Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 49439
Efficient Multiplication
Students will engage with questions to evaluate the students' abilities to select and apply multiplication strategies with fluency and efficiency. The
focus of the lesson is decomposing numbers to multiply using the Distributive property and understanding and applying the Commutative property.
Then, students will reinforce decomposing of factors while playing Decomposition of Factors. The lesson concludes with a real world application
problem on an Exit Slip.
Subject(s): Mathematics
Grade Level(s): 3
Intended Audience: Educators
Suggested Technology: Overhead Projector
Instructional Time: 1 Hour(s)
Freely Available: Yes
Keywords: multiplication, third grade, word problems, multiplication games, decomposing factors, Commutative,
Distributive
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
Decompose factors.docx
Exit_Slip_Efficient_Multiplication.docx
Multiplication Strategies Probe.docx
Rubric for Efficient Multiplication.docx
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will be able to apply decomposition of factors by using the Distributive property of multiplication and the Commutative property of multiplication to solve real
world problems.
Students will be able to decompose factors and use the Commutative property as a strategy of multiplying fluently.
Prior Knowledge: What prior knowledge should students have for this lesson?
The students should already know or have exposure to these standards:
Students should be able to interpret products of whole numbers. For example, interpret 5 X 7 as the total number of objects in 5 groups of 7 objects each.
Students should be able to multiply within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.
Guiding Questions: What are the guiding questions for this lesson?
These guiding questions are associated with the multiplication strategy probe.
page 1 of 4 How does this equation match the word problem?
5x3 and 5x3 represent the original number sentence 5x6. If there are 5 groups of 6, then we can decompose the number sentence to 5x3 and another 5x3 so that we
have a total of 5x6.
Compare your model to this one. What is the same? Different? Why?
Students should compare all three possible answers and discuss each of the possible answers. (The answer key for the multiplication story probe contains detailed
discussion of the possible answers.)
Is there a more efficient way?
Multiplying 5X3 and 5X3 is more efficient because I can quickly recall the fact 5X3, which is 15, so I know that I only need 5 more groups of 3 to have a total of 5X6.
Then, I can quickly add the double 15 + 15, which equals 30.
At this point the teacher may want to suggest to students that they also create their own decomposition of 5X6.
How did you decide which strategies to use?
The strategy of decomposing a factor is easier than adding 5 six times. It is also quicker to decompose the factor than to create an array. The array takes extra time
and if not done correctly will cause mistakes. Our goal is to have fluency and to be efficient with multiplication.
What is the same about all of the solution strategies?
All of the solutions solve the problem and get the same answer. They are all strategies to solve the word problem.
Teaching Phase: How will the teacher present the concept or skill to students?
1. Each student will receive a Multiplication Story Probe (attached).
2. The teacher will read the story probe and the answers with the students, or the students can read the story probe on their own.
3.Then the students will work individually to solve the multiplication story probe. (This is the formative assessment. The teacher can choose to collect these individually
or rotate around the room to monitor student progress in order to gain an insight on the students' knowledge.)
4. The students will work with a partner to discuss how they solved the multiplication story probe, which answer they chose, and why.
5. During this time the teacher will rotate around the room to monitor student discussions.
6. The teacher will then post the multiplication story probe on the board. The students will move back to their seats to work in whole groups at this point.
7. The teacher will ask students to share out their answers. It is important to allow students to share regardless of whether their answer is right or wrong. When a
student provides an incorrect answer, this is a critical point where students with mastery will be able to guide their peers in discussing ways to solve.
8. The teacher needs to guide students though analyzing all of the possible answers on the probe. This should be a student led discussion.
9. Answer A is a correct product. Kevin did calculate 30 erasers correctly. However, it is not the most efficient way to solve. Kevin had to add 5, six times. Adding so
many numbers cannot be done with fluency.
10. Answer B, is also a correct product. However, Julie's calculations are the most efficient. She used what she knew to decompose (or apply the Commutative
property) to the multiplication sentence. She was able to use 5X3 and another 5X3 to get the product. By decomposing the multiplication sentence into more
manageable factors she was able to multiply with fluency. She still has 5 groups of 6, however it has been decomposed into 5 groups of 3 and 5 groups of 3.
11. Teachers will want to note that this is a critical time when you could ask students to create another way to decompose the factors. Students may find that 5X4=20
and 5X2=10, so adding the products will give the sum of 30 as well. (There are additional possible answers.)
12. Answer C is also a correct product. However, Cameron created an array to find the answer. Arrays can take extra time and, if not done correctly will, cause us to
miscalculate the answers. Furthermore, it is not the most efficient way to multiply with fluency.ncy.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
After the students have completed the Multiplication Story Probe, the students will complete 2 practice problems. The students should lead the discussion by sharing
their ideas on how they solved. The following examples demonstrate how students may involve both the Distributive and Commutative property when solving. Students
who finish early may be challenged by finding multiple ways to solve the same multiplication sentence.
Practice problem 1: 7 X 9
This problem should focus on decomposing the multiplication sentence. The students should read the problem first as: seven groups of nine.
Then, students will take a minute to decompose on their own. The teacher should circulate to review student work.
Next, the students will share how they decomposed the problem.
Possible answers: (7X4) + (7X5) Here we have the seven groups of nine separated into seven group of four and seven groups of five (using the Commutative
property). We still have a total of seven groups of nine. I quickly know 7X5 is 35. I also know that 7X4 is 28, so then adding both products I have a sum of 63.
