Wiesen 801 Project 2

  • April 2020
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Chapter 4:Multiplication Facts and Strategies

Foundational “Big” Ideas: Multiplication is best learned through the practice of strategies. Strategies highlight patterns and relationships between numbers, and can work as a visual aid to support learners. Examples of these strategies include the use of manipulative counting blocks, creating drawings and arrays showing what is being done in written algorithms, the idea of repeated addition and equal groups, and the implementation of math properties. The Go Math Curriculum provides multiple examples of how and when to use these various strategies. However, a weakness in the program is the lack of scaffolding provided for English Language Learners. Many of the story problems are very lengthy and full of math vocabulary. It is critical that we provide language support as many students are struggling in math due to these academic vocabulary and complex word problems. To help students reach success with these problems we will be creating a math vocabulary word wall, learning techniques for interpreting contextual problems, and working to incorporate additional, meaningful problems to which students can relate.

CCSS/Grade Level Content Expectations: CCSS.MATH.CONTENT.3.OA.A.3

Use 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. CCSS.MATH.CONTENT.3.OA.A.1

Interpret 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​. Standard for Mathematical Practice That We Will Continue to Develop: CCSS.MATH.PRACTICE.MP4​

Model with mathematics.

Modeling mathematics is an important skill for students to continue to develop as multiplication is a skill that will appear throughout their lives whether it’s academically, in everyday tasks, or in their future careers. It is important to take learning beyond just the classroom, and for students to be able to apply their knowledge in meaningful ways. To support students in developing this, we will continue to relate multiplication to everyday activities, encourage kids to explain their understandings to people outside of the classroom, and find ways that multiplication can relate to other aspects of learning, besides in just our math lessons.

Hello Everyone! Miss. Wiesen here! This next week we are going to continue working on multiplication! I am excited for the students to continue discovering and developing new strategies and methods that will lead to furthering their knowledge of multiplication and numbers. ​Our two learning goals are understanding how to interpret products of whole numbers and knowing how to use math strategies to solve multiplication problems. In order to reach our goals, this week we will practice the many ways to solve multiplication problems, such as drawing a picture, skip counting, using graphs, and arrays. These are all different ways of reaching a product from two factors. It is important to reinforce the idea that whole numbers are made up of smaller parts. In other words, multiplication is really repeated addition. We will continue learning through pre-recorded videos, which allows for each student to move at their own rate of learning and rewatch certain sections as many times as they need before continuing on. This way of learning has been very effective for all learning levels this school year. As you know, the videos are available at all times on SeeSaw! Sometimes these are good refreshers! In terms of homework, expect to see many word problems and questions asking for different models. ​For example: Q: ​Draw an array to model and find the answer to 2x4=? A:

2x4=8. This is shown above in my array as there are 2 groups of 4. By drawing out these problems, students can visualize what it means to ‘multiply’ two numbers and get a product. The students also have access to Imagine Math and Think Central. Both websites have many multiplication games and activities! If you have any questions, feel free to contact me via email: ​[email protected] I look forward to continuing our multiplication unit! Best, Miss. Wiesen

¡Hola a todos!    Señorita. Wiesen aquí! ¡La próxima semana vamos a seguir trabajando en la multiplicación!  Estoy emocionado de que los estudiantes continúen descubriendo y desarrollando nuevas  estrategias y métodos que conduzcan a ampliar sus conocimientos de multiplicación y  números. Nuestros dos objetivos de aprendizaje son entender cómo interpretar productos de  números enteros y saber cómo usar estrategias matemáticas para resolver problemas de  multiplicación.    Con el fin de alcanzar nuestras metas, esta semana practicaremos las muchas maneras de  resolver problemas de multiplicación, como dibujar una imagen, saltar contando, usar gráficos y  matrices. Todas estas son formas diferentes de alcanzar un producto a partir de dos factores.  Es importante reforzar la idea de que los números enteros se componen de partes más  pequeñas. En otras palabras, la multiplicación es realmente una suma repetida.    Continuaremos aprendiendo a través de videos pregrabados, que permiten a cada estudiante  moverse a su propio ritmo de aprendizaje y volver a ver ciertas secciones tantas veces como  sea necesario antes de continuar. Esta forma de aprendizaje ha demostrado ser muy efectiva  para todos los niveles de aprendizaje. Como saben, los videos están disponibles en todo  momento en SeeSaw! A veces estos son buenos refrescos!    En cuanto a la tarea, espere ver muchos problemas de palabras y preguntas sobre diferentes  modelos. Por ejemplo:    P: Dibuja una matriz para modelar y encuentra la respuesta a 2x4 =?  R:

