2nd grade unit 3 overview and standards€¦ · 2nd grade unit 3 overview and standards before you...
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2nd Grade Unit 3 Overview and Standards
Before You Begin this Unit…
Unit at a
Glance
This unit builds on the ideas from Unit 1, with students
becoming familiar with mathematical tools, and developing
strategies for accurately counting a set of objects. They are
also continuing to become fluent with addition combinations.
A large focus is also on making sense of addition and
subtraction story problems. In this unit, start unknown and
change unknown situations are introduced.
It is important to note that the numbers used in the story
problems of Investigation 2 in this unit are kept small so that
students can focus on the situation. Later, students will work
on similar problems with larger numbers.
Even though many students do not need cubes to solve a story
problem, it is important that everyone understands how to
model the situation with cubes.
In this unit, most students are in the process of making a
critical shift from thinking and working primarily in 1s, to
thinking and working in groups of 10. By organizing objects
into groups of tens and ones, students experience that the
number in the tens place represents the groups of 10 and the
number in the ones place represents the number of ones.
Estimated Duration:
32 Days
*Investigation 1: 6 lessons
*Common Core Unit 2
Session 1.1A
*Investigation 2: 8 lessons
*Investigation 3: 7 lessons
*Investigation 4: 6 lessons
Standards Addressed in the Unit
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.
2.OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know
from memory all 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.A1 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:
2.NBT.A2 Count within 1000; skip-count by 5s, 10s, and 100s.
2.NBT.B5 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.B6 Add up to four two-digit numbers using strategies based on place value and
properties of operations.
2.NBT.B9 Explain why addition and subtraction strategies work, using place value and the
properties of operations
2.MD.C8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies,
using $and ¢ symbols appropriately.
Link to CCSS Unpacking Document
2nd Grade Unit 3 Planning Differentiation
Students Who Struggle...
Behaviors Resources How to Use
Difficulty
understanding the
action of a story
problem
Kathy Richardson’s
Developing Number
Sense story boards
Use the story boards as the setting for story
problems. Students can use objects such as
cubes, beans, etc. to model the action of the
story problem on the story board.
Difficulty with
Collect 50 cents Revisit Collect 25 Cents
Revisit Collect 25 Cents and model adding
coins together.
Difficulty imagining
the unknown change
in Cover Up
Use a smaller total of
counters
Keep the numbers small, starting with less
than 18. Help students adjust the total
number of counters to create situations that
are challenging, but not overwhelming. You
may also want to provide problems for
certain children by writing them on their
Cover Up Recording Sheet.
Students Who Have Mastery...
Behaviors Resources How to Use
Knows multiple
ways to Make 50
cents
Variation of Collect 50
Cents
Have students find the fewest number of
coins that makes 50 cents. Also, have
students determine how much more they
need to get to 50 cents.
Shows confidence
when building 2-
digit numbers with
groups of tens and
ones
Stickers
Ten Frames
Open Number
Lines
Blank die with
+10 on 3 sides
and -10 on 3 sides
or a blank die
with +10, +20,
+30 or -10, -20, -
30.
Using these tools, students can practice
adding 10 and multiples of 10 to 2-digit
numbers. Students can record equations to
match their actions.
2nd Grade Unit 3 Planning Each
Investigation and Classroom Routines
Notes About Each Investigation
Investigation 1:
This investigation is focused on fluency with addition number strings.
Students are adding 3 or more numbers by locating known combinations and adding
those first to solve more efficiently.
Students play games such as Close to 20 and Beat the Calculator to practice known
combinations for fluency.
**Before beginning Investigation 2, complete Common Core Unit 2 Lesson 1.1A
Subtraction Facts. **
**Before beginning Investigation 2, complete Common Core Unit 2 Lesson 1.1A
Subtraction Facts. **
Investigation 2:
This investigation is focused on making sense of story problems by visualizing what is
happening and thinking about what we know and need to find out in various
mathematical situations.
Students will make sense of problems with information missing at the start and within
the middle of the story problem.
Students combine numbers with a sum up to 45.
Students will record problems with an unknown and show their work with equations.
