EM2 TEACH Level 1 Module 1 Lesson 1 Thin Slice

1 A Story of Units® Units of Ten

What does this painting have to do with math?

American realist Edward Hopper painted ordinary people and places in ways that made viewers examine them more deeply. In this painting, we are in a restaurant, where a cashier and server are busily at work. What can you count here? If the server gave two of the yellow fruits to the guests at the table, how many would be left in the row? We will learn all about addition and subtraction within 10s in Units of Ten.

On the cover

Tables for Ladies, 1930

Edward Hopper, American, 1882–1967

Oil on canvas

The Metropolitan Museum of Art, New York, NY, USA

Edward Hopper (1882–1967), Tables for Ladies, 1930. Oil on canvas, H. 48 1/4, W. 60 1/4 in (122.6 x 153 cm). George A. Hearn Fund, 1931 (31.62). The Metropolitan Museum of Art. © 2020 Heirs of Josephine N. Hopper/Licensed by Artists Rights Society (ARS), NY. Photo credit: Image copyright © The Metropolitan Museum of Art. Image source: Art Resource, NY

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ISBN 978-1-64497-155-0

Module 1 Counting, Comparison, and Addition

2 Addition and Subtraction Relationships

3 Properties of Operations to Make Easier Problems

4 Comparison and Composition of Length Measurements

5 Place Value Concepts to Compare, Add, and Subtract

6 Attributes of Shapes · Advancing Place Value, Addition, and Subtraction

Before This Module

Overview

Kindergarten Module 3

In kindergarten, students compare the number of objects in a set using language such as more than, fewer than, and the same as. They compare numbers to 10 using language such as greater than, less than, and equal to.

Kindergarten Module 5

Kindergartners represent composition and decomposition situations using number bonds and number sentences. They solve add to with result unknown and put together with total unknown problem types.

Kindergarten Module 6

At the end of kindergarten, students decompose teen numbers as ten ones and some more ones and write the decomposition as a 10+ fact.

Counting, Comparison, and Addition

Topic A

Count and Compare with Data

Data contexts provide natural opportunities for counting. Students collect data by answering questions, sorting sets, and making observations. They create bar graphs, picture graphs, and tally charts to visually represent the data. As students count to find totals and visually compare quantities, they recognize that linear organizations are useful. Students compare what they see using language such as more than, fewer than, and equal to, and represent these statements numerically using the symbols >, <, and =. Number paths and tally marks provide students opportunities for counting on from 5.

There are 14 bears.

There are more medium bears than small bears.

6 > 4

There are fewer large bears than medium bears.

4 < 6

The number of small and large bears is equal.

4 = 4

Topic B

Count On from a Visible Part

Students progress from finding totals by using the Level 1 strategy of counting all objects to using the Level 2 strategy of counting on from a known part. At first, objects are shown as two parts, such as the dots that appear on a pair of dice. Students choose a part they know, or can subitize, without counting one by one. They begin the count by naming the known part and then keep counting the objects in the second part to find the total:

Fooouuur, 5, 6, 7, 8, 9, 10. Students advance to counting on from a part embedded within a total. For example, given a collection of apples, students represent two parts (4 apples and 6 apples) and the total (10 apples) by using number bonds and number sentences. They realize they can count on from either part and get the same total.

Fooouuur, 5, 6, 7, 8, 9, 10

Topic C Count On to Add

Now students count on to find totals for expressions (e.g., 4 + 6) rather than for sets of countable objects. Because the parts are no longer presented as sets of objects that can be counted, students must hold the first addend in mind and count on the second addend by tracking with fingers. Students experiment with counting on from both numbers by using a number path to determine the efficiency of starting with the larger addend. Recognizing this efficiency and knowing that starting with either addend results in the same total, students begin to find totals by strategically counting on from the larger part. Students also look for patterns when adding 0 and 1.

Topic D

Make the Same Total in Varied Ways

This topic deepens understanding about the meaning of the equal sign, which earlier topics introduced through data and counting on. Students recognize that the expressions on both sides of the equal sign have the same total. In this topic, students reason about more complex number sentences to determine whether they are true or false. For example, 4 + 6 = 8 + 2 is true because 4 + 6 = 10 and 8 + 2 = 10. This work leads to decomposing numbers and finding the partners for each (e.g., 10 is 1 and 9, 2 and 8, 3 and 7, 4 and 6, etc.). Their burgeoning number sense allows students to decompose addends to make equivalent, often easier, problems.

