##
* *Reflection: Developing a Conceptual Understanding
Problem Solving with Rational Numbers - Section 2: Explore

The way I approached problem solving, by using whole number substitution, worked very well for my students. They were able to more easily see the operation that they would use. I really pushed that the kids explain to me what was going on in a problem - for example, one student could not figure out that you would divide, but was able to tell me that you would split the punch up evenly among the cups. When I asked him what operation allows you to split up a number - he could tell me division. Additionally, students had trouble with the problem of making 2/3 of a recipe. I asked the students to figure that problem out however they could - with a picture, multiple steps, whatever. Then, I had two students share their work - one that drew a picture and one that said I divided by 4 and then multiplied by three. Then, I explained to them that that is the beauty of fractions! By multiplying by a fraction you are essentially dividing something into groups (the fraction bar and denominator) and choosing a certain number of groups (the numerator).

*Developing a Conceptual Understanding: Explore Reflection*

# Problem Solving with Rational Numbers

Lesson 21 of 23

## Objective: Students will be able to solve real world problems involving rational numbers.

*55 minutes*

#### Launch

*5 min*

**Opener: **As students enter the room, they will immediately pick up and begin working on the opener. Please see my instructional strategy clip for how openers work in my classroom (**Instructional Strategy - Process for openers**). This method of working and going over the opener lends itself to allow students to construct viable arguments and critique the reasoning of others, which is **mathematical practice 3**.

**Learning Target: **After completion of the opener, I will address the day’s learning targets to the students. In today’s lesson, the intended target is, “I can solve real world problems containing rational numbers.” Students will jot the learning target down in their agendas (our version of a student planner, there is a place to write the learning target for every day).

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#### Explore

*40 min*

**Problem Solving with Fractions Notes**: For whatever reason when students see word problems they freak out - and when they see them with fractions the freak out session gains intensity. SO, I have taken problems that are commonly hard for students and rewritten them using only whole numbers. I am going to have the students work out the whole number version of the problem, and then give them the fraction version so that they can see that fractions are not so bad. I do not like to give students key words, I really like them to explain a problem in their own words - usually that is enough to determine what operation to use, without a list of key terms, as key terms are not always black and white. This method of solving problems is a good use of **mathematical practice 7** - as students are using what they already know to solve new problems.

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#### Summarize + Homework

*10 min*

**Breaking Down Problems: **For the last 10 minutes of class, students will work on breaking down a word problem. For this activity, there are four different word problems that students may be assigned. Students are to read the problem, choose an operation - and then explain in complete sentences why they chose that operation. After choosing an operation, they are to draw a picture that would supplement their explanation on why they chose that particular operation. Finally, they are to solve the problem. Since there are a variety of problems to choose from, students will be encouraged to find another student in the room that has the same problem and talk it out with that student.

**Tic-Tac-Toe Assignment: **Students will complete a tic-tac-toe homework assignment. The assignment contains a grid of 9 problems, students need to choose and complete 3 problems that would create a tic tac toe. Philosophy on Homework

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##### Similar Lessons

Environment: Urban

###### Multiplying and Dividing Signed Numbers

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Environment: Urban

Environment: Urban

- UNIT 1: Introduction to Mathematical Practices
- UNIT 2: Proportional Reasoning
- UNIT 3: Percents
- UNIT 4: Operations with Rational Numbers
- UNIT 5: Expressions
- UNIT 6: Equations
- UNIT 7: Geometric Figures
- UNIT 8: Geometric Measurement
- UNIT 9: Probability
- UNIT 10: Statistics
- UNIT 11: Culminating Unit: End of Grade Review

- LESSON 1: Integers and Absolute Value - Are two steps forward and two steps back the same thing?
- LESSON 2: Modeling Addition - Opposites Attract, You Know?!
- LESSON 3: Integer Addition Word Problems - Can You Picture It? (Two Day Lesson)
- LESSON 4: Adding Integers - What's the Rule?
- LESSON 5: Multiple Addends - More than 2 numbers to add?
- LESSON 6: Adding Integers Review
- LESSON 7: Adding Integers Test
- LESSON 8: Subtracting Integers - How does subtraction relate to addition?
- LESSON 9: Subtracting Integers Practice - Can you subtract more than two integers?
- LESSON 10: Addition and Subtraction of Integers - DOMINOES!
- LESSON 11: Adding and Subtracting Integers - Real World Applications
- LESSON 12: Adding and Subtracting Integers - REVIEW!
- LESSON 13: Adding and Subtracting Integers Test
- LESSON 14: Adding and Subtracting Signed Fractions - Remember Those Integer Rules!
- LESSON 15: Adding and Subtracting Signed Fractions Fluency Practice
- LESSON 16: Adding and Subtracting Signed Decimals - Line Up Those Points!
- LESSON 17: Adding and Subtracting Rational Numbers - Practice Makes Perfect!
- LESSON 18: Adding and Subtracting Rational Numbers - Test
- LESSON 19: Multiplying and Dividing Integers
- LESSON 20: Multiplying and Dividing Rational Numbers
- LESSON 21: Problem Solving with Rational Numbers
- LESSON 22: Fractions to Decimals - Terminate or Repeat?
- LESSON 23: Rational Number Unit Test