Students will experience how addition and subtraction are opposite operations through
related story problems.
Students play Cover Up to practice finding a missing part when the other part and total
are known.
Investigation 3:
This investigation is focused on shifting from counting by 1’s to counting in groups.
Students determine if a number is even or odd by arranging the number into groups of
two or two equal groups (partners and teams).
Students identify odd numbers as numbers that cannot be made into two equal groups or
partner groups with no leftovers.
Students count pairs by 2’s, sets of 5 objects by 5’s, and groups of 10 objects by 10’s.
They apply this same pattern when counting pennies, nickels and dimes.
Students experience that the same total is reached whether you count by 1’s, 2’s, 5’s or
10’s.
Investigation 4:
This investigation is focused on building 2-digit numbers in groups of ten and leftover
ones.
Students are introduced to Sticker Station which sells stickers in strips of 10 and singles.
Students will build 2-digit numbers in more than one way by decomposing tens into
ones. (Ex: Students exchange a strip of 10 stickers for 10 single stickers.)
Classroom Routines
Activity Note Standard
Today's
Number
Students will be composing numbers up to 35 with 2 and 3
addends. They will also represent numbers with addition and
subtraction equations. They will also be using near doubles and
coins to represent Today’s Number.
2.OA.2
2.NBT.5
2.NBT.6
2.NBT.9
2.MD.8
Quick
Images
Students will use ten frames to show combinations of 10 and
doubles.
2.OA.2
2.OA.4
2.NBT.5
How Many
Pockets?
Students will count the number of pockets in the class by making
10s with 3 addends. They will also organize the number of pockets
into tens and ones for adding.
2.OA.2
2.NBT.5
What Time
is it?
Students will tell time to the hour and half hour in this unit.
Students will observe how we move around the clock by counting
the minutes. They will identify what time it is, and what time it will
be.
2.MD.7
2.NBT.2
2nd Grade Unit 3 Teaching Standards for
Math Practice
Standards for Mathematical Practice
(behaviors of mathematically proficient students)
Building the Language
of Mathematics
Increasing accountable
talk is the goal for ALL
students in our district.
The following activities are
provided to help ensure
your students are engaging
in mathematical
conversations that address
SMP 3 (Construct Viable
Arguments) and SMP 6
(Attend to Precision)
Words you should hear
students use in
mathematical
conversations: addends, more, less, addition,
subtraction, odd, even
During Investigation 1,
students explore adding
strings of numbers by
adding and subtracting
numbers in different
orders. Students think
about how they can use
combinations that make
ten, doubles, or other
familiar combinations to
add number strings more
quickly. As students work
on student activity pages 3-
5 adding number strings,
play Beat the Calculator,
and play Close to 20, have
students ask each other,
“Why did you choose to
During Investigation 2, Session
2.3 students complete related
problems connecting addition
and subtraction. Have students
represent and describe the action
in the story problems to a
partner. For example, “I put 13
pennies because Sally had
13. Then her mom gave her 12
more. Since Sally got more
pennies that is adding. I can put
12 more pennies. I can write 13
+ 12. Now Sally has 25
pennies. I can write 13 + 12 =
25. Franco started with 25. He
gave 13 to his brother. He will
have less pennies now. So I
move the 13 away. I can write 25
During Investigation 3,
Sessions 3.1 to 3.4, students
investigate whether numbers
can be made into two equal
teams or partners. Have
students explain how they
know a given number can be
made into partners and
teams. Encourage students
use “odd” and “even” to
describe quantities. Students
should explain how they know
a quantity is odd or even using
partners and teams or blocks.
add (7) and (3) together
first?” Then partners
should explain that (7) and
(3) were easy to add
because they (make 10).
– 13 pennies. Now Franco has
12. I can write 25 – 13
=12.” Then ask students to tell
their partner what they notice
about the two problems. How
are these two problems alike?
(Do students see that the
numbers are the same?) How are
the problems different? (Do
students notice that one involves
getting more pennies, while the
other involves removing
pennies? Do students notice that
one problem ends with 25 and
the other begins with 25?)
