Multiplication Meanings & Facts Unit Plan

Lake Washington School District | Unit and Lesson Planning4

Unit Title

Multiplication Meanings and Facts

Grade/Subject

3rd / 4th Grade Mathematics

Author(s)

Kelly Winters

Unit Focus

This unit serves as an introduction to multiplication concepts. Students explore patterns in multiplication and the connections between how repeated addition, equal groups, arrays and skip counting relate to multiplication. Students demonstrate their understanding of the Associative Property and are able to multiply numbers regardless of how they are grouped. Students build automaticity with recall of basic multiplication facts in order to prepare for more complex computational problems.

Connections to the LWSD Student Profile

Interdisciplinary Skills and Attributes

Academic Thinking Skills and Strategies

Questions critically and thinks creatively

Solves problems effectively

Makes connections

Communication and Collaboration Skills

Offers ideas and makes contributions

Works well with others

Respects and values others

Personal Attributes

Exhibits a strong work ethic

Takes personal responsibility

Demonstrates resiliency

Interdisciplinary Content Knowledge

Mathematical Reasoning

Understands and applies mathematical principles and concepts

Solves problems, reasons and communicates mathematically

Guiding Questions

What are equal groups?

What patterns do you see in the multiplication table?

How do you know that 4+ 4 + 4 = 3 x 4?

How can skip counting on a number line help you find 5 x 2?

How can you prove that your number sentence matches your array?

What is the difference between 7 X 4 and 4 X 7?

Why are 0 and 1 special in multiplication?

How can three numbers be multiplied to solve a multiplication problem?

Standards and Levels of Proficiency

Common Core State Standards (CCSS)

Represent and solve problems involving multiplication and division.

1. CCSS.Math.Content.3.OA.A.1Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 7.

2. CCSS.Math.Content.3.OA.A.2Interpret whole-number quotients of whole numbers, e.g., interpret 56 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 8.

3. CCSS.Math.Content.3.OA.A.3Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Understand properties of multiplication and the relationship between multiplication and division.

4. CCSS.Math.Content.3.OA.B.5Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication.) 3 5 2 can be found by 3 5 = 15, then 15 2 = 30, or by 5 2 = 10, then 3 10 = 30. (Associative property of multiplication.) Knowing that 8 5 = 40 and 8 2 = 16, one can find 8 7 as 8 (5 + 2) = (8 5) + (8 2) = 40 + 16 = 56. (Distributive property.)

Multiply and divide within 100.

5. CCSS.Math.Content.3.OA.C.7Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 5 = 40, one knows 40 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

6. CCSS.Math.Content.3.OA.D.9Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

LWSD Power Standard

PS3: Students represent and explain multiplication strategies.

Proficiency Scale

4: Exceeds learning target/standard with more complex content and thinking.

Given a real-world situation, recommend and explain why a chosen strategy is appropriate and effective for solving the problem.

Recommends an effective strategy.

Explains why the strategy they chose is appropriate.

3: Meets learning target/standard.

Students represent and explain multiplication and division strategies.

Illustrate multiplication in a variety of ways (repeated addition, arrays, counting by multiples, equal jumps on a number line).

2: No major errors or omissions regarding foundational knowledge: background knowledge, simpler procedures, terminology.

Student recognizes and identifies strategies for solving multiplication and division problems.

Labels strategies for solving multiplication problems.

Defines strategies (repeated addition, arrays, counting by multiples, equal jumps on a number line).

1: With help, student can perform score 2.0 and 3.0 expectations.

Interdisciplinary Skills

Common Core State Standards (CCSS)

English Language Arts: Speaking and Listening, Grade 3

Comprehension and Collaboration

CCSS.ELA-Literacy.SL.3.1Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 3 topics and texts, building on others' ideas and expressing their own clearly.

CCSS.ELA-Literacy.SL.3.1.bFollow agreed-upon rules for discussions (e.g., gaining the floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion).

CCSS.ELA-Literacy.SL.3.1.cAsk questions to check understanding of information presented, stay on topic, and link their comments to the remarks of others.

CCSS.ELA-Literacy.SL.3.1.dExplain their own ideas and understanding in light of the discussion.

CCSS.ELA-Literacy.SL.3.3Ask and answer questions about information from a speaker, offering appropriate elaboration and detail.

By the end of this unit, students will be able to interpret, represent and explain strategies to solve problems involving multiplication.

Teaching Students the Unit Learning Target

1. Ill ask two students to come to front of the class and hold out their hands with their palms up. Ill count out two counters into each students hand. Ill ask the group how we can find the total number of counters in the four hands.

