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