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TAT2 Task 3: Instructor’s Manual 1

TAT2 Task 3: Instructor’s Manual

Elly Kirkpatrick

June 18, 2019

A Written Project Presented to the Faculty of the Teachers College of

Western Governors University


TAT2 Task 3: Instructor’s Manual

This is a two-week unit on multi-digit whole-number multiplication. This unit of instruction

was designed for typical fourth graders in a public school setting.

Instructional Goal

When given a set of multi-digit multiplication problems, fourth graders will use pencil and paper to

apply appropriate computation strategies to solve multiplication problems fluently and with 90 percent

accuracy.

Intended Audience

The fourth graders in this instructional setting attend Mary G. Fritz Elementary School in

Wallingford, Connecticut. The school houses approximately 350 students in grades 3-5. Students at

this school are predominantly Caucasian, with lower-class/middle-class backgrounds. In this

particular classroom, 79% of the students are white, 16% are Hispanic, and 5% are Asian.

The class is comprised of 19 academically heterogeneous students between the ages of eight

and ten years old. There are ten boys and nine girls in the class. Of the 19 students, two students

have 504 plans for ADHD diagnoses, and two others have IEPs for learning disabilities and receive

special education services. There is a paraprofessional assigned to the classroom for part of the day

to assist in the education of the students with IEPs.

Length of Unit and Delivery Approach

This unit is designed to be taught over two consecutive weeks. There are nine lessons, each

lasting 60 minutes. The tenth math block is intended to be used as an assessment block during

which the final, summative assessment should be given.

In terms of pedagogical approach, the majority of the unit incorporates ideas from the

Constructivist and Cognitivist schools of thought. Because multi-digit multiplication is a difficult

concept for many fourth graders, Cognitivist strategies are well-represented in the unit through the


use of direct instruction. Students will also have many opportunities for collaborative work, which

is characteristic of the Constructivist theory. One lesson in the unit utilizes Behaviorist principles

because it is a whole-group, teacher-led lesson that incorporates lots of positive reinforcement.

Instructional Sequence

Each lesson in this unit typically consists of an anticipatory set to excite and engage students

about the lesson’s content, direct instruction where the teacher presents the content to the students,

independent practice or small-group instruction where students have the opportunity to practice new

skills independently, and a possible formative assessment in the form of an exit slip. The lessons in

the unit build upon each other, so it is recommended that the lessons be taught in order.

Materials Needed

The variety of materials used throughout the unit include hundreds charts, number lines, grid

paper for lining up digits for computation and arrays, construction paper, butcher paper, drawing

paper, scissors, glue, individual whiteboards and dry-erase markers, construction paper, colored

pencils, highlighters, worksheets, task cards, cardboard templates, and a variety of math

manipulatives (e.g.; Base 10 blocks, colored counters, place value dice, etc.).

Resources needed for this unit include Chromebook computers, a document camera,

TouchIT interactive whiteboard, and an Internet connection to access technology resources such as

Arcademic Skill Builders, LearnZillion, and Numberock music videos.

Description of Lessons in Plan of Instruction

Each lesson in this unit was designed to support a corresponding performance objective.

Please see Table 1 for a brief overview of the scope and sequence of the instructional unit.


Table 1

Lesson Performance Objectives Description of Lesson

Lesson 1: Ice Cream Multiples

Given hundreds charts and number lines, students will identify multiples and determine if a whole number is a multiple of a given number in 10 out of 10 trials.

Students play the game, “Fact Pop” to practice naming multiples of a given number, then construct paper ice cream cones to name all the multiples of a given number.

Lesson 2: Multiply by Multiples of Ten

When given a written multiplication problem, students will correctly multiply multiples of 10, 100, and 1000 by one-digit factors in 4 out of 5 trials.

Students learn patterns for multiplying numbers when one factor is a multiple of ten, then use place value die to practice the same skill with a partner. Formatively assessed with an exit slip (Appendix A).

Lesson 3: Multiply Two Digit by One Digit Numbers

When given a written problem, students will multiply a two-digit factor by a one-digit factor in 4 out of 5 trials.

Students use place value die and grid paper to construct arrays that represent multiplication problems.

Lesson 4: Multiply Three and Four Digit Numbers

When given a written problem, students will multiply a three- and/or four- digit factor by a one-digit factor in 4 out of 5 trials.

