 ### Learning Story for Grade 1

Welcome to Grade 1! This year, students will extend their understanding of numbers to 10 into the teen numbers and up to 20. They will learn to see 10 as an important benchmark for counting, comparing, adding and subtracting. Through exploring and visualizing numbers and their part-whole relationships, students will develop understanding in seeing how numbers relate to each other, and how they can be broken apart (decomposing) and put back together (recomposing) in different ways. These important foundations of numbers to 20, including beginning to understand place value, are essential for the number concepts and operations (addition and subtraction) that will be developed in Grade 2 (up to 100) and beyond.

### Key Concepts

#### Counting and Estimating Numbers to 20

Students extend their counting to teen numbers, including sequencing, counting on and back, skip counting, and more. Students will engage in counting collections using a variety of counting materials and strategies, including estimation

#### Composing and Decomposing Numbers to 20

Students learn to build and to see numbers in terms of their part-whole relationships. Students will develop a beginning understanding of place value as they see 10 as a benchmark (eg. ten and some more).

#### Comparing and Ordering Numbers to 20

Students learn to compare and order numbers, including developing a sense of where these numbers exist on a number line in relation to other numbers. Students develop fluency with the number before/after and the concept of one/two more/less. An essential tool for comparing and ordering numbers is an understanding of how numbers to 20 relate to benchmark numbers (5, 10, 15, 20).

#### Adding and Subtracting Numbers to 20

Students are introduced to the different meanings of addition and subtraction, how these relate to each other, and how they are based upon part-whole relationships. These relationships form an important foundation as they start to develop mental math strategies.

#### Key Number Concept 1: Counting and Estimating Numbers to 20

##### Overview
Counting is important because it tells us how many or how much. It goes beyond saying a count sequence to developing a sense of quantity and how numbers relate to each other. Estimating helps students reason about quantity and develop the concept of about how many or how much. In Grade One, students build from their understanding of numbers to 10 to explore numbers to 20. Students begin by counting by ones, and then by groups (2s and 5s) as they move towards understanding place value.
##### Number Sense Foundations:

The following concepts and competencies are foundational in developing understanding of counting in Grade One:
number sequence to 10

• subitizing (recognizing a quantity up to 5 without counting)
• one-to-one correspondence (each object in a collection is counted once)
• cardinality (understanding the last number you say answers the question how many)
• representing quantities using numerals
• applying number sequence to recognize quantities one more or one less than a set without recounting (eg. student recognizes that adding one more to a collection of 5 objects is now 6 objects without recounting)
• visualizes numbers to 10 on a ten frame (recognize amount at a glance)
• understands numbers in context (eg. in a classroom, 6 is a lot of elephants, but a small number of students)
##### Progression:

Throughout this progression, students engage in estimation, and counting verbally, concretely (counting objects), and symbolically (representing their counts using numerals, eg: 12 sticks).

• Number sequence (rote counting) to 20 (forward, then back)
• Applying the number sequence to counting collections of objects, starting with making a range estimate (eg: less than 10, greater than 5)
• Counting on from a known number
• Counting back from a known number
• Skip counting to 20 by 2s and 5s
• Makes reasonable estimates around benchmarks (eg. about 15)
• Use grouping strategies (of 2s and 5s) to count collections
• Ten and some more (beginning understanding of place value), including unitizing ten as one ten (filled ten frame, base-ten rod, a dime).
##### Sample Week at a Glance:
Students are already comfortable counting by 1’s, and they know the count sequence to 20. During this week, they begin a transition to counting by groups (2’s and 5’s) as a more efficient strategy, making sure to always estimate before counting. Students also practice verbal counting by 1’s from one number to another (forward and back).

Before

Read a counting book such as How Many Snails by Paul Giganti and invite students to share how they might count the items on the different pages

During

Counting Collections between 10 and 50 (only assess to 20). Include estimation of quantity.

After

Closing Discussion:

Ask students to share how they counted and what they noticed about their estimates.

Before

Instructional routine (Count Around the Circle): Count forward and back (by 1’s) around the circle with different start and end points

Independent practice where students count up and back from a number symbolically (eg. __, __, 9, __, __)

During

Count around the circle(skip count) Introduce counting forward and back by 2’s by having 1st, 3rd student (for example) whisper their number, while 2nd, 4th, … students say their number out loud

Independent practice where students count by 2’s up and back from a number symbolically (eg. __, __, 8, __, __)

After

Closing Discussion:Ask students what patterns they notice when they count by 2’s and how counting by 2’s is different from counting by 1’s

Before

Formally introduce counting by 2’s and 5’s by asking students how they might count the number of shoes in the class or how much money 6 nickels would be.

