### Learning Story for Grade 2

#### Number and Computational Fluency

For grade 2, students are starting to think about and operate with larger numbers, to 100. Foundational place value concepts are developed in grade 2 along with development of computational strategies for addition and subtraction.

In grade 2, students move from thinking about teen numbers as ten and some more in grade 1 to thinking about numbers to 100 as tens and ones in concrete and visual ways. As they move to grade 3, they extend this thinking to numbers to 1000 and build three-digit numbers. In grade 2, students build on their understanding of addition and subtraction concepts to develop their computational fluency with facts to 20 and use a variety of strategies to add and subtract two-digit numbers. This learning about addition and subtraction continues into grade 3 with three-digit numbers.

### Key Concepts

#### Place value to 100

#### Addition and subtraction to 20 (facts)

#### Addition and subtraction to 100

#### Key Number Concept 1: Place Value to 100

##### Overview

##### Number Sense Foundations:

The following concepts and competencies are foundational in supporting understanding of place value in grade 2:

- Counting by 1s, 2s, 5s forwards and backwards up to and from 20
- Understanding of teen numbers as being composed of a ten and “some more” (ones)
- Ordering and comparing numbers to 20 on a number line with benchmark numbers such as 10
- Connecting number words, symbolic number and quantities in concrete forms
- Concrete, pictorial and symbolic representations of numbers to 20
- Make reasonable estimates of quantities up to 20

##### Progression:

- Place value at grade two builds on students’ understanding of teen numbers in grade 1 (ten and some more/ones)
- Composing ten with concrete materials (like Unifix cubes) and counting a quantity by groups of tens and then counting on the extra ones
- Use ten frames, rekenreks or abacuses to represent two-digit numbers
- Understanding that 100 is made up of ten groups of ten and that the digit 8 in 80 represents 80 or 8 tens based on its place in the number
- Build different decade numbers (20, 40, 70 etc) using concrete materials or pictorial representations (ten frames, tallies, groupings) and record the number in symbolic form
- Build two-digit numbers/quantities with tens and ones in concrete and pictorial form and record using symbolic forms in both standard and expanded form (47, 40+7)
- Play with composing and decomposing two digit numbers in different ways (47 can be 40+7 or 30+10+7, 20+20+5+2, etc)
- With a small collection of two-digit numbers, have students compare and order numbers along a number line, providing benchmark numbers of 0, 50 and 100
- Make reasonable estimates for quantities up to 100 using referents or other visual strategies
- Mentally adding or subtracting 10s to any two-digit number such as 47 + 20
- Apply understanding of place value when adding and subtracting two-digit numbers and using strategies such as decomposing by place value or compensating by using complementary numbers

##### Sample Week at a Glance:

Before this week of lessons, grade 2 students will have developed an understanding of counting by tens and had some experience representing two-digit numbers with concrete materials and symbolic forms. They will have already learned to play the math game **Two-Digit Face Off**.

Before

Record the number 37 on a whiteboard or chart paper. What are all the different ways we can represent or compose this number? How do some of these ways help us to think more about place value?

During

In small groups, have students choose a number between 20-50 and have them complete a ** concept circle** together using concrete, pictorial and symbolic representations for that number.

After

Closing circle – share and discuss the different ways they represented their numbers and how different representations helped them to understand the place values of that number.

Before

** Choral Counting routine:** count by 10s to 120, recording in two rows (first row to 60, second row to 120) – what number patterns do you see?

During

Math Workshop

-Building two-digit numbers with Unifix Cubes and ten frames/counters

–** Counting Collections** between 10-100

-Teacher led small group instruction: reading and writing two-digit numbers

After

Closing Circle – students sharing what they did, what they learned and where they want to go next with their learning about place value

Before

Class discussion having students share what they know about place value.

During

Invite students to choose different materials to help them think about place value in new ways. Include base ten blocks, Cuisenaire Rods, ten frames, grid paper, loose parts, numerals, etc. Invite students to represent numbers in different ways.

After

Closing circle – have students share their findings/what they did with a partner and how materials helped them think about numbers in new ways.