After This Module

Grade 1 Module 2

Graphs provide context for adding to find the total of all the data points.

Students use counting strategies from this module to find unknown addends and to subtract.

Grade 1 Module 3

With Level 1 and Level 2 strategies well established in the first modules, module 3 focuses on Level 3 strategies that involve making easier problems. To access Level 3 strategies such as make ten, students practice

• decomposing numbers 5 through 9,

• finding the partner that makes 10 for any number,

• developing fluency with 10 + n facts, and

• working with three addend expressions.

Grade 1 Module 4 and 5

Students will use number paths as a measuring tool. They will also use >, <, and = symbols to compare measurements.

Students will use familiar >, <, and = symbols to compare two-digit numbers by using place value concepts.

total number of data points

compare categories in a picture graph.

Make the Same Total in Varied Ways

Organize, count, and record a collection of objects.

Why

Counting, Comparison, and Addition

What are the 3 counting levels?

Students in K–2 advance through three strategy levels as they count, add, and subtract. All levels are valid strategies. However, each next level offers greater efficiency for problem solving.

• Level 1, Direct Modeling by Counting All or Taking Away: Students represent problems with groups of objects, fingers, or drawings. They model the action by composing or decomposing groups and then they count the result.

• Level 2, Counting On: Students count to solve, but they shorten the process of counting by starting with the number word of one part. They use different methods, such as fingers, to keep track of the count.

• Level 3, Convert to an Easier Equivalent Problem: Students work flexibly with numbers. They decompose and compose parts to create equivalent, easier problems.

What stages do students move through as they develop skills with counting on?

Counting on is foundational to more efficient addition strategies, mastery of facts within 20, and finding an unknown part. It takes practice for students to trust that counting all and counting on strategies each produce the same total. Several complexities are involved:

• When presented with two parts composed of discrete objects, students intuitively count the objects to find the total. Rather than count all the objects starting at 1, they subitize one part and say how many (the quantity). Then they point to each object in the second part to count on. They understand that the last number stated is the total. They recognize that counting on is addition, recording the parts and total in number bonds and number sentences.

• When given one set of discrete objects, students will subitize an embedded part and count on to find the total. Students may point to the remaining objects as they count on, or they may begin to use their fingers to keep track. Students begin to realize that they can count on from either part and get the same result.

• When presented with an addition expression, students state the first addend (possibly by making a fist). Then they count on the second addend, tracking with fingers. They stop when the number of fingers is the same as the second addend. The last number said is the unknown total.

• Students first experience using one hand to count on, when the addend is 5 or less, and using two hands to count on when the addend is 6 through 9.

• Students will see that the sums are the same, or equal, when counting on from either addend. They use number paths to show that counting on from the larger addend is more efficient. Finally, they choose to count on from the larger addend by thinking of 8 + 4 when presented with 4 + 8.

Which word problem types, or addition and subtraction situations, are used in this module?

The table shows examples of addition and subtraction situations.1 Darker shading in the table indicates the four kindergarten problem types. Students in grades 1 and 2 work with all problem types. Grade 2 students reach proficiency with the unshaded problem types.

Grade 1 students revisit the following problem types that were mastered in kindergarten. However, in grade 1, the problems may use numbers within 20 (not just within 10) and students solve them by using Level 2 and Level 3 strategies.

• Add to with result unknown: Both parts are given. An action joins the parts to form the total.

Hope has 7 rocks. She adds 3 more rocks. How many rocks does she have now? (Lesson 13)

• Put together/take apart with total unknown: Both parts are given. No action joins or separates the parts. Instead, the parts are distinguished by an attribute such as type, color, size, or location.

5 markers are in the box. 3 markers are out of the box. How many markers are there in all? (Lesson 7)

• Put together/take apart with both addends unknown: Only the total is given. Students take apart the total to find both parts. This situation is the most open ended because the parts can be any combination of numbers that make the total.

There are 5 dogs. What are all the ways they can be inside the house or out in the yard? (Lesson 18)

Students are invited to solve word problems intuitively. Each lesson presents an accessible problem that can also be extended. Some students may directly model all components of the problem with manipulatives or by drawing. Others may use their fingers, a number path, or drawing to count on from one part. This variety is important because it presents an opportunity for students to discuss their reasoning.