Students learn the standard algorithm for multiplying a multi-digit factor by a one-digit factor. Formatively assessed with an exit slip (Appendix B).

Lesson 5: Estimating Products

When given a written problem, students will multiply two-, three-, and four-digit factors by a one digit factor and assess the reasonableness of the product in 4 out of 5 trials.

Students use rounding and magnitude estimates to assess the reasonableness of an answer. Students work to complete the magnitude estimate worksheet (Appendix C).

Lesson 6: Multiplication Using the Area Model

When given a written problem, students will multiply two-digit by two-digit factors correctly using the array/area model in 4 out of 5 trials.

Students use butcher paper, base 10 blocks, and dry erase boards to build arrays/use the area model to multiply two two-digit factors.

Lesson 7: Partial Product Sandwiches

When given a written problem, students will multiply two-digit by two-digit factors correctly using four partial products in 4 out of 5 trials.

Students use the partial products method to solve multi-digit multiplication problems. They work with a partner to complete the sandwich task cards.

Lesson 8: Using the Standard Algorithm for Multiplication

When given a written problem, students will multiply one-, two-, and three-digit factors correctly using the standard algorithm in 4 out of 5 trials.

Students use the standard algorithm to multiply two multi-digit factors. Students complete the standard algorithm worksheet (Appendix E).

Lesson 9: Word When given a written task, students Students review all of the


Problems with Multiplication

will solve word problems involving multiplication with one-, two-, and/or three-digit factors in 4 out of 5 trials.

strategies for multi-digit multiplication presented in the unit, then work to solve the Exemplars performance task (Appendix F).

Assessments

Students will be assessed formatively at the end of each lesson. Formative assessments

include exit slips, review of student work, and anecdotal notes. The instructor may choose to use

data from these formative assessments to help drive future instruction, which could include

reteaching and/or reinforcement of a particular skill if necessary. There is also a pencil-and-paper

summative assessment at the end of the unit which consists of 16 multi-digit multiplication

problems (Appendix G). Students will be directed to use any of the strategies presented in the unit

to solve the problems successfully.

Instructional Delivery

The lessons in this unit were designed to be delivered to a heterogeneous class of fourth-

grade students. It is assumed that the classroom will be equipped with desks at which students can

complete independent work, as well as communal spaces such as tables or area rugs so that students

can work collaboratively in pairs or small groups at times. Depending on the lesson or activity,

students may be required to work independently, with partners, or in small groups. Some students

may also need to work with the instructor or paraprofessional in a one-on-one or small group setting

in order to receive the appropriate level of support, depending on the students’ individual ability

levels.

The instructor should expect to spend fewer than 20 minutes of each lesson on direct

instruction. The majority of the 60-minute math block will be spent on student exploration and skill

practice. In general, the instructor’s task is to engage students and spark interest during the


anticipatory set, set the lesson’s learning objective, and briefly deliver necessary content. He or she

will then guide students during the learner participation portion of each lesson. Discourse between

students is essential, and probing questions from the instructor can help guide conversations so that

they are productive.

As this unit was designed with fourth-graders in mind, a certain level of technological

proficiency is expected. Students should be able to power on and log in to a Chromebook computer

and use a web browser to navigate to the correct resource. Additionally, the instructor will need to

present some aspects of the unit plan using the interactive whiteboard and will thus also require a

basic level of proficiency with modern educational technology.

Instructional Materials

Below is a list of instructional materials used throughout the unit:

Arcademic Skill Builders website

Base 10 blocks

Butcher paper

Colored counters

Construction paper

Drawing paper

Dry erase boards (individual)

Dry erase markers

Exit slips (Appendices A and B)

Glue

Grid paper

Highlighters

Hundreds charts


LearnZillion instructional videos

Number lines

Numberock music videos

Place value dice

Scissors

Task cards (Appendix D)

Templates

Unit assessment (Appendix G)

Worksheets (Appendices C, E, and F)

Physical Resources

Below is a list of physical resources used throughout the unit:

Chromebook computers

Document camera

Internet connection

TouchIT interactive whiteboard

Lesson Plans

Lesson Plan #1 Title: Ice Cream Multiples

Performance Objective: Using hundreds charts and number lines, students will correctly identify

at least five multiples of a given number.

