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* *Reflection: Problem-based Approaches
Using Clues to Multiply or Divide - Section 1: Opener

To me, this is a very important lesson. Historically, my students have problems with word problems. Exposing students to problem-based problems help develop thinking, problem-solving skills, and self-directed learning.

By going over clues and giving the students practice finding the clues will make them more aware of applying this skill in the real world. This is a life long skill that the students must know in order to be "thinkers" and "problem-solvers."

*Why teach this lesson?*

*Problem-based Approaches: Why teach this lesson?*

# Using Clues to Multiply or Divide

Lesson 4 of 23

## Objective: SWBAT recognize clue words in word problems to help them multiply.

*45 minutes*

#### Opener

*5 min*

Students need to know clues to help them know when to multiply or divide. I feel that if they learn key words to help them, then all students can master solving real-world problems. Once they find the clue words, they can solve word problems involving multiplicative comparison by using drawings and equations **(4.OA.A.2). **

I have the students think about a time when they may need to multiply or divide? I let one or two students share their thoughts. I tell them that today, they will learn key words to help them know when to multiply or divide. At the beginning of this lesson, I will let the students know that to become really good at solving word-problems, all they need to do is look for clue words. I share with the students the importance of learning "clues" because this skill will be used for years to come, even as adults.

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#### Direct Instruction

*10 min*

I call my students to the carpet as we have whole class direct instruction because I want to be near my students, and I want to make sure that they all are attentive. I show the clue words (Clue Words to Multiply or Divide.pptx) on the Smart board. I give the students a few minutes to study the group of words. I give a practice problem and see if the students can find the clue. My students know that as we discuss anything whole class, they have the freedom to interject to as questions or share their thoughts. Together, we work on a sample problem.

Sample:

Ten students went to the basketball game. They each paid $3.00 to get in. How much money did they pay altogether?

I ask the students a series of questions to help them solve the problem.

1. How many students went to the basketball game?

2. How much did they each pay to get in?

3. What clue word(s) do you see?

4. What operation should you use: addition or multiplication? Why?

5. What is the equation?

From answering the questions, the students should realize that this is a multiplication problem because a number is repeating. The clue word for this problem is "altogether." I tell the students that this is a clue to multiply because we are trying to find a total. Also, I share with the students that they could get the answer through addition, but it is a multiplication problem because the number is repeating.

Sample # 2:

There were 12 people sitting at the table. They shared equally a cake. The cake was cut into 24 slices. How many slices did they each get?

I give the students a few minutes to think about the problem.

1. How many people were at the table?

2. How many slices of cake were there?

3. What clue word(s) do you see?

4. What operation will you use to solve this problem?

5. What is the equation?

I call on the students to answer the questions. From their responses, they should be able to see that this is a division problem. I tell the students that now they will practice the skill in groups.

#### Resources

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#### Group or Partner Activity

*20 min*

To give the students pratice on the skill, I let them work as pairs. I like for my students to work in small groups because it allows all of the students a chance to be heard and share their thoughts or justifications for their answers **(MP3).** Also, they must communicate precisely to others within their groups **(MP6)** using math terminology appropariate for the skill.

I give each group a copy of the clue words (Group Activity Using Clues to Multiply or Divide.docx.) They should use this list of clues to help them solve the real-world problems **(MP5)**. In their groups, the students will work together using a group activity sheet with real world problems. They must reason abstractly by decontextualizing the information and representing it in multiplication equations **(MP2)**. The students should make sense of the problem **(MP1)** by discussing the clues and solving them using the standard algorithm.

As the students work, I walk around to monitor. Some of the students are familiar with the clue words for multiplication and division, but others are not. My whole point of the lesson is to familiarize the students with these clue words so that they will know (without a doubt) what operation to use if they see these words. The students must be able to solve the problems as well. This involves using models and equations to solve.

My early finishers can practice multiplying at the following site: http://quizlet.com/6041106/flashcards

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#### Independent Activity

*10 min*

The students will complete an Independent Assignment Using Clues to multiply and divide. I need to assess students independently to make sure they are all comprehending the skill. I will put a problem on the Smart board for the students to work. The students will use paper and pencil to solve the problem. I will walk around to visually assess the students understanding, keeping track of all students who I will work with in small group for remediation.

My teacher wanted to give her students a special gift. She decided to buy beautiful pencils for each of her students. She bought 20 students 3 pencils each. How many pencils did she give in all?

Clue word: ______________

Equation: _______________

To close the lesson, I have one or two students share their answers. This gives those students who still do not understand another opportunity to learn it. I like to use my document camera to show the students' work during this time. Some students do not understand what is being said, but understand clearly when the work is put up for them to see.

The closure is also the time for students to ask any questions that they may have for me. I do no like to end my class with students being confused about anything.

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- UNIT 1: Fractions
- UNIT 2: Skills Review
- UNIT 3: Algebra
- UNIT 4: Geometry
- UNIT 5: Patterns & Expressions
- UNIT 6: Problem-Solving Strategies
- UNIT 7: Decimals
- UNIT 8: Measurement and Data
- UNIT 9: Multiplication and Division Meanings
- UNIT 10: Place Value
- UNIT 11: Adding and Subtracting Whole Numbers
- UNIT 12: Multiplying and Dividing

- LESSON 1: Multiplying by Multiples of 10 and 100
- LESSON 2: Using Rounding to Estimate
- LESSON 3: Is Your Answer Reasonable?
- LESSON 4: Using Clues to Multiply or Divide
- LESSON 5: Using Mental Math to Multiply 2-Digit Numbers (Are You My Match?)
- LESSON 6: Multiplying 2-Digit Numbers by Multiples of Ten
- LESSON 7: Multiplying Greater Numbers
- LESSON 8: Modeling: Multiplying a 2-digit number by a 1-digit number
- LESSON 9: Multiplying 2-digit number by 1-digit number
- LESSON 10: Multiplying a 3-digit number by a 1-digit number
- LESSON 11: Estimating Products
- LESSON 12: Multiplying 2-Digit by 2-Digit Numbers
- LESSON 13: Multiplication: Arrays and an Expanded Algorithm
- LESSON 14: Multiplication Unit Assessment
- LESSON 15: Using Mental Math to Divide
- LESSON 16: Estimating Quotients
- LESSON 17: Dividing with Remainders
- LESSON 18: Dividing 2-Digit by 1-Digit Numbers
- LESSON 19: Dividing 3-Digit by 1-Digit Numbers
- LESSON 20: Deciding Where to Start Dividing
- LESSON 21: How Much Will They Get?
- LESSON 22: Factors
- LESSON 23: Prime and Composite Numbers