During

– counting quantities by 2’s that are naturally paired (toonies, skates, wings)

– counting quantities by 5’s that are naturally paired (nickels, fingers on a hand, tallies)

– activity cards or counting books where students can practice counting by 2’s and 5’s and recording their responses.

After

Closing Discussion: Is counting by groups helpful or easier than counting by 1’s? Why or why not?

Before

Instructional routine: Day 006 – Estimation 180 How many almonds in the cup? Invite students to provide a range estimate and then discuss how they might count the almonds – by 1s, 2s, 5s?

During

Math workshop:

-counting quantities by 2’s and 5’s, allowing students to decide whether to count by 2’s or 5’s.

-counting collections, including opportunity to estimate first

-symbolic counting from one number to another by 1’s, 2’s, and 5’s

After

Closing Discussion:

What did you learn today? What do you still need to practice?

Before

Read How Many Snails again but this time invite students to use more sophisticated counting strategies.

During

Invite students to create their own counting picture and once finished, exchange with a partner to estimate and count.

After

Closing Discussion: Ask students what they have learned this week about counting, and if their thinking about counting has changed since the beginning of the week.

This week is about the transition from counting by 1’s to counting by groups. After this week and throughout the year, students should have regular practice counting and skip-counting, both of quantities and verbally, from different start and end points.
##### Suggestions for Assessment
What to look for – by the end of grade 1, students will be able to verbally count forward and backward within 20. They will also be able to estimate and count quantities from one, or count on from a given number. Students will be able to skip-count by 2’s and 5’s.

#### Key Number Concept 2: Composing and Decomposing Numbers to 20

##### Overview
Composing and decomposing numbers is essential for understanding how numbers relate to each other, and forms the basis for most strategies for whole number operations. Students will engage in many experiences of building numbers and recognizing their part-whole relationships. Ten frames are a particularly important tool for building and representing numbers as they clearly illustrate how numbers relate to the benchmarks of 5, 10, 15, and 20.
##### Number Sense Foundations:

The following concepts and competencies are foundational in developing understanding of composing and decomposing numbers to 20 in Grade 1:

• Different ways to make ten
• The count sequence
• One-to-one correspondence
• Counting on and counting back
##### Progression:
• Use materials to build a number by counting from one
• Use materials to build a number by counting forward or back from a given number
• Use materials to build a number by counting by 2s or 5s
• Use materials to represent numbers in different ways
• Recognize different part-whole relationships within a number (Being able to see a number in terms of its parts eg. 6 can be 4 and 2 or 5 and 1)
• Use materials to compose and decompose even numbers using doubles
• Use materials to identify the unknown part of a number (given whole and one part, what is the other part?)
• Understand equivalence of different part-whole relationships (eg. given 12 as 7 and 5, move one from the 5 to get 8 and 4)
• Use this equivalence to express teen numbers as ten and some more
• Develop fluency of parts that make ten (eg. 8 and 2, 6 and 4, etc)
##### Sample Week at a Glance
At this point in the year, students will have had many counting experiences – counting by 1’s, counting on and back, and skip-counting.

Before

Instructional Routine: Ways to Make a Number

Invite students to represent a number up to 20 in as many ways as they can (ten-frame, tally marks, equations, base ten blocks, coins, etc.)

During

Discuss the different representations students used, and introduce a part-part-whole representation if it didn’t already come up. (eg. 16 can be 8 and 8 or 10 and 6)

Materials Investigation:

Cuisenaire Rods

Hand each pair of students a set of Cuisenaire Rods and give them some time to explore. Ask them what they notice and what they wonder. Invite students to assign a value to each rod, given that the smallest is 1.

After

Closing discussion: do students see any possible connection between the two activities?

Before

Instructional Routine: Ways to Make a Number

Invite students to represent a number up to 20 in as many ways as they can (ten-frame, tally marks, equations, base ten blocks, coins, etc.)

During

Materials Investigation (cont’d)

Distribute Cuisenaire rods to pairs of students again. Ask students to make one rod with two other rods in as many ways as they can, and record their work using different representations (part-whole diagram, equation, and partitioning scale diagrams of the rods). Try this with several different rods. Ask questions like, what rod would I need to pair with a white rod to make a purple rod?

After

Closing Discussion: ask students what this has taught them about the number 9 for example.

Before

Number Talk: How many different ways can you make 12?

During

– Ways to make a number routine

– More practice composing and decomposing numbers with Cuisenaire Rods

– part-whole centre where students have to fill in the missing component in a part-whole card (students can use Unifix cubes or other materials for this)

After

Ask students if the math workshop gave them any new ideas about how to decompose numbers. Try doing the same number talk except with a different number to see if strategies are different.

Before

Math journal: Story problem involving part-whole relationships. Provide part-part-whole template for students to fill in.