Resources or Materials Needed: Hundred charts (1 per student), colored pencils/crayons,

construction paper, ice cream scoop templates, construction paper ice cream cones, scissors, glue.

Time: 60 minutes


Step 1: Pre-Instructional Activities: Play the game “Math Pop” (while standing in a circle,

students take turns skip counting by a given number. When a student in the circle reaches the

agreed-upon maximum, he/she says “pop!” and must sit down. Skip counting resumes from zero

and continues until only one student is still standing – the winner).

Step 2: Content Presentation: Review previous work with factors. Define the vocabulary word

multiple and illustrate with several examples. Explain to students that their job today is to find all

the multiples of a given number, from 1x-12x. Using the ice cream scoop template, cut out several

scoops from the same color paper. The paper that is used for a given factor should coordinate with

the colors of the factor/multiple dots on the number line hanging in the classroom). Show students

one strategy for finding a multiple of a given number (refer back to the Math Pop game in the

anticipatory set). Discuss other possible strategies. Begin assembling the first few multiples of the

number 2, showing students how to glue the scoops to the paper cone starting with the smallest

multiple and working up.

Step 3: Learner Participation: Divide students into their problem-solving partners. Assign each

group a given number and distribute the materials. Rotate between the groups as the students

identify their multiples. Discuss strategy and problem-solving. When students are finished

assembling their multiples projects, bring the class back together to look at each group’s finished

product. Talk about the process, what they noticed, patterns, and identify what worked and what

didn’t work for their groups. Hang multiples cones on the wall so students can reference them

throughout the unit.

Step 4: Assessment: Small group anecdotal notes; ice cream multiple project.

Step 5: Follow-Through Activities: Regularly incorporate the Math Pop game into the class’

morning meeting routine to help strengthen understanding of multiples.


Lesson Plan #2 Title: Multiply by Multiples of Ten

Performance Objective: When given a written multiplication problem, students will correctly

multiply multiples of 10, 100, and 1,000 by one-digit factors in 4 out of 5 trials.

Resources or Materials Needed: Base Ten Blocks, individual whiteboards, dry erase markers,

place value dice (ones and tens)

Time: 60 minutes

Step 1: Pre-Instructional Activities: Have students practice skip counting by tens aloud, starting

at 10 and stopping at 100. Have them repeat skip counting by hundreds until 1,000, and thousands

until 10,000. Students can skip count together or take turns in a circle.

Step 2: Content Presentation: Explain to students that they will be learning how to multiply a one-

digit number by a multiple of ten, one hundred, or one thousand. On the whiteboard, write a variety

of multiplication equations, such as 3x40 = 120, 5x60 = 300, 8x20 = 160, etc. Each equation should

have one one-digit factor and one two-digit factor that is also a multiple of ten. Ask students to

identify any patterns or similarities between the equations. If necessary, prompt students by saying,

“There is a simple multiplication problem in the larger problem. I can see 3x4 in 3x40. The answer

to 3x4 is 12 and the answer to 3x40 is 120. Since 40 is ten times greater than 4, it makes sense that

120 is ten times greater than 12. After pointing out how the same pattern exists in the other

problems, show students the LearnZillion video on multiplying by tens (Pimentel, 2019).

Step 3: Learner Participation: Students can break up into pairs and take turns rolling the place

value dice (each pair should have a tens die and a ones die). They should use the numbers they roll

as two factors to be multiplied; the problems can be written on the individual whiteboards. Students


can use the Base Ten blocks to model the resulting multiplication problems, or model with drawings

on the whiteboards. Students should be encouraged to check each other’s work.

Step 4: Assessment: Anecdotal notes, exit slip (Appendix A).

Step 5: Follow-Through Activities: Students can refer back to the LearnZillion video if needed.

Lesson Plan #3 Title: Multiply 2-Digit by 1-Digit Numbers

Performance Objective: When given a written multiplication problem, students will correctly

multiply a two-digit factor by a one-digit factor in 4 out of 5 trials.

Resources or Materials Needed: Grid paper, large construction paper, glue sticks, place value dice

(tens place and ones place), colored counters or tiles, scissors

Time: 60 minutes

Step 1: Pre-Instructional Activities: Review the vocabulary term array (items arranged in rows

and columns). Pass out the color counters or tiles and have students practice building possible

arrays for a variety of composite numbers.