Building Mathematically Proficient Students
During this unit, focus student attention on:
Practice 1-Make sense of problems and persevere in solving them
SMP 7-Look for and Make Use of Structure
Unit 3, Investigation 3 focuses on addition and subtraction story problems. Students need to
apply Practice 1-Make sense of problems and preserve in solving them. Students solve change
unknown and start unknown problems. Students must make sense of problems in which the
middle or beginning information is not given. Locate the poster here (page 2) that can be posted
and discussed during these lessons. For example, during in Session 2.4, students are presented
with change unknown situations. Have students retell the mathematical stories in their own
words. Ask students, what information do we know? What are we trying to find out? Do you
think the answer will be more or less than (starting number)? Why? Encourage students to
represent their thinking with blocks, number lines, and equations with an unknown.
Several sessions in Unit 3 also address Practice 7- Reason abstractly and quantitatively. In
Investigation 3 students practice counting in groups in sessions 3.4 through 3.7. As students
count in groups of 2’s, 5’s, and 10’s record numbers. Ask students what they notice about the
patterns in the numbers (ie When we count by 5’s the ones digit changes 5-0-5-0-5,…) Ask
students how the patterns could help them decide what comes next. Introduce Practice 7 using
the poster located here (page 2). You can also note Practice 7 in Investigation 4, Session
4.2. Students build numbers using groups of ten and leftovers. As students work with partners,
encourage them to look for patterns in the number of groups of ten and the leftovers and the
total number (ie 5 groups of ten and 2 leftovers is 52). Students should experience this by
building lots of numbers with tens and ones, rather than simply being told that the left digit is
the “tens” and the right digit is the “ones.”
2nd Grade Unit 3 Assessing Student
Understanding
Resource:
Teaching Suggestion:
2.OA.1
Suggested Tasks:
1a, 2a, 8b
The addition and subtraction lessons in this Investigations unit
introduce add to and separate from problems with change and start
unknown. Also problems with one addend and the total known are
included. All of these problems are with numbers less than 50. The
suggested tasks can be used as additional assessments for students on
these types of problems.
2.MD.8
Illustrative
Mathematics Task
Students are given a set of coins with a value of 33¢ to find the value
of and represent with an equation. Students are then asked to show
another way to make the same amount using different coins.
2.MD.8
Task 2.MD.8a
Students combine 3 dimes and 2 nickels for this task.
2.OA.3
Illustrative
Mathematics Task
This task asks students to determine if several sets of tile designs
could be made with the same number of red and blue tiles. Then
students identify which sets are odd and even.
2.OA.3
Illustrative
Mathematics Task
This task asks students to group given numbers of buttons into
partners to determine if the number is odd or even. Students are then
asked to record an equation to show how they know.
2.NBT.2, 2.MD.8
Illustrative
Mathematics Task
This task asks students to decide if they prefer to get $20 now or $2
every day for the next $15 days. Students will need to count by twos
for 15 times. It may be challenging for some students at this point
because they need to keep track of both the days and counting by
twos. Students are asked to explain why they chose the option they
preferred.
Exit Tickets
Unit 2,
Investigation
1.1A
1.1A Use Student Activity Book Unit 2, page 1B
Investigation 1
1.1 Ruth has 3 green pencils, 9 red pencils, and 7 blue pencils. How many
pencils does she have? Show two different ways to add these numbers.
1.2 Find the sum. Show your work with equations:
4 + 7 + 5 + 3 =
1.3 Use Student Activity Book page 7
1.4 Use Student Activity Book page 10
1.5 What is the sum of 6 + 3 + 7 + 6? Show how you know.
1.6 Use Number Strings Assessment
Investigation 2
2.1 Use Student Activity Book page 21
2.2 Chris had 28 marbles. He gave 14 to Jacob. How many marbles does
Chris have now?
2.3 Use Student Activity Book page 27
2.4 1. There were 16 pencils in the box. Dr. Williams put some more pencils
in the box. Now there are 22 pencils. How many pencils did Dr.
Williams put in the box?
2. Dr. Williams had 22 pencils in her box. She gave some away to
students. Now she has 16 pencils in her box. How many pencils did she
give away?