During

Instructional Routine: Same but different. Give students one whole, with two part-part representations and ask them what is the same and what is different (eg. 13 as 10 and 3 or 6 and 7). Invite students to write different part-whole representations of different numbers.

After: Discussion about what students noticed or learned from the routine.

Before

Instructional routine: Quick images. Give students part-part-whole template in a page protector and a dry erase marker. Show students several different two-coloured dot plates for a few seconds each (Van de Walle) and for each one, have them complete the template. Begin with small quantities and build up.

During

Math workshop:

-Bears in a Cave

-Missing part cards (Van de Walle)

-”I wish I had” (Van de Walle)

After

Closing: Have a discussion with a partner about what you learned this week and where you want to go next with your learning.

The next step after students become comfortable with part-part-whole relationships is practicing the pairs that make 10 and then decomposing and recomposing parts of a whole to make one part a ten. For example, 8 + 5 can be changed to 10 + 3.
##### Suggestions for Assessment
What to look for – by the end of grade 1, students will be able to recall the pairs that make 10, represent numbers to 20 in different ways (tally marks, ten-frames, base-ten blocks, part-part-whole diagrams), and identify (with materials or diagrams) the missing part or whole in a part-part-whole relationship.

#### Key Number Concept 3: Comparing and Ordering Numbers to 20

##### Overview
Being able to compare and order numbers is a critical component of number sense as it helps students come to see the structure of our number system as well as how numbers relate to each other. In Grade 1, students learn to compare and order numbers, including developing a sense of where these numbers exist on a number line in relation to other numbers. Students also start to develop fluency with the numbers before/after and the concept of one/two more/less. An essential tool for comparing and ordering numbers is an understanding of how numbers to 20 relate to benchmark numbers (5, 10, 15, 20). For example, knowing that 17 is between 15 and 20 or that 9 is one less than 10.
##### Number Sense Foundations:

Foundational, supporting concepts and related competencies that are needed to develop this grade level concept

• The count sequence to 20
• Comparing and ordering within 10
##### Progression:
• Recognize which of two numbers is larger/smaller within 20
• Put a series of numbers (within 20) in ascending or descending order
• Say which number is one/two more/less than a given number
• Say how much bigger or smaller one number is than another
• Place numbers within 20 on an open number line up to 20 and space accordingly
##### Sample Week at a Glance
Before this week, students will have had many experiences counting and estimating. They also would have had the opportunity to learn how to represent numbers to 20 in different ways.

Before: Present collections of different-sized objects to the class and have them decide which collection is more or less or if they are the same size. Then discuss how they could decide how many more/less.

Instructional Routine: Quick images: show students two dot plates and/or ten-frames for a few seconds and ask them which one has more dots and how they know.

Instructional Routine: Clothesline number line

(0-20 cards with different representations)

Provide students with empty number lines from 0 to 20. Have them work with a partner to place a selection of numbers on the number line.

Closing: Have students share what they learned from the two number line activities.

Before: Circle activity: teacher places three baskets labeled more, less, and same in the centre of the circle and then invites one student to choose a number between 1 and 20 (although numbers between 5 and 15 work best). Students are each given a few 1-20 number cards (different representations) and invited to take turns putting them in the correct basket.

Students play a partner card game where they each flip over a card from the deck (A to 10 only) and they take turns saying how much larger/smaller one number is than the other. So if a 7 and a 4 are flipped, one student might count on and notice that 7 is 3 more than 4. Students can also use the quantities shown on the cards to compare.

Closing: Have students share one thing they learned from the two activities.

Instructional Routine: Clothesline number line (same as Tuesday)

Math workshop:

-1-2 more/less activity with 1-20 cards showing different representations

-Play Fill the Stairs (1-20)

-Roll and place: students take turns rolling two 10-sided dice and then placing the total on an open number line. The goal is to order the numbers correctly and space them appropriately.

Closing: Discuss which of the math workshop stations students found difficult and why.

Before: Circle activity: teacher places three baskets labeled more, less, and same in the centre of the circle and then invites one student to choose a number between 1 and 20 (although numbers between 5 and 15 work best). Students are each given a few 1-20 number cards (different representations) and invited to take turns putting them in the correct basket.

Play Build and Change: Students flip over two cards (from 1-20) and build each number with snap cubes. They then describe to a partner how to get from one number to the other (eg. if the numbers are 8 and 11, build 8 and add 3 blocks)

Closing: Ask students what activity they liked best from the week and what they learned from it.