Before

** Clothesline**: ordering numbers between 50-80, each pair getting one number and justifying their placement of that number on the clothesline

During

Math Workshop

-Building two-digit numbers with Unifix Cubes and ten frames/counters, Numicon Shapes and base ten blocks

-Mini-clotheslines with numbers from 50-100

-Teacher led small group instruction: provide cards with two-digit numbers and ask students to compare and order, explaining their thinking

After

Closing Circle – students sharing what they did, what they learned and where they want to go next with their learning about place value

** Choral Counting**: by 5s, starting 0 and finishing at 90, recording the oral count in three rows (5-30, 35-60, 65-90); what number patterns do you see?

Assessment tasks completed in centres:

1) How many ways can you compose or decompose 58? Record on a small whiteboard, blank piece of paper or notebook.

2) Order the following number cards in order from least to greatest: 15, 27, 72, 82, 86, 62, 68, 12)

3) Represent 24, 57 or 89 in at least three different ways with concrete materials or pictorial forms

Closing Circle – students share with a partner what they know about place value and two-digit numbers and set a learning goal for next week

##### Suggestions for Assessment

##### Suggested Links and Resources

Choral Counting **https://www.youtube.com/watch?v=LqHfkHfe4vE&list=PLwD5gaAZPrjYCP4AETsSw88PAZ7XXkXsF&index=13&t=4s**

Clothesline routine **https://www.youtube.com/watch?v=fQYjL3m7Xys&list=PLwD5gaAZPrjYCP4AETsSw88PAZ7XXkXsF&index=9&t=25s**

Counting Collections: **https://www.stenhouse.com/content/choral-counting-counting-collections**

About Teaching Mathematics: A K-8 Resource by Marilyn Burns (place value menu tasks and games)

Two-Digit Face-Off Game **https://blogs.sd38.bc.ca/sd38mathandscience/wp-content/uploads/sites/14/2020/05/SD38_Face_Off_Game.pdf**

CGI Math resources: **https://blogs.sd38.bc.ca/sd38mathandscience/cgi-math/**

#### Key Number Concept 2: Addition and Subtraction to 20 (facts)

##### Overview

In grade 2, students are introduced to computational strategies for addition and subtraction facts to/within 20, as part of the computational fluency continuum of development. In grade 1, students learn about the concepts of addition and subtraction, in grade 2 they are introduced to flexible mental math strategies and in grade 3 they are expected to have emerging fluency with the strategies.

In grade 2, students are formally introduced to strategies for adding and subtracting numbers although many of these strategies may have been introduced in grade 1 as part of students’ introduction to addition and subtraction. These strategies include: making or bridging 10, decomposing, related doubles, and adding on to find the difference. Many students will need concrete (cubes, counters, rekenreks) and visual (ten frames, number lines) supports as they learn these strategies.

Please note: The expectation is that students at grade 2 will have flexibility and fluency with multiple mental math strategies for adding and subtracting numbers to and within 20. “Memorization” of addition and subtraction facts is not expected or encouraged at this grade level as students need to make meaning of the concepts and strategies. As we also think about the curricular competencies in mathematics, we need to pay attention to students using multiple strategies and being able to explain and communicate their thinking in many ways. With many experiences and as students develop computational fluency, students will be able to recall many addition and subtraction facts to and within 20.

##### Number Sense Foundations:

The following concepts and competencies are foundational in supporting understanding of addition and subtraction in grade 2:

- Counting with fluency to 20, forward and backwards by 1s, 2s and 5s
- Connecting number words, symbolic numbers, and quantities in concrete and pictorial forms with numbers to 20
- Knowing different ways to make/compose 10 (6 and 4, 5 and 5, 7 and 2 and 1)
- Decompose numbers to 20 in different ways with concrete materials, using pictures or visual tools and using visualization (mental visualization)
- Understanding making and bridging 10 (7 + 5 can be solved by decomposing 5 into 3 and 2 so that the 3 can be added to the 7 to make 10 and then add the 2 to bridge over 10 to 12)
- Use flexible strategies for adding (example: doubles plus/minus/near doubles) and subtracting (example: If I have 13 and you have 9, how many more do I have?)
- Use benchmark numbers of 5 and 10 to support addition and subtraction strategies
- Understanding the commutative property of addition (example: 4+3 = 3+4)
- Make reasonable estimates for sums and differences to and within 20
- Consider the relationship between addition and subtraction and different equation structures such as 8 + __ = 15 and 9 = __ – 5