3. Can you use what you know from problem 1 to help you solve problem
2? How does it help?
2.5A 1. Laura had some books. She gave 14 of her books to her
brother. Now she has 8 books. How many books did Laura have to begin
with?
2. Calvin had some rocks in his collection. He found 13 more rocks. Now
he has 12 rocks. How many rocks did Calvin start with?
2.5 Use Student Activity Book page 34
2.6 Use Student Activity Book page 39
2.7 Assessment M20
Investigation 3
3.1 Use Student Activity Book page 45
3.2 Use Student Activity Book page 50
3.3 Use Student Activity Book page 52
3.4 Use Student Activity Book page 54
3.5 Use Student Activity Book page 55
3.6 Give students a set of 32 blocks. Have students represent with tallies and
show how to count by 5’s with the tallies. Then have students count
another way and record.
3.7 Use Student Activity Book page 61
Investigation 4
4.1 Complete 2’s, 5’s, and 10’s chart for 42 cubes
4.2 1- If I made 7 towers of ten and had 3 leftover, how many cubes?
2- If I have 58 cubes, how many towers of ten can I make?
3-If I have 62 cubes and I put them in towers of 10, how many cubes will I
have leftover?
4-If I have 3 towers of 10 and 5 leftover cubes, how many cubes do I
have?
4.3 1-Renee has 64 cards. If she puts them in rows of 10, how many rows will
she make? How many cards will be leftover?
2-Emily has 58 cents. She only has dimes and pennies. How many dimes
and pennies could she have?
4.4 Use Student Activity Book page 74
4.5 Use Student Activity Book page 77
2nd Grade Unit 3 Digital Resources
Interactive Student Resources
Resource Suggestion for Use: What standard(s) are addressed?
National
Library of
Virtual
Manipulatives
Use this site for modeling how to
build numbers and arrange numbers
for acting out addition and
subtraction situations. Consider
having students explain how they
solved and why their strategy works.
Specifically notice the following
activities:
1. Base Blocks
2. Base Blocks Addition
3. Base Blocks 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.
2.NBT.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.
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.8: Mentally add 10 or 100 to a
given number 100-900, and mentally
subtract 10 or 100 from a given
number 100-900.
2.NBT.9: Explain why addition and
subtraction strategies work, using
place value and the properties of
operations.
Shark Numbers
Students will identify numbers with
base ten pieces by matching a model
to its numeral form.
2.NBT.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.
Coin Combo
Game
Students will create specific
amounts of money, using coins.
Level 1 uses pennies and nickels.
Level 2 adds dimes and Level 3 adds
quarters.
2.MD.8: Solve word problems
involving dollar bills, quarters, dimes,
nickels, and pennies, using $and ¢
symbols appropriately.
Digital Resources for Teachers
Resource Suggestion for Use: What standard(s) are addressed?
Thinking
Blocks
Use this site to model the parts of a
story problem. It is specifically
helpful when determining the
significance of each number in the
story problem. There are options
for part-part-whole, comparison
problems, change and other
“random” types.
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.
Educreations
App
Use this app to model solving story
problem situations, while recording
an audio description of the strategy
and why it works. This is
particularly useful when students
replay it and use it as a guide in
their own work.
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.
2.NBT.9: Explain why addition and
subtraction strategies work, using place
value and the properties of operations.
Close to 20
Video
Watch a teacher interact with
struggling and strong math students
while playing the game. Notice
questions they ask as they play, as
well as explanations of their
teacher moves.
2.OA.2, 2.NBT.2, 2.MD.6
Cover Up
Video
Watch a teacher interact with
struggling and strong math students
while playing the game. Notice
questions they ask as they play, as
2.OA.1, 2.NBT.5, 2.MD.7
well as explanations of their
teacher moves.
Printable Resources for Teachers
Resource Suggestion for Use: What standard(s) are addressed?
Add-To:
Change
Unknown
Story
Problems
Add-To:Start
Unknown
Take-From:
Change
Unknown
Take-From:
Start
Unknown
This document provides story
problems of different types that can
be reproduced for student work. You
might consider cutting them apart
and using as rotations in a jigsaw or
as an addition to your math
workshop. You might also consider
adding a section that asks students to
describe why their strategy works.