Teachers use students’ thinking to advance the class toward the objective. They watch how students solve the problem, select work to share, and ask questions that engage the class in others’ thinking. Observations about how students use counting on in these lessons may be useful for preparing to teach topics B and C. The Read–Draw–Write problem-solving routine begins in module 2.

Why is lesson 25 optional?

Students count a collection of objects in lesson 25. Counting collections lessons engage students in self-directed learning and provide opportunities for informal assessment. This lesson can be used in the module when the timing best meets the needs of the class. Note that counting collections lessons require preparation. Make sure to read the Lesson Preparation in advance.

Counting collections are best used as a frequent routine, as students benefit from opportunities to internalize the procedure, choose new collections, and try new counting strategies. They will be included in future lessons, however, consider doing them more often as time allows.

Why does this module include time?

Lesson 17 briefly introduces telling time to the hour. This initial exposure provides a starting place for ongoing informal practice before module 4, where telling time to the hour and to the half hour are directly addressed. Beginning with lesson 17, consider

• periodically pausing the class at the top of an hour to ask what time it is, and • pointing out the time when events regularly happen on the hour, such as lunch at 12:00 or dismissal at 3:00.

Achievement Descriptors: Overview

Counting, Comparison, and Addition

Achievement Descriptors (ADs) are standards-aligned descriptions that detail what students should know and be able to do based on the instruction. ADs are written by using portions of various standards to form a clear, concise description of the work covered in each module.

Each module has its own set of ADs, and the number of ADs varies by module. Taken together, the sets of module-level ADs describe what students should accomplish by the end of the year.

ADs and their proficiency indicators support teachers with interpreting student work on

• informal classroom observations (recording sheet provided in the module resources),

• data from other lesson-embedded formative assessments,

• Exit Tickets,

• Topic Tickets, and

• Module Assessments.

This module contains the nine ADs listed.

1.Mod1.AD1

Apply the commutative property of addition as a strategy to add.

1.Mod1.AD2

Count on to find the total number of objects in a set and represent the total with an addition number sentence.

1.Mod1.AD3

Add within 20 by using strategies such as counting on or by creating an equivalent but easier problem.

Add fluently within 10.

Fluently decompose totals within 10 in more than one way.

Determine whether addition and/or subtraction number sentences are true or false.

Count on from 10 to find totals between 11 and 19.

Compare category totals in graphs by using the symbols >, =, and <.

Organize and represent data with up to three categories and write how many are in each category.

The first page of each lesson identifies the ADs aligned with that lesson. Each AD may have up to three indicators, each aligned to a proficiency category (i.e., Partially Proficient, Proficient, Highly Proficient). While every AD has an indicator to describe Proficient performance, only select ADs have an indicator for Partially Proficient and/or Highly Proficient performance.

An example of one of these ADs, along with its proficiency indicators, is shown here for reference. The complete set of this module’s ADs with proficiency indicators can be found in the Achievement Descriptors: Proficiency Indicators resource.

ADs have the following parts:

• AD Code: The code indicates the grade level and the module number and then lists the ADs in no particular order. For example, the first AD for grade 1 module 1 is coded as 1.Mod1.AD1.

• AD Language: The language is crafted from standards and concisely describes what will be assessed.

• AD Indicators: The indicators describe the precise expectations of the AD for the given proficiency category.

• Related Standard: This identifies the standard or parts of standards from the Common Core State Standards that the AD addresses.

1.Mod1.AD3 Add within 20 by using strategies such as counting on or by creating an equivalent but easier problem.

RELATED CCSSM

1.OA.C.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows that 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Partially Proficient Proficient Highly Proficient

Add within 20 by representing with objects or a drawing and counting all

Add. Show how you know.

7 + 5 = 12

1.Mod1.AD4 Add fluently within 10.

RELATED CCSSM

Add within 20 by counting on Add. Show how you know.

7 + 5 = 12

I started with 7 and counted on with my fingers: Sevennnn, 8, 9, 1 0 , 1 1, 1 2

Add within 20 by creating an equivalent but easier problem

Add. Show how you know.

