Introduction to Ratios

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Objective

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

Big Idea

What is a ratio? How can we create equivalent ratios? Students work to express and extend relationships using ratios.

Do Now

7 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.  In preparation with working with ratios, I want students to quickly review equivalent fractions.  I want students to recognize and be able to explain why 36/63 is equivalent to 4/7, but 2/3 is not.

I ask students to explain what it means when two fractions are equivalent.  I want students to be able to explain that two fractions are equivalent when they represent the same part of a whole.  Students participate in a Think Pair Share.  I call on students to share out their thinking. If I notice any of the common mistakes mentioned above I present them and have students share their thinking.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

Frosting Cupcakes

7 minutes

Notes:

  • I will have blue and green square tiles available for students who want to create a model.

Before I introduce ratios, I want students to use their skills to solve problems involving ratios.  I have a student read the prompt.  I use square tiles to create one batch of frosting using 2 green tiles and 5 blue tiles.  Then I tell students to work with their neighbor to figure out how much food coloring Knoa will need to color 2 and 5 batches of frosting.  Students should be able to see that we are taking the amount from 1 batch and multiplying it to get the amounts for the larger batches.  I call on two students to share what they came up with in the table.

I ask question 2 and put 1 green tile under the document camera.  Students participate in a Think Pair Share.  Some students may be confused, or say that it isn’t possible.  I call on a couple students to share out their ideas or questions.  My goal is not for students to be able to answer questions 2 and 3 at this point.  I want to plant these questions and we will return to them later in the lesson.

Ratios

7 minutes

I introduce the term ratio and the different ways we can show the relationship.  We go through the examples together.  I want students to understand that the order of the ratio matters.  After students answer problem 2, I ask “Could 5:7 also represent this relationship?  Why or why not?”  I want students to recognize that 5:7 shows the ratio of squares to all shapes, which is different from the ratio of all shapes to squares.

For problem 3, I want students to realize that if the ratio of oranges to apples is 4:6, then that means that for every 2 oranges there are 3 apples.  The ratios 4:6 and 2:3 are equivalent.

Equivalent Ratios and Practice

20 minutes

I introduce the concept of equivalent ratios and we go through the examples on page 1 – 5 together.  I want students to apply their knowledge of equivalent fractions to equivalent ratios.  These skills will also help students work with rates and unit rates later in the unit.

Students work independently on problems 6 – 13.  Students are engaging in MP4: Model with Mathematics.  As students work, I walk around and monitor student progress.

 If students are struggling give them square tiles and put the problem they are working into context.  For instance for number 6, I tell the student that for every 3 red tiles there are 5 yellow tiles.  We create the model using tiles.  Then I ask the student if we want to keep the same ratio between red and yellow tiles, how many red tiles would we need if we had 15 yellow tiles.  If needed, the student can create the model with tiles.  I ask them what they notice.  I want the student to realize that the number of yellow tiles tripled, so the number of red tiles had to triple.  As these students work through the examples I want them to be able to create equivalent ratios without having to create the physical model.

Closure and Ticket to Go

9 minutes

 For Closure I ask a student to explain what a ratio is.  I call on 2-3 more students to add to that student’s definition.  Then I have students return to questions 2 and 3 on the Frosting Cupcakes.  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 if there is only 1 drop of green food coloring, they are cutting the number of green drops in ½ so they must do the same thing to the blue drops.  If a student has a visual, I project it under the document camera.  If there isn’t a visual, I will draw one.

If I have time, I ask students how the frosting problems relate to Nana’s Chocolate Milk problem.

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