COLLABORATIVE
- Build on each other’s ideas through collaboration
- Require full sentence responses
- Use wait time
INTERPRETIVE
- Concrete models (math manipulatives)
- Visuals to support understanding
- Model academic language and vocabulary
PRODUCTIVE
- Graphic organizer to record
- Provide sentence frames
MULTIPLE MEANS OF ENGAGEMENT
- Foster Collaboration and community
- Develop self-assessment and reflection
MULTIPLE MEANS OF REPRESENTATION
- Activate or provide background
- Clarify vocabulary and symbols
MULTIPLE MEANS OF ACTION & EXPRESSION
- Facilitate managing information and resources
- Build fluencies with graduated levels of support for practice and performance
Multiplying Using Partial Products
Lesson Overview
This lesson was designed for a 4th grade class in San Bernardino County, with 1 expanding EL student, 1 bridging EL student, 5 students with special needs and 2 GATE students.
This lesson involves students collaborating to model multiplying using partial products using a visual model with the teacher guiding and monitoring their understanding. The lesson will begin with an engaging ‘same but different’ math talk. Students then work with their shoulder partner on individualized whiteboards to collaborate the similarities and differences of a given image of base ten blocks and place value disks. The students will be given hands-on opportunities with their shoulder partner to develop their understanding of partial products through the use of a manipulative, e.g. place value disks.
Student Learning Goals/Objectives
- Content- Students will be able to multiply a three digit number by a one-digit number using a visual area model and explain the calculation.
- Language- Students will be able to multiply a three digit number by a one-digit number using a visual model using specific words: attributes, describe, contains, consists of, and properties in a class, group, and partner conversational exchanges and discussions.
Lesson Segments
Engage: Math Talk- Same but Different (10 min)
Hooks / SetIn this activity students will be encouraged to make observations of two images. They will compare the images, calling attention to both how they are the same and how they are different. They will think-pair-share orally with their shoulder partner and then with the whole class. This will hook the students into the lesson by sparking their curiosity and get them engaged about the lesson.
Materials
- Slide Deck
- Whiteboard Markers
- Erasers
Instructions:
The teacher displays the slide with the two images (base ten block set and place value disk set)- see slide deck. The teacher asks the students to make an observation of the two images. The teacher asks the students the following guiding questions
- What makes these two pictures the same?
- What makes these two pictures different?
The students are given wait time/time to think about their response. Then students write down their response on their whiteboard. The teacher provides a sentence frame for the students to use
- The two pictures are the same because……
- The two pictures are different because …….
Then the students share their responses orally with their shoulder partner using the sentence frames. Students partner talk, taking turns and actively listening to their partner.
Let students know that their ideas and contributions are valued, and emphasize the importance of respect, active listening, and open-mindedness.
As students share with their shoulder partner, the teacher will walk around to monitor students and informally assess student participation and responses.
After 2 minutes, the teacher asks students to share their responses with the whole class.
The teacher will clarify on the slide deck the base ten block set and the place value disk set are equal in value. The large cube = 1,000, the flat= 100, the stick = 10, and the small cube = 1.
STUDENT EXPECTATIONS
Students actively participate in class by taking turns sharing their responses with a partner through collaboration and discussion.
Students use sentence frames as a scaffold to speak in complete sentences.
Review Multiplication Vocabulary-Mix-Pair-Share (10 min.)
Hooks / SetIn this activity students will mix around the room to music. When the music stops, the students pair up with the classmate closest to them. The teacher then gives the class a review question to discuss with their partner.
Materials
Instructions:
The teacher announces for students to mix around the class while the music is playing. When the music stops, the teacher announces
“Pair Up.” The students pair up with the classmate closest to them. The teacher will display a review question form the slide. The students will discuss their response with their partner. The teacher asks students to share their response to the whole class. Afterwards, the teacher will reveal the answer to the question to confirm the student's responses or correct any misunderstandings. Then the teacher continues the music and repeats the steps until all the review questions have been discussed. As students share with their partner, the teacher will walk around to monitor students and informally assess student participation and responses.
Review Questions:
- What is multiply?
- What is a factor?