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.
2.NBT.9: Explain why addition and
subtraction strategies work, using place
value and the properties of operations.
Counting
Collections
This task card/activity is designed to
help students see how a group of
objects can be counted in various
ways. This would be beneficial to
use with Investigation 3.
2.NBT.2: Count within 1000; skip count
by 2s, 5s, 10s, and 100s.
2nd Grade Unit 3 Professional Learning for
Teachers
Professional
Learning Activities
Things to Discuss with
Your Team
Before beginning Investigation 1, read
TE page 205: Does the Order Matter?
Discuss the following questions with your team:
1-What number properties will students
experience in this Investigation (note that students
use the property, but do not needed to use official
names of the properties)?
2-What is the difference between the two
properties?
3-How do we know when students are making
generalizations about these properties?
4-How does work with these properties support
students who are adding larger numbers later in
second grade?
Before beginning Investigation 2, read
TE pages 214-217: Using Notation to
Record Strategies, Part 2
Discuss the following questions with your team:
1-What is the difference between counting by
ones, adding in groups, and adding by place
value? How can we tell which strategy students
are using by looking at their work?
2-How might different strategies be represented
on a number line or hundred chart?
3-How can teachers model using equations to
record student thinking?
Before beginning Investigation 2, read
TE pages 216-217: Solving Addition
and Subtraction Problems
Discuss the following with your team:
1-Why is it important that students develop the
ability to visualize addition and subtraction
situations rather than relying on keywords?
2-How do students typically progress toward
more efficient strategies for solving addition and
subtraction problems?
3-How can we recognize if children are counting
all, counting on or back, or using numerical
strategies?
4-Why is it important to have students
communicate their strategies to a partner and/or
the teacher?
Before beginning Investigation 3,
read TE pages 223-224: Defining Even
and Odd
Reading NCDPI Unpacking for
2.OA.3 (page 11)
Discuss the following questions with your team:
1-How do second grade students define even and
odd numbers?
2-How can the same representation be used to
show partners and teams simultaneously?
3-What types of observations do second graders
typically make about even and odd?
4-How can equations be used to represent even
and odd numbers?
Before beginning Investigation 4, read
this excerpt from How Children Learn
Number Concepts: A Guide the Critical
Learning Phases by Kathy Richardson*
*This book is an excellent resource for
understanding how children develop
number concepts including place
value. These are short excerpts from a
longer chapter that teams may be
interested in reading.
“The difficulty young children have
understanding place value concepts has not
always been recognized. Because children can
learn the language of tens and ones with relatively
little difficulty, their lack of understanding is
often hidden.” (page 75)
“There are instructional strategies that can help
children develop an understanding of tens and
ones. Primarily they involve organizing quantities
into groups of ten and counting those groups.”
(page 77)
“When children organize a number of counters
into all groups of tens they can, we can see
evidence of different states of thinking in the
ways they determine the total. Children at one
stage of thinking will need to count all the
counters to determine what the total is….At the
next level of thinking, children will be able to
count by tens, and then count by ones to
determine the total…, but they do not yet treat
each group of ten as one unit…Children who
understand this Critical Learning Phase instantly
recognize the total for any number of tens plus
any number of ones…To find out whether the
child understands that 3 tens and 4 is 34, the
teacher would have to ask, ‘How many would
there be if we counted these by ones?’…The
reverse of knowing that 3 groups of ten and 4
ones is 34 is knowing that when you have a group
of 34 counters you can make 3 tens…Children
who understand this Critical Learning Phase will
be able to tell the number of tens they can make
when they know the number of objects in a
group.” (pages 88-89)
Discuss the following questions with your team:
1-How does the work in this Investigation support
student development of place value
understanding?
2-What questions can we ask students to
determine their level of place value
understanding? (You might also look at Assessing
Math Concepts: Ten Frames Assessment and
Grouping Tens Assessment for ideas for
determining where students are in their
understanding of Place Value)