Exemplar Lesson K CRM6 - Austin Independent School...

Lesson Template

Mathematics Department 10/9/2014

Lesson Name: Numbers Tell How Many Estimated timeframe: 520 Minutes (9 Days)

Grading Period/Unit: CRM 6 (2nd Nine Weeks) Grade level/Course: Kindergarten

Lesson Components

Lesson Objectives:

1. The students will be able to compare objects by length and height. 2. The students will be able to order objects from longest to shortest and vice versa. 3. The students will be able to use numbers and counting strategies to compare the quantity of sets of

objects 0-10.

Language Objectives:

1. The students will use language (e.g., longer than, shorter than, taller than) to compare measurements describing length and height.

2. The students will use language (e.g., longest, shortest, tallest) to order objects by length and height. 3. The students will use language (e.g., greater than, more than, less than, fewer than, equal to, the

same number as) to compare the quantity of sets 0-10.

Prior Learning: The child should be able to identify measureable attributes related to length and height and be able to identify which of two sets is more than, greater than, less than, fewer than, or the same as.

Standards(Texas Essential Knowledge and Skills): K.2B read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures;

K.2G compare sets of objects up to at least 20 in each set using comparative language;

K.7A give an example of a measurable attribute of a given objects, including length, capacity, and weight; and

K.7B compare two objects with a common measurable attribute to see which object has more of/less of the attribute and describe the difference;

Essential Questions: 1. How do you know when you have just enough, too many, or too few? 2. How is measuring different/ similar to counting? 3. How is (any number 1-10) different from (any number 1-10)? 4. How can you tell if an object is longer, shorter, and taller?

Vocabulary Lesson Preparation Measure, long, tall, short, wide, narrow, far, near, distance, numeral, counting, quantity, number words 1-10, set, one-to-one correspondence, greater than, more than, fewer than, less than, as many as, equal

x Big Dog, Little Dog by PD. Eastman x Chart Paper x Various lengths of sting or yarn. x Connecting cubes x Adding machine tape x Writing utensils (e.g., markers) x Pathway to Grandma’s House Grid (See attachment) x Pathway Graph (See attachment) x Comparison Data Recording Sheet (See attachment)

Lesson Template


Lesson Cycle Engage

x Sing “Over the River and Through the Woods” in celebration of the upcoming Thanksgiving holiday.

Verse 1 Verse 2 Over the river and thru the wood, To grandfather's house we go; The horse knows the way To carry the sleigh, Thru the white and drifted snow, oh! Over the river and thru the wood, Oh, how the wind does blow! It stings the toes, And bites the nose, As over the ground we go.

Over the river and thru the wood, To have a first-rate play; Oh, hear the bell ring, "Ting-a-ling-ling!" Hurrah for Thanksgiving Day-ay! Over the river and thru the wood, Trot fast my dapple gray! Spring over the ground, Like a hunting hound! For this is Thanksgiving Day.

x Relate what the students are learning related to the transportation introduced in the Treasures resource to the concept of travel and distance: o Do you think that the journey to Grandmother’s house described in this song is a long or short

trip? Why? What clues in the song would indicate to you that it is a long/ short distance from the child’s home to his/ her grandmother’s house?

x Challenge the children to think how they could use their hands to show how long something is. If no one suggests, demonstrate this gesture by spreading your hands far apart. Emphasize that the distance in between your hands refers to the attribute of length.

x Likewise, challenge the children to use their hands to indicate that an object is short. Explain that in order to make the space in between your hands shorter; you had to bring your hands closer together.

x Encourage the children to look around the room from where they are seated and identify a center that appears to be a long distance away from the circle area.

x Select a volunteer to take the end of a ball of yarn/string and travel to a center that seems to be the farthest away. Once the child arrives, instruct her/him to lift the string just above her/his head and pull tightly so that it is not obstructed by furniture arranged around the classroom and makes a straight line from where you are standing (the starting point) and the child is standing (the end point). Use scissors to detach/ cut the string/ yarn from the ball.

x Select another volunteer to repeat the same procedure for a center that appears to be the closest to the circle/ gathering area.

x Discuss how to arrange the two strings of yarn so that you can compare their respective lengths: o Where should I hold the ends of both strings so that we can see which is longer?

x Purposefully arrange the shortest string incorrectly along the length of the longer one so that its endpoint extends further out from where the latter ends. o Is this a fair way to compare the length of these two strings? Why/ Why not?

x Lead the children to understand that both ends of each string must match up at the baseline in order

to make an accurate measurement. x Allocate sufficient time to introduce new math station activities before dismissing the children to

conduct the partner/ dual language activity outlined in the next section titled “Exploration”.