2. Students may suggest counting the counters by ones (1+1+1+1+1+1+1+1=8) or counting by twos (2+2+2+2=8).

3. Ill explain that we can write the repeated addition sentence as a multiplication sentence. For example, 2+2+2+2=8 is the same as 4x2=8. Ill explain that this number sentence can be read as 4 times 2 equals 8 and 4 groups of 2 equals 8 counters total.

4. Well discuss which number sentence is easier to write so that students understand why we use multiplication.

5. I will then direct students to a posted learning target for the unit, explaining that they will be learning different strategies to solve problems that involve multiplication.

6. Well discuss the meaning of each of the words in the learning target.

7. I will present examples of each of the strategies.

8. Ill ask students restate the posted target in unison and then record the target in their own words on their tracking sheet.

9. Students will then turn to a partner to restate it again, in their own words.

10. I will assess students understanding of the learning target with an exit slip that students will need to complete prior to being dismissed. Ill erase the learning target from the white board and have students write, in their own words, what the learning target is for our multiplication unit.

Determining Students Baseline Knowledge

Students will be given a pre-assessment taken from the Focus Math curriculum to serve as baseline data for this unit. This will assess students knowledge of a variety of strategies used to solve multiplication problems, including multiplication as repeated addition, equal groups, arrays and skip counting on a number line. It will also assess students ability to solve a word problem that involves basic multiplication and their ability to find the product of a multiplication problem that includes three factors.

Vocabulary

Equal groups, repeated addition, multiplication sentence, multiply, times, product, array, number line, skip count, double, factors, twice

Connecting to the Learner

What do you THINK might be student preconceptions related to this unit?

The x symbol may be confused with the + symbol. Students may believe that multiplication is the same as addition.

Based on my previous experiences, some students may be initially intimidated by multiplication before they have an understanding of it. I have had some students tell me that it was going to be too difficult for them to learn. I will want to keep this in mind as I introduce the unit by reassuring students and helping them build their confidence.

How will you determine/what strategies will you use at the beginning of the school year or prior to the unit that will help you learn the students life experiences, interests, and biases? How will you use this information to develop your lessons and activities for the unit?

There are a few strategies that Im interested in implementing at the beginning of the school year in order to learn of my students life experiences, interests and biases. The first thing that I would like to do is have my students complete a questionnaire. This will help build a positive classroom climate and give me information about my students learning preferences, strengths and needs. (See Student Profile document.) I would also like to establish dialogue journals to use with students. These would lend opportunity for students to have a written conversation with me. I would like to use these at the beginning of the unit to have students reflect on their previous experiences and general feelings about math. The dialogue journals may uncover some possible misconceptions and allow me to differentiate my unit accordingly. Another strategy that I would like do at the start of this unit is to engage my students in an open conversation where they can discuss their interests and what they hope to accomplish this year. While this same information may present itself through the questionnaire and dialogue journals, I feel that getting students comfortable to talk about themselves amongst the group is a powerful way for students to feel a part of the classroom community. It will likely result in students being more comfortable to ask questions and take risks throughout the unit. I will use this information to create activities that align with students backgrounds, experiences, interests and learning preferences. It will be critical that I get to know my students well at the start of the school year and that my unit addresses their individual needs accordingly.

What might the students struggle with in the unit (based on your prior experiences)? What might be common student errors in reasoning?

I plan to analyze the students preassessments in order to determine whether or not any of the following misconceptions exist. This way I will be able to ensure that they are addressed within the unit.

Confusion between multiplication (x) and addition (+).

4 x 3 may have little meaning without context. At the early stages of learning, Ill want to be sure that the x symbol be used alongside other forms of representation, such as pictures or actual objects. This will help develop a more firm conceptual understanding of multiplication.

Students may believe that when you multiply two numbers the product is larger than the factors. We know this isnt true when multiplying by 0 or 1.

Some students may struggle with the memorization of basic multiplication facts. I will want to provide daily experiences for students to practice their math fluency. These activities could include practice with flash cards, daily timed tests, games and computer programs.

Instructional Plan Progression of Learning

What is it we expect our students to learn?

Assessment Plan

How will we know if each student has learned it?

Differentiation Plan

How will we respond when some students do not learn it?

How will we respond when some students already know it?

1. INTRODUCTION OF THE UNIT

How will you introduce the unit to your students? What strategies will you use?