Related Standards

1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows that 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Partially Proficient Proficient Highly Proficient

Add fluently within 5. Add. 2 + 3 =

Add fluently within 10. Add. 3 + 6 =

Copyright © Great Minds PBC

AD Indicators

Topic A Count and Compare with Data

Topic A gives students a chance to extend their kindergarten counting and comparing skills within real-life data contexts. These lessons provide opportunities for students to mathematize their world.

Students collect data by sorting sets, making choices, and tracking observations. They represent their data by using cubes, colored number paths, symbols, and tally marks. Students come to see that each piece of data can be represented by an object or mark. They also have opportunities to express which representations are most helpful to collect, represent, and interpret data.

As students interpret data, they see that organizing helps them find totals and compare categories. Students ask and answer questions such as How many animals are in the park? or Do more children ride the bus or walk to school? To answer, they may compare data by noticing that one category is longer than another or that there are “extras.” They may also compare numerically by noticing which total is greater.

At first, students use everyday words to share what they notice about the totals, and then they transition to more formal comparison terms. Finally, they connect the terms to the comparative symbols >, <, and =. Students write numbers to complete number sentence frames that use these symbols.

Students will progress from counting all to counting on to add in topic A and topic B. Representations such as the number path and tally marks, which use 5-groups, support the transition throughout topic A.

Comparison concepts are revisited later in module 1 as students explore equality; in module 2 when students find how many more; and in module 5 when students use place value reasoning.

Please note that lessons 1, 3, and 5 include sets of objects that students count. They require advance preparation, as described in the materials section of each lesson.

Progression of Lessons

Lesson 1

Organize to find how many and compare.

Lesson 2

Organize and represent data to compare two categories.

Lesson 3

Sort to represent and compare data with three categories.

Organizing on a number path helps me count and compare.

I see my choice on the graph! More of us like to listen to music.

I can tell there are more blue cubes than red cubes. 8 is greater than 4.

Lesson 4

Find the total number of data points and compare categories in a picture graph.

Lesson 5

Organize and represent categorical data.

Lesson 6

Use tally marks to represent and compare data.

I counted the checkmarks to find out that there are 12 butterflies. There are the same number of small butterflies and large butterflies, 3 = 3.

Look! I have 41 cubes. I sorted them by color. I chose to show my collection by coloring a graph.

Tally marks show groups of 5. There are 5, 6, 7, 8, 9 animals! There are fewer stop signs than bridges, 6 < 9.

Name

Count out 8 cubes

Color how many cubes.

Organize to find how many and compare.

Lesson at a Glance

Students explore ways to organize by counting a set. With guidance, they organize their set on a number path. Students compare and reason about the totals on the number path and discover the usefulness of linear organization. Finally, they use color to represent and compare sets on number paths.

Key Question

• How can we show objects so they are easy to count and compare?

Achievement Descriptor

Count out 6 cubes.

Color how many cubes.

This lesson is foundational to the work of grade 1 and builds from K.CC.C.6 and K.CC.C.7. Lesson content is intended to serve as a formative assessment and is therefore not included on summative assessments in grade 1.

Agenda Materials

Fluency 10 min

Launch 5 min

Learn 35 min

• Count a Set

• Organize to Count and Compare

• Problem Set

Land 10 min

Teacher

• 20-bead rekenrek

• Unifix® Cubes (16)

• Large number path

• Teacher computer or device*

• Projection device*

• Teach book*

Students

• Bag of Unifix® Cubes

• Large number path

• Pencil*

• Learn book*

• Personal whiteboard*

• Dry-erase marker*

• Whiteboard eraser*

* These materials are only listed in lesson 1. Ready these materials for every lesson.

Lesson Preparation

• Gather 16 Unifix Cubes: 7 of one color and 9 of a different color.

• Assemble one bag of 10–15 Unifix Cubes per student. Vary the number in each collection, but make sure that each bag contains only one color.

• Write a sentence frame for display: is greater than .

Fluency

Counting on the Rekenrek by Ones Within 5

Materials—T: Rekenrek

Students count by ones to prepare for work with the number path.

Show the rekenrek with the side panel attached. Start with all the beads behind the panel.

Say how many beads there are as I slide them over.