Step 2: Content Presentation: Tell students that they will be learning how to multiply a 2-digit

number by a 1-digit number using an array strategy. Show students the LearnZillion video on

multiplying by a 2-digit by 1-digit number (Lewis, 2019).

Step 3: Learner Participation: Students should be split into pairs. Each pair will need grid paper,

construction paper, scissors, and place value dice (one ones-place die and one tens-place die).

Students should roll the ones place die to get a one-digit product and the ones- and tens-place dice

to get a combined two-digit product. Students then work with their partners to create an array


representing the multiplication problem they created with the dice. They should cut out the grid

paper and glue it on the construction paper before writing the full equation next to their array.

Step 4: Assessment: Anecdotal notes, students’ finished projects.

Step 5: Follow-Through Activities: Students can refer back to the LearnZillion video if needed.

Lesson Plan #4 Title: Multiply 3- and 4-Digit Numbers

Performance Objective: When given a written problem, students will correctly multiply a three-

and/or four-digit factor by a one-digit factor in 4 out of 5 trials.

Resources or Materials Needed: Dry-erase boards, dry-erase markers

Time: 60 minutes

Step 1: Pre-Instructional Activities: As a fun review of place value, show students the

Numberock music video on place value (Numberock, 2019). Students will need a strong

understanding of place value to be successful in this lesson.

Step 2: Content Presentation: This is students’ first introduction to the standard algorithm for

multiplication. Show students how to line up a two-digit by one-digit multiplication problem so that

the digit in the ones place for both factors are lined up. Proceed to show students how to multiply

using the standard algorithm. Students may need to be shown several examples of this type of

problem before they feel comfortable trying it on their own.

Step 3: Learner Participation: When they are ready, pass out the dry-erase boards and post a new

multiplication problem on the board. Have students work the problem on their dry-erase boards.

Circulate around the room to monitor student work and identify any student misconceptions. After a

few minutes, demonstrate how to solve the problem on the board before posting a new one. When


students seem comfortable, teach student to extend the algorithm to multiply a three-digit factor by

a one-digit factor. Repeat the activity from before, using a three-digit factor in each problem.

Step 4: Assessment: Exit slip, anecdotal notes (Appendix B).

Step 5: Follow-Through Activities: Students can practice their math fact fluency using Arcademic

Skill Builders (Arcademics, 2019).

Lesson Plan #5 Title: Estimating Products

Performance Objective: When given a written multiplication problem, students will multiply two-,

three-, and four-digit factors by a one-digit factor and assess the reasonableness of the product in 4

out of 5 trials.

Resources or Materials Needed: Magnitude estimate worksheets

Time: 60 minutes

Step 1: Pre-Instructional Activities: As a fun review of rounding, show students the Numberock

music video on rounding (Numberock, 2019).

Step 2: Content Presentation: Review the rules for rounding. Discuss why it can be important to

use rounding to assess the reasonableness of a product. Let students know that they will be

performing magnitude estimates today, which are very rough estimates of what a product might be.

Students should be thinking, Is the product in the tens, hundreds, or thousands place? Students can

use these rough estimates to check the reasonableness of their answers when multiplying large

numbers.

Step 3: Learner Participation: Post the following problem on the board: 15x19. Ask students

whether the product is in the tens, hundreds, or thousands place. They should not calculate the


actual product. Guide students to the realization that the product of 15 and 19 must be greater than

10x10 (100), but less than 20x20 (400), so the answer must be in the hundreds place. Pose a few

more examples so that students become comfortable with magnitude estimates, then have students

work on the magnitude estimate worksheet.

Step 4: Assessment: Magnitude estimate worksheet (Appendix C).

Step 5: Follow-Through Activities: Students can practice their math fact fluency using Arcademic

Skill Builders (Arcademics, 2019).

Lesson Plan #6 Title: Multiplication Using the Area Model

Performance Objective: When given a written problem, students will multiply two-digit by two-

digit factors correctly using the array/area model in 4 out of 5 trials.

