6th Grade - Ratios
A. Focus and CoherenceCommon Core Standards:
 6.RP.1
 6.RP.3
Student Prior knowledge:
 Rate and ratio language (for example, “3 girls
for every 2 boys” could be written as “3:2”
and read as “3 to 2”)
 Solving ratio problems by writing and solving
equations
Focus of the lesson:
 Understanding ratios through tape diagrams
 Creating a visual representation of ratio
problems
 Using ratios to solve real-world problems
Where will students use/apply what they have
learned in this lesson later this year:
 Tape diagrams or bar modeling could be used
for a variety of fraction problems and percent
problems.
B. What will students produce when they are making
sense, persevering, attending to precision and/or
modeling, in relation to the focus of the lesson?
(Evidence of the Standards for Mathematical
Practices, 1, 4, and/or 6)
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Students will write and talk about what they
know about the problem before jumping in
Students will make a plan for solving the
problem with their tape diagram – they will
decide what labels to use and how many bars
to draw, then decide what value each bar
represents
Students will be able to solve a ratio problem
in more than 1 way (tape diagram or
equation)
Students will label diagrams accurately when
using a table or a tape diagram
Students will explain their ideas orally and in
writing
Materials: individual whiteboards and markers, post-its (2 different colors), “Ratio Problems” worksheet (attached)
C. What are the learning experiences that provide for rigor (fluency, deep understanding, application and
dual intensity)? What are the learning experiences that provide for evidence of the Standards for
Mathematical Practices?
Warm up:
A cake recipe says to use 3 cups of flower and 1 cup of sugar. You want to triple the recipe to make a really
big cake. How many cups of flower and how many cups of sugar will you use?
(Show responses in a table; talk about how if you triple one quantity, you must do the same to the other
quantity if you want your cake to taste the same)
Input/Modeling
1) “We want to know how many girls are in class today, how many boys are in class today, and the total
number of students here today.”
Record data:
Girls: ____
Boys: ____
Total: ____
 On your individual whiteboard, write a ratio sentence comparing two of the quantities above
(for example, “The ratio of girls to boys is 12:14”)
Whole-group share out
2) I want a visual representation for the ratio of boys to girls.
Show tape diagram on the board using different color post-its. (blue for boys, pink for girls)
Boys
Girls
Total
Pose question to the class: What if my class is double in size but the ratio of boys to girls stays the same?
 How can I figure out how many boys there are and how many girls there are?
 How can I represent that using the post-its? (Put a “2” in each post-it)
What if there are 320* students total in the school, and the ratio of boys to girls remains the same?
How many boys are there? How many girls are there?
(*change total number of students as needed; each box should represent an integer number).
Explain how when using tape diagrams each box represents the same number and we can find that number.
Boys
320
Girls
3) How else could you have set up and/or solved this problem?
3
x
Writing an equation: 
5 320
Using a table:
*whatever you do
to one quantity, you
must do to the others
Boys 3
Girls 5
Total 8
12
20
32
120
200
320
Guided Practice
Practice using tape diagrams to solve problems. Students may use other methods to check their answers,
but we want to see a visual representation as well.
Pass out “Ratio Problems” worksheet
Steps to solving word problems:
Step 1: Read the problem
*Step 2: Write an answer sentence with a blank where the answer will go (*IMPORTANT)
Step 3: Find relevant information and make a plan for solving
Step 4: Solve
Step 5: Check and put the appropriate answer in the blank of your answer sentence
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Do #1 as a class, following the steps above
Students do #2 in small groups
o Solve the problem (using the 5 steps)
o Create a poster showing your method and answer
o Be prepared to share with the rest of the class
 Start #3 as a class – students finish it on their own.
Closure
Ticket out the door:
Explain how you solved #3, including any pictures, tables, or equations you used.
Independent Practice
Homework worksheet: 3 ratio problems
Name: _____________________________________
Ratio Problems
1. The ratio of boys to girls at a party was 2:3. If there were 9 girls, how many boys were at the party?
2. The ratio of cheese pizzas to pepperoni pizzas sold at Sal's Pizzeria last Thursday was 7:5. There were 45 pepperoni
pizzas sold that day. How many pizzas were sold in all on Thursday?
3. The ratio of flutists to trumpeters to drummers in the school bank is 3:4:1. If there are 5 drummers, how many
flutists are there? How many trumpeters are there?
Name: ______________________________
Homework
1. The ratio of soda to popcorn to candy sold at the movie theater last weekend was 8:5:6. There were 18 packages of
candy sold. How many sodas were sold?
2. Jasmine went shopping with $180 total. She spent her money on cd's, movies, and games in a ratio of 1:3:5. How
much more did Jasmine spend on games than on movies?
3. Yolanda makes a juice mixture using 3 cups of orange juice and 4 cups cranberry. She wants to make a bigger batch
of juice by tripling the recipe. How much total juice will she have after tripling it?