Introduce the unit to my students by teaching them the unit target. (See Teaching Students the Unit Learning Target in Standards and Levels of Proficiency section.)

Students use tracking sheet advanced organizer to record:

Unit learning target: By the end of this unit, I will be able to interpret, represent and explain strategies to solve problems involving multiplication.

What I will be able to do: I will explore patterns in multiplication and the connections between how equal groups, repeated addition and skip counting relate to multiplication. I will construct arrays to model multiplication and demonstrate my understanding of the Associative property. I will build fluency of multiplication facts.

How I will know if they met the target for the unit: I will be able to use different strategies to solve multiplication problems.

Students complete a before unit/after unit anticipation guide about multiplication strategies

How will you teach the Learning Target(s) for the unit to your students?

Post learning target and underline verbs

Connect to prior knowledge and experiences

Discuss the learning target as a group and share why we are learning it

Provide clear expectations and examples

Students use tracking sheet to record daily learning target

Students set personal learning goals

How will you determine if the students had a clear understanding of the learning targets for the unit? What evidence will you gather to show student understanding?

KWL chart

Use of questioning strategies through open discussions (collaborative conversations)

One-on-one discussions with students

Quick-checks

Use of ActiVotes

Students review posted learning target at the end of each lesson and verbally self-assess level of understanding

Exit passes

If your students do NOT understand the learning target(s) for the unit, what will you do to help them understand the targets?

Stop and revisit/reteach learning targets

Use a variety of questioning strategies to determine knowledge gaps

Correct misconceptions

Provide additional examples

Have a peer explain (in his/her own words) learning target to a student who does not understand

1. How will you pre-assess the students knowledge in order to gather baseline information for your starting point? Will you use a curriculum generated pre-assessment or one you create yourself? Be sure to explain how this is aligned to the learning target for the unit. How will you share the results of this with your students?

Students will be given a curriculum generated pre-assessment in order to gather baseline information for my starting point. This assessment aligns with the units learning target in a number of ways. It will determine students initial understanding of equal groups, the relation between addition and multiplication, arrays, skip counting on a number line and using multiplication sentences to compare amounts. When I share the results of the pre-assessment with my students, Ill tell them that the assessment is only being used to teach me what they already know and what they need to learn. Ill emphasize the fact that the scores they received are not being recorded in my grade book.

1. Please provide examples what types of lessons, strategies and activities you will use to both extend and enrich and/or to modify/adapt your curriculum.

For students who are struggling with the mastery of their basic multiplication facts, I will provide a multiplication chart for them to refer to when doing the practice portion of their daily time tests.

Manipulatives will be made available to students who need them as we are learning about multiplication as equal groups.

The following vocabulary words will be posted for students to refer to throughout the lesson:

Equal groups

Repeated addition

Multiplication sentence

Multiply

Product,

Array

Number line

Doubles

I will provide 1:1 assistance during recess for students who need extra support or practice with a skill.

Students who have a strong understanding of the strategies taught throughout this unit will be given an opportunity to create questions for other students to solve.

Higher achieving students will be peer leaders and assist students who are struggling.

Students with a strong understanding of their basic multiplication facts using the strategies taught will be introduced to the procedure of solving two-digit times one-digit multiplication problems.

2. BODY OF THE UNIT

What lessons will you teach to develop students understanding of vocabulary, concepts, and skills? What will be the scaffolded sequence of the lessons?

1. Understand that addition and multiplication are related.

2. Understand multiplication using equal groups.

3. Build arrays to model multiplication situations.

4. Skip count using a number line to solve multiplication problems.

5. Use multiplication sentences to compare amounts.

What strategies will you use to teach the lessons?

Direct instruction (I do, we do, you do)

Student workbooks

Notetaking

Cooperative learning

Advanced graphic organizers

Varied questioning strategies (one-on-one and in a small group)

Technology to support lessons (XtraMath.com, MobyMath.com)

Flash cards

Nonlinguistic representations

Support resources (manipulatives, visual aids, charts, outlines)

Games

What instruction will you provide regarding how to create/read/use a rubric?

Provide rubric in student-friendly language

Review the expectations for a 4, 3, 2 and 1

Provide examples

Students self-assess performance using rubric

What instruction will you provide to help students effectively complete self and/or peer assessments?

Use of tracking sheet

Rubric in student-friendly language as a tool for students to self-assess

Students self-assess orally within the small group following each lesson to identify what went well, something that challenged them and something they will do differently next time

Closely monitor student responses to determine level of accuracy

Provide correction, redirection and reteaching as needed

How will you use student work or self-assessment to make instructional decisions?