Slide the red beads from behind the panel, one at a time, as students count to 5. 1, 2, 3, 4, 5

Slide the red beads back behind the panel, one at a time, as students count down to 0. 5, 4, 3, 2, 1, 0

Watch closely! Say how many beads there are as I slide them over.

Slide the red beads, one at a time, to the left or to the right in the following sequence as students count:

Continue counting on the rekenrek within 5. Change directions occasionally, emphasizing where students hesitate or count inaccurately. Invite play and promote focus by varying the pace or inserting dramatic pauses.

Ready, Set, Compare

Students compare values within 5 to prepare for comparing quantities by using the number path.

Let’s play Ready, Set, Compare. Have students form pairs and stand facing each other.

Model the action: Make a fist, and shake it on each word as you say, “Ready, set, compare.” At “compare,” open your fist, and hold up any number of fingers.

Tell students that they will make the same motion. At “compare,” they will show their partner any number of fingers. Consider doing a practice round with students.

Clarify the following directions:

• To show zero, show a closed fist at “compare.”

• Showing more fingers is not a win.

• Try to use different numbers each time to surprise your partner.

“I’m showing more fingers.” “4 is greater than 2.”

Each time partners show fingers, have them compare amounts. They might say, “I’m showing more fingers,” “I’m showing fewer fingers,” or “We’re showing the same number of fingers.” See the sample dialogue under the photograph.

Invite partners to use the word greater. For example, “ is greater than .”

Circulate as students play the game to ensure they are trying a variety of numbers within 5.

Differentiation: Support

If students need support with comparing, they can use the one-to-one matching strategy of touching fingertips to compare their numbers.

Consider also having students say their counts as they touch fingertips so that they experience the greater number being said last.

Launch

Students recognize that organizing objects is useful for comparing the size of groups.

Gather students and display the scattered yellow bears and blue bears.

I will show you yellow bears and blue bears. See if you can tell just by looking whether there are more yellow bears or more blue bears.

Show the bears only for a few seconds.

Facilitate a brief discussion by using questions such as the following:

• Are there more yellow bears or blue bears?

• Is it easy or hard to tell which group has more? Why?

Repeat with the rows of blue bears and yellow bears.

Then display the scattered bears and rows of bears side by side.

Language Support

Consider using strategic, flexible grouping throughout the module.

• Pair students who have different levels of mathematical proficiency.

• Pair students who have different levels of English language proficiency.

• Join pairs of students to form small groups of four.

As applicable, complement any of these groupings by pairing students who speak the same native language.

Draw attention to the usefulness of organization by asking the following question. Is it easier to compare the bears in the first picture or in the second? Why?

It is easier in the second picture, because there are extra yellow bears on the bottom line.

Revoice the correct answer using the term organize in your response. The second picture makes comparing easier, because the bears are organized or lined up.

Transition to the next segment by framing the work. Today, we will organize Unifix Cubes to help us count and compare.

Learn Count a Set

Materials—S: Bag of Unifix Cubes

Students explore ways to organize and count a collection.

Distribute a bag of cubes to each student, and prompt them to count the items in their bags. Tell students that mathematicians take their time. Provide limited guidance so that you may circulate and informally assess the following counting behaviors:

• Do students show one-to-one correspondence (say one and only one number word per cube)?

• Do students understand that the last number said when counting is the total?

• Do students organize their count in some way?

• Do students say the counting sequence fluently?

Identify two or three students who have varied approaches to organizing and counting, such as organizing in a line or in an array or by using 5-groups, as shown.

Invite the students you identified to share their work with the class. Use prompts such as the following to show the value of organization.

Teacher Note

The following terms within this lesson are familiar from kindergarten:

• Organize

• Compare

• Is more than

• Is greater than

Tell us how you organized and counted.

How did organizing help our friend count?

It was easy for them to know what they already counted. It helped them count each one (cube) only once. They didn’t skip any when they lined them up.

Organize to Count and Compare

Materials—T: Large number path, Unifix Cubes; S: Large number path Students use a number path to organize, count, and compare.

Distribute a number path, numbered side up, to each student.

Model counting to 5 by using a number path. Have students follow along on their own paths. Start at 1, place a cube on each number, and count out loud. When the class reaches 5, invite students to clear their number paths and repeat the process to organize and count their own collections.