##### Progression:

- Addition and subtraction at grade 2 builds on students’ understanding of addition and subtraction concepts in grade 1 – What does it mean to add and subtract? What are the actions/processes?
- Record addition and subtraction equations symbolically.
- Through number talks, have students share their counting and mental math strategies. A typical progression at this grade level might be:
- Addition: counting all, counting on, making a ten, bridging over ten by decomposing to make a 10, doubles, related doubles
- Subtraction: removal (concrete or pictorial), counting back, parts-whole relationship and related to addition, adding on or counting up to compare and find the difference

- Developing ability to explain mental math strategies for addition and subtraction using mathematically correct and efficient language

##### Sample Week at a Glance

Before

Read Bunny Money by Rosemary Wells. Provide students with “money” (one five and 10 one dollar bills cut from pieces of paper) to act out the story as you read it. Record the subtraction equations for each interaction in the story.

During

Invite students to draw, write or build their own subtraction story and record the related subtraction equations.

After

Closing circle – share and discuss how stories help us think of different easy to think about subtraction

Before** Number Talk Image**: Choose an image with a missing part such as a dozen eggs with only 9 eggs in the carton. How many? How do you know? How could subtraction help you think about this image?

During

Math Workshop

-Race to Zero (from 20 with two ten frames filled with counters, roll one die and remove that amount, repeat until ten frames are cleared)

–** Subtraction Face-Off** (use cards Ace-10, each student turns over two and subtracts the smaller number from the greater number and compares differences)

-half-sheet of five subtraction questions within 20 (solve and show each in at least two ways)

-Teacher led small group instruction: mini number talk with focus on subtraction strategies

After

Closing Circle – students sharing what they did, what they learned and where they want to go next with their learning about subtraction

Before

During

Subtraction Stories with Materials

Invite students to choose different materials to tell a story about subtraction. Include base ten blocks, Cuisenaire Rods, ten frames, loose parts, numerals, etc. What context would make sense for a subtraction story? What actions might be happening (removal/separating/taking away or comparing to find the difference) in the story?

After

Closing circle – Have students share their subtraction stories with a partner and how the materials and actions of storytelling helped them think about subtraction in new ways. For example, how does using Cuisenaire rods help you think about subtraction as comparing to find the difference?

Before**Number Talk/String**: 8 – 6, 13 – 6, 18 – 6

Show use of an open number line to represent adding on or counting up if students do not share this particular strategy. Connect to how students can visualize this in their minds.

During

Math Workshop

-Subtraction questions on mini whiteboards using open number line to record

–**Subtraction Track (BoxCars game)** using ten-sided or twelve-sided dice

-half-sheet of five subtraction questions to solve using adding on/counting up strategy

-Teacher led small group instruction: Roll two ten-sided dice, have students represent with Cuisenaire rods and then compare to find the difference, recording the subtraction equation

After

Closing Circle – students sharing what they did, what they learned and where they want to go next with their learning about subtraction

Before

Open Question: If 5 is the answer, what could the subtraction question be?

Record student ideas on a chart or whiteboard for all to see and discuss.

During

Present a start or change unknown separate/subtraction **CGI problem** such as: When we started playing the video game we had 648 points. Then we lost some points and ended with 362. How many points did we lose? Invite students to solve the problem and represent their thinking with pictures, numbers and words. Have students share and compare their approaches in small groups. Invite students to pose their own subtraction problems for others to solve next week.

