Lesson Plan Template: Confirmatory or Structured Inquiry
Learning Objectives: What will students know and be able to do as a result of this lesson?
Students will gain a stronger understanding of division which they will show in the following ways:
Students will use place value blocks to solve a division problem with a dividend of 3 digits in which the hundreds block must be decomposed to 10 tens. Students will use precise place value language to justify their solution.
Students will efficiently use multiplication to solve division problems with 3-digit dividends and 1 or 2-digit divisors. Students will accurately record each equation.
Students will break apart 3 digit numbers mentally to solve division problems then record and explain their strategies.
Prior Knowledge: What prior knowledge should students have for this lesson?
- Students should be able to decompose and recompose numbers in multiple ways.
- Students should be familiar with products of two one-digit numbers.
- Students should be able to apply the distributive property of multiplication and division to problems resulting in products or quotients less than 100.
- Students should be able to solve a division problem as an unknown-factor problem.
- Students should have some ability to make sense of problems and persevere in solving them as they do math.
Guiding Questions: What are the guiding questions for this lesson?
- What does division do to a quantity?
- What is the relationship between multiplication and division? How are they the same? How are they different?
Introduction: How will the teacher introduce the lesson to the students?
The"Hook" and Activation of Prior Knowledge
Open the lesson with the Formative Assessment "My Favorite No" using a missing factor problem in an area model.
1. Have each student write his/her name and response on an index card.
2. Post the following array problem and ask the students to find the missing factors and partial product
3. Collect the cards. Then sort the cards saying aloud "yes" for the cards which are correct and "no" for the cards which have an error. This can be done with a touch of drama so that students will begin to moan when they hear a "no" and cheer when they hear a "yes."
4. Select an incorrect response that has the most frequent misconception or through analyzing this error an important point could be reviewed.
5. Record the student's response on the board.
6. Ask the students what is correct about this response. Have students describe what knowledge is evident in this response.
7. Then ask the students what error is in the response and why they think a student might make this error. A quick check of the cards will tell you which students are confused and what misconceptions students still have. If students miss this problem, consider having them begin with the division problem that requires the use of the manipulatives.
Investigate: What question(s) will students be investigating? What process will students follow to collect information that can be used to answer the question(s)?
The "Hook" for this lesson.
You may do this activity as centers or print the handout (4 slides) mode of the PowerPoint and give each student a copy.
Tell a story similar to the following to the students.
T: When a group of kids get together, what do they like to brag about? What do you like to brag about?
T: Well, there are some very special kids, I know, who like to brag about how great they are at math. (Let the students joke about this.) Did you know I brag about your math abilities? Sure, I do … since you are all great mathematicians.
- These kids, Billy Bob, Marybelle, and Bubba have little math quirks. (Show the first PowerPoint slide.) Your mission today is to see if you can solve some division problems and be as quirky as they are.
- Billy Bob loves to prove that he is right in simple yet clear ways. He says he can use place value blocks to solve any division problem. So, at this center you will use the place value blocks to represent this division problem. When you have finished, record one idea about division that this center points out.
- Marybelle loves to figure out ways to break apart numbers to make the math easier to do. At this center, your mission is to mentally solve these division problems like Marybelle. Think about the number and strategically figure out how to break one of them apart so it is easy to find an answer mentally. Today, please record each step and be ready to explain why you chose to solve it as you did. When you have finished, record one idea about division that this activity brings out.
- Finally, we have Bubba. Bubba just doesn't like to divide so he multiplies constantly. See if you can solve these division problems by multiplying … well you might have to do a little subtraction also. When you have finished, record one idea about division that this activity points out.
Divide the students into three groups and let them begin. Allow about 15 minutes per rotation.
Analyze: How will students organize and interpret the data collected during the investigation?
Circulate around the room to observe and help students. As you circulate make notes of the specific examples you wish to show during the closure. The following discusses Student Feedback that can be given at each center.
At Billy Bob's place value block center, ask the students what division does to numbers. (It splits a number into equal groups to tell you how many groups you have or how many are in each group.)
Questions might include,
- "Where are your 4 equal groups?"
- "What roadblock is stopping you from creating the 4 groups?" (There are only 3 100 flats.)
- "What can you do to the hundred flats so that you can then share equally between 4 groups?"
- "How many tens do you have after decomposing the 300?" "How many are in each group?"
At Bubba's multiplying center, check to see the students are recording their work in an organized efficient manner. They could use T-charts or just write the equations neatly.
Questions might include,
- "How are you organizing your work so that you can clearly see your answers?"
- "What is the total amount you have in all?" (ex. 486)
- "Could you start with 100 groups of 9 or 100 x 9?" (No, that's too big, 900.)
- "Then where would you like to start?" If a student says 10 x 9, consider encouraging them to chunk the numbers a bit more but still keep a simple multiplication problem. For example, "Could you make 50 groups of 9 or 50 x 9?" (Yes, that would be 450.) "How many more do you need to make 486?" (36)
- "What multiplication sentence would you like to try now?"
- "So, how many groups of 9 do you have?"
- "What piece of knowledge did you learn about division from this activity?" or
- "What piece of knowledge about division does this activity point out?"
At Marybelle's decomposition center, ask the students what division does to numbers. (See Billy Bob's explanation.)
Scaffolding questions might include,
- "How many hundreds to you have in 369? How many would be in each group if you split it between 3 groups?"
- Repeat the same interaction with the tens and the ones.
- Note that in 408/4 there are no tens to be shared equally.
- And, in the 126/2 problem they will need to think of having 12 tens to split between 2 equal groups.
- "What piece of knowledge about division does this activity point out?
Closure: What will the teacher do to bring the lesson to a close? How will the students make sense of the investigation?
Show the picture of the place value block center. Ask a student to explain their thinking on how they solved it. Be sure to discuss the necessity to decompose the hundreds so that the quantity could be divided. Record a piece of knowledge that could be noted about division from this center on a document camera or the board. Students could copy this sentence into their notebooks if they haven't already noted a piece of knowledge for this center.
Process the multiplication center. Be sure to show the most efficient strategies and ask the students why someone would want to solve the problem this way. (It's less work.) Discuss why they had to subtract at this center. (You have to subtract to find out how much still needs to be divided. Just as you do in the standard algorithm.) Again, record a sentence about a piece of knowledge from this center.
Finally, discuss different students' strategies for the mental division and note a piece of knowledge from this center. Point to all that is on the board and ask the students what is the same about every strategy that is on the board.
While the students may note some worthy similarities, the following should be highlighted:
- Every strategy involved finding equal groups. That's important because that is what division does.
- Every strategy involved breaking apart numbers. We do that a lot in mathematics so we want to get strategic or efficient in the way we break apart numbers.
Be sure students have pieces of knowledge written in their notebook and applaud their hard work and brilliant thinking. Suggest they go home and brag about their work in math today.
Listening to student conversations during the Guided Practice and the Closure will provide a teacher with information on the students' understanding; a more formal assessment is attached. The questions require reasoning and explanations. Answering 3 out 4 questions would indicate a strong understanding of the topic. Please see the answer key for model responses to the explanations.
summative assessment answer key.docx
My Favorite No... there is a video of a teacher using this strategy on Teaching Channel. Video: Open video.
For this lesson, the quick assessment will focus on finding a missing factor in an area representation. See the Teaching Phase for each step. A quick check of the cards will tell you which students are confused and what misconceptions students still have. If students miss this problem, consider having them begin with the division problem that requires the use of the manipulatives.
Feedback to Students
During the activity, circulate among the students to monitor their work, probe their thinking and scaffold the task for students needing assistance. The Guided Practice section includes specific feedback for each center.