  2x4 = 8. Esto se muestra arriba en mi matriz ya que hay 2 grupos de 4.    Al extraer estos problemas, los estudiantes pueden visualizar lo que significa "multiplicar" dos  números y obtener un producto. Los estudiantes también tienen acceso a Imagine Math y Think  Central. Ambos sitios web tienen muchos juegos de multiplicación y actividades!    Si tiene alguna pregunta, no dude en comunicarse conmigo por correo electrónico:  [email protected]  ¡Espero continuar nuestra unidad de multiplicación!    Mejor,  Señorita Wiesen 

Section 3: Formative Assessments:    Exit Tickets​: I like the idea of at the end of each lesson handing the students a half sheet of  paper with a review of what we learned that day in order to gage how well they understood the  lesson and what parts of the lesson we need to go back to the following day or during  intervention time. This formative assessment is simple yet very helpful to track student learning.  An example of what would be given to the students is: “Today we learned to multiply with 2 and  4, give me two examples of when you could multiply with 2 and 4 in your everyday life”. This is  simple but it gets the students connecting multiplication to their daily lives.     Take Home Assignments: ​On Mondays and Wednesdays the students will take home a  worksheet that reviews the previous lessons information. This formative assessment will allow  for them to continuously be thinking of previous things they have learned and be able to relate  the new information back! This will keep me aware of how students are doing as we move  towards more complex strategies. I like the idea of take home because it takes the time  pressure aspect away. We will go over these assignments as a whole group and discuss any  problems the students struggled with.     Be The Teacher:​ Students will take home the worksheet they completed that day in class and be  asked to teach a sibling, adult, or parent the math concept they learned in the given lesson. They  will have to get the worksheet signed to verify that they completed this task. This will not count  against them if they are unable to complete this task, but it is encouraged! We will also offer Dr.  Wood or myself to be taught the concept during their intervention time.     *Looking at each formative assessment, we will keep a running track of how students are doing  and where they are in their learning of the content (below expectations, at expectations, above  expectations). With this information, we can know which concepts to review and practice during  intervention time.     Mid-Chapter Check-Point: F ​ or this summative assessment, it will be important to remind the  students of this upcoming assessment to eliminate anxiety. In our morning meetings, in the  days leading up to the mid-chapter check-point, we will strategically start practicing very similar  questions that the students will see on the assessment. This will get students familiar with the  problems and allow for a practice of strategies to help them find success on this assessment.                  

Section 4: Sequence of Lessons:    Date:10/31 

Date:11/1 

Date:11/2 

Objective: ​The students  will know how to multiply  with 2 and 4.  CCSS:3.0A.A.3 

Objective: ​The students  will know how to multiply  with 5 and 10.  CCSS:3.0A.A.3 

Objective:​ The students  will know how to multiply  with 3 and 6  CCSS:3.0A.A.3 

Brief  Description/Overview:  Introduction:​ Use  manipulative blocks to  count by 2s, talk about  how this relates to  multiplication. Then count  by 4s with blocks.  We do:​ Together we will  work through unlocking  the problem on page 191.  You do:​ Students will  complete the worksheet  on their own, then work  with partners, that we  have selected ahead of  time, to check their  answers before sharing  out as a class.    Students will complete an  exit ticket at the end of  the assignment.   

Brief  Description/Overview:  Introduction: ​Review the  idea of skip counting,  refresher on skip counting  with 10s and 5s​.   Activity: ​To get kids  moving, we will get in a  circle, the instructor  (myself), will call out a  random number (with a  factor of either 10 or 5)  and we will go around the  circle until everyone has  participated in skip  counting! If students need  help with the counting,  they can ask a classmate  for help!  We do: ​Together we will  work through unlocking  the problem on page 197.  You do: S ​ tudents will  complete the worksheet  on their own, then work  with partners to check  their answers before  sharing out as a class.  Students will work with a  partner on the application  problems, 32-35, with a  partner as formative  assessment.  