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Lesson Template


Exploration

Dual Language Activity 1: (This activity is also appropriate for all classrooms) x Instruct the children to build a tower that is 10 connecting cubes long.

Once their tower is completed, direct the children to team up with a partner and to check each other’s work to be sure that they have counted out 10 connecting cubes.

x Dismiss each pair to locate two items in the classroom—one that is longer than the connecting cube tower, and another one that is shorter. Assign one partner the responsibility of locating the longer object and the other friend the task of finding an item that is shorter.

x Encourage each partner to use the appropriate space on the recording sheet (see attachment) to illustrate and write the name of the item he/she located.

x Assessment (Informal Observation): Observe and make note of how the children use their connecting cube tower to compare and measure other objects in the classroom by length.

Math Stations/ Centers: In addition to any other math centers or games you might have available (including many of the choice time activities referenced in Unit 2, “Counting and Comparing” of the Investigations in Number, Data, and Space resource), introduce any or all of the following activity suggestions:

x Block sort: Place an assortment of Geoblocks (or unit blocks) inside a container. Instruct the children to compare the length of the edges on each block and then use a dot sticker to indicate which edge is the longest. Make available a dry erase board and marker for the children to trace along the edges of the blocks so that they can justify their answer to the following prompt: How do you know the edge you selected is the longest?

x Play dough ropes: Instruct the children to roll two dot cubes and build a connecting cube tower with that many cubes. Then, direct the children to roll a (+/-) cube to determine the length of the rope they will mold and make out of play dough. Inform the children that if the plus/minus cube lands on (+), they must make the rope of play dough longer than their connecting cube tower. Similarly, if the plus/minus cube lands on (-), they must make the rope shorter than the connecting cube tower.

x Name Towers (Refer to Session 2.7 on page 110 of Unit 2, “Counting and Comparing,” from the

Investigations in Number, Data, and Space teacher guide): Make sheets of white or yellow dot stickers available at the writing center. Instruct the children to write each letter of their name on a corresponding dot. Then, direct the children to count out as many connecting cubes as there are letters in their name and attach one dot/letter to each cube. Tell the children to place their name tower inside a bin, from which they will be able to select other classmates’ names and compare during tomorrow’s math station time.

Lesson Template


x Thick and Thin Contest (Art Easel): Place a thick brush on one side of the art easel and a thin brush on the opposite side of the easel. Assign one partner to one side of the easel and the other child to the opposite side. Instruct the children to use their assigned brush to cover a sheet of paper with paint. Before they start the contest, allow the partners to verify that the sheet of paper they are covering is the same size/ dimension. The child who finishes the assignment first can use his/her brush to help the other partner complete painting his/her sheet of paper. Allow the two children to compare the bristles on their respective brushes. Ask: Was this competition fair? Why/ Why not?

x (Optional) Cuisenaire Rods: Allow the children to explore a container of Cuisenaire rods. (NOTE: If you do not own these rods, many upper elementary grades that teach fractions have these materials available. Ask these teachers if you may borrow a set. If not, check your campus or district library.) As the children explore, challenge them to order and compare the rods by length.

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Explanation

DAY 1 Debriefing Session (15 to 20 minutes maximum): x Play a game of Simon Says as you gather the children together as a class to debrief the work they

accomplished during math stations/ centers: Simon says, “Make your body tall/ short; spread your arms out wide; make the space between your knees narrow; etc.”

x As the children focus, encourage them to share and discuss the strategies they used to determine which objects in the classroom were longer than 10 connecting cubes and which were shorter. Refer back to the observation/ informal assessment suggestions that accompanied the dual language/ partner activity outlined in the previous section titled, “Explore.” As the volunteers share out, encourage them to demonstrate how they oriented the connecting cube tower as they aligned it along the length of the object they were measuring: o How did you determine you were measuring the longest edge of the object? o How do you know it is longer/ shorter than the connecting cube tower?

x Anchor of Support: Make a list of proper techniques for measuring (a “Strategies for Measuring Length” chart)—e.g., orienting both objects at the baseline, locating the longest edge of the item being compared, etc. Take picture of children implementing these techniques.