The next step for students would be learning addition and subtraction.
##### Suggestions for Assessment
What to look for – by the end of this grade 1, students will be able to compare and order numbers, visualize to place numbers to 20 on a number line in relation to other numbers, recall the numbers before/after or one/two more/less than a given number. Students will be able to explain or show how numbers to 20 relate to benchmark numbers (5, 10, 15, 20). For example, knowing that 17 is between 15 and 20 or that 9 is one less than 10.

Marc Garneau’s number representation cards (for Clothesline Math): https://clotheslinemath.com/

#### Key Number Concept 4: Adding and Subtracting Numbers to 20

##### Overview
Developing a deep conceptual understanding of the meaning of addition and subtraction is complex and takes time. Grade 1 is the beginning of this journey for students. Students are exposed to different types of addition and subtraction applications, and begin to recognize what types of situations relate to what operations. Students also begin to develop their repertoire of mental math strategies. In Grade 1, students learn to use and name some initial strategies, but are not yet expected to use them fluently.
##### Number Sense Foundations:

The following concepts and competencies are foundational in supporting understanding adding and subtracting numbers to 20 in Grade 1:

• Counting sequence to 20 forward and back
• Composing/decomposing numbers to 20 (part-part-whole)
• Recognizing pairs that make ten
• Understanding meaning of doubles and developing familiarity
##### Progression:

Throughout this progression, students begin making sense at a concrete level with materials as symbolic representations are introduced, then gradually develop understanding of pictorial representations like a number line and mental math strategies.

• Experience meanings of addition and subtraction problems (joining, separating, part-part-whole, comparing) by modeling concretely. Symbolic notation is introduced.
• Make connections between addition and subtraction (eg. fact families)
• Develop strategies for addition and subtraction to 20 initially by modeling concretely, then building towards pictorially (eg. number line) and mental math strategies:
• Counting on, counting back
• Counting on/back from a known fact
• Making tens
• Using doubles, then one away from a double
##### Sample Week at a Glance
Focus this week: making ten to add; addition (joining) story problems and using the making 10 strategy to solve the story problem.

Pairs that Make Ten

Show students a ten-wand made using multi-link cubes (5 of one colour connected to 5 of another colour). Pretend you’re clumsy and ‘accidentally’ break it. Show the two parts and ask the class what they notice. They should notice the two parts that make ten (eg. 7 and 3), but also notice that the 7 is 2 more than 5 and perhaps that the 3 is 2 less than 5.

Have the class make their own ten wands, and ask them to explore different ways they can ‘break’ their wand into two parts. Ask them to record what they discovered using pictures and numbers.

Share, discuss, and record the different pairs of numbers that make ten, then re-arrange them in order (ie. 1+9, 2+8, …). Ask the class if they see any connections between these. For example, they may notice that they can change one pair into another by moving one cube from one part to the other.

Number
String: Using Ten

Use two magnetic ten frames (or draw them on a white board), and write the expression 10 + 4. Ask the class how you could model the sum using the ten frames (ie. fill one frame and put 4 counters in the other), and ask what is the sum and how they know.

Number strings are a series of expressions which are intended to develop a concept. They are presented and thought about one at a time, and each stage connects to the previous stage, but pushes the thinking further.

Provide double ten-frames and counters for pairs of students. For each problem in the number string below, ask them to build, model, and record the sum, then have a class discussion. Encourage them to build each new expression from the previous one rather than starting over each time.

6 + 10

10 + 6

9 + 7

8 + 8

8 + 7

Share and discuss how 10 (a full ten frame) was helpful to think about for each expression.

Before: Do a numberless word problem as a class (join type) to think about meaning of story problem before working with numbers

Students practice join problems using ten-frames

Closing: Can students come up with a joining story problem and share it with the class?

Before: Do a numberless word problem as a class (join type) to think about meaning of story problem before working with numbers

Number Talk: Invite students to solve a joining story problem. DIscuss strategies and see if anyone made 10 to add.

Math Workshop:

• Students are given a collection of numberless word problems and have to determine which of them are joining problems. Students can then insert their own numbers and solve.
• Students practice making 10s to add using ten-frames
• Students work with ten-wands to practice the pairs that make 10

Closing: Have a discussion about what students learned about story problems this week and how 10 can help them solve the problems.

In the following weeks and months, students will develop more familiarity with making ten to add and story problems, including:

• More problem types
• Explore the strategy using a number line
• Develop it as a mental math strategy
• Make decisions about when it is a useful strategy in comparison to other strategies

They will also continue exploring and developing other strategies as they build understanding at a concrete level towards number line representations and mental math.

##### Suggestions for Assessment
What to look for – by the end of grade 1, students will be able to identify what operation to use given a story problem. They will be able to use a variety of tools to add and subtract (number lines, ten-frames, base ten blocks), and they will be able to name, describe, and use a variety of mental math strategies including near doubles, and making/bridging 10 to add/subtract.