Brief  Description/Overview:  Introduction: ​Play  counting by 3s song for  students, have them sing  along and get interested.  Talk about 6 being twice  the size of 3. Reflect back  on the skip counting  activity.   Activity: ​To show 6 being  twice the amount of 3, we  will use m&m’s to solve  different problems as  review and to really get  the students to visually  notice the pattern. Each  student will be give 24  m&m’s. A multiplication  problem will be on the  board and they will have  to show how to solved it  on their plate which will  have an outline of a  multiplication sentence  (___ x___=__).   We do: ​Together we will  work through unlocking  the problem on page 203.  You do: S ​ tudents will  complete the worksheet  on their own, then work  on the share and show 

part of the worksheet. As  students begin to finish  up, they will talk with a  partner about any  questions they have on  the worksheet before we  review as a whole class.   Materials Needed:  Counting cubes  Go Math textbook 

Materials Needed:  Go Math Book 

Materials Needed:  3’s video  Go Math Book 

Formative Assessment:  Students will complete an  exit ticket at the end of  the assignment.  “There are 2 groups of 5.  Draw a picture and write  out the math sentence for  this problem.  BONUS QUESTION: Tell  about a time you would  use multiplication by 2 or  by 4 in your everyday life.  Explain." 

Formative Assessment:  Students will work with a  partner on the application  problems, 32-35, with a  partner as formative  assessment. These  problems are more  complex than the  previous work with 5s and  10s and allow the  students to look at 5s and  10s in a different way.  

Formative Assessment:  Students will be matched  up with two other  students in the classroom  to work on an exit ticket  that will show us their  learning. On this exit  ticket it will ask “Use 5s  facts and addition to find  the answer to 6 x 6.  Explain with a model and  show your work.” If  students finish this  quickly, they will be asked  to independently create a  story problem involving  3s and 6s. The story  problems will be switched  among the group of 3 to  be completed.  

Strategies for meeting  the needs of all learners:  -Partner work is allowed  for their assessment as it  provides support for  students learning this  new content.  -Allow for students to use  number lines or counting  blocks 

Strategies for meeting  the needs of all learners:  - I will print off number  lines that count by 3s and  6s. These are two  numbers that I initially  struggled with so support  is important.  -Students will have  access to manipulatives. I 

(This may seem surface level,  but it is important for students  to have this practice and really  master 2s and 4s before we  continue onto other numbers.) 

Strategies for meeting  the needs of all learners:  -Some students may  benefit from using a  number line  -All students are allowed  to use their math journals,  which have examples of  arrays and models of  multiplication which can 

serve as a reminder.  -I will check in multiple  times throughout  independent work time  with M.C. and A.T.,  encourage both students  to continue using the  counting cubes. 

-check in with A.V. and  M.C.  -Review with I.G. counting  by 5s and 10s, go through  number line to help  visualize this skip  counting.  

will work on the first few  problems with C, A, and  M.C..   -Check in with K.B. to  make sure she is on task  and working through the  tasks.  

Date: 11/5 

Date:11/7 

Date:11/8 

Objective: ​The students  will know how to use the  distributive property.   CCSS:3.0A.A.3 

Objective: ​The students  will be able to connect the  concept of arrays to the  distributive property.   CCSS:3.0A.A.3 

Objective:​ Students will  continue to practice using  the distributive property  and how to multiply with  7.   CCSS:3.0A.A.3 

Brief  Description/Overview:  Introduction: W ​ e will talk  about the word distribute,  and have students talk  about what that could  mean in math. Together  walk through what the  distributive property is.  Create an anchor chart  together to explain to  others the distributive  property. This will be  displayed for the whole  class.   We do: ​Together we will  work through the activity,  using counting blocks to  model. Do the first  problem of the worksheet  before the students go off 

Brief  Description/Overview:  Introduction:  Think-pair-share on the  distributive property and  arrays. How they could be  connected.   We do: ​Use manipulatives  to create arrays on ELMO  and in small groups  based on product of using  distributive property.   You do:​ Students will  work on an Engage NY  module independently  before we review the  worksheet as a class.  

