Grade 3
Lesson: 6-8
Reference to English
Multiplying to find Combinations
Math Standard(s): 3.OA.3
Domain: Operation and Algebraic Thinking
Content objective(s):
Language Objective(s):
Students will use objects, pictures, and multiplication to find
Students will explain how they solved a combination problem.
the number of possible combinations of data or objects in a
I can explain how I solved a combination problem.
problem.
I can use objects, pictures, and multiplication to find the number
of possible combinations of data or objects in a problem.
Essential Understanding
Required Academic Vocabulary for Word Wall:
Finding the number of combinations that are possible between
Listen: organized list
the members of one group and the members of another group
Read:
is one meaning of multiplication.
Write:
Speak: combination
Sentence Frame:
Materials:
Additional Lesson Vocabulary:
Shirt, pants, clothes, pizza, drinks, cups, thin crust, thick crust,
 Different cups (tall, short, mugs, fancy….)
pineapple, pepperoni, cheese
 Different drinks (juice box, soda, water…)
 Two-color Counters (teaching tool 16) (1 set per pair)
 Two-color tiles (Teaching Tool 16) (1 set per pair)
 Whiteboards, erasers and markers
 Guided Practice page 158 - 159
Lesson:
Instructional Time: 30 minutes
Opening: (3 minutes)
T: “You have learned how to make organized lists to solve problems. Today, you will learn how to find all possible combinations
of objects from two sets. This is new, so you will want to pay really close attention today!”
 Display different kinds of cups (tall, short, mugs, fancy…) and different drinks (juice box, soda, water…)
T: “You often have options as to how to pair things. Such as what to drink and what kind of glass to put the drink in. Look up at
all the different glasses and all the different drinks on the table. How many different combinations could we make?”
S: will answer.
T: “When else might you have different options? Tell your neighbor.”
S: will say, “when choosing a pizza style and toppings” or “when choosing combinations of clothes to wear.”
T: “You are right, there are so many times we have options to choose from.”
Introduction to New Material (Direct Instruction): (8 minutes)
T: “Let me tell you a story. Delia is tying strings onto balloons. She has green and blue balloons and red and yellow string. I will
draw them on the board. What are the colors of the balloons again?”
S: will say, “green and blue balloons.”
T: “Perfect, I drew 1 green and 1 blue balloon. What are the colors of strings?”
S: will say, “red and yellow string.”
T: “With these two balloons I am going to use red strings. Is that the only combination I can make? Thumbs up or down.”
S: will show thumbs down.
T: “You are right, I can make at least one more combination. What could it be? Tell your neighbor.”
S: will tell their neighbor and other combination.
T: “I am going to draw two more balloons on the board. One blue one and one green one. This time I am going to give them
yellow string.”
T: “Are there any more combinations? Thumbs up or down.”
S: will show thumbs up.
T: “What is another combination?”
S: will say, “a red string with a green balloon and a yellow string with a blue balloon.”
T: “Okay, I will draw that yellow with green and red with blue.”
T: “Are there any other combinations?”
S: will say, “red with blue and yellow with green.”
T: “You are right, I will draw that one on the board too. Are there any other combinations?”
S: will say, “no.”
T: “How many possible combinations of a balloon and a piece of string can Delia make?”
S: will say, “there are 4 combinations.”
T:

T:
S:

T:
S:

T:
S:

T:
S:
T:
“You can make a table to find all of the possible combinations too. Let’s try it.”
On the board, draw a table with two columns and two rows.
“We need to label this table. How can you label the columns and rows with the different options for balloons and string?
will say, “label the columns green balloon and blue balloon and the rows red string and yellow string.”
Label the table on the board.
“The cells in the table will show the possible combinations. How do you know what to write in each cell?”
will say, “put the balloon color of the column that the cell is in and the string color of the row the cell is in.”
Work through the table until all cells are filled.
“Are there any possible combinations that are not listed here?”
will say, “no.”
Make sure students understand that the possible combinations cannot have the same two objects.
“How many possible combinations of a balloon and a piece of string are there?”
will say, “4 possible combinations.”
“So, you can draw a picture or you can draw a table. You choose which way works best for you.”
Guided Practice: (8 minutes)
Use the modeling cycle:
Teacher Does:
 Pass out whiteboards, erasers and markers.
T: “Let’s do one more problem together to practice. Please write down the important information on your whiteboard.”
T: “Kerrie was ordering a pizza. She could choose thin crust or thick crust. She could also choose her toppings – cheese,
pepperoni, or pineapple. How many possible combinations of pizza are there?”
T: “How many kinds of crust?”
S: will say, “2 kinds of crust.”
T: “How many kinds of toppings?”
S: will say, “3 kinds of toppings.”
T: “Let’s draw it first. What should we draw first?”
S: will respond, “thin crust pizza.”
T: “I will draw three thin crust pizzas.”
T: “What should we draw now?”
S: will respond, “thick crust pizza.”
T: “Okay, I will draw three thick crust pizzas.”
T: “You should be drawing too!”
T: “Now let’s draw the toppings. We need how many cheese pizzas?”
S: will say, “1 thin crust pizza and 1 thick crust pizza.”
T: “Perfect. Let’s do the same with pepperoni and pineapples. One thick crust of each and one thin crust of each.”
T: “How many combinations do we have? Tell you neighbor.”
S: will say, “there are 6 combinations.”
T: “Now let’s do the table. I want you to try and draw it on your whiteboard without my help first. You can work with a
neighbor if you want.”
S: will draw the table on their boards.
T: “Show me your boards.”
T: “Let’s put pizza on the side with 2 rows. I will write thin and thick.”
 Start drawing and labeling the table.
T: “Now let’s write the toppings on the top. I will actually draw them- cheese, pepperoni and pineapple.”
T: “Now let’s write ‘X’ for each combination in each box in the table.”
T: “How many combinations are there?”
S: will say, “there are 6 combinations.”
T: “Well done!!”
All Students Do:
T: “Now I want you to work with a partner and try one more problem. I will read it and I want you to write the important
information on you whiteboard.”
T: “Martin has red and yellow caps. He also has orange, blue, and green sweatshirts. How may different combinations of a cap
and a sweatshirt can Martin wear?”
T: “Remember to draw the picture as well as draw the table. Raise your hand if you need help.”
S: will work in pairs to solve the problem.
 Teacher will walk around the room checking student work and helping students as needed.
T: “You have one more minute. Then I want to go over the problem together.”
 Go over the problem as a whole group.
Independent Practice: (6 minutes)
T: “Please open your books to page 158. You will need to solve problems 1, 2, 5, 6 and 8. You will have 5 minutes to solve these
problems.”
S: will pull out their books and start to solve the problems.
 Teacher will walk around the room helping students as needed.
T: “You have 1 more minute.”
T: “10,9,8,7,6,5,4,3,2,1. Time is up. Please clean up your desks, turn in your papers, pick up your whiteboards and comes sit on
the carpet.”
Closing: (5 minutes)
T: “We are going to do one more problem together. I will read a story problem and I need you to write the important
information on your whiteboard.”
T: “Wanda is choosing a shirt and pants. She has 4 different color shirts: green, pink, red, and yellow. How many different colors
of shirts does Wanda have?”
S: will say, “4 different shirts.”
T: “She has 3 different color pants: blue, white and black. How many different colors of pants does she have?”
S: will say, “3 different pants.”
T: “How many different combinations of a shirt and pants can she make? Work with your neighbor and use an organized list.”
S: will work with their partner and solve the problem.
T: “Please show me your boards.”
S: will show the teacher their boards with the organized list on it.
 Teacher needs to check the lists to make sure the students solved the problem correctly.
T: “How did you solve the problem?”
S: will explain to the class how they solved the problem.
T: “Are they right?”
S: will say, “yes” or “no”
T: “WHY?”
S: will explain why the person who solved the problem is correct or incorrect.
T: “Ok. So if there are 4 shirts and 3 pants, you would draw an organized list like this?”
 Draw an organized list on the board. (if you want to have fun with your students, draw it incorrectly and make them correct
you).
T: “Let’s count them up, there are 12 combos that can be made. Is that the answer you got?”
Assessment:
Guided Practice problems 1, 2, 5, 6, 8.