Bar Models and Ratios

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SWBAT use bar models to represent and solve scenarios involving two or more ratios.

Big Idea

Students work in partnered pairs to use bar models to solve ratio word problems

Do Now

10 minutes

Students enter silently according to the Daily Entrance Routine.  For today's Do Now a timer is set for a problem solving challenge:

Finish in 6 minutes with at least 80% correct to earn 2 achievement points**

For this task, students will enter their answers into clickers, which speeds up the checking process to determine which students earned the extra points. I am walking around the room during these 6 minutes helping students and motivating them to stay on task.

I expect the most commonly missed answers to be #1 and #4. My students are still making errors when multiplying or dividing rational numbers. This is a skill I continue to work toward remediating with the appropriate students. 


** I am using the Online Stopwatch to provide a visual timer for students.

Class Notes

15 minutes

Any red font included in the Class Notes - Bar Models and Rates resource is meant to be copied off the board by students.  For each example, I model for students how bar models help me visualize and solve this problem.


Students may also opt to use the larger drawings of the bar models on the back of the page.  A common misconception is failing to see the boxes as parts of an entire unit, as well as being able to isolate information from the word problem to identify the quantities being compared and the question being asked. Thus, it is important to ensure all students write all information off the board and understand how to use this information to continue to study the concept.

Another common misunderstanding is the language behind fractions of a year (i.e. a quarter of a year is one fourth of the year). Again, it is important to push students to understand these concepts visually as shown on the back of the class notes paper.  


20 minutes

After answering any student questions about the Do Now assignment, I distribute their Bar Models and Ratios Task for today.  It is titled "Locations" as each set of questions is located in a different “setting” of the story.  For example, the first set of 3 questions is set in a 6th grade class room where the ratio of boys to girls is 2 : 3. The questions asked must be answered using this information.

I also have 3 stations set up around the room. There is a station in the booths for the last location in the classwork: inside an M&M bag. There are baskets at the booths with different chip counters (or actual bowls of M&Ms?) students will be able to use as manipulatives to further visualize the problem. The 16 tables in the center of the room are divided into two groups. All students are asked to move so that they begin on the right hand side of the room, this is the first location. There are baskets at most tables with counting bears or other manipulatives with two distinct category colors (boys/girls). These manipulatives will hopefully help students further visualize the first setting. On the left side of the room I will have baskets with plastic toy farm animals also playing a role as a manipulative for the second location. Students will get to move to the next location by raising their hands with the correct work and answers on their papers.

I will most likely spend most of my time working with a small group of students as they move from station to station. This is a group of students that understands they must ask for help rather than expect me to know they need it. This is a big character piece I have been focusing on recently as I have a group of students that do not advocate for their needs under the fear that they are “bad” for not understanding. 


10 minutes

In the closing I review the answers to the first 6 problems and ask students to complete the rest for homework.

When reviewing the answers I make sure to call on different students to explain the answers to those questions. Getting students to discuss the topic and describe the placement of the numbers within the boxes is important. Students discussing and defending their answers and the answers of others are in use of MP3.