After

Closing Circle – student sharing and comparing strategies, set goal for next week about subtraction

##### Suggestions for Assessment

##### Suggested Links and Resources

Number Talk Images **http://ntimages.weebly.com/**

Subtraction Face-Off **https://blogs.sd38.bc.ca/sd38mathandscience/wp-content/uploads/sites/14/2020/05/SD38_Face_Off_Game.pdf**

Subtraction Track game by BoxCars (adapt from video to use with ten-sided or twelve-sided dice) **https://www.youtube.com/watch?v=E0K9hNl–sM**

Bunny Money by Rosemary Wells (picture book)

CGI Resources **https://blogs.sd38.bc.ca/sd38mathandscience/cgi-math/**

#### Key Number Concept 3: Addition and Subtraction to 100

##### Overview

In grade 2, students build on their understanding and strategies for adding and subtracting numbers to and within 20 from grade 1 to develop a variety of strategies to add and subtract two-digit numbers to 100. After beginning the year with a focus on building and representing numbers to 100 in different ways, addition and subtraction with two-digit numbers is introduced by the end of the first term. Two-digit addition and subtraction questions are initially presented horizontally so students focus on the whole numbers and not the “digits” and make sense of the quantities through estimating the sums and differences. **Number talks** (as a whole class or in small groups) is an essential practice for students to learn to explain their strategies and hear different strategies from their classmates. Many of these strategies can be done mentally and do not require students writing their computations on paper. Towers of ten Unifix cubes with additional cubes and base ten blocks (tens and ones) provide concrete support at grade 2 for the process of regrouping numbers when adding and subtracting two-digit numbers. The use of ten frames is also an essential visual support for the process of adding and subtracting two-digit numbers. Students develop their understanding of strategies such as decomposing and compensating. Students practice taking apart (example: decomposing using friendly numbers and compensating) and combining numbers in various ways which can also be considered regrouping (example 56+28 = 50+20+6+8=70+14=84). For subtraction strategies, students learn to use concrete materials for the process of removal (“take away”) or comparing quantities and number lines to compare numbers, to count back and to add on to find the difference (example 42-17 can be thought of as 17+3 to make 20 then add 20 to make 40 and add 2 to make 42 then compose those add ons to find the difference of 25). Students will have two or more strategies to solve two-digit addition and subtraction questions and may have a preference for strategies that make sense to them. Students apply their understanding of addition and subtraction to 100 through contextual problems such as Cognitively Guided Instruction (CGI) problem types.

**Please note**: The expectation is that students at grade 2 will have flexibility and fluency with multiple strategies for adding and subtracting numbers to 100.. Students may have learned the “traditional algorithm” from outside of school sources and this can be acknowledged when students share this method during a number talk but they are expected to have other strategies to add and subtract than this.

##### Number Sense Foundations:

The following concepts and competencies are foundational in supporting understanding of addition and subtraction to 100 in grade 2:

- Skip-counting by 1s, 2s, 5s, forward and back within 100
- Understanding making and bridging 10, including over decade numbers like 30 and 70
- Use of some flexible mental math strategies for adding and subtracting (ie counting on, comparing quantities)
- Reading and writing two-digit numbers
- Understanding the commutative property of addition (example: 5+3 = 3+5)
- Connecting number words, symbolic number and quantities in concrete forms
- Conceptualize numbers as whole numbers and units (what is ten more than 44?)
- Decomposing two-digit numbers into tens and ones
- Concrete, pictorial and symbolic representations of two-digit numbers
- Make reasonable estimates within 100

##### Progression:

Addition and Subtraction to 100

- Developing fluency with mental math strategies for adding and subtracting single-digit numbers (making ten, bridging over ten, decomposing, etc)
- Add single-digit numbers to a teen number to bridge over 20, for example, one way of adding 16 + 7 would be to decompose 7 into 3 and 4 so that 4 can be added to the 16 to make 20 and then add the 3 to the 20 to make 23
- Build numbers using concrete materials such as Unifix cubes in groups of tens and ones and base ten blocks (tens and ones) and compose and decompose considering place value (for numbers to 100); with materials, model the processes of addition and subtraction with two-digit numbers
- Add two-digit numbers using different strategies (start with questions written horizontally to allow students to decompose by place value for more flexible thinking), with students explaining and sharing their strategies such as decomposing and compensating using concrete materials such as base ten blocks or visual tools such as ten frames and an open number line
- Subtract two-digit numbers using different strategies (finding the difference, compensating) using concrete materials such as Unifix cubes and base ten blocks or visual tools such as ten frames or an open number line
- Demonstrate various ways to solve addition and subtraction problems to and within 100 using concrete, pictorial and symbolic forms.
- Use appropriate place value language when explaining their thinking and strategies.

