ALEX Lesson Plan


Painter Problems

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  This lesson provided by:  
Author:Tim McKenzie
The event this resource created for:CCRS
  General Lesson Information  
Lesson Plan ID: 33035


Painter Problems


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.

 Associated Standards and Objectives 
Content Standard(s):
MA2015 (2016)
Grade: 6
1 ) Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. [6-RP1]

Examples: "The ratio of wings to beaks in the bird house at the zoo was 2:1 because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."

NAEP Framework
NAEP Statement::
4NPO4a: Use simple ratios to describe problem situations.

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

NAEP Statement::
8NPO4a: Use ratios to describe problem situations.

NAEP Statement::
8NPO4b: Use fractions to represent and express ratios and proportions.

NAEP Statement::
8NPO4d: Solve problems involving percentages (including percent increase and decrease, interest rates, tax, discount, tips, or part/whole relationships).

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.1- Select a ratio to match a given statement and representation.

MA2015 (2016)
Grade: 6
3 ) Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. [6-RP3]

a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. [6-RP3a]

b. Solve unit rate problems including those involving unit pricing and constant speed. [6-RP3b]

Example: If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours' At what rate were lawns being mowed'

c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. [6-RP3c]

d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [6-RP3d]

NAEP Framework
NAEP Statement::
8M2b: Solve problems involving conversions within the same measurement system such as conversions involving square inches and square feet.

NAEP Statement::
8M2c: Estimate the measure of an object in one system given the measure of that object in another system and the approximate conversion factor. For example:
  • Distance conversion: 1 kilometer is approximately 5/8 of a mile.
  • Money conversion: U.S. dollars to Canadian dollars.
  • Temperature conversion: Fahrenheit to Celsius.

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

NAEP Statement::
8NPO4a: Use ratios to describe problem situations.

NAEP Statement::
8NPO4b: Use fractions to represent and express ratios and proportions.

NAEP Statement::
8NPO4d: Solve problems involving percentages (including percent increase and decrease, interest rates, tax, discount, tips, or part/whole relationships).

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.3- Solve simple real-world problems using ratio/rate reasoning.
M.AAS.6.3a- Answer simple questions about a table of equivalent ratios with whole-number measurements.
M.AAS.6.3b- Calculate unit-rate problems, including those involving unit pricing.
M.AAS.6.3c- Identify a percentage equivalent to a fraction (e.g., 1/2, 1/4, 1).
M.AAS.6.3d- Identify the decimal equivalent of a percentage (limited to 10%, 20%, 25%, 40%, and 50%).

Local/National Standards:

Math Practice Standards: 

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others. 

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning. 

Primary Learning Objective(s):

I CAN identify and develop ratios in real world situations.

I CAN identify equivalent ratios.


Additional Learning Objective(s):

 Preparation Information 

Total Duration:

61 to 90 Minutes

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

Access to search engine (individually or whole group)


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. 



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). 

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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.



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


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.

View the Special Education resources for instructional guidance in providing modifications and adaptations for students with significant cognitive disabilities who qualify for the Alabama Alternate Assessment.