Brief  Description/Overview:  Introduction​: Watch video  on the distributive model.  Do a think-pair-share on  what we learned from the  video. Show strong  examples of their exit  tickets from the previous  lesson as a way to refresh  on the distributive model  (try to find exit tickets that  used the number 7!). Talk  about the commutative  property that we learned a  few weeks ago. These  can be labeled on an  anchor chart that we  create in this intro.  We do: ​Talk about  strategies we can use 

     

when multiplying by 7, how  these properties can help  us. ​Guide students through  the Unlock the Problem  together. They should  follow along and complete  the work alongside of the  teacher demonstration.  Walk students through the  rest of the worksheet and  what is expected of them  by the end of math time.   You Do: S ​ tudents will  independently complete  the rest of the worksheet.  An adult in the classroom  will check the share and  show section as a  formative assessment/exit  ticket.    

to independently work.  You do: ​Students will  independently complete  the engage NY module  before we check it as a  class. They are  encouraged to use their  counting blocks.   Students will be given an  exit ticket.   Activity:​ (for morning  circle before math) We  will play the beach ball  game. On the beach ball  will be multiplication  problems with numbers  we have already learned  about. This will be a  quick, but active review.   Materials Needed:  Counting blocks  Engage NY sheet 

Materials Needed:  Counting  blocks/manipulatives   Engage NY sheets 

Materials Needed:  Go Math book  Anchor chart  

Formative Assessment:  Exit Ticket:​ Explain the  distributive property in  writing and then explain  your explanation to a  partner, make sure you  get a partner initials to  confirm that you  explained the distributive  property. If time, write  down two times they  would use the distributive  property to find products.  

Formative Assessment:  Exit Ticket: ​Students will  each write out an  equation where the  distributive property is  used. They will exchange  these equations with  partners, where they will  each solve the problem  and use model arrays to  show the problem. These  will be handed in to be  checked by the teacher.   

Formative Assessment:  An adult will check that  students have completed  the share and show  section of the worksheet.  These 5 problems will  allow the students to  show their understanding  of the concepts. If  multiple students seem to  not understand, we will  review the concepts and  work as a small group  until we are all on the  same page.  

Strategies for meeting 

Strategies for meeting 

Strategies for meeting 

the needs of all learners:  -Encourage the use of  counting  blocks/manipulatives  -allow for students to  check in with table mates  if they are struggling.  -check in with A to make  sure she can explain what  the distributive property  is.   -Check in periodically  throughout the lesson  with M.C. and I.G. 

the needs of all learners:  -Check in to review  concepts with M.C. and  I.G.  -Encourage manipulatives   -remind students that  their math journals are  there to help.   -Allow A to work with E.V.  if necessary  

the needs of all learners:  -Place the anchor chart  with examples in a clear  area for the students  -Remind A, M.C. and A.T.  that they can use their  math journals to remind  them of these concepts.   -Check in with I.G. after a  few minutes of  independent work time  -Sit with A and have her  repeat the concepts.  

  Date:11/9  Objective: ​Students will review the new concepts they have learned in this chapter  and apply their skills during a mid-chapter checkpoint.  CCSS:3.0A.A.3   Brief Description/Overview:  Intro: ​As a group we will verbally make a list of all we have learned/practiced over  the past few lessons. Ask students if they want to review anything that is still  confusing for them. Work through any questions the students have. (Use  knowledge of previous exit tickets/assessments to help aid this discussion).   We do:​ Together we will look at the mid-chapter checkpoint, walk through what is  expected in each section. We will complete the vocabulary section as a group.   You do: ​Students will independently work to complete the checkpoint.   Materials Needed: ​Go math book  Formative Assessment: T ​ he students will be assessed based on their  performance on the mid-chapter checkpoint. It is important to look at their learning  and the progress they are making. It will help me to see areas where students are  still confused and to help me adjust my teaching.   Strategies for meeting the needs of all learners:   - Be sure to provide language support with the math vocabulary   -Remind students of strategies we have learned   -Have I.G., A, and M.C. sit with adult to make sure they are focused   -make sure to be circulating to see that all students are working.  

  Date: 11/12 

Date: 11/14 

Date:11/15 

Objective: ​The students  will know how find and  identify patterns on the  multiplication table.  CCSS:3.0A.A.3 

Objective:​ The students  will know how to multiply  with the number 8.   CCSS:3.0A.A.3 

Objective: ​The students  will know how to multiply  with the number 9.  CCSS:3.0A.A.3  

Brief  Description/Overview:  Introduction:​ Discuss  what a pattern is, where in  math or in everyday life  we see patterns.   We do:​ Display an image  of a multiplication table  ask the students if they  see any sort of patterns.  Highlight/write down  students ideas. Together,  work through Unlock the  Problem.   You do:​ Have students  complete the rest of the  worksheet independently.  Make sure students  complete the exit ticket  as a formative  assessment.    