Orient the objects at a common baseline

Find the longest edge of the object you compare.

Lesson Template


DAY 2 Introduction: x Refer the two charts you developed with the children during the debriefing session you conducted at

the conclusion of yesterday’s math time. Inform the children that they will be able to refer back to these charts as they continue to explore the activities that were available at math stations yesterday as well as a few additional projects that you will introduce today.

x Introduce Big Dog, Little Dog by PD Eastman. Encourage the children to compare the heights of the two dogs shown on the cover of the book: What words would you use to describe the dog wearing green? How is he different from the dog wearing red? What does the dog dressed in green appear to be doing with the ruler? What do you do with a ruler?

x Encourage a volunteer to show how they would use a ruler to measure a friend’s height. Allow the volunteer to select a classmate/ friend to demonstrate the process: o Where do you begin measuring? What do the numbers on the ruler tell you? How do you use

them (the numerals)? x Before dismissing the children to centers, demonstrate how the children will use a roll of adding

machine tape to measure the height of a partner. (See the Dual Language Activity 2 in the section that follows))

NOTE: For DAYS 3-9, consult other math resources (e.g., Go Math, Investigations in Data, Number, and Space, etc.) for whole group lesson suggestions. You will also want to designate a portion of these whole group sessions for introducing new math stations and center activities followed by a brief (10 minutes maximum) debrief during which the children refine their new learning and developing understandings related to the essential questions about length, height, and quantity comparisons. Refer to the following section titled, “Elaboration,” for additional small group lessons and center activities that are designed to extend and deepen the children’s thinking.

Elaboration

Math Centers/ Stations (DAYS 2-9): x Science/ Block Center (Ramps): Encourage the children to make ramps for racing cars. Guide the

children to think about different ways to assemble the blocks, making adjustments in the height and length of the ramps so as to determine the optimal slope that will increase the speed by which a race card will travel down the track and thereby achieve the maximum distance forward. Make balls of yarn, strips of construction paper, or connecting cubes available for the children to keep track of and record the distance the car travels after each adjustment. Guiding Question: How far does the car travel when you make the ramp taller/shorter/longer? NOTE: You might want to integrate this center activity/ investigation with the science focus for this week, which relates to the concept of force and motion.

Lesson Template


x Social Studies/ Language Center: Allow the children to sort picture cards of various vehicles into two distinct categories: Vehicles that are better suited for traveling long distances (e.g., airplanes, trains, cars, etc.)/ Vehicles that are better suited for traveling short distances (e.g., bicycle, scooter, etc.)

x Writing Center (Comparing Names): Direct the children to compare their connecting cube name tower (which they created on Day 1) to their classmates’ name towers. Tell the children to locate the names of two classmates—one whose name is shorter (or has fewer letters in his/her name) and another whose name is longer (or has more letters in his/her name)—and record this data on a sheet of paper. Inform the child in the class who has the fewest letters in his/her name that it is okay if he/she cannot find a classmate with a shorter name and to simply leave that information blank on the recording sheet. Make the same assurance/ accommodation for the child who has the most letters in his/her name.

x Optional Manipulative Center (Cuisenaire Rods): Challenge the children to assign each rod a numerical value. Guiding Questions: How many white cubes (the shortest rod) will make the length of the red rod (the longest rod)? How could you find out? Which numeral would show this information? NOTE: In addition to the stations suggested in the above, consider introducing the Choice Time activity per day from Unit 2, Session 2 of the Investigations in Number, Data, and Space 2nd Edition resource—e.g., Session 2.1 (“Measurement Towers,” p. 82); Session 2.3 (“Counting Backwards,” p. 88; Session 2.4 (“Grab and Count: Compare” p. 94); Session 2.5 (“The Game of Compare,” p. 100); Session 2.6 (“Comparing Two Inventory Bags,” p. 105); Session 2.10 (“Grab and Count: Ordering,” p. 128); Session 2.11 (“Ordering Names,” p. 133); and Session 2.12 (“Ordering Cards,” p. 138).

