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)