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### Overview

This lesson will allow students to become familiar with ratios. In this investigative lesson students will compare ratios and determine equivalent ratios. This is an introductory lesson to be used as part of a unit.

This is a College- and Career-Ready Standards showcase lesson plan.

## UP:MA19.6.1

### Vocabulary

• Ratio
• Ratio Language
• Part-to-Part
• Part-to-Whole
• Attributes
• Quantity
• Measures
• Fraction

### Knowledge

Students know:
• Characteristics of multiplicative situations

### Skills

Students are able to:
• Compare and contrast additive vs. multiplicative contextual situations.
• Identify all ratios and describe them using "For every…, there are…"
• Identify a ratio as a part-to-part or a part-to whole comparison.
• Represent multiplicative comparisons in ratio notation and language (e.g., using words such as "out of" or "to" before using the symbolic notation of the colon and then the fraction bar. for example, 3 out of 7, 3 to 5, 6:7 and then 4/5).

### Understanding

Students understand that:
• In a multiplicative comparison situation one quantity changes at a constant rate with respect to a second related quantity. -Each ratio when expressed in forms: ie 10/5, 10:5 and/or 10 to 5 can be simplified to equivalent ratios, -Explain the relationships and differences between fractions and ratios.

## UP:MA19.6.3

### Vocabulary

• Rate
• Ratio
• Rate reasoning
• Ratio reasoning
• Transform units
• Quantities
• Ratio Tables
• Double Number Line Diagram
• Percents
• Coordinate Plane
• Ordered Pairs
• Tape Diagrams
• Unit Rate
• Constant Speed

### Knowledge

Students know:
• Strategies for representing contexts involving rates and ratios including. tables of equivalent ratios, changing to unit rate, tape diagrams, double number lines, equations, and plots on coordinate planes.
• Strategies for finding equivalent ratios,
• Strategies for using ratio reasoning to convert measurement units.
• Strategies to recognize that a conversion factor is a fraction equal to 1 since the quantity described in the numerator and denominator is the same.
• Strategies for converting between fractions, decimals and percents.
• Strategies for finding the whole when given the part and percent in a mathematical and contextual situation.
• Strategies for finding the part, given the whole and the percent in mathematical and contextual situation.
• Strategies for finding the percent, given the whole and the part in mathematical and contextual situation.

### Skills

Students are able to:
• Represent ratio and rate situations using a variety of strategies (e.g., tables of equivalent ratios, changing to unit rate, tape diagrams, double number line diagrams, equations, and plots on coordinate planes).
• Use ratio, rates, and multiplicative reasoning to explain connections among representations and justify solutions in various contexts, including measurement, prices and geometry.
• Understand the multiplicative relationship between ratio comparisons in a table by writing an equation.
• Plot ratios as ordered pairs.
• Solve and justify solutions for rate problems including unit pricing, constant speed, measurement conversions, and situations involving percents.
• Solve problems and justify solutions when finding the whole given a part and the percent.
• Model using an equivalent fraction and decimal to percents.
• Use ratio reasoning, multiplication, and division to transform and interpret measurements.

### Understanding

Students understand that:
• A unit rate is a ratio (a:b) of two measurements in which b is one.
• A symbolic representation of relevant features of a real-world problem can provide for resolution of the problem and interpretation of the situation.
• When computing with quantities the transformation and interpretation of the resulting unit is dependent on the particular operation performed.

### Primary Learning Objectives

I CAN identify and develop ratios in real world situations.

I CAN identify equivalent ratios.

### Procedures/Activities

1. The teacher will conduct a math discussion on ratios, using the Discussion Cards (found in attachments). The teacher will display Ratio card 1. The teacher will ask students to give the fraction of the red tiles, and ask the students "What does a fraction tell us?" The students will give feedback on the significance of the numerator and denominator. The teacher will then introduce “ratio” as a math word. The teacher will identify a ratio as a number that compares two quantities and provide the three ways to write a ratio (a to b; a/b; a:b). The teacher will ask, “What is the ratio of red tiles to white tiles?” “White to red?” “Red to the total amount?” The teacher will continue this discussion with the remaining cards. The teacher will ask the students the main difference between a fraction and a ratio.

2. Once the discussion subsides, the teacher will allow students time to search "Ratios in Advertisements." Students will discuss the different ratios they view on the Web (an example: 2 out of 3 people choose us). If every student cannot individually search, students may work in groups or teacher can lead a whole group search.