Dual Language Activity 2 (DAYS 2-5): (This activity is also appropriate for all classrooms) x (Day 2): Pair the children with partners. Instruct each pair to take

turns using a roll of adding machine tape to measure the height of their assigned partner. Encourage children to refer to the “What Good Measuring Looks Like” chart as they determine where to mark off the baseline (e.g., at the base of their partner’s shoes) and cut off the top of the strip (at the endpoint on the top of the head) from the roll of adding machine tape. Tell the children to write their name on the strip once they are finished cutting and measuring.

x (Days 3-5 Extension): Affix photos of each child to his/her adding machine height measurement strip. Laminate the strips and encourage the children to work with their partner to compile a list of five friends that is ordered by students’ heights (i.e., from shortest to tallest) in preparation for group picture day. Informal Assessment (Observation and Work Samples):” Observe the children as they discuss and experiment with how to arrange the strips on the carpet from shortest to tallest. Encourage the children to submit their completed class list for your inspection and group approval. (You can use this as a work sample for both partners’ portfolio.

Small Group/ Guided Math (DAYS 6-7): x Display the Pathways to Grandma’s House Counting Grid. Sing, “Over the River and Through the

Woods,” which you introduced on Day 1. Instruct the children to look closely at each path, which all lead to the house located in the center of the grid. Ask: “Which path would be the shortest to

Lesson Template


Grandma’s house?” “How do you know?” “If you are not sure, what could you do to figure which path would be the shortest distance to walk?”

x Discuss how it might be difficult to estimate which path is the shortest because of the way each one bends. If no one suggests, point out that counting the squares in each path would help to confirm which one was the shortest/ longest.

x Invite children to select a path on the grid and count the number of squares starting at the point of origin along the edge of the grid all the way to the entrance to Grandma’s house. Allow the children to use connecting cubes that match the color of the squares along their assigned path, placing them one by one on top of each square as they count. Emphasize that the last counting word the children say as they enumerate the squares and cubes tells how many (or how long the path is).

x Direct each child to assemble the cubes they arranged along his assigned path into a tower. Gather each tower and order/compare them by height. Which is tallest/ shortest? How does this information help you decide which path would provide the quickest route to the park?

x Emphasize the one more/ one less relationship between each quantity—e.g., 6 is one less than 7; 9 is one more than 8, etc.

x Color in the bar-type graph that accompanies the Pathways to Grandma’s House Counting Grid to represent and compare the measurement data. Point out how the vertical (up and down) display of the numerals 1-10 in the left-hand column on the graph correspond to the height (distance) recorded for each color path. Ask: Up to which numeral does the last square on the green bar reach?

Evaluation (check for understanding)

Formative: x Anecdotal Records/ Informal Observations of the children’s work during math stations/ small groups. x Refer to the Session 2.13, End-of-Unit Assessment and Ordering, on p. 142 of Investigations 2nd

Edition, Unit 2. Before conferencing with each individual student, read the following Teacher Notes: Assessing Students’ Counting (p. 153) and Observing Kindergarteners as they Count (p. 152).

x Refer to the Session 2.14, End-of-Unit Assessment and Ordering our Names, on p. 145 of Investigations 2nd Edition, Unit 2. The students continue to count, compare and order quantities during Math Workshop, while students who have not yet met the benchmarks meet individually with the teacher.

Summative (DAYS 8-9): x Interview and work with individual or pairs of children as you play the “Make My Name the Same”

game. Provide the following instruction to introduce the game: 1. Compare and select a classmate’s connecting cube name tower that has more or fewer letters

than your name—do not select a classmate whose name has as many letters as your name. 2. Roll a plus/minus cube to determine if you should add or take away cubes to make your tower the

Lesson Template


same length as your classmate’s name. 3. Explain and record how many cubes you had to add/ take away.

x Encourage the children to use numbers to compare the quantity of letters in theirs and their classmate’s name towers: How many fewer/ more letters are in your name than (classmate’s) name? How do you know?

x Use the child’s recording as a portfolio/ work sample entry.

