 ### 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.

### Key Concepts

#### Place value to 100

Building on students’ beginning understanding of place value in teen numbers(ten and some more), students build and represent numbers to 100 using tens and ones. Students may use materials like towers of ten Unifix cubes or base ten blocks (rods and units). Students compare and order numbers along a number line, using benchmarks such as 50.

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

Students are introduced to computational strategies for addition and subtraction facts to/within 20. Students apply their understanding of ten to practice mental math strategies such as bridging and making ten as well as using known facts to solve unknown facts.

#### Addition and subtraction to 100

Students begin to apply their understanding of place value to add and subtract two-digit numbers using strategies such as decomposing and compensating. Students add and subtract two-digit numbers using both mental math strategies and building and representing with concrete and visual materials.

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

##### Overview
Building on students’ beginning understanding of place value with the teen numbers in grade one (ten and some more), students build and represent numbers in different forms (concrete, pictorial and symbolic) to 100 (99) using tens and ones and are able to read and write two-digit numbers. At grade 2, students may hear the number “twenty-seven” and write 207 as they write the number the way they say it. This reveals a developing understanding of how the digit 2 in the number 27 represents 2 tens based on its place in the number. Grade 2 students build a sense of tens and ones by building sets of ten made of ten units such as bundling ten straws or popsicle sticks or stacking ten Unifix cubes together. After experiences with one-to-one concrete representations of tens and ones, students can begin to use more representational materials such as base ten blocks. Students in grade 2 compare and order numbers to 100 along a number line, using benchmarks such as 25 and 50. Students estimate quantities within 100. Students compose and decompose numbers to 100 flexibly and fluently, for example, by thinking of all the ways to make “57” using both place value understanding and other benchmark numbers. Students apply their understanding of place value when adding and subtracting two-digit numbers and related strategies.
##### 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

Two-Digit Face Off game

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?

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

Based on formative assessment information from this week, next week’s planning would include extending ways to represent two-digit numbers in different and more flexible ways, including expanded notation. Rekenreks or abacuses may be introduced as another way to think about place value and represent two-digit numbers.
##### Suggestions for Assessment
By the end of grade 2, students will be able to think about two-digit numbers flexibly and fluently. This would look like being able to represent and compose and decompose two-digit numbers in different ways using different forms (concrete, pictorial and symbolic) and order and compare two-digit numbers and explain their thinking and justify their choices. Students will be able to use materials like Unifix cubes and base ten blocks as well as ten frames and counters to represent two-digit numbers concretely. Routines such as choral counting, counting collections and clothesline help students to make connections between different representations of numbers, see patterns and practice symbolic notation of numbers and can be a rich source of observational assessment information – watch and listen as students engage in whole class or small group discussions using these routines.

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

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 this week of lessons, grade 2 students will have practiced and developed some strategies for subtraction to 20. Students will likely have had more experience with addition and might connect addition and subtraction strategies. This week focuses primarily on expanding students’ thinking of subtraction beyond “take away”.

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

Based on formative assessment information from this week, next week’s planning would include ways to practice and apply subtracting numbers within 20. Students will continue to develop strategies such as decomposing, compensating or adding on to find the difference. Contextual story/word problems are one way for students to apply their understanding. Have students share the problems they posed for others to solve. Students are encouraged to record their mathematical thinking in ways that are meaningful to them, but also understandable by someone who reads it.
##### Suggestions for Assessment
By the end of grade 2, most students will be able to use two or more flexible mental math strategies to add and subtract numbers to and within 20. Students can use strategies such as finding related doubles, bridging over 10, decomposing, finding the difference, and the commutative property and can share their thinking in multiple ways. Students can use their understanding of the relationship between addition and subtraction to think about computation to and within 20.

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

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:

• 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 this week of lessons, students have had many experiences with adding and subtracting two-digit numbers earlier in the school year. Students have at least one or two strategies they can use for addition and subtraction to and within 100. This week’s plan will focus on further developing students’ understanding and application of addition and subtraction to 100.

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
By the end of grade 2, students will be able to apply their understanding of place value of tens and ones to flexible strategies for adding and subtracting two-digit numbers. Students will be able to add and subtract two-digit numbers flexibly and fluently using both mental math strategies, using concrete materials, and recording with pencil and paper. Students will be able to use two or more strategies, use different forms (concrete, pictorial and symbolic), and justify their thinking. Strategies most students will be able to use for adding two-digit numbers include decomposing by place value, compensating and using benchmark numbers to add on using an open number line. For subtracting two-digit numbers, students will use both removal/take-away and finding the difference strategies and use strategies such as decomposing by place value, compensating and using adding on with an open number line to find the difference. All of these strategies focus on connecting place value understanding and number sense. Observe if students use mental math where appropriate as this demonstrates their growing number sense.