3. The teacher will transition students into the investigative activity, Painter Problems. To build background knowledge the teacher will explain how paint is mixed at the local hardware store. "Using a white base, workers must provide the appropriate drops of dye to get the desired color. Today there are computers for this, but many times computers fail." To introduce the activity the teacher will tell the students that they have a summer job at a paint store where the computer does not work. Using the ratios provided, they must fulfill the orders for the customers.

4. The students will begin the investigation. Students may work individually or collaboratively.

5. Once adequate time (30-45 minutes) is given, the students will share their finding on the document camera. (If a document camera is not available, students may present their work in the front of the class, this is where the students would need chart paper). As the students are sharing, the teacher is acting as the facilitator and coach asking questions that drive ratio understanding. "How do you know that ratio is equivalent to the first ratio?" "How did you know to do _______?" "Did someone do this differently or find a different answer?"

6. Toward the end of class, the teacher will distribute the Exit Slip (found in attachments).

1. The teacher will conduct a math discussion on ratios, using the Discussion Cards (found in attachments). The teacher will display Ratio card 1. The teacher will ask students to give the fraction of the red tiles, and ask the students "What does a fraction tell us?" The students will give feedback on the significance of the numerator and denominator. The teacher will then introduce “ratio” as a math word. The teacher will identify a ratio as a number that compares two quantities and provide the three ways to write a ratio (a to b; a/b; a:b). The teacher will ask, “What is the ratio of red tiles to white tiles?” “White to red?” “Red to the total amount?” The teacher will continue this discussion with the remaining cards. The teacher will ask the students the main difference between a fraction and a ratio.

2. Once the discussion subsides, the teacher will allow students time to search "Ratios in Advertisements." Students will discuss the different ratios they view on the Web (an example: 2 out of 3 people choose us). If every student cannot individually search, students may work in groups or teacher can lead a whole group search.

3. The teacher will transition students into the investigative activity, Painter Problems. To build background knowledge the teacher will explain how paint is mixed at the local hardware store. "Using a white base, workers must provide the appropriate drops of dye to get the desired color. Today there are computers for this, but many times computers fail." To introduce the activity the teacher will tell the students that they have a summer job at a paint store where the computer does not work. Using the ratios provided, they must fulfill the orders for the customers.

4. The students will begin the investigation. Students may work individually or collaboratively.

5. Once adequate time (30-45 minutes) is given, the students will share their finding on the document camera. (If a document camera is not available, students may present their work in the front of the class, this is where the students would need chart paper). As the students are sharing, the teacher is acting as the facilitator and coach asking questions that drive ratio understanding. "How do you know that ratio is equivalent to the first ratio?" "How did you know to do _______?" "Did someone do this differently or find a different answer?"

6. Toward the end of class, the teacher will distribute the Exit Slip (found in attachments).

### Assessment Strategies

Formal Formative Assessment: Ratio Exit Slip (found in attachments)

Formal Assessment: Using the Investigative Activity Rubric (found in attachments) teacher will evaluate students' work.

Informal Formative Assessment: As the students are working, the teacher will act as the facilitator and coach. Teacher will ask questions to evaluate students (i.e. How do you know ______? What did you do to get that?) Teacher may pull small groups during investigation on a needs basis.

### Acceleration

The investigation has an included extension on the Painter Problem Activity Sheet (found in attachments).

### Intervention

Because this is part of a unit, teacher may develop small groups based on the Ratio Exit Slip or informal questioning as part of the investigative activity.

### Total Duration

61 to 90 Minutes

### Background/Preparation

The teacher must prepare the appropriate number of math tool boxes for the class; several students can use one tool box.

The teacher must make the appropriate number of copies of the Painter Problems Activity guide; to promote student collaboration several students may use one guide.

The teacher must prepare Ratio Discussion Cards (found in attachments) or ratio models may be created on the interactive whiteboard software or the application of paint.

The teacher must make the appropriate number of Ratio Exit Slips (found in attachments); each student will need one Exit Slip.

The students must have prior knowledge of fractions and how to develop equivalent fractions.

### Materials and Resources

Discussion Cards (provided in the attachment section)

Ratio Exit Slip (provided in the attachment section)

Painter Problems Activity Guide

Investigative Activity Rubric

Chart paper

Math Toolbox which include the following: pencil, paper, graph paper, markers, scissors, glue, calculator, and sticky notes

### Technology Resources Needed

Interactive Whiteboard (Optional) with required software

Document camera or projector