English Language Proficiency Standards

2(E) use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language;

Anchors of Support Develop and add to a “Strategies for Measuring Length” chart with the children during each brief debriefing session that follows the exploration time. Take picture of the children implementing these strategies as they are working during math station/ exploration time. Encourage the children to refer to this chart as they continue to explore.

College and Career Readiness

I.C.1 (Numeric Reasoning) Compare real numbers.

VIII.C.1 (Problem Solving and Reasoning) Formulate a solution to a real world situation based on the solution to a mathematical problem.

21st Century Skills

x Assume shared responsibility for collaborative work, and value the individual contributions made by each team member

Differentiation strategies

Special Education: Before assigning a color path to individual children during the Pathways to Grandma’s House Counting Grid small group activity (see the Elaboration section, Days 6 and 7 in the above), allow each child to stand/ sit in front of the point of origin on the grid that corresponds to her/his color so that she/he can see the direction forward to the park. Otherwise, some children can become disoriented when trying to determine which way is up or down/ forward and backward.

“He needs to take two cubes off because he has two more letters in his name than I do.”

“I need to add two cubes because I have two fewer letters in my name than he does.”

Lesson Template


English Language Learners: After reading Big Dog Little Dog, develop an “opposites” chart divided in two columns—one labeled “Words associated with big”, and the other, “Words associated with little/small.” As you write the list, encourage the children to more accurately describe each word they assign to one of the respective columns—e.g., “Why do you associate the word short with the word little?” Other associations with the term little/small you may want prompt the children to explain include narrow, near, close, shallow, and low. Lead the children to understand that each of these words is closely related because they refer to a small proportional distance/ space between two endpoints—e.g., the point of origin and the top/ bottom/ left side/ right side, etc. Likewise, the word big—again, referring to the distance between two endpoints-- might be associated with the terms tall, long, wide, deep, high, or far.

Extension for Learning: x Shared/ Interactive Writing Extension: Schedule another time during the day (or on another day) to

compile on chart paper a list of the items the children compared for the dual language/ partner activity. Divide the chart in two columns. Label one column, “Items longer than 10 connecting cubes,” and the other column, “Items longer than 10 connecting cubes.” This activity is designed to encourage children to write words as a way to show their math work.

CRM Planning Schedule

Monday Tuesday Wednesday Thursday Friday EEnnggaaggee & EExxpplloorree sections of the Exemplar Lesson Investigations: Unit 2, Session 2.1

EExxppllaaiinn section of the Exemplar Lesson Investigations: Unit 2, Session 2.2

EEllaabboorraattee section of the Exemplar Lesson Go Math: Lesson 6.1 Investigations: Unit 2, Session 2.3





EEvvaalluuaattiioonn section of the Exemplar Lesson Go Math: Lesson 6.6 Investigations: Unit 2, Session 2.11

EEvvaalluuaattiioonn section of the Exemplar Lesson Investigations: Unit 2, Session 2.12

Other resources include Teaching Student-Centered Mathematics: Grades K-3; Activity 8.1 (p. 228) and ETA Hands-On Standards (PK and K) Number and Operations Lesson 9 (Order of Numbers p. 32) and Lesson 10 (Ordinal Numbers, p. 34)/ Algebra Lesson 6 (Extend Growing Patterns, p. 102)/ Measurement Lesson 1 (Nonstandard Measurement of Height, p. 112), Lesson 2 (Sorting by Height, p. 114), and Lesson 3 (Sorting by Length, p. 116);). These can be integrated within this time line where you see fit. RREEMMEEMMBBEERR,, iiff yyoouu ccaannnnoott ggeett ttoo eevveerryy aaccttiivviittyy ssuuggggeesstteedd,, tthhaatt iiss ookkaayy.. CChhoooossee aanndd ppiicckk wwiisseellyy..

Lesson Template


Pathway Graph

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Green Yellow Blue Red

Lesson Template


Longer than 10 connecting cubes

Shorter than 10 connecting cubes

Completed by ___________ and ___________

Comparison Data Sheet

Exemplar Lesson K CRM6 - Austin Independent School...

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