Brief  Description/Overview:  Introduction: ​Begin with a  class discussion on what  we learned about patterns  in multiplication the last  lesson and how we can  use this when helping us  learn how to multiply with  the number 8.   Activity:​ We will play the  beach ball game. On the  beach ball will be  multiplication problems  with numbers we have  already learned about.  This will be a quick, but  active review.   We do: ​Together we will  work on Unlock the  Problem. I will review  strategies with the  students on how to  properly complete the rest  of the worksheet.   You do:​ Students will  work in small groups (a  mix of learning levels to  allow those with a greater  understanding to support  those struggling) to  complete the rest of the  worksheet. As a group 

Brief  Description/Overview:  Introduction: ​Talk about  the idea of repeated  addition, the tools we  have learned in  multiplication in the  previous lesson. (possibly  teach the finger trick)  -Think-pair-share of how  we can use previous  knowledge of  multiplication in our  current learning of 9s.   We do: ​Together work  through unlock the  problem. Walk through  expectations of the rest  of the worksheet.  You do: S ​ tudents will  work independently on  the rest of the worksheet.  Have the students pair up  to compare answers  before we check as a  group.  

they will have to agree on  all their answers and be  able to explain their  reasonings before we  review the worksheet as a  whole class.   Materials Needed:  Go math textbook  Multiplication tables  

Materials Needed:  Go Math textbook   

Materials Needed:  Go Math textbook    

Formative Assessment:  Students will be matched  up with another student in  the classroom, not  someone they sit next to  as we want them to get  some movement in. With  their partner they will  discuss how  multiplication is related to  addition and draw a  model that explains this.  They can use  manipulatives or other  objects in the classroom  and then take a picture to  turn into Seesaw.       SUGGESTED HOMEWORK  BUT NOT GRADED:​ Each  student will take home a  copy of the multiplication  table and discuss with a  parent, sibling, or adult  the patterns they  discovered in the  multiplication table and  how this can be help them  as we continue with  multiplication. They will 

Formative Assessment:  3-2-1 EXIT TICKET:  Students will tell 3 facts  they learned in this lesson  or in previous lessons in  this chapter, 2  questions/points of  confusion they still have  about what we have  learned, and 1 thing they  feel they have mastered  and could teach to  someone else.  (This will allow me to  keep track of individual  student progress and to  see if I can match  students up to help teach  each other things that one  student may still be  struggling with. A new  perspective and way to  look at math can be all it  takes for it to click with a  student!) 

Formative Assessment:  Have students share a  problem where they had  different answers, how  each of them solved it,  and how they came to the  conclusion of which  answer was right. This is  a great way to have the  students walk through  their thinking and identify  any misunderstandings.  In an exit slip, they will  explain the correct way of  working through the  problem and what they  learned from seeing a  partners work.  

have to write out what  they explained and how  they taught the other  other person. This forces  the students to reflect on  their knowledge and  learning.   Strategies for meeting  the needs of all learners:  -We will recommend  using different colors for  different patterns   -I will make sure A, I.G.,  are correctly identifying  patterns and highlighting  accurately.   -I will circulate to make  sure all students are on  task.   -As circulating, point out  any misunderstandings  

Strategies for meeting  the needs of all learners:  -Encourage students to  create number lines if that  will help them  -Remind students of the  patterns and tools we  have learned when  applying multiplication   -Allow for manipulatives  to be used  -Sit next to A to make  sure she is on the right  track   -Check in with M.C. to  make sure she is on the  right track 

Strategies for meeting  the needs of all learners:  -Encourage the use of  manipulatives  -Remind students of  previous tools   -Check in with A, I.G., and  M.C.   -If enough students are  struggling, call them back  to review multiplying by  9s.   -If some students finish  early, have them help  those who are still  struggling  

  Ideas for Intervention time:     -Beach ball that has multiplication problems written on it. Small group will play catch with the  ball, where your thumb lands is the problem you write on the board and either answers yourself  or phone a friend for help. After each lesson, we will add the new numbers we learned to  multiply by.     -The Cookie Challenge game, created in TE801.     -multiplication flash cards for students to do independently      

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