##
* *Reflection: Intervention and Extension
Ratio Tables - Section 3: Task

This year I was able to have two smaller groups of instruction for this lesson. One half of the students were able to complete the original card activity independently lead by each other. The other half needed to see more examples of the use of ratio tables to solve word problems. I have attached the worksheet and drawn tables I used with this smaller group. The last page also includes blank ratio tables to use in other word problems. I find that some students, especially those with IEPs, benefit greatly from repetition. The four examples included in that document are meant to show them how the use of ratio tables can help them find missing information.

Knowing where to begin is usually a common problem for students. What is the first step? We have to show our students what it means to understand what is happening in the problem rather than immediately focusing on the process. Thus, the first step is to

- think, "which two units are being compared? is it miles per hour? dollars per hour? something else?".
- After identifying these units, students must write them into the table and
- identity the information given in the problem and the information needed to solve the problem.
- identify the operations needed between each step

Whenever students ask for a procedure throughout this rates and ratios unit, these are the steps I ask them to follow.

*Intervention and Extension: Additional Practice*

# Ratio Tables

Lesson 4 of 21

## Objective: SWBAT use ratio tables to determine whether two quantities are in a proportional relationship.

#### Do Now

*10 min*

Students enter silently according to the Daily Entrance Routine. Today’s Do Now includes a set of 6 proportion problems. Students will be given 5 minutes to word independently with a timer displayed at the board. After those 5 minutes, partnered pairs will get 2 minutes to:

**1) **Read off their answers

**2) **Finish any questions they didn’t get to finish

**3) **Explain how to solve for the **unknown**

I expect to hear students following these directions. I find that class runs much smoother when concrete, clear expectations are both given and displayed during class. In the last 2 minutes, I will be cold calling to get the answers read out loud.

*expand content*

#### Class Notes

*10 min*

Students are asked to take out a blank sheet of paper and set it up using Cornell Notes Style. Once their paper has been set up they must raise their hand to show me and then retrieve a red textbook from the back of the room. The Big Ideas Math company has Dynamic Student edition online.* *

I instructed students to turn to page 114 in their books(pg 174 in online version). I modeled the use of ratio tables to answer question #5:

I ask students to solve the next two problems using ratio tables. I display the tables I would like them to show on the board.

As I walk around I am looking out for students drawing and using these tables appropriately. Some students may only show two equivalent ratios in their table and thus must be pushed to show everything in the sample tables at the board.

After 10 minutes group work is stopped and we review the answers. I cold-call students to give me each of the values in the table and answer the question: Tell whether the ratios form a proportion. It is important to push students to use the vocabulary as much as possible through this review by answering the question in a complete sentence such as, “yes, the ratios 1/3 and 7/21 form a proportion”.

Some students may struggle to understand the concept of proportionality. Going over the activity on page 111 about “Fairness” using equivalent ratios could help. Once again, these examples may be found in the Big Ideas Math has Dynamic Student edition online.

#### Resources

*expand content*

#### Task

*20 min*

Students must complete questions 8 – 10 and 17 – 19 on the same page we reviewed in the class notes. They must show their work through complete ratio tables. If they need help figuring out how to set up the table, they may raise their hands and I will come over to help. The following general expectations for showing work are displayed on the board:

1) You must draw ratio table

2) Include the units given for questions 17 – 19

3) Answer each question in a complete sentence:

** Yes/No**, the ratios _______ and ______

**a proportion**

*form/do not form*

After 15 minutes have passed all students are asked to return to their seats to work silently for 5 minutes to finish up this task. Students who finished the entire assignment by this time will be asked to put their work up on the chalkboard.

**Mathematical Practice 5** is in use through the tables in this lesson. The tables aid problem solving and also help students understand proportional relationships through repeated reasoning (**MP8**).

#### Resources

*expand content*

#### Closing

*10 min*

Students who were able to put their work on the board will be asked to review their answers with the class and will be responsible for answering student questions. If I cannot get work on the board then I will be cold calling students to give me answers, as well as pushing students who did not finish continuing working. To show that it is valued when one finishes what they are given for class work, I give positive paycheck comments or achievement points which students may redeem for homework passes.

Students receive homework and are advised to look at the class website for guidelines on neat homework.

*expand content*

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- UNIT 1: Integers
- UNIT 2: Operations with Rational Numbers
- UNIT 3: Expressions and Equations - The Basics
- UNIT 4: Multi-step Equations, Inequalities, and Factoring
- UNIT 5: Ratios and Proportional Relationships
- UNIT 6: Percent Applications
- UNIT 7: Statistics and Probability
- UNIT 8: Test Prep
- UNIT 9: Geometry

- LESSON 1: Mastering Rational Numbers
- LESSON 2: Introducing Ratios and Rates in Word Problems
- LESSON 3: Best Buy
- LESSON 4: Ratio Tables
- LESSON 5: Quiz + Graphing Proportional Relationships
- LESSON 6: Bar Models and Ratios
- LESSON 7: Unit Rates and Ratio Tables
- LESSON 8: The Constant of Proportionality
- LESSON 9: Quiz + The Constant of Proportionality in Equations and Tables
- LESSON 10: Put it Together - Equations y = kx
- LESSON 11: Equations and Bar Models + The Constant of Proportionality
- LESSON 12: Identifying the Constant of Proportionality
- LESSON 13: Determine and Interpret Proportionality through Table and Graphs - Day 95
- LESSON 14: Quiz + Similar Figures
- LESSON 15: Scale Drawings
- LESSON 16: Map Scales
- LESSON 17: Let's Dream About a Different Place...
- LESSON 18: Practice Test
- LESSON 19: Unit 5 Test
- LESSON 20: Unit 5 Test Debrief
- LESSON 21: MAP it Out: Part 2