numbers. MA.2.a. By the end of grade 2, know from memory related subtraction facts of sums of two one-digit numbers.
2.OA.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting
them by 2s; write an equation to express an even number as a sum of two equal addends.
Day
Lesson
Student Learning Objective(s)
Notes
6
7
See Glossary, Table 1.
See standard 1.OA.6 for a list of mental strategies.
North Adams Public Schools
Lesson 17
Problems with
Not Enough,
Extra, or Hidden
Information
MX pp. 117-126
2015-2016
Grade 2 Math Unit 1:
Addition and Subtraction within 20 (29 days)
Skip this lesson; not in the standard.
Wed.
Lesson 18
9/23/15 More Complex
Compare
Problems
MX pp. 127-132

Thu.
Lesson 19
9/24/15 Two-Step Word
Problems
MX pp. 133-140
(This lesson may
take two days)

Fri.
Continue Lesson
9/25/15 19
Use comparison bars to solve more complex
Compare problems.
Formative Assessment
p. 130 Check for Understanding. Explain how
stating the comparison both ways makes
problems easier to understand.
Identify and answer first-step questions to
solve two-step word problems.
Formative Assessment
p. 138 Check for Understanding. What is meant
by a hidden or first-step question in a two-step
word problem?
See TE p. 128 Teaching Note. The language in these
problems can be challenging. These problems
illustrate why key words can be misleading. It may
be helpful to act these out with students and
objects.
See TE p. 134 Teaching Note. Teaching students to
read word problems for understanding is a top
priority. Acting out these problems is a good way to
help students begin to visualize situations for
understanding.
North Adams Public Schools
Mon.
Lesson 20
9/28/15 Mixed Word
Problems
Tue.
Lesson 21
9/29/15 Focus on
Mathematical
Practices
Wed.
Test 1
9/30/15
2015-2016


Grade 2 Math Unit 1:
Addition and Subtraction within 20 (29 days)
Categorize problem types using the class poster of
Represent and solve a variety of word
problem types.
problems.
Practice Make-a-Ten strategy for
PREP: Blue Make-a-Ten cards from SAB pp. 61-64
subtraction.
Formative Assessment
p. 144 Check for Understanding. Choose a
problem from SAB p. 59 or 60. Explain how you
solved it.
 Use reasoning to find patterns in numbers.
 Represent and solve a variety of word
problems.
Test Objectives
 1A: Fluently add and subtract within 20
(2.OA.2)
 1B: Determine if a group of objects (up to
20) has an even or an odd number; write an
equation to express an even number as the
sum of two equal addends (2.OA.3)
 1C: Add three or four 1-digit addends
(2.OA.2, 2.NBT.6)
 1D: Use addition and subtraction within 20
to solve one- and two- step word problems.
(2.OA.1, 2.OA.2)
Skip SAB p. 66 Extra Information; not in the
standard.
Discuss meaning of pattern; have students think of
other ways to express a pattern, i.e. red, yellow,
yellow (repeat 3 times) could be R, Y, Y, etc.
Use p. 155-157 for Re-teaching Activities and
Common Errors and Prescription for additional
learning activities to meet students’ needs.
North Adams Public Schools
2015-2016
Grade 2 Math Unit 1:
Addition and Subtraction within 20 (29 days)
North Adams Public Schools
2015-2016
Grade 2 Math Unit 1:
Addition and Subtraction within 20 (29 days)