Extending and Comparing Ratios

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SWBAT: • Define a ratio as a way to show a relationship between two different quantities. • Represent a ratio in 3 ways • Use multiplication and division to extend a ratio • Compare ratios

Big Idea

Which pictures have the same ratio of trucks to boxes? Students continue to work on understanding and comparing ratios.

Do Now

8 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today, I want students to review how to create ratios.  Problem 1d pushes students to look at the current ratio of 5:8 and reason what to add to the picture to create a ratio of 3:4 (or 6:8).  Students are engaging in MP2: Reason abstractly and quantitatively.

I call on students to share out their answers and share whether they agree or disagree with one another.  I present a ratio with the numbers switched and ask students if this will work.  I want students to remember that the order of the values does matter.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others

Trucks and Boxes

10 minutes


  • I will have square tiles available for students who want to compare ratios using tiles.

I want to give students an opportunity to show what they know about equivalent ratios.  I read the prompt and tell students to work for a few minutes on their own.

After a few minutes, I prompt students to participate in a Think Pair Share.  I ask students to compare their ratios of trucks to boxes.  I call on students to share out their ratios.  I ask for one student to share a match he/she found.  I ask students if they agree or disagree and why.  I use the tiles as another way of proving whether the ratios are equivalent.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

Some students may be confused, or having difficulty finding multiple matches.  This is okay.  I want to plant these questions and we will return to them later in the lesson.

Ratios and Tables

5 minutes

I present ratio tables as one tool to help us understand the relationship between the two categories.  We work through the bouquet problem together.  I want students to be able to recognize the pattern and vocalize that the ratio of daisies to tulips is 2:1.

Guided Practcie

7 minutes

We work through the reading example together.  A common mistake is for students to misread the problem and place 30 as the amount of pages Thaisha reads.  Also, some students may try and find an additive relationship instead of a multiplicative relationship.  If this occurs, I will create fractions comparing Thaisha and her brother’s pages (15/5 = ___ / 15).  I want students to make connections with creating equivalent fractions.

Question c  is more complicated because it gives the total of pages read, rather than the amount of pages read by Thaisha or her brother.  I have students participate in a Think Pair Share about how to attack this problem.  Some students may look at the ratio of 15:5 and think that Thaisha reads 3 out of the total 4 read and that her brother reads 1 pages out of the total 4 read.  If Thaisha reads ¾ of the total pages, then she will read 30 of the 40 pages and her brother will read 10 pages.  Other students may guess and check by creating ratios that are equivalent to 3:1 and then add the pages together.  Other students may add 3+1 to get 4 total pages.  If you multiply 4 x 11 you get 44, so you would then multiply both sides of the ratio by 11, so Thaisha read 33 pages and her brother read 11 pages.  Other students may create a Singapore bar model to help them.  This is a strategy that students will use in the next lesson when they work on with thinking blocks at Math Playground

I have students share out their different strategies.  If students did not use a presented strategy, I tell them to record what the student did.  This can serve as helpful notes if students get stuck later.

More Practice

10 minutes

Students work independently on problems 1-5.  Students are engaging in MP1: Make sense of problems and persevere in solving them and MP2: Reason Abstractly and Quantitatively.  As students work, I walk around and monitor student progress.

 If students are struggling I may intervene in one or more of the following ways:

  • Read the problem out loud and have student identify key information
  • Use tiles so student can create a visual of the ratio they are working on
  • Ask the student how they can use a table to help them
  • Have student refer to the guided notes and examples to see how we used a table

I Post A Key.  As students complete their work, they raise their hand.  I quickly scan their work and if they are on the right track I send them to check their work.  If students are able to correctly create equivalent ratios, I ask them to return to the Trucks and Boxes problem and create a visual showing which ratios are equivalent.

Closure and Ticket to Go

10 minutes

 For Closure I ask a student to explain how tables can help us work with ratios.  I call on 2-3 more students to add to that student’s idea.  Then I have students return to the Trucks and Boxes problem.  I ask students to share what they are thinking now. Students are engaging in MP2: Reason Abstractly and Quantitatively and MP3: Construct viable arguments and critique the reasoning of others.  I want students to realize that pictures A, C, and F all are equivalent to 1 truck: 3 boxes and that pictures B, D, and E are all equivalent to 1 truck: 4 boxes.  Picture D is confusing to some students, since there are 1 ½ trucks.  A visual with blocks may help.  Other students may see the connection that if you double the ratio in picture D you end up with the ratio in picture E. 

With a few minutes left, I pass out the Ticket to Go and the HW Comparing and Extending Ratios.