Resources or Materials Needed: Base Ten blocks, butcher or bulletin board paper (1 long piece

per pair of students), dry erase boards, dry erase markers

Time: 60 minutes

Step 1: Pre-Instructional Activities: Pose the following question to students:

Marcus and Abby are two friends who are each building a garden. Marcus’ rectangular

garden is 35 feet by 20 feet, and Abby’s rectangular garden is 40 feet by 15 feet. Whose

garden has the larger area?

Instead of, or in addition to, the problem above, show students the Numberock video for the area

model of multiplication (Numberock, 2019).


Step 2: Content Presentation: Present students with the materials that will be available to them

during the activity (Base Ten blocks, butcher paper). Review the names of each Base Ten block so

that students use the correct terminology when discussing their work.

Step 3: Learner Participation: Split students into their problem solving pairs and let them work

out the problem using the blocks and the paper. Students may model using the blocks or draw on the

paper, or both. Circulate among the groups, asking students to explain their strategies and

mathematical reasoning. When needed, guide students toward using the blocks to create actual

arrays that represent the areas of both gardens so that they may see them and compare them. Push

students to quantify the areas of both gardens.

When students have had an ample amount of time to explore the problem, bring the class back

together to discuss strategies. What worked for the groups? Show students how they can take the

arrays they built using the Base Ten blocks and turn them into a more conceptualized drawn model.

Using the dry erase boards and markers, have students work through a few problems using their

newly-discovered area model for multiplication together as a class, then pose a few problems for

students to work through on their own.

Step 4: Assessment: Anecdotal notes, review of student work on butcher paper, pictures of student

arrays built with Base Ten blocks.

Step 5: Follow-Through Activities: Create task cards with additional multiplication problems that

lend themselves to the area model strategy. Laminate the cards and place them in the computation

center for students to use during station time. Instead of using task cards, students could work

through similar problems using the technology resource Arcademic Skill Builders.


Lesson Plan #7 Title: Partial Product Sandwiches

Performance Objective: When given a written problem, students will multiply two-digit by two-

digit factors correctly using four partial products in 4 out of 5 trials.

Resources or Materials Needed: Dry erase boards, dry erase markers, laminated sandwich task

cards (Appendix D).

Time: 60 minutes

Step 1: Pre-Instructional Activities: Review with students some of the ways they have learned to

multiply large numbers throughout the unit (standard algorithm, area model). Tell students that they

will be learning an additional strategy they can add to their problem-solving toolkits today: the

partial products method of multiplication.

Step 2: Content Presentation: Demonstrate for students the partial products strategy for

multiplication. Students should be following along as the teacher works through several problems

on the board. When students seem ready, students should use the individual whiteboards to work

through problems along with the teacher. Finally, the teacher may present a few problems and have

students work through them on their own. The teacher should circulate among students, checking

students’ work.

Step 3: Learner Participation: When students seem reasonably comfortable with the partial

products method, invite them to use the task cards to build a partial product “sandwich.” Students

should choose a problem card (the “bread”) and solve the problem that is printed on it using the

partial products method. The other sandwich ingredient cards (cheese, various veggies, various

meats) have possible partial products written on them. Students should work through their problem,

identifying all partial products and then selecting the matching sandwich ingredient card. When


they have arrived at the correct product, they can finish their sandwich off by finding another bread

card that matches the product. Students should be challenged to complete as many multiplication

sandwiches as possible in the time they have.

Step 4: Assessment: Students can fill out a recording sheet as they work through the different

sandwich problems and turn it in at the end of the activity. The teacher will be able to assess the

number of problems students were able to complete (fluency) and also the accuracy of students’

computation.

Step 5: Follow-Through Activities: This activity can be modified to include three digit factors

once students become very comfortable with the partial products strategy. It would be a good option

to offer to students who finish other classwork quickly and need something to work on, or to add to

classroom math stations.

Lesson Plan #8 Title: Using the Standard Algorithm for Multiplication

Performance Objective: When given a written problem, students will multiply one-, two-, and

three-digit factors correctly using the standard algorithm in 4 out of 5 trials.

Resources or Materials Needed: Individual whiteboards, dry-erase markers, standard algorithm

worksheet

Time: 60 minutes

Step 1: Pre-Instructional Activities: Let students know that they will be learning the standard

algorithm for multi-digit multiplication. In order to do this, they needed to master more conceptual

methods of multiplication, and they are finally ready!