I will assess student work and self assessment and ask myself the following questions:

Have students mastered the learning target? Are we ready to move on to the next lesson as a group?

If not

What strategies can I use with the whole group to support learning?

Which student(s) needs additional support or intervention? Where are the knowledge gaps? What strategies should I use to address his/her needs?

Which student(s) have mastered the learning target and need enrichment? Which strategies might best meet his/her needs?

When and how will you teach your students how to track their progress (toward learning target)?

Students will use the tracking sheet following each lesson to track their progress. At the conclusion of each lesson, students will revisit the daily learning target and determine whether or not they felt they met the target. Ill ask students to provide specific evidence to defend their answer and record that information on the tracking sheet.

How will you build critical thinking and/or problem solving into your lessons?

Each lesson has a reasoning question that expects students to apply the learned multiplication strategy to a word problem. Each problem requires students to determine the relevant numbers, correct operation and question being asked. Other opportunities for students to analyze, evaluate and create will include cooperative learning activities, use of manipulatives and other nonlinguistic representations.

How will you help students see that the use of critical thinking and/or problem solving is moving them toward mastery of the unit learning target(s)?

Connect word problems to each daily learning target

Have students reference tracking sheet

How will you provide ongoing feedback to your students regarding their progress throughout the unit?

Designate specific time each day/week to provide both verbal and written feedback

Give formative assessments throughout and review results with students

Provide students with specific feedback throughout the unit so that they have an opportunity to reflect and improve their work

Facilitate group and one-on-on discussion regarding student progress

Correct students self-assessments as needed

How will you teach your students the ethical use of technology prior to the unit?

I plan to teach Digital Citizenship and the norms of safe, responsible behavior with technology use at the start of the school year. I plan to teach this through the use of the lesson plans available on the Common Sense Media website. These free materials are designed to empower students to think critically about their participation in the digital world.

How will you use technology effectively in your lesson instruction and assessment?

ActivBoard

Teaching websites to retrieve additional resources to supplement teaching as needed (interventions and enrichment tools)

ActiVotes as formative assessment tool

How will the students use technology during the lessons and in assessment?

Math websites

ActiVotes as formative assessment tool

2. What types of formative assessments will you use during the unit to check for ongoing understanding of concepts and skills? How will these assessments be directly tied to your learning targets for the unit? What will each measure? How will students know their scores and track their progress through the use of formative assessments to know they are making progress toward the Learning Target for the unit?

I plan to use a variety of short answer (constructed response) and multiple-choice (selected response) formative assessments throughout the unit to assess students understanding of the concepts and skills that are addressed. I will provide an opportunity for students to explain their answers or reasoning throughout the process through collaborative conversations as well. Being that my target is for students to interpret, represent and explain strategies to solve multiplication problems, Ill assess students abilities to use those strategies throughout the unit. These strategies include relating addition to multiplication, understanding equal groups, building arrays, skip counting on a number line and using multiplication sentences to compare amounts. Students will monitor their progress throughout the unit using a self-assessment tracking sheet following each formative assessment. I will work closely with them as they complete these tracking sheets so that they have an understanding as to whether or not they are making progress towards the learning target for the unit.

2. How will you address the needs of IEP and 504 students?

I will be sure to make the appropriate modifications and accommodations documented for students on IEPs and 504 Plans. Since all of the students that I work with have an IEP, it will be important that I take data on their goals throughout the unit. This data should be closely monitored and shared with students and their families.

3. CLOSURE TO THE UNIT

How will you wrap up the unit prior to the summative assessment?

Use of questioning strategies with whole group and one-on-one to facilitate discussion to determine student level of understanding

Will you do any type(s) of review activities? If so, what strategies will you be using?

Use white boards to review lessons and to assess students readiness for summative assessment

How will students reflect on their learning and determine if they have met the learning target(s)?

Have students refer to tracking sheet and review each lesson target and unit target

Have students self-assess mastery of unit target

After the summative assessment how will you provide feedback to the students?

I will provide students with specific, immediate feedback following the summative assessment. I plan to share the results with them privately and stress the importance of keeping the scores to themselves. If there are any students who struggled significantly with the assessment, I plan to conference with them one-on-one to get more information about what they felt they had a hard time with. I also want to provide time for all students to reflect on their successes and what it is they may still help with. I also want to give my students an opportunity to correct their work for any items they may have missed.