(7X3) + (7X3) + (7X3) Here we have the seven groups of nine separated into seven groups of three, three times (using the Distributive property). Although students
will want to create this decomposition of factors, it is critical that the students discuss that this is not an efficient way to solve.
Practice problem 2: 9X6
This problem should focus on decomposing the multiplication sentence. The students should read the problem first as: nine groups of six.
Then, students will take a minute to decompose on their own. The teacher should circulate to review student work.
Next, the students will share how they decomposed the problem.
page 2 of 4 Possible answers: 9 X (4+2). I know that 9X2 is equal to 18. I also know that 9X4 is equal to 36. So the sum of both products is 54. Here the student used the
Distributive property to decompose the factor of 6 into 4 and 2. The student then multiplied both factors by 9.
6 X (3+6). I know that 6X3 is equal to 18. I also know that 6X6 is equal to 36. So the sum of both products is 54. Here the Distributive property is used again with the
factor 9 being decomposed into 3 and 6. The student then multiplied both factors by 6.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
The students will complete the game Decompose the Factors (attached). This game allows students the opportunity to decompose factors in an exciting and engaging
game.
1. Students should be placed into groups of two. Each group will need: one game board, a recording sheet for each player (this may be a piece of handwriting paper),
two place holder chips (this could be eraser caps), two pencils for recording, a number cube, and each player will need one crayon (a different color from their
partner).
2. Students can roll the number cube to determine who is player 1 (the higher number is player 1).
3. Player 1 will roll the number cube to see how many spaces to move from the start. The number sentence that player 1 lands on will be the factors that both players
record and decompose.
4. After player 1 lands on his/her space, both players decompose the number sentence. Then, both students can compare strategies for decomposing efficiently.
5. If player 1 correctly decomposed and found the correct product, he or she may color in the space they are on. If they are wrong, they may not color in the space.
6. Next will be player 2's turn to roll the number cube. The students will continue to play until they both reach the finish line. The player with the most spaces colored
in is the winner.
An extension to the game may be that students who show mastery play a second game and as they decompose the number sentences, they create as many
decomposed factors as possible. The player with the most decomposed factors for each original multiplication sentence is allowed to color in the square.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
After the activity the teacher will ask students if they were able to decompose all of the factors efficiently. Did you use the Commutative property to change the order
of the factors? Did you use the Distributive property to decompose the factors? Could you solve the multiplication sentences in more than one way? Why or Why not?
The students will complete a Summative Assessment. The students will read the real world problem and the Commutative question for an Exit Slip (attached). This
assessment requires students to review a real world problem, decompose factors, and explain the Commutative property.
The teacher may choose to review the exit slips prior to the next lesson or before the end of the math lesson with the class.
Summative Assessment
The teacher will evaluate the students' ability to use the Commutative property of multiplication and Distributive property of multiplication (decomposing factors) with
efficiency applied to a real world situation. The Summative Assessment is paired with a rubric to evaluate student progress with decomposing factors and the
Commutative property. This assessment is titled Exit Slip Efficient Multiplication and is located under uploaded files.
Formative Assessment
The teacher will gather information about the students' understanding by using the multiplication strategies probe. This probe will allow students to demonstrate their
levels of thinking prior to the lesson. This assessment gives teachers insight into student fluency of utilizing multiplication strategies. The teacher can then use the
student data gathered from the probe to group students into pairs with different levels of abilities.
Feedback to Students
After completing the probe, students will pair up with a partner to share their answers. Then, the students will share out as a whole to discuss their reasoning behind
their answers. The teacher should be sure to not only have the students with correct answers share out, but more specifically the students with incorrect answers
should share out. This will help students to understand their mistakes as well as allow students with mastery to guide the instruction.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Students needing additional assistance may work in a small group with the teacher.
Students may need to use a blank game board and roll a number cube that has only numbers 1-4 to fill in the board.
Extensions:
Students who have mastery of the multiplication strategies may choose to use the blank game board. The students may fill in the board by rolling the number cube
twice. Upon the first roll students will add the digits for the first number. Upon the second roll students will add those digits for the second number. Both of the new
numbers will be then used as the factors on the blank game board.
Students may choose to create their own game on the blank game board at home as a school-to-home connection.
Suggested Technology: Overhead Projector
Special Materials Needed:
Decompose the Factors Game board (one per team - attached)
Pencil (one per player)
Place chip (one per player)
Two number cubes per team of two (for blank boards)
One number cube for teams playing on the pre-filled game board
Recording sheets (one per player) This may be a blank piece of paper for recording equations during the game.
page 3 of 4 Multiplication Probe (one per student - attached)
Multiplication Exit Slip (one per student - attached)
Crayons, one per student (they need to be different colors)
Further Recommendations:
Students may want to take the game home for practice. Therefore, you may want to make extra copies of the game board or send home blank game boards.
The game can be used as a center for students to use for reinforcement post the completion of this activity.
Additional Information/Instructions
By Author/Submitter
This resource is likely to support student engagement in the following the Mathematical Practice: MAFS.K12.MP.5.1; Use appropriate tools strategically.
SOURCE AND ACCESS INFORMATION
Contributed by: Lindsey Johannessen
Name of Author/Source: Lindsey Johannessen
District/Organization of Contributor(s): Brevard
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.3.OA.2.5:
Description
Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24
is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or
by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16,
one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
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