Step 2: Content Presentation: Show students the LearnZillion video on the standard algorithm for

multiplication of large numbers (Baldwin, 2019). Pass out the individual whiteboards to the

students. Demonstrate a few examples of two-digit by two-digit multiplication on the whiteboard.

Students should be following along as the teacher works through several problems on the board.

When students seem ready, students should use the individual whiteboards to work through

problems along with the teacher. Finally, the teacher may present a few problems and have students

work through them on their own. The teacher should circulate among students, checking students’

work.

Step 3: Learner Participation: Students should work on the standard algorithm worksheet

(Appendix E) independently, then get the work checked with the teacher when they finish. Students

should keep working until all of their answers are correct.

Step 4: Assessment: Standard algorithm worksheet.

Step 5: Follow-Through Activities: Students can watch the Numberock music video on

multiplication using the standard algorithm (Numberock, 2019) to reinforce the steps of the

standard algorithm.

Lesson Plan #9 Title: Word Problems with Multiplication

Performance Objective: When given a written task, students will correctly solve word problems

involving multiplication with one-, two-, and/or three-digit factors in 4 out of 5 trials.

Resources or Materials Needed: Exemplars word problem task (Exemplars, 2019), large drawing

paper, colored pencils or crayons, highlighters

Time: 60 minutes


Step 1: Pre-Instructional Activities: Review all of the strategies for multi-digit multiplication

included in this unit (area model, partial products, and standard algorithm). If needed, model a

problem using each method. Tell students that today, they will be using their preferred strategy to

solve word problems involving multiplication.

Step 2: Content Presentation: Show students the LearnZillion video on understanding a word

problem (King, 2019). Make sure students know they need to actively thing about what is going on

in the word problem. They may want to use highlighters or colored pencils to mark important

information and numbers in the text.

Step 3: Learner Participation: Students can work in pairs to solve the Exemplars word problem

(Appendix F). When the pairs finish and their work is correct, they can work together to make a

poster of their problem and solution. Remind students they need to show their thinking using

numbers, models, and words. If there is time, students can present their posters to the class.

Step 4: Assessment: Anecdotal notes, Exemplars word problem task

Step 5: Follow-Through Activities: Students can refer back to any of the technology resources

used in this unit (LearnZillion videos, Numberock songs, Arcademic games) to help prepare for the

upcoming unit assessment.

Lesson Plan #10 Title: Unit Assessment

Students should work to complete the unit assessment (Appendix G) independently. Information

from the assessment can be used to plan future instruction.


References

Arcademics. (2019). Multiplication games. Retrieved from https://www.arcademics.com/games?

subject=multiplication

Baldwin, G. (2019). Use the standard algorithm for multiplication [Video file]. Retrieved

from https://learnzillion.com/assignments/R2RC626

Exemplars. (2019). Retrieved from https://library.exemplars.com/

Numberock. (2019). Area model multiplication [Video file]. Retrieved from https://numberock.com/

lessons/area-model/

Numberock (2019). Place value [Video file]. Retrieved from https://numberock.com/lessons/place

value/

Numberock (2019). Rounding numbers [Video file]. Retrieved from https://numberock.com/lessons/

rounding-whole-numbers/

Numberock (2019). Multi-digit multiplication [Video file]. Retrieved from https://numberock.com/

lessons/long-multiplication/

King, H. (2019). Understand a word problem [Video file]. Retrieved from https://learnzillion.com/

assignments/ VZ79586

Lewis, M. (2019). Use an array to multiply a two-digit number by a one-digit number [Video file].

Retrieved from https://learnzillion.com/assignments/SW43775


Pimentel, I. (2019). Multiply by multiples of 10 with base ten blocks [Video file]. Retrieved from

https://learnzillion.com/assignments/GM62493


Appendix A

Exit Slip for Lesson 2: Multiply by Multiples of Ten


Appendix B

Exit Slip for Lesson 4: Multiply Three- and Four-Digit Numbers


Appendix C

Magnitude Estimate Worksheet for Lesson 5: Estimating Products


Appendix D

Sandwich Task Cards for Lesson 7: Partial Product Sandwiches


Appendix E

Standard Algorithm Worksheet for Lesson 8: Using the Standard Algorithm for Multiplication


Appendix F

Exemplars Worksheet for Lesson 9: Word Problems with Multiplication


Appendix G

Unit Assessment

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