Differentiation: Support

Consider making brief mention of incorrect counting behaviors, such as

• placing more than 1 cube in a space,

• skipping numbers on the number path as you place cubes, or

• starting at a number other than 1 when placing cubes.

Invite students to begin. As they finish, guide a class discussion.

Peek at the number under your last cube. That number is the total. Tell a partner your total.

How does the number path help you organize your cubes?

The cubes are in a line now. Each cube has its own spot.

How does using the number path make it easier to find the total?

The number under the last cube shows the total, so I don’t have to count. Have students set their work aside and turn their attention to the class number path. Place 9 cubes along the top and 7 cubes of another color along the bottom.

Promoting the Standards for Mathematical Practice

When students use the number path and are careful to start at 1, not skip any spaces, and only put 1 item in each space, they attend to precision (MP6).

Ask the following questions to promote MP6:

• When using the number path, what do you need to be extra careful with?

• What mistakes are easy to make when using the number path?

Ask students how many there are of each color. Then ask which color has more.

How can we tell there are more green cubes?

The green line of cubes is longer.

9 is more than 7.

We can match each blue cube with a green cube. 2 green cubes don’t have a match, or a partner, because there are more green cubes.

Tell students that we can also compare totals on the number path without using cubes. On the number path, circle the total of each color group, and then remove the cubes as shown. Point to the circled numbers as you refer to them.

Differentiation: Challenge

Consider asking the following questions:

• If you didn’t have a number path, how would you compare two amounts?

• Which numbers on the number path are greater than 7? Which numbers on the path are greater than 9?

7 is one total, and 9 is the other total.

Without cubes, how can we tell that 9 is more than 7?

9 comes after 7.

9 objects are more than 7 objects.

Display the prepared sentence frame and use it to compare the totals: 9 is greater than 7 .

We say 9 is greater than 7. Let’s say this statement together. 9 is greater than 7.

If students are ready, briefly introduce the greater than symbol (>) by recording a comparison on a whiteboard, such as 9 > 7.

Although the concept of difference is not taught until module 2, some students may notice how many more or how many fewer there are in one set than another.

For these students, ask the following questions:

• How many extra blue cubes are there?

• How many more green cubes would we need to make the groups the same?

Have students return to their cubes and work with a partner to compare totals by using one or both of their number paths. Listen to student conversations, and prompt them to use the language more than or greater than as they discuss.

If time allows, consider having students trade bags of cubes to count and compare by using their number paths.

Problem Set

Differentiate the set by selecting problems for students to finish within the timeframe. Problems are organized from simple to complex.

In lesson 1, students may benefit from the support of guided practice, and the directions may be read aloud. Help students recognize the word count in print. Invite students to underline it as you read it aloud. Please note that students will continue to use their cubes and number path.

Teacher Note

The Problem Set transitions students from counting concretely with cubes to pictorial practice.

Notice that the image of the dogs adds the complexity of a scattered arrangement. If students need a strategy to organize and count accurately, suggest they use their pencils to mark and count each dog.

Some students may need to continue to organize and count cubes in lieu of counting static images.

Land

Debrief 5 min

Objective: Organize to find how many and compare.

Display student work from page 2 of the Problem Set.

Facilitate a discussion within the given timeframe. Use some combination of the following questions to help students synthesize their experience from the lesson. Encourage students to build on one another’s ideas as they discuss the purpose of today’s lesson.

Which is easier to compare: the pictures or the number paths? Why?

The number paths are easier because you can see the numbers.

The number paths are easier because you can see which is longer.

How does organizing on the number path help us count?

We don’t forget to count anything.

We don’t count anything twice.

The number path shows the numbers in order.

I can look under the last cube to see the total.

How does organizing on the number path help us compare?

It makes it easy to see which group has extras. You can tell which group has more.

Exit Ticket 5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Teacher Note

Have students clean up their bags of cubes by making sticks of 10 and other sticks of the leftover cubes. This will aid with the preparation for the bags of cubes in lesson 3.

UDL: Representation

Consider making a graph in another format. Download the digital 1-20 Floor Number Path. Have students line up on either side of the Number Path based on their category choice.

UDL: Engagement

Allow students to choose what to count and compare. For example, students might suggest comparing information about their classmates, such as tied and non-tied shoes, siblings and no siblings, or other categories that they find interesting or familiar.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.