##### Sample Week at a Glance

Before

Read Two of Everything by Lily Toy Hong, stopping to have students share their mental math strategies for calculating the number of items in the pot.

During

Problem-posing: Invite students to create their own doubling math stories using numbers between 10-100 and solve them using at least two different strategies.

After

Have students prepare their problem at their table/desk for others to solve via a gallery walk and stop to solve. Have students share some of the strategies they used for solving the problems. The teacher records the strategies on a whiteboard/ chart.

Before

Math Routine: **Number Talk/ String** (15-8=, 45-8=, 75-38=, include adding up to subtract as a strategy)

During

Math Workshop: Students choose learning experiences focused on the concepts of addition and subtraction.

–**Find Sums app** (100 grid focusing on complementary numbers)

–**Addition Face-Off** card game with three cards (adding a two digit and a one-digit number)

-Addition and subtraction question cards to solve on mini whiteboards or in notebooks.

Teacher led small group instruction: use of an open number line to represent mental math strategies for addition and subtraction questions.

After

Closing circle with students share what they did, what they learned and what they want to practice next.

Before

In table groups, have students discuss what their learning goals are for addition and subtraction.

During

Provide a selection of addition and subtraction questions on the whiteboard for students to choose from and invite students to investigate the concepts of addition and subtraction through materials. Offer: Unifix cubes, Cuisenaire rods, Numicon Shapes, Base Ten blocks, ten frames and counters, and drawing materials.

After

Closing circle: Using an artifact or record of learning, invite students to share what materials they used and how they helped them think about addition or subtraction in new ways. Invite students to reflect on what materials they would choose to support their learning.

Before

Math Routine: **Number Talk Images** (choose two or three images for students to discuss and teacher records +/- equations to represent their thinking)

During

Math Workshop: Students choose learning experiences focused on the concepts of addition and subtraction.

–**Find Sums app** (100 grid focusing on complementary numbers)

–** Subtraction Face-Off** card game with three cards (subtracting a one-digit number from a two-digit number)

–

**CGI**addition and subtraction question cards to inspire problem posing (record on mini-whiteboards or in notebooks)

Teacher led small group instruction: practicing addition and subtraction strategies (in response to formative assessment observations and discussions)

After

Closing circle with students share what they did, what they learned and what they want to practice next

Before

Math Routine: Number Talk/ String ( 17+5=, 57+5=, 67+25=)

During

CGI-based math stories: students choose addition or subtraction equation cards to inspire a math story based on the equation structure. Students are encouraged to use characters and materials to act out the mathematical actions and communicate their strategies to a partner as they tell their story.

After

Closing circle: Teacher has video-recorded some of the students’ math stories and shares them with the class to discuss strategy use and new ideas for math stories

##### Suggestions for Assessment

##### Suggested Links and Resources

Number Talks **https://www.youtube.com/watch?v=2osLQRH2HbQ**

Number Talk Images **http://ntimages.weebly.com/**

Find Sums app **http://www.mathtappers.com/2010/08/mathtappers-find-sums-free-app-designed.html**

Addition and Subtraction Face-Off **https://blogs.sd38.bc.ca/sd38mathandscience/wp-content/uploads/sites/14/2020/05/SD38_Face_Off_Game.pdf**

Cognitively Guided Instruction (CGI) resources: **https://blogs.sd38.bc.ca/sd38mathandscience/cgi-math/**

Two of Everything by Lily Toy Hong (picture book)