- What is a product?
- What is a equation?
The teacher provides the following sentence frames for language support
- I think _________ because ______________
- I agree with ________ because ___________
- I disagree with _______ because __________
Student Expectations
Students actively participate in class by taking turns sharing their responses with a partner through collaboration and discussion.
Students connect the questions and observations to prior knowledge or experiences.
Students build on each other’s ideas, ask follow-up questions, or respectfully disagree with their partner’s thoughts.
Model Multiplying Using Partial Products (30 minutes)
Demo / ModelingIn this activity students are given a set of place value disks (includes 100, 10, and 1). They will work with their shoulder partner to multipy a three digit number by a one-digit number using place value disks to create partial products.
Materials:
- bag set of place value disks (includes 100, 10, and 1)
or template of place value disks for students to cut (see template)
- multiplication work mat
- multiplication worksheet
Instructions:
The teacher will refer back to the Same but Different slide on the slide deck.
The teacher will remind students that the base ten block set and the place value disk set are equal in value.
The teacher will model on the slide deck how to multiply a three digit number by a one-digit number using place value disks. The equation that will be model is 3 x 231.
The teacher will display the multiplication work mat on the slide deck. The teacher will display the equation 3 x 231 in the given box on the work mat. Next, the teacher will diplay the factor 3 in the given box on the work mat. Afterwards, the number 231 will be expanded based on its place value. The 2 will be above the hundreds, the 3 will be above the tens, and the 1 will be above the ones on the work mat.
The teacher will clarify that the number 231 is being multiplied by 3, which means there are 3 groups of 231. The teacher will use place value disks to represent the number 231 on the work mat. The teacher will display 3 groups of 2 place value disks labeled 100 to represent 200 on the work mat. Next, the teacher will display 3 groups of 3 place value disks labeled 10 to represent 30 on the work mat. Finally, the teacher will display 3 groups of 1 place value disks labeled 1 to represent 1 on the work mat.
The teacher will have the students orally count by 100s to add up the total number of place value disks in the hundreds sections of the work mat. The teacher will display the sum equals 600.
The teacher will have the students orally count by 10s to add up the total number of place value disks in the tens sections of the work mat. The teacher will display the sum equals 90.
The teacher will have the students orally count by 1s to add up the total number of place value disks in the ones sections of the work mat. The teacher will display the sum equals 3.
Afterwards, the teacher will discussion that the numbers 600, 90, and 3 are called partial products. The teacher will display the definition- a product of two numbers when a number is broken up into parts, multiply the parts separately, and then add them together on the slide deck. To find the product of 3 x 231, you will need to add up the partial products. The product is 693.
The teacher will distribute the multiplication work mat and place value disks for shoulder partners to share.
The teacher will provide a worksheet with multiplication equations with three digit numbers multiplied by a one-digit number. The students will solve the multiplication equations on the work mat using the place value disks. Afterwards, the students will add the partial products to find the product of the multiplication equations for the worksheet.
Students will work collaboratively and discuss their understanding of multiplying a three digit number by a one-digit number using partial products with their shoulder partner.
*Teacher Note- Alternate visual model to represent numbers on the work mat include base ten blocks
STUDENT EXPECTATIONS
Students are collaborating with their shoulder partner to multiply a three digit number by a one-digit number with a visual model using partial products.
Students express their ideas, listen to others’ ideas, and work together to solve the given problems.
Assessment
Informational Checks for Understanding: (Students choose how to respond using models or drawings)
Student questioning
Student responses/ student collaboration
Student participation and engagement
- Sharing ideas, use of visual models, disagreeing/agreeing
In this activity students will reflect on their learning of multiply a three digit number by a one-digit number with a visual model using partial products.
Materials:
- 3-2-1 Exit Ticket (free download)
Instructions:
The teacher will provide students a student self-reflection exit ticket. Students will reflect on 3 things they learned about multiplication using partial produts, 2 things they found interesting about multiplication using partial produts, and 1 question they still have about multiplication using partial produts.
Students also monitor their progress by reflecting on whether they met their learning goals or not yet, and on how to adjust their learning moving forward to meet their learning goals.