3. How will you incorporate student self-assessment through the use of a scoring rubric? How do you anticipate that this will impact student learning? How will you use technology for assessment purposes?

I plan to use a scoring rubric that is written in student-friendly language so that students are able to use it as a self-assessment tool. I will present models of student work that is matched to the criteria so that students are able to see how the criterion translates into actual products. If students have access to the rubric before, during and after a given task they will likely feel more in control and know exactly what they need to do to meet the goal as well as what to do in order to go above standard. I plan to use ActiVotes as a technology assessment tool. This student response system will allow me to poll students at any time to assess progress and adjust my teaching to address student need. These could be used for students to answer content related questions or to share how they feel they are doing with a particular skill we are working on.

3. How will you address the needs of ELL students?

Vocabulary will be posted on the wall throughout the unit to refer to. Ill be sure that ELL students have a firm understanding of what those words mean. Ill revisit each word often, asking students to provide definitions and examples. I will work closely with the ELL teacher at my school to determine what goals each student is working on so that they can be supported in the Resource Room as well.

4. What will you use as your leveled summative assessment?

I have adapted the summative assessment that is provided in the curriculum so that it is leveled and aligned with the LWSD Proficiency Scale. (See Summative Assessment document.)

4. How will you be building in problem solving and/ or critical thinking for all of your students?

Story problems are integrated into the curriculum and included in each lesson throughout the unit. These help develop students critical thinking skills by going a step further and challenging them to apply their understanding of a variety of methods used for solving problems that involve multiplication to a real life situation.

5. How are your differentiated lessons, activities, and strategies linked to the achievement of the learning targets?

The differentiated lessons, activities and strategies that I plan to implement will support the learning targets throughout the unit. They that serve as additional supports for students who may be struggling, as well as those proficient and advanced students who need to be challenged. I will use formative assessments throughout my unit to determine the need for each differentiation strategy. Depending on student need, I will adjust my instruction accordingly.

Learning Environment

Resources

What lesson-specific considerations are needed for respect and rapport, culture for learning, classroom procedures, managing student behavior and classroom physical space?

Establishment of a safe and supportive classroom environment

Establishing classroom behavior expectations as a group

Managing positive peer relationships amongst students

Welcome all student questions and comments without criticism

Practice classroom routines

Acknowledge appropriate student behavior

Assign seating of peer leaders next to students who may need additional help

What resources, technologies, materials, adopted curriculum, equipment, and/or tools will be needed to teach this unit?

Focus Math teachers manual and student workbooks

Tracking sheet

ActivBoard

ActiVotes

Netbooks

Document camera

Math manipulatives (counters)

Flash cards

Multiplication tables

Number lines

How will students use the resources, materials, and technologies during the unit?

The use of the above materials will be integrated into lessons throughout the unit. The Focus Math student workbooks will be used throughout the unit to record student work. The tracking sheet will be used for students to self-assess and monitor progress towards the learning targets and the unit target. Students will use the ActivBoard to work through problems as a group and the ActiVotes will be used as a formative assessment tool. Students will use netbooks to access online programs for extended learning opportunities and to practice multiplication facts. Students can use the document camera to display their work. Math manipulatives will be used to solidify student understand and engage students. Flash cards and the multiplication tables will serve as tools for students to improve math fluency. The number lines serve as a tool when learning how to skip count to solve multiplication problems.

How and when will you ensure that students use technology appropriately for their age level and build digital citizenship?

Prior to the start of the unit, I will teach my students the importance of being effective digital citizens. I also plan to closely monitor student use of technology throughout the unit.

Parent/Family Connection

Local and/or Global Connections

What opportunities might this unit present for communicating and collaborating with parents/families?

This unit lends itself opportunity to connect with families by sharing student progress towards the unit target and learning targets. This will be done through a parent newsletter. I also plan to work closely with families as part of an IEP team to develop and monitor each students individual math goals. In addition to that, students will have occasional homework assignments that require them to involve family participation. This will allow parents to be more informed of what their child is working on in school.

What opportunities might this unit present for communicating and collaborating with the extended community?

Throughout this unit, I will help students make connections to self and/or world. Ill discuss with students how being able to solve a multiplication problem is an important skill in and outside of school.

How will the lessons learning activities engage students with problem solving and real world connections?

If students are taught a variety of strategies to solve multiplication problems, they will be able to choose one of those strategies when faced with a real world situation that requires them to use multiplication. Real world examples are embedded throughout the unit.

Reflection

Unit Planning Template (continued)

Lake Washington School District | Unit and Lesson Planning2